%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL942^2 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:15:16 AM UTC 2026
% Result : Theorem 13.86s 2.21s
% Output : Refutation 13.86s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% 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,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_18,type,
qmltpeq: $i > $i > mworld > $o ).
thf(func_def_19,type,
inv: $i > $i ).
thf(func_def_20,type,
op: $i > $i > $i ).
thf(func_def_21,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_23,type,
vNOT: $o > $o ).
thf(func_def_24,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
vAND: $o > $o > $o ).
thf(func_def_26,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
vOR: $o > $o > $o ).
thf(func_def_28,type,
vIMP: $o > $o > $o ).
thf(func_def_29,type,
vIFF: $o > $o > $o ).
thf(func_def_30,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_34,type,
sK0: mworld ).
thf(func_def_35,type,
sK1: mworld > mworld ).
thf(func_def_36,type,
sK2: mworld > mworld ).
thf(func_def_37,type,
sK3: mworld > mworld ).
thf(func_def_38,type,
sK4: mworld > mworld ).
thf(func_def_39,type,
sK5: mworld > mworld ).
thf(func_def_40,type,
sK6: mworld > mworld ).
thf(func_def_41,type,
sK7: mworld > mworld ).
thf(func_def_42,type,
sK8: mworld > mworld ).
thf(func_def_43,type,
sK9: mworld > mworld ).
thf(func_def_44,type,
sK10: mworld > mworld ).
thf(func_def_45,type,
sK11: mworld > mworld ).
thf(func_def_46,type,
sK12: mworld > mworld ).
thf(func_def_47,type,
sK13: mworld > mworld ).
thf(func_def_48,type,
sK14: mworld > mworld ).
thf(func_def_49,type,
sK15: mworld > mworld ).
thf(func_def_50,type,
sK16: mworld > mworld ).
thf(func_def_51,type,
sK17: mworld > mworld ).
thf(func_def_52,type,
sK18: mworld > mworld ).
thf(func_def_53,type,
sK19: mworld > mworld ).
thf(func_def_54,type,
sK20: mworld > mworld ).
thf(func_def_55,type,
sK21: mworld > mworld ).
thf(func_def_56,type,
sK22: mworld > mworld ).
thf(func_def_57,type,
sK23: mworld > mworld ).
thf(func_def_58,type,
sK24: mworld > mworld ).
thf(func_def_59,type,
sK25: mworld > mworld ).
thf(func_def_60,type,
sK26: mworld > mworld ).
thf(func_def_61,type,
sK27: mworld > mworld ).
thf(func_def_62,type,
sK28: mworld > mworld ).
thf(func_def_63,type,
sK29: mworld > mworld ).
thf(func_def_64,type,
sK30: mworld > mworld ).
thf(func_def_65,type,
sK31: mworld > mworld ).
thf(func_def_66,type,
sK32: mworld > mworld ).
thf(func_def_67,type,
sK33: mworld > mworld ).
thf(func_def_68,type,
sK34: mworld > mworld ).
thf(func_def_69,type,
sK35: mworld > mworld ).
thf(func_def_70,type,
sK36: mworld > mworld ).
thf(func_def_71,type,
sK37: mworld > mworld ).
thf(func_def_72,type,
sK38: mworld > mworld ).
thf(func_def_73,type,
sK39: mworld > mworld ).
thf(func_def_74,type,
sK40: mworld > mworld ).
thf(func_def_75,type,
sK41: mworld > mworld ).
thf(func_def_76,type,
sK42: mworld > mworld ).
thf(func_def_77,type,
sK43: mworld > mworld ).
thf(func_def_78,type,
sK44: mworld > mworld ).
thf(func_def_79,type,
sK45: mworld > mworld ).
thf(func_def_80,type,
sK46: mworld > mworld ).
thf(func_def_81,type,
sK47: mworld > mworld ).
thf(func_def_82,type,
sK48: mworld > mworld ).
thf(func_def_83,type,
sK49: mworld > mworld ).
thf(func_def_84,type,
sK50: mworld > mworld ).
thf(func_def_85,type,
sK51: mworld > mworld ).
thf(func_def_86,type,
sK52: mworld > mworld ).
thf(func_def_87,type,
sK53: mworld > mworld ).
thf(func_def_88,type,
sK54: mworld > mworld ).
thf(func_def_89,type,
sK55: mworld > mworld ).
thf(func_def_90,type,
sK56: mworld > mworld ).
thf(func_def_91,type,
sK57: mworld > mworld ).
thf(func_def_92,type,
sK58: mworld > mworld ).
thf(func_def_93,type,
sK59: mworld > mworld ).
thf(func_def_94,type,
sK60: mworld > mworld ).
thf(func_def_95,type,
sK61: mworld > mworld ).
thf(func_def_96,type,
sK62: mworld > mworld ).
thf(func_def_97,type,
sK63: mworld > mworld ).
thf(func_def_98,type,
sK64: mworld > mworld ).
thf(func_def_99,type,
sK65: mworld > mworld ).
thf(func_def_100,type,
sK66: mworld > mworld ).
thf(func_def_101,type,
sK67: mworld > mworld ).
thf(func_def_102,type,
sK68: mworld > mworld ).
thf(func_def_103,type,
sK69: mworld > mworld ).
thf(func_def_104,type,
sK70: mworld > mworld ).
thf(func_def_105,type,
sK71: mworld > mworld ).
thf(func_def_106,type,
sK72: mworld > mworld ).
thf(func_def_107,type,
sK73: mworld > mworld ).
thf(func_def_108,type,
sK74: mworld > mworld ).
thf(func_def_109,type,
sK75: mworld > mworld ).
thf(func_def_110,type,
sK76: mworld > mworld ).
thf(func_def_111,type,
sK77: mworld > mworld ).
thf(func_def_112,type,
sK78: mworld > mworld ).
thf(func_def_113,type,
sK79: mworld > mworld ).
thf(func_def_114,type,
sK80: mworld > mworld ).
thf(func_def_115,type,
sK81: mworld > mworld ).
thf(func_def_116,type,
sK82: mworld > mworld ).
thf(func_def_117,type,
sK83: mworld > mworld ).
thf(func_def_118,type,
sK84: mworld > mworld ).
thf(func_def_119,type,
sK85: mworld > mworld ).
thf(func_def_120,type,
sK86: mworld > mworld ).
thf(func_def_121,type,
sK87: mworld > mworld ).
thf(func_def_122,type,
sK88: mworld > mworld ).
thf(func_def_123,type,
sK89: mworld > mworld ).
thf(func_def_124,type,
sK90: mworld > mworld ).
thf(func_def_125,type,
sK91: mworld > mworld ).
thf(func_def_126,type,
sK92: mworld > mworld ).
thf(func_def_127,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_128,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_129,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_130,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_131,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_132,type,
sK93: $i > mworld > $i > mworld ).
thf(func_def_133,type,
sK94: $i > mworld > $i > mworld ).
thf(func_def_134,type,
sK95: $i > mworld > $i > mworld ).
thf(func_def_135,type,
sK96: mworld > $i > $i > mworld ).
thf(func_def_136,type,
sK97: $i > mworld > $i > mworld ).
thf(func_def_137,type,
sK98: $i > mworld > $i > mworld ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f2,axiom,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_def) ).
thf(f3,axiom,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(f4,axiom,
( mor
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor_def) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f9,axiom,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(f29,conjecture,
mlocal @ ( mbox @ ( mnot @ ( mand @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) @ ( mbox @ ( mnot @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
thf(f30,negated_conjecture,
~ ( mlocal @ ( mbox @ ( mnot @ ( mand @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) @ ( mbox @ ( mnot @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
thf(f31,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f32,plain,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f33,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f34,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f35,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f36,plain,
( mor
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f37,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f42,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f43,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f46,plain,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
inference(rectify,[],[f9]) ).
thf(f47,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f46]) ).
thf(f86,plain,
~ ( mlocal @ ( mbox @ ( mnot @ ( mand @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) @ ( mbox @ ( mnot @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f30]) ).
thf(f87,plain,
( ( mlocal @ ( mbox @ ( mnot @ ( mand @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) @ ( mbox @ ( mnot @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f86]) ).
thf(f88,plain,
( ( mlocal @ ( mbox @ ( mnot @ ( mand @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) @ ( mbox @ ( mnot @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f87]) ).
thf(f89,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f90,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f91,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f92,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f95,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f97,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f47]) ).
thf(f117,plain,
( ( mlocal @ ( mbox @ ( mnot @ ( mand @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) @ ( mbox @ ( mnot @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f88]) ).
thf(f137,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] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ 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 ) ) )
@ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) )
@ ( ^ [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 ) ) )
@ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) )
@ ( ^ [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 ) ) )
@ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ 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 ) ) )
@ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) )
@ ( ^ [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 ) ) )
@ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) )
@ ( ^ [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 ) ) )
@ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ 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 ) ) )
@ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) )
@ ( ^ [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 ) ) )
@ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) )
@ ( ^ [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 ) ) )
@ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) )
@ ( ^ [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 ) ) )
@ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) )
@ ( ^ [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 ) ) )
@ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) )
@ ( ^ [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 ) ) )
@ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ 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 ) ) )
@ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) )
@ ( ^ [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 ) ) )
@ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) )
@ ( ^ [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 ) ) )
@ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ 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 ) ) )
@ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) )
@ ( ^ [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 ) ) )
@ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) )
@ ( ^ [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 ) ) )
@ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ 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 ) ) )
@ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) )
@ ( ^ [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 ) ) )
@ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) )
@ ( ^ [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 ) ) )
@ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) )
@ ( ^ [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 ) ) )
@ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) )
@ ( ^ [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 ) ) )
@ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) )
@ ( ^ [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 ) ) )
@ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f117,f89,f95,f90,f91,f92,f91,f95,f91,f95,f91,f95,f95,f92,f91,f95,f91,f95,f91,f95,f95,f92,f91,f95,f91,f95,f91,f95,f95,f91,f95,f91,f95,f91,f95,f95,f95,f90,f92,f91,f95,f91,f95,f91,f95,f95,f92,f91,f95,f91,f95,f91,f95,f95,f92,f91,f95,f91,f95,f91,f95,f95,f91,f95,f91,f95,f91,f95,f95]) ).
thf(f138,plain,
( $true
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y1 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y2 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y2 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y2 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f137]) ).
thf(f139,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y1 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y2 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y2 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y2 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y2 ) ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f138]) ).
thf(f140,plain,
( $false
= ( ( mrel @ mactual @ sK0 )
=> ~ ( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ~ ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
( $false
= ( ~ ( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ~ ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f140]) ).
thf(f143,plain,
( $true
= ( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ~ ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f141]) ).
thf(f144,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ~ ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y1 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f143]) ).
thf(f145,plain,
( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f143]) ).
thf(f146,plain,
( ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( ( $true
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f149,plain,
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f148]) ).
thf(f150,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f148]) ).
thf(f151,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f151]) ).
thf(f154,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f154]) ).
thf(f157,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f157]) ).
thf(f160,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f158]) ).
thf(f167,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f158]) ).
thf(f168,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f168]) ).
thf(f170,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f166]) ).
thf(f175,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f166]) ).
thf(f176,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f178,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f174]) ).
thf(f183,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f184,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f155]) ).
thf(f189,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f155]) ).
thf(f190,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f190]) ).
thf(f193,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f193]) ).
thf(f195,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f191]) ).
thf(f200,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f191]) ).
thf(f201,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f203,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f199]) ).
thf(f208,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f199]) ).
thf(f209,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f209]) ).
thf(f211,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f211]) ).
thf(f213,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f212]) ).
thf(f214,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f207]) ).
thf(f216,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f218]) ).
thf(f220,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f188]) ).
thf(f222,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f188]) ).
thf(f223,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f222]) ).
thf(f224,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f223]) ).
thf(f226,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f226]) ).
thf(f228,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f224]) ).
thf(f233,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f224]) ).
thf(f234,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f233]) ).
thf(f235,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f234]) ).
thf(f236,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f237]) ).
thf(f239,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f238]) ).
thf(f240,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f232]) ).
thf(f241,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f232]) ).
thf(f242,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f242]) ).
thf(f244,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f243]) ).
thf(f245,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f244]) ).
thf(f246,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f245]) ).
thf(f247,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f246]) ).
thf(f248,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f240]) ).
thf(f249,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f248]) ).
thf(f250,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f249]) ).
thf(f251,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f250]) ).
thf(f252,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f251]) ).
thf(f253,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f252]) ).
thf(f254,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f221]) ).
thf(f255,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f254]) ).
thf(f256,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f254]) ).
thf(f257,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f256]) ).
thf(f258,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f257]) ).
thf(f259,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f258]) ).
thf(f260,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f259]) ).
thf(f261,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f260]) ).
thf(f262,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f261]) ).
thf(f263,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f255]) ).
thf(f264,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f255]) ).
thf(f265,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f264]) ).
thf(f266,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f265]) ).
thf(f267,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f266]) ).
thf(f268,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f267]) ).
thf(f269,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f268]) ).
thf(f270,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f269]) ).
thf(f271,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f263]) ).
thf(f272,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f263]) ).
thf(f273,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f272]) ).
thf(f274,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f273]) ).
thf(f275,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f274]) ).
thf(f276,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f275]) ).
thf(f277,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f276]) ).
thf(f278,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f277]) ).
thf(f279,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f271]) ).
thf(f280,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f279]) ).
thf(f281,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f280]) ).
thf(f282,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f281]) ).
thf(f283,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f282]) ).
thf(f284,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f283]) ).
thf(f285,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f152]) ).
thf(f286,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f152]) ).
thf(f287,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f286]) ).
thf(f288,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f287]) ).
thf(f289,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f287]) ).
thf(f290,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f289]) ).
thf(f291,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f290]) ).
thf(f292,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f290]) ).
thf(f293,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f292]) ).
thf(f294,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f293]) ).
thf(f295,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f294]) ).
thf(f296,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f295]) ).
thf(f297,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f296]) ).
thf(f298,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f297]) ).
thf(f299,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f291]) ).
thf(f300,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f291]) ).
thf(f301,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f300]) ).
thf(f302,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f301]) ).
thf(f303,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f302]) ).
thf(f304,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f303]) ).
thf(f305,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f304]) ).
thf(f306,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f305]) ).
thf(f307,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f299]) ).
thf(f308,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f299]) ).
thf(f309,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f308]) ).
thf(f310,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f309]) ).
thf(f311,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f310]) ).
thf(f312,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f311]) ).
thf(f313,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f312]) ).
thf(f314,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f313]) ).
thf(f315,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f307]) ).
thf(f316,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f315]) ).
thf(f317,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f316]) ).
thf(f318,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f317]) ).
thf(f319,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f318]) ).
thf(f320,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f319]) ).
thf(f321,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f288]) ).
thf(f322,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f288]) ).
thf(f323,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f322]) ).
thf(f324,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f323]) ).
thf(f325,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f323]) ).
thf(f326,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f325]) ).
thf(f327,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f326]) ).
thf(f328,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f327]) ).
thf(f329,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f328]) ).
thf(f330,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f329]) ).
thf(f331,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f330]) ).
thf(f332,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f324]) ).
thf(f333,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f324]) ).
thf(f334,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f333]) ).
thf(f335,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f334]) ).
thf(f336,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f335]) ).
thf(f337,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f336]) ).
thf(f338,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f337]) ).
thf(f339,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f338]) ).
thf(f340,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f332]) ).
thf(f341,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f332]) ).
thf(f342,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f341]) ).
thf(f343,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f342]) ).
thf(f344,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f343]) ).
thf(f345,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f344]) ).
thf(f346,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f345]) ).
thf(f347,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f346]) ).
thf(f348,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f340]) ).
thf(f349,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f348]) ).
thf(f350,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f349]) ).
thf(f351,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f350]) ).
thf(f352,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f351]) ).
thf(f353,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f352]) ).
thf(f354,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f321]) ).
thf(f355,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f321]) ).
thf(f356,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f355]) ).
thf(f357,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f356]) ).
thf(f358,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f356]) ).
thf(f359,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f358]) ).
thf(f360,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f359]) ).
thf(f361,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f360]) ).
thf(f362,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f361]) ).
thf(f363,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f362]) ).
thf(f364,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f363]) ).
thf(f365,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f357]) ).
thf(f366,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f357]) ).
thf(f367,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f366]) ).
thf(f368,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f367]) ).
thf(f369,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f368]) ).
thf(f370,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f369]) ).
thf(f371,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f370]) ).
thf(f372,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f371]) ).
thf(f373,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f365]) ).
thf(f374,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f365]) ).
thf(f375,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f374]) ).
thf(f376,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f375]) ).
thf(f377,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f376]) ).
thf(f378,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f377]) ).
thf(f379,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f378]) ).
thf(f380,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f379]) ).
thf(f381,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f373]) ).
thf(f382,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f381]) ).
thf(f383,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f382]) ).
thf(f384,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f383]) ).
thf(f385,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f384]) ).
thf(f386,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f385]) ).
thf(f387,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f354]) ).
thf(f388,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f387]) ).
thf(f389,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f387]) ).
thf(f390,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f389]) ).
thf(f391,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f390]) ).
thf(f392,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f391]) ).
thf(f393,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f392]) ).
thf(f394,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f393]) ).
thf(f395,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f394]) ).
thf(f396,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f388]) ).
thf(f397,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f388]) ).
thf(f398,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f397]) ).
thf(f399,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f398]) ).
thf(f400,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f399]) ).
thf(f401,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f400]) ).
thf(f402,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f401]) ).
thf(f403,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f402]) ).
thf(f404,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f396]) ).
thf(f405,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f396]) ).
thf(f406,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f405]) ).
thf(f407,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f406]) ).
thf(f408,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f407]) ).
thf(f409,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f408]) ).
thf(f410,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f409]) ).
thf(f411,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f410]) ).
thf(f412,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f404]) ).
thf(f413,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f412]) ).
thf(f414,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f413]) ).
thf(f415,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f414]) ).
thf(f416,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f415]) ).
thf(f417,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f416]) ).
thf(f418,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f285]) ).
thf(f419,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f285]) ).
thf(f420,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f419]) ).
thf(f421,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f420]) ).
thf(f422,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f420]) ).
thf(f423,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f422]) ).
thf(f424,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f423]) ).
thf(f425,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f423]) ).
thf(f426,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f425]) ).
thf(f427,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f426]) ).
thf(f428,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f427]) ).
thf(f429,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f428]) ).
thf(f430,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f429]) ).
thf(f431,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f430]) ).
thf(f432,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f424]) ).
thf(f433,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f424]) ).
thf(f434,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f433]) ).
thf(f435,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f434]) ).
thf(f436,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f435]) ).
thf(f437,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f436]) ).
thf(f438,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f437]) ).
thf(f439,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f438]) ).
thf(f440,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f432]) ).
thf(f441,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f432]) ).
thf(f442,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f441]) ).
thf(f443,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f442]) ).
thf(f444,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f443]) ).
thf(f445,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f444]) ).
thf(f446,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f445]) ).
thf(f447,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f446]) ).
thf(f448,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f440]) ).
thf(f449,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f448]) ).
thf(f450,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f449]) ).
thf(f451,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f450]) ).
thf(f452,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f451]) ).
thf(f453,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f452]) ).
thf(f454,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f421]) ).
thf(f455,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f421]) ).
thf(f456,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f455]) ).
thf(f457,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f456]) ).
thf(f458,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f456]) ).
thf(f459,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f458]) ).
thf(f460,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f459]) ).
thf(f461,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f460]) ).
thf(f462,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f461]) ).
thf(f463,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f462]) ).
thf(f464,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f463]) ).
thf(f465,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f457]) ).
thf(f466,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f457]) ).
thf(f467,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f466]) ).
thf(f468,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f467]) ).
thf(f469,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f468]) ).
thf(f470,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f469]) ).
thf(f471,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f470]) ).
thf(f472,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f471]) ).
thf(f473,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f465]) ).
thf(f474,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f465]) ).
thf(f475,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f474]) ).
thf(f476,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f475]) ).
thf(f477,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f476]) ).
thf(f478,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f477]) ).
thf(f479,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f478]) ).
thf(f480,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f479]) ).
thf(f481,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f473]) ).
thf(f482,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f481]) ).
thf(f483,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f482]) ).
thf(f484,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f483]) ).
thf(f485,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f484]) ).
thf(f486,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f485]) ).
thf(f487,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f454]) ).
thf(f488,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f454]) ).
thf(f489,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f488]) ).
thf(f490,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f489]) ).
thf(f491,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f489]) ).
thf(f492,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f491]) ).
thf(f493,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f492]) ).
thf(f494,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f493]) ).
thf(f495,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f494]) ).
thf(f496,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f495]) ).
thf(f497,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f496]) ).
thf(f498,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f490]) ).
thf(f499,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f490]) ).
thf(f500,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f499]) ).
thf(f501,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f500]) ).
thf(f502,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f501]) ).
thf(f503,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f502]) ).
thf(f504,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f503]) ).
thf(f505,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f504]) ).
thf(f506,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f498]) ).
thf(f507,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f498]) ).
thf(f508,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f507]) ).
thf(f509,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f508]) ).
thf(f510,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f509]) ).
thf(f511,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f510]) ).
thf(f512,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f511]) ).
thf(f513,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f512]) ).
thf(f514,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f506]) ).
thf(f515,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f514]) ).
thf(f516,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f515]) ).
thf(f517,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f516]) ).
thf(f518,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f517]) ).
thf(f519,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f518]) ).
thf(f520,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f487]) ).
thf(f521,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f520]) ).
thf(f522,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f520]) ).
thf(f523,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f522]) ).
thf(f524,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f523]) ).
thf(f525,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f524]) ).
thf(f526,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f525]) ).
thf(f527,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f526]) ).
thf(f528,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f527]) ).
thf(f529,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f521]) ).
thf(f530,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f521]) ).
thf(f531,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f530]) ).
thf(f532,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f531]) ).
thf(f533,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f532]) ).
thf(f534,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f533]) ).
thf(f535,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f534]) ).
thf(f536,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f535]) ).
thf(f537,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f529]) ).
thf(f538,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f529]) ).
thf(f539,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f538]) ).
thf(f540,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f539]) ).
thf(f541,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f540]) ).
thf(f542,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f541]) ).
thf(f543,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f542]) ).
thf(f544,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f543]) ).
thf(f545,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f537]) ).
thf(f546,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f545]) ).
thf(f547,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f546]) ).
thf(f548,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f547]) ).
thf(f549,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f548]) ).
thf(f550,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f549]) ).
thf(f551,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f418]) ).
thf(f552,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f551]) ).
thf(f553,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f551]) ).
thf(f554,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f553]) ).
thf(f555,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f554]) ).
thf(f556,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f554]) ).
thf(f557,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f556]) ).
thf(f558,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f557]) ).
thf(f559,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f558]) ).
thf(f560,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f559]) ).
thf(f561,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f560]) ).
thf(f562,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f561]) ).
thf(f563,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f555]) ).
thf(f564,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f555]) ).
thf(f565,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f564]) ).
thf(f566,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f565]) ).
thf(f567,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f566]) ).
thf(f568,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f567]) ).
thf(f569,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f568]) ).
thf(f570,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f569]) ).
thf(f571,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f563]) ).
thf(f572,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f563]) ).
thf(f573,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f572]) ).
thf(f574,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f573]) ).
thf(f575,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f574]) ).
thf(f576,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f575]) ).
thf(f577,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f576]) ).
thf(f578,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f577]) ).
thf(f579,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f571]) ).
thf(f580,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f579]) ).
thf(f581,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f580]) ).
thf(f582,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f581]) ).
thf(f583,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f582]) ).
thf(f584,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f583]) ).
thf(f585,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f552]) ).
thf(f586,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f552]) ).
thf(f587,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f586]) ).
thf(f588,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f587]) ).
thf(f589,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f587]) ).
thf(f590,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f589]) ).
thf(f591,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f590]) ).
thf(f592,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f591]) ).
thf(f593,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f592]) ).
thf(f594,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f593]) ).
thf(f595,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f594]) ).
thf(f596,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f588]) ).
thf(f597,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f588]) ).
thf(f598,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f597]) ).
thf(f599,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f598]) ).
thf(f600,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f599]) ).
thf(f601,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f600]) ).
thf(f602,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f601]) ).
thf(f603,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f602]) ).
thf(f604,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f596]) ).
thf(f605,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f596]) ).
thf(f606,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f605]) ).
thf(f607,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f606]) ).
thf(f608,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f607]) ).
thf(f609,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f608]) ).
thf(f610,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f609]) ).
thf(f611,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f610]) ).
thf(f612,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f604]) ).
thf(f613,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f612]) ).
thf(f614,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f613]) ).
thf(f615,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f614]) ).
thf(f616,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f615]) ).
thf(f617,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f616]) ).
thf(f618,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f585]) ).
thf(f619,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f585]) ).
thf(f620,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f619]) ).
thf(f621,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f620]) ).
thf(f622,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f620]) ).
thf(f623,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f622]) ).
thf(f624,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f623]) ).
thf(f625,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f624]) ).
thf(f626,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f625]) ).
thf(f627,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f626]) ).
thf(f628,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f627]) ).
thf(f629,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f621]) ).
thf(f630,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f621]) ).
thf(f631,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f630]) ).
thf(f632,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f631]) ).
thf(f633,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f632]) ).
thf(f634,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f633]) ).
thf(f635,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f634]) ).
thf(f636,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f635]) ).
thf(f637,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f629]) ).
thf(f638,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f629]) ).
thf(f639,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f638]) ).
thf(f640,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f639]) ).
thf(f641,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f640]) ).
thf(f642,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f641]) ).
thf(f643,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f642]) ).
thf(f644,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f643]) ).
thf(f645,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f637]) ).
thf(f646,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f645]) ).
thf(f647,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f646]) ).
thf(f648,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f647]) ).
thf(f649,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f648]) ).
thf(f650,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f649]) ).
thf(f651,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f618]) ).
thf(f652,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f651]) ).
thf(f653,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f651]) ).
thf(f654,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f653]) ).
thf(f655,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f654]) ).
thf(f656,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f655]) ).
thf(f657,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f656]) ).
thf(f658,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f657]) ).
thf(f659,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f658]) ).
thf(f660,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f652]) ).
thf(f661,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f652]) ).
thf(f662,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f661]) ).
thf(f663,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f662]) ).
thf(f664,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f663]) ).
thf(f665,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f664]) ).
thf(f666,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f665]) ).
thf(f667,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f666]) ).
thf(f668,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f660]) ).
thf(f669,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f660]) ).
thf(f670,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f669]) ).
thf(f671,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f670]) ).
thf(f672,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f671]) ).
thf(f673,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f672]) ).
thf(f674,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f673]) ).
thf(f675,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f674]) ).
thf(f676,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f668]) ).
thf(f677,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f676]) ).
thf(f678,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f677]) ).
thf(f679,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f678]) ).
thf(f680,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f679]) ).
thf(f681,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f680]) ).
thf(f682,plain,
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f149]) ).
thf(f683,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f149]) ).
thf(f684,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f683]) ).
thf(f685,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f684]) ).
thf(f686,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f684]) ).
thf(f687,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f686]) ).
thf(f688,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f687]) ).
thf(f689,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f687]) ).
thf(f690,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f689]) ).
thf(f691,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f690]) ).
thf(f692,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f690]) ).
thf(f693,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f692]) ).
thf(f694,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f693]) ).
thf(f695,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f694]) ).
thf(f696,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f695]) ).
thf(f697,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f696]) ).
thf(f698,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f697]) ).
thf(f699,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f691]) ).
thf(f700,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f691]) ).
thf(f701,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f700]) ).
thf(f702,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f701]) ).
thf(f703,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f702]) ).
thf(f704,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f703]) ).
thf(f705,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f704]) ).
thf(f706,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f705]) ).
thf(f707,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f699]) ).
thf(f708,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f699]) ).
thf(f709,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f708]) ).
thf(f710,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f709]) ).
thf(f711,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f710]) ).
thf(f712,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f711]) ).
thf(f713,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f712]) ).
thf(f714,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f713]) ).
thf(f715,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f707]) ).
thf(f716,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f715]) ).
thf(f717,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f716]) ).
thf(f718,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f717]) ).
thf(f719,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f718]) ).
thf(f720,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f719]) ).
thf(f721,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f688]) ).
thf(f722,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f688]) ).
thf(f723,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f722]) ).
thf(f724,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f723]) ).
thf(f725,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f723]) ).
thf(f726,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f725]) ).
thf(f727,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f726]) ).
thf(f728,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f727]) ).
thf(f729,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f728]) ).
thf(f730,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f729]) ).
thf(f731,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f730]) ).
thf(f732,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f724]) ).
thf(f733,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f724]) ).
thf(f734,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f733]) ).
thf(f735,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f734]) ).
thf(f736,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f735]) ).
thf(f737,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f736]) ).
thf(f738,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f737]) ).
thf(f739,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f738]) ).
thf(f740,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f732]) ).
thf(f741,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f732]) ).
thf(f742,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f741]) ).
thf(f743,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f742]) ).
thf(f744,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f743]) ).
thf(f745,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f744]) ).
thf(f746,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f745]) ).
thf(f747,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f746]) ).
thf(f748,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f740]) ).
thf(f749,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f748]) ).
thf(f750,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f749]) ).
thf(f751,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f750]) ).
thf(f752,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f751]) ).
thf(f753,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f752]) ).
thf(f754,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f721]) ).
thf(f755,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f721]) ).
thf(f756,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f755]) ).
thf(f757,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f756]) ).
thf(f758,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f756]) ).
thf(f759,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f758]) ).
thf(f760,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f759]) ).
thf(f761,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f760]) ).
thf(f762,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f761]) ).
thf(f763,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f762]) ).
thf(f764,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f763]) ).
thf(f765,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f757]) ).
thf(f766,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f757]) ).
thf(f767,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f766]) ).
thf(f768,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f767]) ).
thf(f769,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f768]) ).
thf(f770,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f769]) ).
thf(f771,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f770]) ).
thf(f772,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f771]) ).
thf(f773,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f765]) ).
thf(f774,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f765]) ).
thf(f775,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f774]) ).
thf(f776,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f775]) ).
thf(f777,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f776]) ).
thf(f778,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f777]) ).
thf(f779,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f778]) ).
thf(f780,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f779]) ).
thf(f781,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f773]) ).
thf(f782,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f781]) ).
thf(f783,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f782]) ).
thf(f784,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f783]) ).
thf(f785,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f784]) ).
thf(f786,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f785]) ).
thf(f787,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f754]) ).
thf(f788,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f787]) ).
thf(f789,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f787]) ).
thf(f790,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f789]) ).
thf(f791,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f790]) ).
thf(f792,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f791]) ).
thf(f793,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f792]) ).
thf(f794,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f793]) ).
thf(f795,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f794]) ).
thf(f796,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f788]) ).
thf(f797,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f788]) ).
thf(f798,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f797]) ).
thf(f799,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f798]) ).
thf(f800,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f799]) ).
thf(f801,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f800]) ).
thf(f802,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f801]) ).
thf(f803,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f802]) ).
thf(f804,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f796]) ).
thf(f805,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f796]) ).
thf(f806,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f805]) ).
thf(f807,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f806]) ).
thf(f808,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f807]) ).
thf(f809,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f808]) ).
thf(f810,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f809]) ).
thf(f811,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f810]) ).
thf(f812,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f804]) ).
thf(f813,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f812]) ).
thf(f814,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f813]) ).
thf(f815,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f814]) ).
thf(f816,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f815]) ).
thf(f817,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f816]) ).
thf(f818,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f685]) ).
thf(f819,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f685]) ).
thf(f820,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f819]) ).
thf(f821,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f820]) ).
thf(f822,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f820]) ).
thf(f823,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f822]) ).
thf(f824,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f823]) ).
thf(f825,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f823]) ).
thf(f826,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f825]) ).
thf(f827,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f826]) ).
thf(f828,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f827]) ).
thf(f829,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f828]) ).
thf(f830,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f829]) ).
thf(f831,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f830]) ).
thf(f832,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f824]) ).
thf(f833,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f824]) ).
thf(f834,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f833]) ).
thf(f835,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f834]) ).
thf(f836,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f835]) ).
thf(f837,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f836]) ).
thf(f838,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f837]) ).
thf(f839,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f838]) ).
thf(f840,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f832]) ).
thf(f841,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f832]) ).
thf(f842,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f841]) ).
thf(f843,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f842]) ).
thf(f844,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f843]) ).
thf(f845,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f844]) ).
thf(f846,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f845]) ).
thf(f847,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f846]) ).
thf(f848,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f840]) ).
thf(f849,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f848]) ).
thf(f850,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f849]) ).
thf(f851,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f850]) ).
thf(f852,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f851]) ).
thf(f853,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f852]) ).
thf(f854,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f821]) ).
thf(f855,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f821]) ).
thf(f856,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f855]) ).
thf(f857,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f856]) ).
thf(f858,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f856]) ).
thf(f859,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f858]) ).
thf(f860,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f859]) ).
thf(f861,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f860]) ).
thf(f862,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f861]) ).
thf(f863,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f862]) ).
thf(f864,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f863]) ).
thf(f865,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f857]) ).
thf(f866,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f857]) ).
thf(f867,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f866]) ).
thf(f868,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f867]) ).
thf(f869,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f868]) ).
thf(f870,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f869]) ).
thf(f871,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f870]) ).
thf(f872,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f871]) ).
thf(f873,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f865]) ).
thf(f874,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f865]) ).
thf(f875,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f874]) ).
thf(f876,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f875]) ).
thf(f877,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f876]) ).
thf(f878,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f877]) ).
thf(f879,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f878]) ).
thf(f880,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f879]) ).
thf(f881,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f873]) ).
thf(f882,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f881]) ).
thf(f883,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f882]) ).
thf(f884,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f883]) ).
thf(f885,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f884]) ).
thf(f886,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f885]) ).
thf(f887,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f854]) ).
thf(f888,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f854]) ).
thf(f889,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f888]) ).
thf(f890,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f889]) ).
thf(f891,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f889]) ).
thf(f892,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f891]) ).
thf(f893,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f892]) ).
thf(f894,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f893]) ).
thf(f895,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f894]) ).
thf(f896,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f895]) ).
thf(f897,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f896]) ).
thf(f898,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f890]) ).
thf(f899,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f890]) ).
thf(f900,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f899]) ).
thf(f901,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f900]) ).
thf(f902,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f901]) ).
thf(f903,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f902]) ).
thf(f904,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f903]) ).
thf(f905,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f904]) ).
thf(f906,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f898]) ).
thf(f907,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f898]) ).
thf(f908,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f907]) ).
thf(f909,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f908]) ).
thf(f910,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f909]) ).
thf(f911,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f910]) ).
thf(f912,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f911]) ).
thf(f913,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f912]) ).
thf(f914,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f906]) ).
thf(f915,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f914]) ).
thf(f916,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f915]) ).
thf(f917,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f916]) ).
thf(f918,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f917]) ).
thf(f919,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f918]) ).
thf(f920,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f887]) ).
thf(f921,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f920]) ).
thf(f922,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f920]) ).
thf(f923,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f922]) ).
thf(f924,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f923]) ).
thf(f925,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f924]) ).
thf(f926,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f925]) ).
thf(f927,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f926]) ).
thf(f928,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f927]) ).
thf(f929,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f921]) ).
thf(f930,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f921]) ).
thf(f931,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f930]) ).
thf(f932,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f931]) ).
thf(f933,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f932]) ).
thf(f934,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f933]) ).
thf(f935,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f934]) ).
thf(f936,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f935]) ).
thf(f937,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f929]) ).
thf(f938,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f929]) ).
thf(f939,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f938]) ).
thf(f940,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f939]) ).
thf(f941,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f940]) ).
thf(f942,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f941]) ).
thf(f943,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f942]) ).
thf(f944,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f943]) ).
thf(f945,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f937]) ).
thf(f946,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f945]) ).
thf(f947,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f946]) ).
thf(f948,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f947]) ).
thf(f949,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f948]) ).
thf(f950,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f949]) ).
thf(f951,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f818]) ).
thf(f952,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f818]) ).
thf(f953,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f952]) ).
thf(f954,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f953]) ).
thf(f955,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f953]) ).
thf(f956,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f955]) ).
thf(f957,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f956]) ).
thf(f958,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f956]) ).
thf(f959,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f958]) ).
thf(f960,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f959]) ).
thf(f961,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f960]) ).
thf(f962,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f961]) ).
thf(f963,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f962]) ).
thf(f964,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f963]) ).
thf(f965,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f957]) ).
thf(f966,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f957]) ).
thf(f967,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f966]) ).
thf(f968,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f967]) ).
thf(f969,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f968]) ).
thf(f970,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f969]) ).
thf(f971,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f970]) ).
thf(f972,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f971]) ).
thf(f973,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f965]) ).
thf(f974,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f965]) ).
thf(f975,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f974]) ).
thf(f976,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f975]) ).
thf(f977,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f976]) ).
thf(f978,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f977]) ).
thf(f979,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f978]) ).
thf(f980,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f979]) ).
thf(f981,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f973]) ).
thf(f982,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f981]) ).
thf(f983,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f982]) ).
thf(f984,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f983]) ).
thf(f985,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f984]) ).
thf(f986,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f985]) ).
thf(f987,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f954]) ).
thf(f988,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f954]) ).
thf(f989,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f988]) ).
thf(f990,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f989]) ).
thf(f991,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f989]) ).
thf(f992,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f991]) ).
thf(f993,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f992]) ).
thf(f994,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f993]) ).
thf(f995,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f994]) ).
thf(f996,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f995]) ).
thf(f997,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f996]) ).
thf(f998,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f990]) ).
thf(f999,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f990]) ).
thf(f1000,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f999]) ).
thf(f1001,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1000]) ).
thf(f1002,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1001]) ).
thf(f1003,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1002]) ).
thf(f1004,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1003]) ).
thf(f1005,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1004]) ).
thf(f1006,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f998]) ).
thf(f1007,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f998]) ).
thf(f1008,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1007]) ).
thf(f1009,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1008]) ).
thf(f1010,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1009]) ).
thf(f1011,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1010]) ).
thf(f1012,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1011]) ).
thf(f1013,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1012]) ).
thf(f1014,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1006]) ).
thf(f1015,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1014]) ).
thf(f1016,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1015]) ).
thf(f1017,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1016]) ).
thf(f1018,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1017]) ).
thf(f1019,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1018]) ).
thf(f1020,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f987]) ).
thf(f1021,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f987]) ).
thf(f1022,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1021]) ).
thf(f1023,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1022]) ).
thf(f1024,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1022]) ).
thf(f1025,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1024]) ).
thf(f1026,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1025]) ).
thf(f1027,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1026]) ).
thf(f1028,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1027]) ).
thf(f1029,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1028]) ).
thf(f1030,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1029]) ).
thf(f1031,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1023]) ).
thf(f1032,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1023]) ).
thf(f1033,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1032]) ).
thf(f1034,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1033]) ).
thf(f1035,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1034]) ).
thf(f1036,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1035]) ).
thf(f1037,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1036]) ).
thf(f1038,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1037]) ).
thf(f1039,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1031]) ).
thf(f1040,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1031]) ).
thf(f1041,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1040]) ).
thf(f1042,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1041]) ).
thf(f1043,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1042]) ).
thf(f1044,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1043]) ).
thf(f1045,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1044]) ).
thf(f1046,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1045]) ).
thf(f1047,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1039]) ).
thf(f1048,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1047]) ).
thf(f1049,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1048]) ).
thf(f1050,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1049]) ).
thf(f1051,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1050]) ).
thf(f1052,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1051]) ).
thf(f1053,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1020]) ).
thf(f1054,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1053]) ).
thf(f1055,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1053]) ).
thf(f1056,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1055]) ).
thf(f1057,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1056]) ).
thf(f1058,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1057]) ).
thf(f1059,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1058]) ).
thf(f1060,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1059]) ).
thf(f1061,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1060]) ).
thf(f1062,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1054]) ).
thf(f1063,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1054]) ).
thf(f1064,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1063]) ).
thf(f1065,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1064]) ).
thf(f1066,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1065]) ).
thf(f1067,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1066]) ).
thf(f1068,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1067]) ).
thf(f1069,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1068]) ).
thf(f1070,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1062]) ).
thf(f1071,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1062]) ).
thf(f1072,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1071]) ).
thf(f1073,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1072]) ).
thf(f1074,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1073]) ).
thf(f1075,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1074]) ).
thf(f1076,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1075]) ).
thf(f1077,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1076]) ).
thf(f1078,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1070]) ).
thf(f1079,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1078]) ).
thf(f1080,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1079]) ).
thf(f1081,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1080]) ).
thf(f1082,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1081]) ).
thf(f1083,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1082]) ).
thf(f1084,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f951]) ).
thf(f1085,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1084]) ).
thf(f1086,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1084]) ).
thf(f1087,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1086]) ).
thf(f1088,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1087]) ).
thf(f1089,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1087]) ).
thf(f1090,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1089]) ).
thf(f1091,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1090]) ).
thf(f1092,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1091]) ).
thf(f1093,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1092]) ).
thf(f1094,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1093]) ).
thf(f1095,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1094]) ).
thf(f1096,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1088]) ).
thf(f1097,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1088]) ).
thf(f1098,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1097]) ).
thf(f1099,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1098]) ).
thf(f1100,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1099]) ).
thf(f1101,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1100]) ).
thf(f1102,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1101]) ).
thf(f1103,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1102]) ).
thf(f1104,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1096]) ).
thf(f1105,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1096]) ).
thf(f1106,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1105]) ).
thf(f1107,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1106]) ).
thf(f1108,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1107]) ).
thf(f1109,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1108]) ).
thf(f1110,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1109]) ).
thf(f1111,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1110]) ).
thf(f1112,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1104]) ).
thf(f1113,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1112]) ).
thf(f1114,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1113]) ).
thf(f1115,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1114]) ).
thf(f1116,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1115]) ).
thf(f1117,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1116]) ).
thf(f1118,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1085]) ).
thf(f1119,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1085]) ).
thf(f1120,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1119]) ).
thf(f1121,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1120]) ).
thf(f1122,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1120]) ).
thf(f1123,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1122]) ).
thf(f1124,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1123]) ).
thf(f1125,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1124]) ).
thf(f1126,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1125]) ).
thf(f1127,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1126]) ).
thf(f1128,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1127]) ).
thf(f1129,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1121]) ).
thf(f1130,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1121]) ).
thf(f1131,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1130]) ).
thf(f1132,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1131]) ).
thf(f1133,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1132]) ).
thf(f1134,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1133]) ).
thf(f1135,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1134]) ).
thf(f1136,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1135]) ).
thf(f1137,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1129]) ).
thf(f1138,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1129]) ).
thf(f1139,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1138]) ).
thf(f1140,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1139]) ).
thf(f1141,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1140]) ).
thf(f1142,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1141]) ).
thf(f1143,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1142]) ).
thf(f1144,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1143]) ).
thf(f1145,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1137]) ).
thf(f1146,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1145]) ).
thf(f1147,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1146]) ).
thf(f1148,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1147]) ).
thf(f1149,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1148]) ).
thf(f1150,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1149]) ).
thf(f1151,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1118]) ).
thf(f1152,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1118]) ).
thf(f1153,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1152]) ).
thf(f1154,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1153]) ).
thf(f1155,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1153]) ).
thf(f1156,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1155]) ).
thf(f1157,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1156]) ).
thf(f1158,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1157]) ).
thf(f1159,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1158]) ).
thf(f1160,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1159]) ).
thf(f1161,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1160]) ).
thf(f1162,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1154]) ).
thf(f1163,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1154]) ).
thf(f1164,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1163]) ).
thf(f1165,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1164]) ).
thf(f1166,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1165]) ).
thf(f1167,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1166]) ).
thf(f1168,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1167]) ).
thf(f1169,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1168]) ).
thf(f1170,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1162]) ).
thf(f1171,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1162]) ).
thf(f1172,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1171]) ).
thf(f1173,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1172]) ).
thf(f1174,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1173]) ).
thf(f1175,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1174]) ).
thf(f1176,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1175]) ).
thf(f1177,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1176]) ).
thf(f1178,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1170]) ).
thf(f1179,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1178]) ).
thf(f1180,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1179]) ).
thf(f1181,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1180]) ).
thf(f1182,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1181]) ).
thf(f1183,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1182]) ).
thf(f1184,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1151]) ).
thf(f1185,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1184]) ).
thf(f1186,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1184]) ).
thf(f1187,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1186]) ).
thf(f1188,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1187]) ).
thf(f1189,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1188]) ).
thf(f1190,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1189]) ).
thf(f1191,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1190]) ).
thf(f1192,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1191]) ).
thf(f1193,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1185]) ).
thf(f1194,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1185]) ).
thf(f1195,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1194]) ).
thf(f1196,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1195]) ).
thf(f1197,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1196]) ).
thf(f1198,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1197]) ).
thf(f1199,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1198]) ).
thf(f1200,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1199]) ).
thf(f1201,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1193]) ).
thf(f1202,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1193]) ).
thf(f1203,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1202]) ).
thf(f1204,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1203]) ).
thf(f1205,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1204]) ).
thf(f1206,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1205]) ).
thf(f1207,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1206]) ).
thf(f1208,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1207]) ).
thf(f1209,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1201]) ).
thf(f1210,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1209]) ).
thf(f1211,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1210]) ).
thf(f1212,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1211]) ).
thf(f1213,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1212]) ).
thf(f1214,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1213]) ).
thf(f1215,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f682]) ).
thf(f1216,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f682]) ).
thf(f1217,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1216]) ).
thf(f1218,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1217]) ).
thf(f1219,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1217]) ).
thf(f1220,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1219]) ).
thf(f1221,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1220]) ).
thf(f1222,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1220]) ).
thf(f1223,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1222]) ).
thf(f1224,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1223]) ).
thf(f1225,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1223]) ).
thf(f1226,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1225]) ).
thf(f1227,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1226]) ).
thf(f1228,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1227]) ).
thf(f1229,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1228]) ).
thf(f1230,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1229]) ).
thf(f1231,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1230]) ).
thf(f1232,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1224]) ).
thf(f1233,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1224]) ).
thf(f1234,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1233]) ).
thf(f1235,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1234]) ).
thf(f1236,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1235]) ).
thf(f1237,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1236]) ).
thf(f1238,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1237]) ).
thf(f1239,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1238]) ).
thf(f1240,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1232]) ).
thf(f1241,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1232]) ).
thf(f1242,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1241]) ).
thf(f1243,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1242]) ).
thf(f1244,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1243]) ).
thf(f1245,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1244]) ).
thf(f1246,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1245]) ).
thf(f1247,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1246]) ).
thf(f1248,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1240]) ).
thf(f1249,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1248]) ).
thf(f1250,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1249]) ).
thf(f1251,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1250]) ).
thf(f1252,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1251]) ).
thf(f1253,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1252]) ).
thf(f1254,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1221]) ).
thf(f1255,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1221]) ).
thf(f1256,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1255]) ).
thf(f1257,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1256]) ).
thf(f1258,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1256]) ).
thf(f1259,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1258]) ).
thf(f1260,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1259]) ).
thf(f1261,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1260]) ).
thf(f1262,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1261]) ).
thf(f1263,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1262]) ).
thf(f1264,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1263]) ).
thf(f1265,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1257]) ).
thf(f1266,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1257]) ).
thf(f1267,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1266]) ).
thf(f1268,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1267]) ).
thf(f1269,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1268]) ).
thf(f1270,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1269]) ).
thf(f1271,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1270]) ).
thf(f1272,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1271]) ).
thf(f1273,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1265]) ).
thf(f1274,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1265]) ).
thf(f1275,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1274]) ).
thf(f1276,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1275]) ).
thf(f1277,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1276]) ).
thf(f1278,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1277]) ).
thf(f1279,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1278]) ).
thf(f1280,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1279]) ).
thf(f1281,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1273]) ).
thf(f1282,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1281]) ).
thf(f1283,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1282]) ).
thf(f1284,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1283]) ).
thf(f1285,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1284]) ).
thf(f1286,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1285]) ).
thf(f1287,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1254]) ).
thf(f1288,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1254]) ).
thf(f1289,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1288]) ).
thf(f1290,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1289]) ).
thf(f1291,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1289]) ).
thf(f1292,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1291]) ).
thf(f1293,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1292]) ).
thf(f1294,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1293]) ).
thf(f1295,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1294]) ).
thf(f1296,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1295]) ).
thf(f1297,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1296]) ).
thf(f1298,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1290]) ).
thf(f1299,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1290]) ).
thf(f1300,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1299]) ).
thf(f1301,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1300]) ).
thf(f1302,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1301]) ).
thf(f1303,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1302]) ).
thf(f1304,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1303]) ).
thf(f1305,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1304]) ).
thf(f1306,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1298]) ).
thf(f1307,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1298]) ).
thf(f1308,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1307]) ).
thf(f1309,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1308]) ).
thf(f1310,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1309]) ).
thf(f1311,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1310]) ).
thf(f1312,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1311]) ).
thf(f1313,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1312]) ).
thf(f1314,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1306]) ).
thf(f1315,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1314]) ).
thf(f1316,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1315]) ).
thf(f1317,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1316]) ).
thf(f1318,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1317]) ).
thf(f1319,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1318]) ).
thf(f1320,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1287]) ).
thf(f1321,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1320]) ).
thf(f1322,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1320]) ).
thf(f1323,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1322]) ).
thf(f1324,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1323]) ).
thf(f1325,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1324]) ).
thf(f1326,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1325]) ).
thf(f1327,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1326]) ).
thf(f1328,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1327]) ).
thf(f1329,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1321]) ).
thf(f1330,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1321]) ).
thf(f1331,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1330]) ).
thf(f1332,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1331]) ).
thf(f1333,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1332]) ).
thf(f1334,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1333]) ).
thf(f1335,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1334]) ).
thf(f1336,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1335]) ).
thf(f1337,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1329]) ).
thf(f1338,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1329]) ).
thf(f1339,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1338]) ).
thf(f1340,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1339]) ).
thf(f1341,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1340]) ).
thf(f1342,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1341]) ).
thf(f1343,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1342]) ).
thf(f1344,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1343]) ).
thf(f1345,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1337]) ).
thf(f1346,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1345]) ).
thf(f1347,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1346]) ).
thf(f1348,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1347]) ).
thf(f1349,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1348]) ).
thf(f1350,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1349]) ).
thf(f1351,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1218]) ).
thf(f1352,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1218]) ).
thf(f1353,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1352]) ).
thf(f1354,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1353]) ).
thf(f1355,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1353]) ).
thf(f1356,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1355]) ).
thf(f1357,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1356]) ).
thf(f1358,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1356]) ).
thf(f1359,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1358]) ).
thf(f1360,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1359]) ).
thf(f1361,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1360]) ).
thf(f1362,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1361]) ).
thf(f1363,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1362]) ).
thf(f1364,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1363]) ).
thf(f1365,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1357]) ).
thf(f1366,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1357]) ).
thf(f1367,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1366]) ).
thf(f1368,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1367]) ).
thf(f1369,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1368]) ).
thf(f1370,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1369]) ).
thf(f1371,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1370]) ).
thf(f1372,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1371]) ).
thf(f1373,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1365]) ).
thf(f1374,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1365]) ).
thf(f1375,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1374]) ).
thf(f1376,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1375]) ).
thf(f1377,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1376]) ).
thf(f1378,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1377]) ).
thf(f1379,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1378]) ).
thf(f1380,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1379]) ).
thf(f1381,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1373]) ).
thf(f1382,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1381]) ).
thf(f1383,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1382]) ).
thf(f1384,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1383]) ).
thf(f1385,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1384]) ).
thf(f1386,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1385]) ).
thf(f1387,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1354]) ).
thf(f1388,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1354]) ).
thf(f1389,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1388]) ).
thf(f1390,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1389]) ).
thf(f1391,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1389]) ).
thf(f1392,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1391]) ).
thf(f1393,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1392]) ).
thf(f1394,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1393]) ).
thf(f1395,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1394]) ).
thf(f1396,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1395]) ).
thf(f1397,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1396]) ).
thf(f1398,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1390]) ).
thf(f1399,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1390]) ).
thf(f1400,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1399]) ).
thf(f1401,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1400]) ).
thf(f1402,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1401]) ).
thf(f1403,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1402]) ).
thf(f1404,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1403]) ).
thf(f1405,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1404]) ).
thf(f1406,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1398]) ).
thf(f1407,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1398]) ).
thf(f1408,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1407]) ).
thf(f1409,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1408]) ).
thf(f1410,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1409]) ).
thf(f1411,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1410]) ).
thf(f1412,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1411]) ).
thf(f1413,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1412]) ).
thf(f1414,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1406]) ).
thf(f1415,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1414]) ).
thf(f1416,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1415]) ).
thf(f1417,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1416]) ).
thf(f1418,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1417]) ).
thf(f1419,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1418]) ).
thf(f1420,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1387]) ).
thf(f1421,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1387]) ).
thf(f1422,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1421]) ).
thf(f1423,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1422]) ).
thf(f1424,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1422]) ).
thf(f1425,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1424]) ).
thf(f1426,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1425]) ).
thf(f1427,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1426]) ).
thf(f1428,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1427]) ).
thf(f1429,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1428]) ).
thf(f1430,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1429]) ).
thf(f1431,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1423]) ).
thf(f1432,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1423]) ).
thf(f1433,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1432]) ).
thf(f1434,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1433]) ).
thf(f1435,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1434]) ).
thf(f1436,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1435]) ).
thf(f1437,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1436]) ).
thf(f1438,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1437]) ).
thf(f1439,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1431]) ).
thf(f1440,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1431]) ).
thf(f1441,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1440]) ).
thf(f1442,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1441]) ).
thf(f1443,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1442]) ).
thf(f1444,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1443]) ).
thf(f1445,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1444]) ).
thf(f1446,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1445]) ).
thf(f1447,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1439]) ).
thf(f1448,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1447]) ).
thf(f1449,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1448]) ).
thf(f1450,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1449]) ).
thf(f1451,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1450]) ).
thf(f1452,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1451]) ).
thf(f1453,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1420]) ).
thf(f1454,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1453]) ).
thf(f1455,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1453]) ).
thf(f1456,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1455]) ).
thf(f1457,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1456]) ).
thf(f1458,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1457]) ).
thf(f1459,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1458]) ).
thf(f1460,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1459]) ).
thf(f1461,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1460]) ).
thf(f1462,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1454]) ).
thf(f1463,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1454]) ).
thf(f1464,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1463]) ).
thf(f1465,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1464]) ).
thf(f1466,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1465]) ).
thf(f1467,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1466]) ).
thf(f1468,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1467]) ).
thf(f1469,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1468]) ).
thf(f1470,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1462]) ).
thf(f1471,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1462]) ).
thf(f1472,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1471]) ).
thf(f1473,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1472]) ).
thf(f1474,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1473]) ).
thf(f1475,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1474]) ).
thf(f1476,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1475]) ).
thf(f1477,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1476]) ).
thf(f1478,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1470]) ).
thf(f1479,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1478]) ).
thf(f1480,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1479]) ).
thf(f1481,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1480]) ).
thf(f1482,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1481]) ).
thf(f1483,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1482]) ).
thf(f1484,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1351]) ).
thf(f1485,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1351]) ).
thf(f1486,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1485]) ).
thf(f1487,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1486]) ).
thf(f1488,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1486]) ).
thf(f1489,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1488]) ).
thf(f1490,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1489]) ).
thf(f1491,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1489]) ).
thf(f1492,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1491]) ).
thf(f1493,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1492]) ).
thf(f1494,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1493]) ).
thf(f1495,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1494]) ).
thf(f1496,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1495]) ).
thf(f1497,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1496]) ).
thf(f1498,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1490]) ).
thf(f1499,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1490]) ).
thf(f1500,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1499]) ).
thf(f1501,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1500]) ).
thf(f1502,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1501]) ).
thf(f1503,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1502]) ).
thf(f1504,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1503]) ).
thf(f1505,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1504]) ).
thf(f1506,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1498]) ).
thf(f1507,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1498]) ).
thf(f1508,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1507]) ).
thf(f1509,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1508]) ).
thf(f1510,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1509]) ).
thf(f1511,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1510]) ).
thf(f1512,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1511]) ).
thf(f1513,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1512]) ).
thf(f1514,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1506]) ).
thf(f1515,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1514]) ).
thf(f1516,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1515]) ).
thf(f1517,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1516]) ).
thf(f1518,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1517]) ).
thf(f1519,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1518]) ).
thf(f1520,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1487]) ).
thf(f1521,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1487]) ).
thf(f1522,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1521]) ).
thf(f1523,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1522]) ).
thf(f1524,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1522]) ).
thf(f1525,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1524]) ).
thf(f1526,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1525]) ).
thf(f1527,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1526]) ).
thf(f1528,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1527]) ).
thf(f1529,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1528]) ).
thf(f1530,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1529]) ).
thf(f1531,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1523]) ).
thf(f1532,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1523]) ).
thf(f1533,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1532]) ).
thf(f1534,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1533]) ).
thf(f1535,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1534]) ).
thf(f1536,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1535]) ).
thf(f1537,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1536]) ).
thf(f1538,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1537]) ).
thf(f1539,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1531]) ).
thf(f1540,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1531]) ).
thf(f1541,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1540]) ).
thf(f1542,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1541]) ).
thf(f1543,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1542]) ).
thf(f1544,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1543]) ).
thf(f1545,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1544]) ).
thf(f1546,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1545]) ).
thf(f1547,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1539]) ).
thf(f1548,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1547]) ).
thf(f1549,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1548]) ).
thf(f1550,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1549]) ).
thf(f1551,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1550]) ).
thf(f1552,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1551]) ).
thf(f1553,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1520]) ).
thf(f1554,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1520]) ).
thf(f1555,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1554]) ).
thf(f1556,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1555]) ).
thf(f1557,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1555]) ).
thf(f1558,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1557]) ).
thf(f1559,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1558]) ).
thf(f1560,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1559]) ).
thf(f1561,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1560]) ).
thf(f1562,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1561]) ).
thf(f1563,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1562]) ).
thf(f1564,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1556]) ).
thf(f1565,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1556]) ).
thf(f1566,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1565]) ).
thf(f1567,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1566]) ).
thf(f1568,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1567]) ).
thf(f1569,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1568]) ).
thf(f1570,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1569]) ).
thf(f1571,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1570]) ).
thf(f1572,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1564]) ).
thf(f1573,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1564]) ).
thf(f1574,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1573]) ).
thf(f1575,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1574]) ).
thf(f1576,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1575]) ).
thf(f1577,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1576]) ).
thf(f1578,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1577]) ).
thf(f1579,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1578]) ).
thf(f1580,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1572]) ).
thf(f1581,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1580]) ).
thf(f1582,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1581]) ).
thf(f1583,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1582]) ).
thf(f1584,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1583]) ).
thf(f1585,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1584]) ).
thf(f1586,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1553]) ).
thf(f1587,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1586]) ).
thf(f1588,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1586]) ).
thf(f1589,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1588]) ).
thf(f1590,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1589]) ).
thf(f1591,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1590]) ).
thf(f1592,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1591]) ).
thf(f1593,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1592]) ).
thf(f1594,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1593]) ).
thf(f1595,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1587]) ).
thf(f1596,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1587]) ).
thf(f1597,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1596]) ).
thf(f1598,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1597]) ).
thf(f1599,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1598]) ).
thf(f1600,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1599]) ).
thf(f1601,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1600]) ).
thf(f1602,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1601]) ).
thf(f1603,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1595]) ).
thf(f1604,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1595]) ).
thf(f1605,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1604]) ).
thf(f1606,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1605]) ).
thf(f1607,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1606]) ).
thf(f1608,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1607]) ).
thf(f1609,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1608]) ).
thf(f1610,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1609]) ).
thf(f1611,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1603]) ).
thf(f1612,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1611]) ).
thf(f1613,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1612]) ).
thf(f1614,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1613]) ).
thf(f1615,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1614]) ).
thf(f1616,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1615]) ).
thf(f1617,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1484]) ).
thf(f1618,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1617]) ).
thf(f1619,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1617]) ).
thf(f1620,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1619]) ).
thf(f1621,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1620]) ).
thf(f1622,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1620]) ).
thf(f1623,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1622]) ).
thf(f1624,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1623]) ).
thf(f1625,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1624]) ).
thf(f1626,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1625]) ).
thf(f1627,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1626]) ).
thf(f1628,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1627]) ).
thf(f1629,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1621]) ).
thf(f1630,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1621]) ).
thf(f1631,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1630]) ).
thf(f1632,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1631]) ).
thf(f1633,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1632]) ).
thf(f1634,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1633]) ).
thf(f1635,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1634]) ).
thf(f1636,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1635]) ).
thf(f1637,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1629]) ).
thf(f1638,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1629]) ).
thf(f1639,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1638]) ).
thf(f1640,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1639]) ).
thf(f1641,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1640]) ).
thf(f1642,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1641]) ).
thf(f1643,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1642]) ).
thf(f1644,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1643]) ).
thf(f1645,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1637]) ).
thf(f1646,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1645]) ).
thf(f1647,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1646]) ).
thf(f1648,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1647]) ).
thf(f1649,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1648]) ).
thf(f1650,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1649]) ).
thf(f1651,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1618]) ).
thf(f1652,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1618]) ).
thf(f1653,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1652]) ).
thf(f1654,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1653]) ).
thf(f1655,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1653]) ).
thf(f1656,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1655]) ).
thf(f1657,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1656]) ).
thf(f1658,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1657]) ).
thf(f1659,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1658]) ).
thf(f1660,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1659]) ).
thf(f1661,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1660]) ).
thf(f1662,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1654]) ).
thf(f1663,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1654]) ).
thf(f1664,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1663]) ).
thf(f1665,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1664]) ).
thf(f1666,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1665]) ).
thf(f1667,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1666]) ).
thf(f1668,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1667]) ).
thf(f1669,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1668]) ).
thf(f1670,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1662]) ).
thf(f1671,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1662]) ).
thf(f1672,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1671]) ).
thf(f1673,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1672]) ).
thf(f1674,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1673]) ).
thf(f1675,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1674]) ).
thf(f1676,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1675]) ).
thf(f1677,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1676]) ).
thf(f1678,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1670]) ).
thf(f1679,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1678]) ).
thf(f1680,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1679]) ).
thf(f1681,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1680]) ).
thf(f1682,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1681]) ).
thf(f1683,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1682]) ).
thf(f1684,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1651]) ).
thf(f1685,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1651]) ).
thf(f1686,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1685]) ).
thf(f1687,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1686]) ).
thf(f1688,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1686]) ).
thf(f1689,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1688]) ).
thf(f1690,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1689]) ).
thf(f1691,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1690]) ).
thf(f1692,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1691]) ).
thf(f1693,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1692]) ).
thf(f1694,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1693]) ).
thf(f1695,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1687]) ).
thf(f1696,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1687]) ).
thf(f1697,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1696]) ).
thf(f1698,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1697]) ).
thf(f1699,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1698]) ).
thf(f1700,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1699]) ).
thf(f1701,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1700]) ).
thf(f1702,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1701]) ).
thf(f1703,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1695]) ).
thf(f1704,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1695]) ).
thf(f1705,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1704]) ).
thf(f1706,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1705]) ).
thf(f1707,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1706]) ).
thf(f1708,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1707]) ).
thf(f1709,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1708]) ).
thf(f1710,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1709]) ).
thf(f1711,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1703]) ).
thf(f1712,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1711]) ).
thf(f1713,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1712]) ).
thf(f1714,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1713]) ).
thf(f1715,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1714]) ).
thf(f1716,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1715]) ).
thf(f1717,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1684]) ).
thf(f1718,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1717]) ).
thf(f1719,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1717]) ).
thf(f1720,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1719]) ).
thf(f1721,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1720]) ).
thf(f1722,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1721]) ).
thf(f1723,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1722]) ).
thf(f1724,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1723]) ).
thf(f1725,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1724]) ).
thf(f1726,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1718]) ).
thf(f1727,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1718]) ).
thf(f1728,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1727]) ).
thf(f1729,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1728]) ).
thf(f1730,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1729]) ).
thf(f1731,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1730]) ).
thf(f1732,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1731]) ).
thf(f1733,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1732]) ).
thf(f1734,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1726]) ).
thf(f1735,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1726]) ).
thf(f1736,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1735]) ).
thf(f1737,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1736]) ).
thf(f1738,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1737]) ).
thf(f1739,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1738]) ).
thf(f1740,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1739]) ).
thf(f1741,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1740]) ).
thf(f1742,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1734]) ).
thf(f1743,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1742]) ).
thf(f1744,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1743]) ).
thf(f1745,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1744]) ).
thf(f1746,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1745]) ).
thf(f1747,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1746]) ).
thf(f1748,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1215]) ).
thf(f1749,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1748]) ).
thf(f1750,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1748]) ).
thf(f1751,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1750]) ).
thf(f1752,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1751]) ).
thf(f1753,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1751]) ).
thf(f1754,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1753]) ).
thf(f1755,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1754]) ).
thf(f1756,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1754]) ).
thf(f1757,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1756]) ).
thf(f1758,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1757]) ).
thf(f1759,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1758]) ).
thf(f1760,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1759]) ).
thf(f1761,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1760]) ).
thf(f1762,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1761]) ).
thf(f1763,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1755]) ).
thf(f1764,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1755]) ).
thf(f1765,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1764]) ).
thf(f1766,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1765]) ).
thf(f1767,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1766]) ).
thf(f1768,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1767]) ).
thf(f1769,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1768]) ).
thf(f1770,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1769]) ).
thf(f1771,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1763]) ).
thf(f1772,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1763]) ).
thf(f1773,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1772]) ).
thf(f1774,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1773]) ).
thf(f1775,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1774]) ).
thf(f1776,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1775]) ).
thf(f1777,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1776]) ).
thf(f1778,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1777]) ).
thf(f1779,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1771]) ).
thf(f1780,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1779]) ).
thf(f1781,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1780]) ).
thf(f1782,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1781]) ).
thf(f1783,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1782]) ).
thf(f1784,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1783]) ).
thf(f1785,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1752]) ).
thf(f1786,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1752]) ).
thf(f1787,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1786]) ).
thf(f1788,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1787]) ).
thf(f1789,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1787]) ).
thf(f1790,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1789]) ).
thf(f1791,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1790]) ).
thf(f1792,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1791]) ).
thf(f1793,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1792]) ).
thf(f1794,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1793]) ).
thf(f1795,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1794]) ).
thf(f1796,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1788]) ).
thf(f1797,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1788]) ).
thf(f1798,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1797]) ).
thf(f1799,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1798]) ).
thf(f1800,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1799]) ).
thf(f1801,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1800]) ).
thf(f1802,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1801]) ).
thf(f1803,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1802]) ).
thf(f1804,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1796]) ).
thf(f1805,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1796]) ).
thf(f1806,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1805]) ).
thf(f1807,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1806]) ).
thf(f1808,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1807]) ).
thf(f1809,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1808]) ).
thf(f1810,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1809]) ).
thf(f1811,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1810]) ).
thf(f1812,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1804]) ).
thf(f1813,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1812]) ).
thf(f1814,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1813]) ).
thf(f1815,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1814]) ).
thf(f1816,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1815]) ).
thf(f1817,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1816]) ).
thf(f1818,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1785]) ).
thf(f1819,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1785]) ).
thf(f1820,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1819]) ).
thf(f1821,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1820]) ).
thf(f1822,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1820]) ).
thf(f1823,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1822]) ).
thf(f1824,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1823]) ).
thf(f1825,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1824]) ).
thf(f1826,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1825]) ).
thf(f1827,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1826]) ).
thf(f1828,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1827]) ).
thf(f1829,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1821]) ).
thf(f1830,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1821]) ).
thf(f1831,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1830]) ).
thf(f1832,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1831]) ).
thf(f1833,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1832]) ).
thf(f1834,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1833]) ).
thf(f1835,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1834]) ).
thf(f1836,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1835]) ).
thf(f1837,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1829]) ).
thf(f1838,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1829]) ).
thf(f1839,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1838]) ).
thf(f1840,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1839]) ).
thf(f1841,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1840]) ).
thf(f1842,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1841]) ).
thf(f1843,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1842]) ).
thf(f1844,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1843]) ).
thf(f1845,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1837]) ).
thf(f1846,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1845]) ).
thf(f1847,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1846]) ).
thf(f1848,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1847]) ).
thf(f1849,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1848]) ).
thf(f1850,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1849]) ).
thf(f1851,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1818]) ).
thf(f1852,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1851]) ).
thf(f1853,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1851]) ).
thf(f1854,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1853]) ).
thf(f1855,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1854]) ).
thf(f1856,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1855]) ).
thf(f1857,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1856]) ).
thf(f1858,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1857]) ).
thf(f1859,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1858]) ).
thf(f1860,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1852]) ).
thf(f1861,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1852]) ).
thf(f1862,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1861]) ).
thf(f1863,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1862]) ).
thf(f1864,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1863]) ).
thf(f1865,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1864]) ).
thf(f1866,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1865]) ).
thf(f1867,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1866]) ).
thf(f1868,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1860]) ).
thf(f1869,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1860]) ).
thf(f1870,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1869]) ).
thf(f1871,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1870]) ).
thf(f1872,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1871]) ).
thf(f1873,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1872]) ).
thf(f1874,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1873]) ).
thf(f1875,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1874]) ).
thf(f1876,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1868]) ).
thf(f1877,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1876]) ).
thf(f1878,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1877]) ).
thf(f1879,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1878]) ).
thf(f1880,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1879]) ).
thf(f1881,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1880]) ).
thf(f1882,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1749]) ).
thf(f1883,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1749]) ).
thf(f1884,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1883]) ).
thf(f1885,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1884]) ).
thf(f1886,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1884]) ).
thf(f1887,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1886]) ).
thf(f1888,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1887]) ).
thf(f1889,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1887]) ).
thf(f1890,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1889]) ).
thf(f1891,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1890]) ).
thf(f1892,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1891]) ).
thf(f1893,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1892]) ).
thf(f1894,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1893]) ).
thf(f1895,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1894]) ).
thf(f1896,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1888]) ).
thf(f1897,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1888]) ).
thf(f1898,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1897]) ).
thf(f1899,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1898]) ).
thf(f1900,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1899]) ).
thf(f1901,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1900]) ).
thf(f1902,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1901]) ).
thf(f1903,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1902]) ).
thf(f1904,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1896]) ).
thf(f1905,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1896]) ).
thf(f1906,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1905]) ).
thf(f1907,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1906]) ).
thf(f1908,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1907]) ).
thf(f1909,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1908]) ).
thf(f1910,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1909]) ).
thf(f1911,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1910]) ).
thf(f1912,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1904]) ).
thf(f1913,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1912]) ).
thf(f1914,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1913]) ).
thf(f1915,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1914]) ).
thf(f1916,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1915]) ).
thf(f1917,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1916]) ).
thf(f1918,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1885]) ).
thf(f1919,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1885]) ).
thf(f1920,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1919]) ).
thf(f1921,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1920]) ).
thf(f1922,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1920]) ).
thf(f1923,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1922]) ).
thf(f1924,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1923]) ).
thf(f1925,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1924]) ).
thf(f1926,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1925]) ).
thf(f1927,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1926]) ).
thf(f1928,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1927]) ).
thf(f1929,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1921]) ).
thf(f1930,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1921]) ).
thf(f1931,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1930]) ).
thf(f1932,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1931]) ).
thf(f1933,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1932]) ).
thf(f1934,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1933]) ).
thf(f1935,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1934]) ).
thf(f1936,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1935]) ).
thf(f1937,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1929]) ).
thf(f1938,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1929]) ).
thf(f1939,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1938]) ).
thf(f1940,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1939]) ).
thf(f1941,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1940]) ).
thf(f1942,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1941]) ).
thf(f1943,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1942]) ).
thf(f1944,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1943]) ).
thf(f1945,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1937]) ).
thf(f1946,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1945]) ).
thf(f1947,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1946]) ).
thf(f1948,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1947]) ).
thf(f1949,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1948]) ).
thf(f1950,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1949]) ).
thf(f1951,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1918]) ).
thf(f1952,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1918]) ).
thf(f1953,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1952]) ).
thf(f1954,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1953]) ).
thf(f1955,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1953]) ).
thf(f1956,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1955]) ).
thf(f1957,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1956]) ).
thf(f1958,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1957]) ).
thf(f1959,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1958]) ).
thf(f1960,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1959]) ).
thf(f1961,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1960]) ).
thf(f1962,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1954]) ).
thf(f1963,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1954]) ).
thf(f1964,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1963]) ).
thf(f1965,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1964]) ).
thf(f1966,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1965]) ).
thf(f1967,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1966]) ).
thf(f1968,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1967]) ).
thf(f1969,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1968]) ).
thf(f1970,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1962]) ).
thf(f1971,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1962]) ).
thf(f1972,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1971]) ).
thf(f1973,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1972]) ).
thf(f1974,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1973]) ).
thf(f1975,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1974]) ).
thf(f1976,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1975]) ).
thf(f1977,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1976]) ).
thf(f1978,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1970]) ).
thf(f1979,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1978]) ).
thf(f1980,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1979]) ).
thf(f1981,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1980]) ).
thf(f1982,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1981]) ).
thf(f1983,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1982]) ).
thf(f1984,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1951]) ).
thf(f1985,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1984]) ).
thf(f1986,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1984]) ).
thf(f1987,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1986]) ).
thf(f1988,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1987]) ).
thf(f1989,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1988]) ).
thf(f1990,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1989]) ).
thf(f1991,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1990]) ).
thf(f1992,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1991]) ).
thf(f1993,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1985]) ).
thf(f1994,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1985]) ).
thf(f1995,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f1994]) ).
thf(f1996,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1995]) ).
thf(f1997,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1996]) ).
thf(f1998,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f1997]) ).
thf(f1999,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1998]) ).
thf(f2000,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1999]) ).
thf(f2001,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1993]) ).
thf(f2002,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1993]) ).
thf(f2003,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2002]) ).
thf(f2004,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2003]) ).
thf(f2005,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2004]) ).
thf(f2006,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2005]) ).
thf(f2007,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2006]) ).
thf(f2008,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2007]) ).
thf(f2009,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2001]) ).
thf(f2010,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2009]) ).
thf(f2011,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2010]) ).
thf(f2012,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2011]) ).
thf(f2013,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2012]) ).
thf(f2014,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2013]) ).
thf(f2015,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1882]) ).
thf(f2016,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1882]) ).
thf(f2017,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2016]) ).
thf(f2018,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2017]) ).
thf(f2019,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2017]) ).
thf(f2020,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2019]) ).
thf(f2021,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2020]) ).
thf(f2022,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2020]) ).
thf(f2023,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2022]) ).
thf(f2024,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2023]) ).
thf(f2025,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2024]) ).
thf(f2026,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2025]) ).
thf(f2027,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2026]) ).
thf(f2028,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2027]) ).
thf(f2029,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2021]) ).
thf(f2030,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2021]) ).
thf(f2031,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2030]) ).
thf(f2032,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2031]) ).
thf(f2033,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2032]) ).
thf(f2034,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2033]) ).
thf(f2035,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2034]) ).
thf(f2036,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2035]) ).
thf(f2037,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2029]) ).
thf(f2038,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2029]) ).
thf(f2039,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2038]) ).
thf(f2040,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2039]) ).
thf(f2041,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2040]) ).
thf(f2042,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2041]) ).
thf(f2043,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2042]) ).
thf(f2044,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2043]) ).
thf(f2045,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2037]) ).
thf(f2046,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2045]) ).
thf(f2047,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2046]) ).
thf(f2048,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2047]) ).
thf(f2049,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2048]) ).
thf(f2050,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2049]) ).
thf(f2051,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2018]) ).
thf(f2052,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2018]) ).
thf(f2053,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2052]) ).
thf(f2054,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2053]) ).
thf(f2055,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2053]) ).
thf(f2056,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2055]) ).
thf(f2057,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2056]) ).
thf(f2058,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2057]) ).
thf(f2059,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2058]) ).
thf(f2060,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2059]) ).
thf(f2061,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2060]) ).
thf(f2062,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2054]) ).
thf(f2063,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2054]) ).
thf(f2064,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2063]) ).
thf(f2065,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2064]) ).
thf(f2066,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2065]) ).
thf(f2067,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2066]) ).
thf(f2068,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2067]) ).
thf(f2069,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2068]) ).
thf(f2070,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2062]) ).
thf(f2071,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2062]) ).
thf(f2072,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2071]) ).
thf(f2073,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2072]) ).
thf(f2074,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2073]) ).
thf(f2075,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2074]) ).
thf(f2076,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2075]) ).
thf(f2077,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2076]) ).
thf(f2078,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2070]) ).
thf(f2079,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2078]) ).
thf(f2080,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2079]) ).
thf(f2081,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2080]) ).
thf(f2082,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2081]) ).
thf(f2083,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2082]) ).
thf(f2084,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2051]) ).
thf(f2085,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2051]) ).
thf(f2086,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2085]) ).
thf(f2087,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2086]) ).
thf(f2088,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2086]) ).
thf(f2089,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2088]) ).
thf(f2090,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2089]) ).
thf(f2091,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2090]) ).
thf(f2092,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2091]) ).
thf(f2093,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2092]) ).
thf(f2094,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2093]) ).
thf(f2095,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2087]) ).
thf(f2096,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2087]) ).
thf(f2097,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2096]) ).
thf(f2098,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2097]) ).
thf(f2099,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2098]) ).
thf(f2100,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2099]) ).
thf(f2101,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2100]) ).
thf(f2102,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2101]) ).
thf(f2103,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2095]) ).
thf(f2104,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2095]) ).
thf(f2105,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2104]) ).
thf(f2106,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2105]) ).
thf(f2107,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2106]) ).
thf(f2108,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2107]) ).
thf(f2109,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2108]) ).
thf(f2110,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2109]) ).
thf(f2111,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2103]) ).
thf(f2112,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2111]) ).
thf(f2113,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2112]) ).
thf(f2114,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2113]) ).
thf(f2115,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2114]) ).
thf(f2116,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2115]) ).
thf(f2117,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2084]) ).
thf(f2118,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2117]) ).
thf(f2119,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2117]) ).
thf(f2120,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2119]) ).
thf(f2121,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2120]) ).
thf(f2122,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2121]) ).
thf(f2123,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2122]) ).
thf(f2124,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2123]) ).
thf(f2125,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2124]) ).
thf(f2126,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2118]) ).
thf(f2127,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2118]) ).
thf(f2128,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2127]) ).
thf(f2129,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2128]) ).
thf(f2130,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2129]) ).
thf(f2131,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2130]) ).
thf(f2132,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2131]) ).
thf(f2133,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2132]) ).
thf(f2134,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2126]) ).
thf(f2135,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2126]) ).
thf(f2136,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2135]) ).
thf(f2137,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2136]) ).
thf(f2138,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2137]) ).
thf(f2139,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2138]) ).
thf(f2140,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2139]) ).
thf(f2141,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2140]) ).
thf(f2142,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2134]) ).
thf(f2143,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2142]) ).
thf(f2144,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2143]) ).
thf(f2145,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2144]) ).
thf(f2146,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2145]) ).
thf(f2147,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2146]) ).
thf(f2148,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2015]) ).
thf(f2149,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2148]) ).
thf(f2150,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2148]) ).
thf(f2151,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2150]) ).
thf(f2152,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2151]) ).
thf(f2153,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2151]) ).
thf(f2154,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2153]) ).
thf(f2155,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2154]) ).
thf(f2156,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2155]) ).
thf(f2157,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2156]) ).
thf(f2158,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2157]) ).
thf(f2159,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2158]) ).
thf(f2160,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2152]) ).
thf(f2161,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2152]) ).
thf(f2162,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2161]) ).
thf(f2163,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2162]) ).
thf(f2164,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2163]) ).
thf(f2165,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2164]) ).
thf(f2166,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2165]) ).
thf(f2167,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2166]) ).
thf(f2168,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2160]) ).
thf(f2169,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2160]) ).
thf(f2170,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2169]) ).
thf(f2171,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2170]) ).
thf(f2172,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2171]) ).
thf(f2173,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2172]) ).
thf(f2174,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2173]) ).
thf(f2175,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2174]) ).
thf(f2176,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2168]) ).
thf(f2177,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2176]) ).
thf(f2178,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2177]) ).
thf(f2179,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2178]) ).
thf(f2180,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2179]) ).
thf(f2181,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2180]) ).
thf(f2182,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2149]) ).
thf(f2183,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2149]) ).
thf(f2184,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2183]) ).
thf(f2185,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2184]) ).
thf(f2186,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2184]) ).
thf(f2187,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2186]) ).
thf(f2188,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2187]) ).
thf(f2189,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2188]) ).
thf(f2190,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2189]) ).
thf(f2191,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2190]) ).
thf(f2192,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2191]) ).
thf(f2193,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2185]) ).
thf(f2194,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2185]) ).
thf(f2195,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2194]) ).
thf(f2196,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2195]) ).
thf(f2197,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2196]) ).
thf(f2198,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2197]) ).
thf(f2199,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2198]) ).
thf(f2200,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2199]) ).
thf(f2201,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2193]) ).
thf(f2202,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2193]) ).
thf(f2203,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2202]) ).
thf(f2204,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2203]) ).
thf(f2205,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2204]) ).
thf(f2206,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2205]) ).
thf(f2207,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2206]) ).
thf(f2208,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2207]) ).
thf(f2209,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2201]) ).
thf(f2210,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2209]) ).
thf(f2211,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2210]) ).
thf(f2212,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2211]) ).
thf(f2213,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2212]) ).
thf(f2214,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2213]) ).
thf(f2215,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2182]) ).
thf(f2216,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2182]) ).
thf(f2217,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2216]) ).
thf(f2218,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2217]) ).
thf(f2219,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2217]) ).
thf(f2220,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2219]) ).
thf(f2221,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2220]) ).
thf(f2222,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2221]) ).
thf(f2223,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2222]) ).
thf(f2224,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2223]) ).
thf(f2225,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2224]) ).
thf(f2226,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2218]) ).
thf(f2227,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2218]) ).
thf(f2228,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2227]) ).
thf(f2229,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2228]) ).
thf(f2230,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2229]) ).
thf(f2231,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2230]) ).
thf(f2232,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2231]) ).
thf(f2233,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2232]) ).
thf(f2234,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2226]) ).
thf(f2235,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2226]) ).
thf(f2236,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2235]) ).
thf(f2237,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2236]) ).
thf(f2238,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2237]) ).
thf(f2239,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2238]) ).
thf(f2240,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2239]) ).
thf(f2241,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2240]) ).
thf(f2242,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2234]) ).
thf(f2243,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2242]) ).
thf(f2244,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2243]) ).
thf(f2245,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2244]) ).
thf(f2246,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2245]) ).
thf(f2247,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2246]) ).
thf(f2248,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f2215]) ).
thf(f2249,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2248]) ).
thf(f2250,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2248]) ).
thf(f2251,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2250]) ).
thf(f2252,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2251]) ).
thf(f2253,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2252]) ).
thf(f2254,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2253]) ).
thf(f2255,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2254]) ).
thf(f2256,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2255]) ).
thf(f2257,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f2249]) ).
thf(f2258,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2249]) ).
thf(f2259,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2258]) ).
thf(f2260,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2259]) ).
thf(f2261,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2260]) ).
thf(f2262,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2261]) ).
thf(f2263,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2262]) ).
thf(f2264,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2263]) ).
thf(f2265,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2257]) ).
thf(f2266,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2257]) ).
thf(f2267,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2266]) ).
thf(f2268,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2267]) ).
thf(f2269,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2268]) ).
thf(f2270,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2269]) ).
thf(f2271,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2270]) ).
thf(f2272,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2271]) ).
thf(f2273,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f2265]) ).
thf(f2274,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f2273]) ).
thf(f2275,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2274]) ).
thf(f2276,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( ( mrel @ sK0 @ X3 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f2275]) ).
thf(f2277,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( ( mrel @ sK0 @ X4 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f2276]) ).
thf(f2278,plain,
! [X2: mworld,X3: mworld,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2277]) ).
thf(f2279,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ~ ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y1 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f144]) ).
thf(f2280,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ sK0 @ X1 )
=> ~ ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2279]) ).
thf(f2281,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ~ ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2280]) ).
thf(f2282,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f2281]) ).
thf(f2283,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f2282]) ).
thf(f2284,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f2282]) ).
thf(f2285,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2284]) ).
thf(f2286,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2285]) ).
thf(f2287,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2286]) ).
thf(f2288,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ ( sK1 @ X1 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f2287]) ).
thf(f2289,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ ( sK1 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f2288]) ).
thf(f2290,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ ( sK1 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ ( sK3 @ X1 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f2289]) ).
thf(f2291,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ Y0 ) )
@ ( sK1 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ Y0 ) )
@ ( sK3 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ Y0 ) )
@ ( sK4 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f2290]) ).
thf(f2292,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ( mrel @ X1 @ ( sK1 @ X1 ) )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK2 @ X1 ) )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK3 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK4 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2291]) ).
thf(f2293,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK2 @ X1 ) )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK3 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK4 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2292]) ).
thf(f2294,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK2 @ X1 ) )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK3 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK4 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2292]) ).
thf(f2295,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK3 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK4 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2294]) ).
thf(f2296,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK1 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK2 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK3 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK4 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2294]) ).
thf(f2297,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK1 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK2 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK4 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2296]) ).
thf(f2298,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK1 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK2 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK4 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2296]) ).
thf(f2299,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK3 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK2 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2298]) ).
thf(f2300,plain,
! [X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK4 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK1 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK2 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2298]) ).
thf(f2301,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK2 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2297]) ).
thf(f2302,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK4 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK2 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2297]) ).
thf(f2303,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK4 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2295]) ).
thf(f2304,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK4 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2295]) ).
thf(f2305,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2304]) ).
thf(f2306,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK4 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK1 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2304]) ).
thf(f2307,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2303]) ).
thf(f2308,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK4 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2303]) ).
thf(f2309,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK3 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK4 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2293]) ).
thf(f2310,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK2 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK3 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK4 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2293]) ).
thf(f2311,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK2 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK4 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2310]) ).
thf(f2312,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK2 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK4 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2310]) ).
thf(f2313,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK3 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK2 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2312]) ).
thf(f2314,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK4 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK2 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2312]) ).
thf(f2315,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK2 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2311]) ).
thf(f2316,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK4 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK2 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2311]) ).
thf(f2317,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK4 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2309]) ).
thf(f2318,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK4 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2309]) ).
thf(f2319,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2318]) ).
thf(f2320,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK4 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2318]) ).
thf(f2321,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sK4 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2317]) ).
thf(f2322,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK4 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2317]) ).
thf(f2323,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f2283]) ).
thf(f2324,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f2283]) ).
thf(f2325,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2324]) ).
thf(f2326,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2325]) ).
thf(f2327,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2326]) ).
thf(f2328,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ ( sK5 @ X1 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f2327]) ).
thf(f2329,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ ( sK5 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ ( sK6 @ X1 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f2328]) ).
thf(f2330,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ ( sK5 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ ( sK6 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ ( sK7 @ X1 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f2329]) ).
thf(f2331,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ Y0 ) )
@ ( sK5 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ Y0 ) )
@ ( sK6 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ Y0 ) )
@ ( sK7 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ Y0 ) )
@ ( sK8 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f2330]) ).
thf(f2332,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ( mrel @ X1 @ ( sK5 @ X1 ) )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK6 @ X1 ) )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK7 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK8 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2331]) ).
thf(f2333,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK6 @ X1 ) )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK7 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK8 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2332]) ).
thf(f2334,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK6 @ X1 ) )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK7 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK8 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2332]) ).
thf(f2335,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK7 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK8 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2334]) ).
thf(f2336,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK5 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK7 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK8 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2334]) ).
thf(f2337,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK5 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK8 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2336]) ).
thf(f2338,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK5 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK6 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK8 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2336]) ).
thf(f2339,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK7 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK6 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2338]) ).
thf(f2340,plain,
! [X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK8 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK5 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK6 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2338]) ).
thf(f2341,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK6 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2337]) ).
thf(f2342,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK8 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK6 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2337]) ).
thf(f2343,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK8 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2335]) ).
thf(f2344,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK8 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2335]) ).
thf(f2345,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2344]) ).
thf(f2346,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK8 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK5 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2344]) ).
thf(f2347,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2343]) ).
thf(f2348,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK8 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2343]) ).
thf(f2349,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK7 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK8 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2333]) ).
thf(f2350,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK7 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK8 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2333]) ).
thf(f2351,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK8 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2350]) ).
thf(f2352,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK6 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK8 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2350]) ).
thf(f2353,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK7 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2352]) ).
thf(f2354,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK8 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK6 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2352]) ).
thf(f2355,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2351]) ).
thf(f2356,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK8 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2351]) ).
thf(f2357,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK8 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2349]) ).
thf(f2358,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK8 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2349]) ).
thf(f2359,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2358]) ).
thf(f2360,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK8 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2358]) ).
thf(f2361,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sK8 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2357]) ).
thf(f2362,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK8 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2357]) ).
thf(f2363,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f2323]) ).
thf(f2364,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f2323]) ).
thf(f2365,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2364]) ).
thf(f2366,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2365]) ).
thf(f2367,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2366]) ).
thf(f2368,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ ( sK9 @ X1 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f2367]) ).
thf(f2369,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ ( sK9 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ ( sK10 @ X1 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f2368]) ).
thf(f2370,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ ( sK9 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ ( sK10 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ ( sK11 @ X1 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f2369]) ).
thf(f2371,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ Y0 ) )
@ ( sK9 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ Y0 ) )
@ ( sK10 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ Y0 ) )
@ ( sK11 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ Y0 ) )
@ ( sK12 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f2370]) ).
thf(f2372,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ( mrel @ X1 @ ( sK9 @ X1 ) )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK10 @ X1 ) )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK11 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK12 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2371]) ).
thf(f2373,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK10 @ X1 ) )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK11 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK12 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2372]) ).
thf(f2374,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK9 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK10 @ X1 ) )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK11 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK12 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2372]) ).
thf(f2375,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK9 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK11 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK12 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2374]) ).
thf(f2376,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK9 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK10 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK11 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK12 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2374]) ).
thf(f2377,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK9 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK10 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK12 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2376]) ).
thf(f2378,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK9 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK10 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK11 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK12 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2376]) ).
thf(f2379,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK11 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK10 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK9 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2378]) ).
thf(f2380,plain,
! [X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK12 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK9 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK10 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK11 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2378]) ).
thf(f2381,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK10 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK9 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2377]) ).
thf(f2382,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK12 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK10 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK9 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2377]) ).
thf(f2383,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK9 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK12 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2375]) ).
thf(f2384,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK9 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK11 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK12 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2375]) ).
thf(f2385,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK11 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK9 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2384]) ).
thf(f2386,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK12 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK9 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK11 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2384]) ).
thf(f2387,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK9 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2383]) ).
thf(f2388,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK12 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK9 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2383]) ).
thf(f2389,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK11 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK12 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2373]) ).
thf(f2390,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK10 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK11 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK12 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2373]) ).
thf(f2391,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK10 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK12 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2390]) ).
thf(f2392,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK10 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK11 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK12 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2390]) ).
thf(f2393,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK11 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK10 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2392]) ).
thf(f2394,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK12 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK10 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK11 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2392]) ).
thf(f2395,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK10 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2391]) ).
thf(f2396,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK12 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK10 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2391]) ).
thf(f2397,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK12 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2389]) ).
thf(f2398,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK11 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK12 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2389]) ).
thf(f2399,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK11 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2398]) ).
thf(f2400,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK12 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK11 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2398]) ).
thf(f2401,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sK12 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2397]) ).
thf(f2402,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK12 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2397]) ).
thf(f2403,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2363]) ).
thf(f2404,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2403]) ).
thf(f2405,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f2404]) ).
thf(f2406,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ ( sK13 @ X1 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f2405]) ).
thf(f2407,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ ( sK13 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ ( sK14 @ X1 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f2406]) ).
thf(f2408,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ ( sK13 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ ( sK14 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ ( sK15 @ X1 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f2407]) ).
thf(f2409,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ Y0 ) )
@ ( sK13 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ Y0 ) )
@ ( sK14 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ Y0 ) )
@ ( sK15 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ Y0 ) )
@ ( sK16 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f2408]) ).
thf(f2410,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( ( mrel @ X1 @ ( sK13 @ X1 ) )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK14 @ X1 ) )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK15 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK16 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f2409]) ).
thf(f2411,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK14 @ X1 ) )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK15 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK16 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2410]) ).
thf(f2412,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK13 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK14 @ X1 ) )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK15 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK16 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2410]) ).
thf(f2413,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK13 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK15 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK16 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2412]) ).
thf(f2414,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK13 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK14 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK15 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK16 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2412]) ).
thf(f2415,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK13 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK14 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK16 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2414]) ).
thf(f2416,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK13 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK14 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK15 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK16 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2414]) ).
thf(f2417,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK14 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK13 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2416]) ).
thf(f2418,plain,
! [X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK16 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK13 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK14 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK15 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2416]) ).
thf(f2419,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK14 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK13 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2415]) ).
thf(f2420,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK16 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK14 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK13 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2415]) ).
thf(f2421,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK13 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK16 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2413]) ).
thf(f2422,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK13 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK15 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK16 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2413]) ).
thf(f2423,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK15 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK13 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2422]) ).
thf(f2424,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK16 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK13 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK15 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2422]) ).
thf(f2425,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK13 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2421]) ).
thf(f2426,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK16 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK13 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2421]) ).
thf(f2427,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK15 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK16 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2411]) ).
thf(f2428,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK14 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK15 @ X1 ) )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK16 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2411]) ).
thf(f2429,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK14 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK16 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2428]) ).
thf(f2430,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK14 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK15 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK16 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2428]) ).
thf(f2431,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK14 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2430]) ).
thf(f2432,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK16 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK14 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK15 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2430]) ).
thf(f2433,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK14 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2429]) ).
thf(f2434,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK16 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK14 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2429]) ).
thf(f2435,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK16 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2427]) ).
thf(f2436,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK15 @ X1 ) ) )
| ( $false
= ( ( mrel @ X1 @ ( sK16 @ X1 ) )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f2427]) ).
thf(f2437,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK15 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2436]) ).
thf(f2438,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK16 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK15 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2436]) ).
thf(f2439,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sK16 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2435]) ).
thf(f2440,plain,
! [X1: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X1 ) ) )
| ( $true
= ( mrel @ X1 @ ( sK16 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X1 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X1 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f2435]) ).
thf(f4503,definition,
( spl99_37
<=> ! [X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_37])],[avatar_definition]) ).
thf(f4504,plain,
( ! [X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) ) )
| ~ spl99_37 ),
inference(avatar_component_clause,[],[f4503]) ).
thf(f4509,definition,
( spl99_39
<=> ! [X3: mworld] :
( ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_39])],[avatar_definition]) ).
thf(f4510,plain,
( ! [X3: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) ) )
| ~ spl99_39 ),
inference(avatar_component_clause,[],[f4509]) ).
thf(f4515,definition,
( spl99_41
<=> ! [X2: mworld] :
( ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_41])],[avatar_definition]) ).
thf(f4516,plain,
( ! [X2: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) ) )
| ~ spl99_41 ),
inference(avatar_component_clause,[],[f4515]) ).
thf(f4521,definition,
( spl99_43
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_43])],[avatar_definition]) ).
thf(f4522,plain,
( ! [X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) )
| ~ spl99_43 ),
inference(avatar_component_clause,[],[f4521]) ).
thf(f4523,plain,
( spl99_37
| spl99_39
| spl99_41
| spl99_43 ),
inference(avatar_split_clause,[],[f165,f4521,f4515,f4509,f4503]) ).
thf(f4546,definition,
( spl99_45
<=> ! [X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_45])],[avatar_definition]) ).
thf(f4547,plain,
( ! [X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) ) )
| ~ spl99_45 ),
inference(avatar_component_clause,[],[f4546]) ).
thf(f4552,definition,
( spl99_47
<=> ! [X3: mworld] :
( ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_47])],[avatar_definition]) ).
thf(f4553,plain,
( ! [X3: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) ) )
| ~ spl99_47 ),
inference(avatar_component_clause,[],[f4552]) ).
thf(f4558,definition,
( spl99_49
<=> ! [X2: mworld] :
( ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_49])],[avatar_definition]) ).
thf(f4559,plain,
( ! [X2: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) ) )
| ~ spl99_49 ),
inference(avatar_component_clause,[],[f4558]) ).
thf(f4564,definition,
( spl99_51
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_51])],[avatar_definition]) ).
thf(f4565,plain,
( ! [X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) )
| ~ spl99_51 ),
inference(avatar_component_clause,[],[f4564]) ).
thf(f4566,plain,
( spl99_45
| spl99_47
| spl99_49
| spl99_51 ),
inference(avatar_split_clause,[],[f872,f4564,f4558,f4552,f4546]) ).
thf(f4595,definition,
( spl99_53
<=> ! [X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_53])],[avatar_definition]) ).
thf(f4596,plain,
( ! [X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) ) )
| ~ spl99_53 ),
inference(avatar_component_clause,[],[f4595]) ).
thf(f4601,definition,
( spl99_55
<=> ! [X3: mworld] :
( ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_55])],[avatar_definition]) ).
thf(f4602,plain,
( ! [X3: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) ) )
| ~ spl99_55 ),
inference(avatar_component_clause,[],[f4601]) ).
thf(f4607,definition,
( spl99_57
<=> ! [X2: mworld] :
( ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_57])],[avatar_definition]) ).
thf(f4608,plain,
( ! [X2: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) ) )
| ~ spl99_57 ),
inference(avatar_component_clause,[],[f4607]) ).
thf(f4613,definition,
( spl99_59
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_59])],[avatar_definition]) ).
thf(f4614,plain,
( ! [X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) )
| ~ spl99_59 ),
inference(avatar_component_clause,[],[f4613]) ).
thf(f4615,plain,
( spl99_53
| spl99_55
| spl99_57
| spl99_59 ),
inference(avatar_split_clause,[],[f1579,f4613,f4607,f4601,f4595]) ).
thf(f4673,definition,
( spl99_62
<=> ! [X4: mworld] :
( ( $false
= ( mrel @ sK0 @ X4 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_62])],[avatar_definition]) ).
thf(f4674,plain,
( ! [X4: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ X4 ) )
| ( $false
= ( mrel @ sK0 @ X4 ) ) )
| ~ spl99_62 ),
inference(avatar_component_clause,[],[f4673]) ).
thf(f4679,definition,
( spl99_64
<=> ! [X3: mworld] :
( ( $false
= ( mrel @ sK0 @ X3 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_64])],[avatar_definition]) ).
thf(f4680,plain,
( ! [X3: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ X3 ) )
| ( $false
= ( mrel @ sK0 @ X3 ) ) )
| ~ spl99_64 ),
inference(avatar_component_clause,[],[f4679]) ).
thf(f4685,definition,
( spl99_66
<=> ! [X2: mworld] :
( ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_66])],[avatar_definition]) ).
thf(f4686,plain,
( ! [X2: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) ) )
| ~ spl99_66 ),
inference(avatar_component_clause,[],[f4685]) ).
thf(f4691,definition,
( spl99_68
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_68])],[avatar_definition]) ).
thf(f4692,plain,
( ! [X1: mworld] :
( ( $true
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) )
| ~ spl99_68 ),
inference(avatar_component_clause,[],[f4691]) ).
thf(f4693,plain,
( spl99_62
| spl99_64
| spl99_66
| spl99_68 ),
inference(avatar_split_clause,[],[f2278,f4691,f4685,f4679,f4673]) ).
thf(f5040,plain,
( spl99_45
| spl99_39
| spl99_41
| spl99_51 ),
inference(avatar_split_clause,[],[f706,f4564,f4515,f4509,f4546]) ).
thf(f5079,plain,
( spl99_45
| spl99_39
| spl99_49
| spl99_59 ),
inference(avatar_split_clause,[],[f1372,f4613,f4558,f4509,f4546]) ).
thf(f5127,plain,
( spl99_45
| spl99_55
| spl99_49
| spl99_59 ),
inference(avatar_split_clause,[],[f1438,f4613,f4558,f4601,f4546]) ).
thf(f5190,plain,
( spl99_45
| spl99_55
| spl99_57
| spl99_59 ),
inference(avatar_split_clause,[],[f1571,f4613,f4607,f4601,f4546]) ).
thf(f5270,plain,
( spl99_45
| spl99_64
| spl99_57
| spl99_59 ),
inference(avatar_split_clause,[],[f1602,f4613,f4607,f4679,f4546]) ).
thf(f5346,definition,
( spl99_75
<=> ( $true
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_75])],[avatar_definition]) ).
thf(f5347,plain,
( ( $true
!= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| spl99_75 ),
inference(avatar_component_clause,[],[f5346]) ).
thf(f5348,plain,
( ( $true
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ~ spl99_75 ),
inference(avatar_component_clause,[],[f5346]) ).
thf(f5350,definition,
( spl99_76
<=> ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_76])],[avatar_definition]) ).
thf(f5351,plain,
( ( $true
!= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| spl99_76 ),
inference(avatar_component_clause,[],[f5350]) ).
thf(f5352,plain,
( ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ~ spl99_76 ),
inference(avatar_component_clause,[],[f5350]) ).
thf(f5433,plain,
( spl99_45
| spl99_47
| spl99_57
| spl99_59 ),
inference(avatar_split_clause,[],[f1538,f4613,f4607,f4552,f4546]) ).
thf(f5622,plain,
( spl99_62
| spl99_47
| spl99_41
| spl99_43 ),
inference(avatar_split_clause,[],[f220,f4521,f4515,f4552,f4673]) ).
thf(f5823,plain,
( spl99_62
| spl99_47
| spl99_49
| spl99_43 ),
inference(avatar_split_clause,[],[f353,f4521,f4558,f4552,f4673]) ).
thf(f5824,plain,
( spl99_62
| spl99_47
| spl99_41
| spl99_51 ),
inference(avatar_split_clause,[],[f753,f4564,f4515,f4552,f4673]) ).
thf(f5825,plain,
( spl99_62
| spl99_47
| spl99_41
| spl99_68 ),
inference(avatar_split_clause,[],[f1817,f4691,f4515,f4552,f4673]) ).
thf(f5854,plain,
( spl99_62
| spl99_55
| spl99_41
| spl99_59 ),
inference(avatar_split_clause,[],[f1319,f4613,f4515,f4601,f4673]) ).
thf(f6240,plain,
( spl99_62
| spl99_47
| spl99_41
| spl99_59 ),
inference(avatar_split_clause,[],[f1286,f4613,f4515,f4552,f4673]) ).
thf(f7169,definition,
( spl99_98
<=> ( $true
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_98])],[avatar_definition]) ).
thf(f7170,plain,
( ( $true
!= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| spl99_98 ),
inference(avatar_component_clause,[],[f7169]) ).
thf(f7171,plain,
( ( $true
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_98 ),
inference(avatar_component_clause,[],[f7169]) ).
thf(f7173,definition,
( spl99_99
<=> ( $true
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_99])],[avatar_definition]) ).
thf(f7174,plain,
( ( $true
!= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| spl99_99 ),
inference(avatar_component_clause,[],[f7173]) ).
thf(f7175,plain,
( ( $true
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ~ spl99_99 ),
inference(avatar_component_clause,[],[f7173]) ).
thf(f7472,plain,
( spl99_37
| spl99_47
| spl99_41
| spl99_68 ),
inference(avatar_split_clause,[],[f1795,f4691,f4515,f4552,f4503]) ).
thf(f7733,plain,
( spl99_45
| spl99_55
| spl99_41
| spl99_51 ),
inference(avatar_split_clause,[],[f772,f4564,f4515,f4601,f4546]) ).
thf(f8032,plain,
( spl99_45
| spl99_39
| spl99_41
| spl99_68 ),
inference(avatar_split_clause,[],[f1770,f4691,f4515,f4509,f4546]) ).
thf(f8092,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_62 ),
inference(constrained_superposition,[],[f4674,f2394]) ).
thf(f8095,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_62 ),
inference(trivial_inequality_removal,[],[f8092]) ).
thf(f8188,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_37 ),
inference(constrained_superposition,[],[f4504,f2386]) ).
thf(f8191,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_37 ),
inference(trivial_inequality_removal,[],[f8188]) ).
thf(f8371,plain,
( spl99_45
| spl99_55
| spl99_41
| spl99_68 ),
inference(avatar_split_clause,[],[f1836,f4691,f4515,f4601,f4546]) ).
thf(f8394,definition,
( spl99_105
<=> ( $true
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_105])],[avatar_definition]) ).
thf(f8395,plain,
( ( $true
!= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| spl99_105 ),
inference(avatar_component_clause,[],[f8394]) ).
thf(f8396,plain,
( ( $true
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ~ spl99_105 ),
inference(avatar_component_clause,[],[f8394]) ).
thf(f8398,definition,
( spl99_106
<=> ( $true
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_106])],[avatar_definition]) ).
thf(f8399,plain,
( ( $true
!= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| spl99_106 ),
inference(avatar_component_clause,[],[f8398]) ).
thf(f8400,plain,
( ( $true
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_106 ),
inference(avatar_component_clause,[],[f8398]) ).
thf(f8532,plain,
( spl99_45
| spl99_64
| spl99_41
| spl99_68 ),
inference(avatar_split_clause,[],[f1867,f4691,f4515,f4679,f4546]) ).
thf(f8902,plain,
( spl99_53
| spl99_64
| spl99_41
| spl99_68 ),
inference(avatar_split_clause,[],[f1875,f4691,f4515,f4679,f4595]) ).
thf(f9018,plain,
( spl99_53
| spl99_55
| spl99_41
| spl99_68 ),
inference(avatar_split_clause,[],[f1844,f4691,f4515,f4601,f4595]) ).
thf(f9300,plain,
( spl99_45
| spl99_47
| spl99_41
| spl99_68 ),
inference(avatar_split_clause,[],[f1803,f4691,f4515,f4552,f4546]) ).
thf(f9872,plain,
( spl99_53
| spl99_47
| spl99_41
| spl99_68 ),
inference(avatar_split_clause,[],[f1811,f4691,f4515,f4552,f4595]) ).
thf(f9966,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_53 ),
inference(constrained_superposition,[],[f2385,f4596]) ).
thf(f9967,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_53 ),
inference(constrained_superposition,[],[f2379,f4596]) ).
thf(f9970,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) ) )
| ~ spl99_53 ),
inference(trivial_inequality_removal,[],[f9967]) ).
thf(f9971,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_53 ),
inference(trivial_inequality_removal,[],[f9966]) ).
thf(f9978,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_37
| ~ spl99_53 ),
inference(constrained_superposition,[],[f4504,f9971]) ).
thf(f9981,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) ) )
| ~ spl99_37
| ~ spl99_53 ),
inference(trivial_inequality_removal,[],[f9978]) ).
thf(f9990,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_37
| ~ spl99_53 ),
inference(constrained_superposition,[],[f9981,f8191]) ).
thf(f10034,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_53 ),
inference(duplicate_literal_removal,[],[f9990]) ).
thf(f10035,plain,
( ( $true
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_53 ),
inference(trivial_inequality_removal,[],[f10034]) ).
thf(f10045,plain,
( ( $true
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_53
| spl99_105 ),
inference(forward_subsumption_resolution,[],[f10035,f8395]) ).
thf(f10049,plain,
( ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_53
| spl99_105
| spl99_106 ),
inference(forward_subsumption_resolution,[],[f10045,f8399]) ).
thf(f10055,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_53
| spl99_105
| spl99_106 ),
inference(forward_demodulation,[],[f10049,f97]) ).
thf(f10056,plain,
( ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_53
| spl99_105
| spl99_106 ),
inference(trivial_inequality_removal,[],[f10055]) ).
thf(f10083,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_53 ),
inference(constrained_superposition,[],[f9970,f2380]) ).
thf(f10135,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_53 ),
inference(duplicate_literal_removal,[],[f10083]) ).
thf(f10136,plain,
( ( $true
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_53 ),
inference(trivial_inequality_removal,[],[f10135]) ).
thf(f10142,plain,
( ( $true
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_53
| spl99_105 ),
inference(forward_subsumption_resolution,[],[f10136,f8395]) ).
thf(f10146,plain,
( ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_53
| spl99_105
| spl99_106 ),
inference(forward_subsumption_resolution,[],[f10142,f8399]) ).
thf(f10153,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_53
| spl99_105
| spl99_106 ),
inference(forward_demodulation,[],[f10146,f97]) ).
thf(f10154,plain,
( ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_53
| spl99_105
| spl99_106 ),
inference(trivial_inequality_removal,[],[f10153]) ).
thf(f10178,plain,
( ( $true = $false )
| ~ spl99_37
| ~ spl99_53
| spl99_105
| spl99_106 ),
inference(constrained_superposition,[],[f10056,f10154]) ).
thf(f10182,plain,
( $false
| ~ spl99_37
| ~ spl99_53
| spl99_105
| spl99_106 ),
inference(trivial_inequality_removal,[],[f10178]) ).
thf(f10183,plain,
( ~ spl99_37
| ~ spl99_53
| spl99_105
| spl99_106 ),
inference(avatar_contradiction_clause,[],[f10182]) ).
thf(f10226,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_53 ),
inference(constrained_superposition,[],[f4596,f2393]) ).
thf(f10229,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_53 ),
inference(trivial_inequality_removal,[],[f10226]) ).
thf(f10236,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_53
| ~ spl99_62 ),
inference(constrained_superposition,[],[f4674,f10229]) ).
thf(f10239,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_53
| ~ spl99_62 ),
inference(trivial_inequality_removal,[],[f10236]) ).
thf(f10255,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_53
| ~ spl99_62 ),
inference(constrained_superposition,[],[f8095,f10239]) ).
thf(f10274,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_53
| ~ spl99_62 ),
inference(duplicate_literal_removal,[],[f10255]) ).
thf(f10275,plain,
( ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_53
| ~ spl99_62 ),
inference(trivial_inequality_removal,[],[f10274]) ).
thf(f10488,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ~ spl99_53
| ~ spl99_62 ),
inference(forward_demodulation,[],[f10275,f97]) ).
thf(f10489,plain,
( ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ~ spl99_53
| ~ spl99_62 ),
inference(trivial_inequality_removal,[],[f10488]) ).
thf(f10712,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_47 ),
inference(constrained_superposition,[],[f4553,f2342]) ).
thf(f10715,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_47 ),
inference(trivial_inequality_removal,[],[f10712]) ).
thf(f10781,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_64 ),
inference(constrained_superposition,[],[f4680,f2354]) ).
thf(f10784,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_64 ),
inference(trivial_inequality_removal,[],[f10781]) ).
thf(f10832,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_55 ),
inference(constrained_superposition,[],[f4602,f2339]) ).
thf(f10835,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_55 ),
inference(trivial_inequality_removal,[],[f10832]) ).
thf(f10849,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_55 ),
inference(constrained_superposition,[],[f2340,f10835]) ).
thf(f10850,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_55 ),
inference(duplicate_literal_removal,[],[f10849]) ).
thf(f10851,plain,
( ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_55 ),
inference(trivial_inequality_removal,[],[f10850]) ).
thf(f10867,plain,
( ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_55
| spl99_76 ),
inference(forward_subsumption_resolution,[],[f10851,f5351]) ).
thf(f10871,plain,
( ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_55
| spl99_75
| spl99_76 ),
inference(forward_subsumption_resolution,[],[f10867,f5347]) ).
thf(f10895,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ~ spl99_55
| spl99_75
| spl99_76 ),
inference(forward_demodulation,[],[f10871,f97]) ).
thf(f10896,plain,
( ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ~ spl99_55
| spl99_75
| spl99_76 ),
inference(trivial_inequality_removal,[],[f10895]) ).
thf(f10910,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_55 ),
inference(constrained_superposition,[],[f4602,f2345]) ).
thf(f10913,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_55 ),
inference(trivial_inequality_removal,[],[f10910]) ).
thf(f10920,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_39
| ~ spl99_55 ),
inference(constrained_superposition,[],[f4510,f10913]) ).
thf(f10923,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_39
| ~ spl99_55 ),
inference(trivial_inequality_removal,[],[f10920]) ).
thf(f10995,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_39 ),
inference(constrained_superposition,[],[f4510,f2346]) ).
thf(f10998,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_39 ),
inference(trivial_inequality_removal,[],[f10995]) ).
thf(f11003,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_55 ),
inference(constrained_superposition,[],[f10998,f10923]) ).
thf(f11017,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_55 ),
inference(duplicate_literal_removal,[],[f11003]) ).
thf(f11018,plain,
( ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_55 ),
inference(trivial_inequality_removal,[],[f11017]) ).
thf(f11021,plain,
( ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_55
| spl99_76 ),
inference(forward_subsumption_resolution,[],[f11018,f5351]) ).
thf(f11023,plain,
( ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_55
| spl99_75
| spl99_76 ),
inference(forward_subsumption_resolution,[],[f11021,f5347]) ).
thf(f11026,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_55
| spl99_75
| spl99_76 ),
inference(forward_demodulation,[],[f11023,f10896]) ).
thf(f11027,plain,
( ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_55
| spl99_75
| spl99_76 ),
inference(trivial_inequality_removal,[],[f11026]) ).
thf(f11031,plain,
( ( $true = $false )
| ~ spl99_39
| ~ spl99_55
| spl99_75
| spl99_76 ),
inference(forward_demodulation,[],[f11027,f97]) ).
thf(f11032,plain,
( $false
| ~ spl99_39
| ~ spl99_55
| spl99_75
| spl99_76 ),
inference(trivial_inequality_removal,[],[f11031]) ).
thf(f11033,plain,
( ~ spl99_39
| ~ spl99_55
| spl99_75
| spl99_76 ),
inference(avatar_contradiction_clause,[],[f11032]) ).
thf(f11071,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_55 ),
inference(constrained_superposition,[],[f4602,f2353]) ).
thf(f11074,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_55 ),
inference(trivial_inequality_removal,[],[f11071]) ).
thf(f11081,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_55
| ~ spl99_64 ),
inference(constrained_superposition,[],[f4680,f11074]) ).
thf(f11084,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_55
| ~ spl99_64 ),
inference(trivial_inequality_removal,[],[f11081]) ).
thf(f11099,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_55
| ~ spl99_64 ),
inference(constrained_superposition,[],[f10784,f11084]) ).
thf(f11103,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_55
| ~ spl99_64 ),
inference(duplicate_literal_removal,[],[f11099]) ).
thf(f11104,plain,
( ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_55
| ~ spl99_64 ),
inference(trivial_inequality_removal,[],[f11103]) ).
thf(f11191,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_39 ),
inference(constrained_superposition,[],[f4510,f2360]) ).
thf(f11194,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_39 ),
inference(trivial_inequality_removal,[],[f11191]) ).
thf(f11201,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_39
| ~ spl99_64 ),
inference(constrained_superposition,[],[f4680,f11194]) ).
thf(f11204,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_39
| ~ spl99_64 ),
inference(trivial_inequality_removal,[],[f11201]) ).
thf(f11271,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_47 ),
inference(constrained_superposition,[],[f4553,f2362]) ).
thf(f11274,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_47 ),
inference(trivial_inequality_removal,[],[f11271]) ).
thf(f11359,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_47 ),
inference(constrained_superposition,[],[f4553,f2356]) ).
thf(f11362,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_47 ),
inference(trivial_inequality_removal,[],[f11359]) ).
thf(f11623,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_47 ),
inference(constrained_superposition,[],[f4553,f2348]) ).
thf(f11626,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_47 ),
inference(trivial_inequality_removal,[],[f11623]) ).
thf(f11690,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ~ spl99_55
| ~ spl99_64 ),
inference(forward_demodulation,[],[f11104,f97]) ).
thf(f11691,plain,
( ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ~ spl99_55
| ~ spl99_64 ),
inference(trivial_inequality_removal,[],[f11690]) ).
thf(f11763,plain,
( ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ~ spl99_55
| ~ spl99_64
| spl99_75 ),
inference(forward_subsumption_resolution,[],[f11691,f5347]) ).
thf(f11764,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ~ spl99_55
| ~ spl99_64
| spl99_75
| ~ spl99_76 ),
inference(forward_demodulation,[],[f11763,f5352]) ).
thf(f11765,plain,
( ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ~ spl99_55
| ~ spl99_64
| spl99_75
| ~ spl99_76 ),
inference(trivial_inequality_removal,[],[f11764]) ).
thf(f11772,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_55 ),
inference(constrained_superposition,[],[f4602,f2359]) ).
thf(f11775,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_55 ),
inference(trivial_inequality_removal,[],[f11772]) ).
thf(f11782,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_39
| ~ spl99_55 ),
inference(constrained_superposition,[],[f4510,f11775]) ).
thf(f11785,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_39
| ~ spl99_55 ),
inference(trivial_inequality_removal,[],[f11782]) ).
thf(f11792,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_39
| ~ spl99_55
| ~ spl99_64 ),
inference(constrained_superposition,[],[f4680,f11785]) ).
thf(f11795,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_39
| ~ spl99_55
| ~ spl99_64 ),
inference(trivial_inequality_removal,[],[f11792]) ).
thf(f11805,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_55
| ~ spl99_64 ),
inference(constrained_superposition,[],[f11795,f11204]) ).
thf(f11841,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_55
| ~ spl99_64 ),
inference(duplicate_literal_removal,[],[f11805]) ).
thf(f11842,plain,
( ( $true
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_55
| ~ spl99_64 ),
inference(trivial_inequality_removal,[],[f11841]) ).
thf(f11854,plain,
( ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_55
| ~ spl99_64
| spl99_75 ),
inference(forward_subsumption_resolution,[],[f11842,f5347]) ).
thf(f11857,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_55
| ~ spl99_64
| spl99_75
| ~ spl99_76 ),
inference(forward_demodulation,[],[f11854,f5352]) ).
thf(f11858,plain,
( ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_55
| ~ spl99_64
| spl99_75
| ~ spl99_76 ),
inference(trivial_inequality_removal,[],[f11857]) ).
thf(f11861,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_55
| ~ spl99_64
| spl99_75
| ~ spl99_76 ),
inference(forward_demodulation,[],[f11858,f11765]) ).
thf(f11862,plain,
( ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_55
| ~ spl99_64
| spl99_75
| ~ spl99_76 ),
inference(trivial_inequality_removal,[],[f11861]) ).
thf(f11866,plain,
( ( $true = $false )
| ~ spl99_39
| ~ spl99_55
| ~ spl99_64
| spl99_75
| ~ spl99_76 ),
inference(forward_demodulation,[],[f11862,f97]) ).
thf(f11867,plain,
( $false
| ~ spl99_39
| ~ spl99_55
| ~ spl99_64
| spl99_75
| ~ spl99_76 ),
inference(trivial_inequality_removal,[],[f11866]) ).
thf(f11868,plain,
( ~ spl99_39
| ~ spl99_55
| ~ spl99_64
| spl99_75
| ~ spl99_76 ),
inference(avatar_contradiction_clause,[],[f11867]) ).
thf(f12085,definition,
( spl99_107
<=> ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_107])],[avatar_definition]) ).
thf(f12086,plain,
( ( $false
!= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| spl99_107 ),
inference(avatar_component_clause,[],[f12085]) ).
thf(f12087,plain,
( ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ~ spl99_107 ),
inference(avatar_component_clause,[],[f12085]) ).
thf(f12127,plain,
( spl99_45
| spl99_55
| spl99_49
| spl99_68 ),
inference(avatar_split_clause,[],[f1969,f4691,f4558,f4601,f4546]) ).
thf(f12348,plain,
( spl99_45
| spl99_64
| spl99_49
| spl99_68 ),
inference(avatar_split_clause,[],[f2000,f4691,f4558,f4679,f4546]) ).
thf(f12463,plain,
( spl99_45
| spl99_64
| spl99_66
| spl99_68 ),
inference(avatar_split_clause,[],[f2264,f4691,f4685,f4679,f4546]) ).
thf(f12478,plain,
( spl99_45
| spl99_64
| spl99_57
| spl99_68 ),
inference(avatar_split_clause,[],[f2133,f4691,f4607,f4679,f4546]) ).
thf(f13048,definition,
( spl99_110
<=> ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_110])],[avatar_definition]) ).
thf(f13049,plain,
( ( $true
!= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| spl99_110 ),
inference(avatar_component_clause,[],[f13048]) ).
thf(f13050,plain,
( ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ~ spl99_110 ),
inference(avatar_component_clause,[],[f13048]) ).
thf(f13052,definition,
( spl99_111
<=> ( $true
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_111])],[avatar_definition]) ).
thf(f13053,plain,
( ( $true
!= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| spl99_111 ),
inference(avatar_component_clause,[],[f13052]) ).
thf(f13054,plain,
( ( $true
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ~ spl99_111 ),
inference(avatar_component_clause,[],[f13052]) ).
thf(f13543,plain,
( spl99_45
| spl99_64
| spl99_66
| spl99_51 ),
inference(avatar_split_clause,[],[f1200,f4564,f4685,f4679,f4546]) ).
thf(f14142,plain,
( spl99_37
| spl99_64
| spl99_66
| spl99_51 ),
inference(avatar_split_clause,[],[f1192,f4564,f4685,f4679,f4503]) ).
thf(f14185,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ~ spl99_53
| ~ spl99_62
| ~ spl99_106 ),
inference(forward_demodulation,[],[f10489,f8400]) ).
thf(f14186,plain,
( ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ~ spl99_53
| ~ spl99_62
| ~ spl99_106 ),
inference(trivial_inequality_removal,[],[f14185]) ).
thf(f14191,definition,
( spl99_112
<=> ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_112])],[avatar_definition]) ).
thf(f14192,plain,
( ( $true
!= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| spl99_112 ),
inference(avatar_component_clause,[],[f14191]) ).
thf(f14193,plain,
( ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_112 ),
inference(avatar_component_clause,[],[f14191]) ).
thf(f14194,plain,
( spl99_105
| spl99_112
| ~ spl99_53
| ~ spl99_62
| ~ spl99_106 ),
inference(avatar_split_clause,[],[f14186,f8398,f4673,f4595,f14191,f8394]) ).
thf(f14378,plain,
( spl99_45
| spl99_64
| spl99_57
| spl99_51 ),
inference(avatar_split_clause,[],[f1069,f4564,f4607,f4679,f4546]) ).
thf(f14888,plain,
( spl99_45
| spl99_64
| spl99_49
| spl99_51 ),
inference(avatar_split_clause,[],[f936,f4564,f4558,f4679,f4546]) ).
thf(f14982,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) ) )
| ~ spl99_51 ),
inference(constrained_superposition,[],[f2434,f4565]) ).
thf(f14983,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) ) )
| ~ spl99_51 ),
inference(constrained_superposition,[],[f2440,f4565]) ).
thf(f14988,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) ) )
| ~ spl99_51 ),
inference(trivial_inequality_removal,[],[f14983]) ).
thf(f14989,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) ) )
| ~ spl99_51 ),
inference(trivial_inequality_removal,[],[f14982]) ).
thf(f15117,definition,
( spl99_114
<=> ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl99_114])],[avatar_definition]) ).
thf(f15118,plain,
( ( $true
!= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| spl99_114 ),
inference(avatar_component_clause,[],[f15117]) ).
thf(f15119,plain,
( ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ~ spl99_114 ),
inference(avatar_component_clause,[],[f15117]) ).
thf(f15124,plain,
( spl99_45
| spl99_64
| spl99_66
| spl99_43 ),
inference(avatar_split_clause,[],[f667,f4521,f4685,f4679,f4546]) ).
thf(f15491,plain,
( spl99_45
| spl99_39
| spl99_66
| spl99_43 ),
inference(avatar_split_clause,[],[f570,f4521,f4685,f4509,f4546]) ).
thf(f15678,plain,
( spl99_37
| spl99_39
| spl99_66
| spl99_43 ),
inference(avatar_split_clause,[],[f562,f4521,f4685,f4509,f4503]) ).
thf(f15698,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) ) )
| ~ spl99_37 ),
inference(constrained_superposition,[],[f2400,f4504]) ).
thf(f15701,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) ) )
| ~ spl99_37 ),
inference(trivial_inequality_removal,[],[f15698]) ).
thf(f15756,plain,
( spl99_53
| spl99_39
| spl99_66
| spl99_43 ),
inference(avatar_split_clause,[],[f578,f4521,f4685,f4509,f4595]) ).
thf(f15847,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) ) )
| ~ spl99_45 ),
inference(constrained_superposition,[],[f2396,f4547]) ).
thf(f15848,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) ) )
| ~ spl99_45 ),
inference(constrained_superposition,[],[f2402,f4547]) ).
thf(f15853,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) ) )
| ~ spl99_45 ),
inference(trivial_inequality_removal,[],[f15848]) ).
thf(f15854,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) ) )
| ~ spl99_45 ),
inference(trivial_inequality_removal,[],[f15847]) ).
thf(f15882,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) ) )
| ~ spl99_45
| ~ spl99_62 ),
inference(constrained_superposition,[],[f4674,f15854]) ).
thf(f15885,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ X0 ) ) ) )
| ~ spl99_45
| ~ spl99_62 ),
inference(trivial_inequality_removal,[],[f15882]) ).
thf(f15981,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_53 ),
inference(constrained_superposition,[],[f2395,f4596]) ).
thf(f15982,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_53 ),
inference(constrained_superposition,[],[f2399,f4596]) ).
thf(f15983,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_53 ),
inference(constrained_superposition,[],[f2401,f4596]) ).
thf(f15984,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_53 ),
inference(trivial_inequality_removal,[],[f15983]) ).
thf(f15985,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_53 ),
inference(trivial_inequality_removal,[],[f15982]) ).
thf(f15986,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_53 ),
inference(trivial_inequality_removal,[],[f15981]) ).
thf(f16001,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_45
| ~ spl99_53 ),
inference(constrained_superposition,[],[f4547,f15986]) ).
thf(f16004,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_45
| ~ spl99_53 ),
inference(trivial_inequality_removal,[],[f16001]) ).
thf(f16011,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62 ),
inference(constrained_superposition,[],[f4674,f16004]) ).
thf(f16014,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ X0 ) ) ) )
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62 ),
inference(trivial_inequality_removal,[],[f16011]) ).
thf(f16028,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62 ),
inference(constrained_superposition,[],[f15885,f16014]) ).
thf(f16029,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62 ),
inference(duplicate_literal_removal,[],[f16028]) ).
thf(f16030,plain,
( ( $false
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62 ),
inference(trivial_inequality_removal,[],[f16029]) ).
thf(f16046,plain,
( ( $false
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62
| spl99_112 ),
inference(forward_subsumption_resolution,[],[f16030,f14192]) ).
thf(f16078,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62
| ~ spl99_105
| spl99_112 ),
inference(forward_demodulation,[],[f16046,f8396]) ).
thf(f16079,plain,
( ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62
| ~ spl99_105
| spl99_112 ),
inference(trivial_inequality_removal,[],[f16078]) ).
thf(f16086,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62
| ~ spl99_105
| spl99_112 ),
inference(forward_demodulation,[],[f16079,f97]) ).
thf(f16087,plain,
( ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62
| ~ spl99_105
| spl99_112 ),
inference(trivial_inequality_removal,[],[f16086]) ).
thf(f16107,plain,
( ( $true = $false )
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62
| ~ spl99_105
| ~ spl99_106
| spl99_112 ),
inference(constrained_superposition,[],[f16087,f8400]) ).
thf(f16111,plain,
( $false
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62
| ~ spl99_105
| ~ spl99_106
| spl99_112 ),
inference(trivial_inequality_removal,[],[f16107]) ).
thf(f16112,plain,
( ~ spl99_45
| ~ spl99_53
| ~ spl99_62
| ~ spl99_105
| ~ spl99_106
| spl99_112 ),
inference(avatar_contradiction_clause,[],[f16111]) ).
thf(f16283,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_37
| ~ spl99_53 ),
inference(constrained_superposition,[],[f4504,f15985]) ).
thf(f16286,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_37
| ~ spl99_53 ),
inference(trivial_inequality_removal,[],[f16283]) ).
thf(f16293,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_37
| ~ spl99_53
| ~ spl99_62 ),
inference(constrained_superposition,[],[f4674,f16286]) ).
thf(f16296,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ X0 ) ) ) )
| ~ spl99_37
| ~ spl99_53
| ~ spl99_62 ),
inference(trivial_inequality_removal,[],[f16293]) ).
thf(f16388,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_45
| ~ spl99_53 ),
inference(constrained_superposition,[],[f4547,f15984]) ).
thf(f16389,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_45
| ~ spl99_53 ),
inference(trivial_inequality_removal,[],[f16388]) ).
thf(f16394,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53 ),
inference(constrained_superposition,[],[f4504,f16389]) ).
thf(f16395,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53 ),
inference(trivial_inequality_removal,[],[f16394]) ).
thf(f16400,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62 ),
inference(constrained_superposition,[],[f4674,f16395]) ).
thf(f16401,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ X0 ) ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62 ),
inference(trivial_inequality_removal,[],[f16400]) ).
thf(f16463,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) ) )
| ~ spl99_37
| ~ spl99_45 ),
inference(constrained_superposition,[],[f4504,f15853]) ).
thf(f16466,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sK9 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) ) )
| ~ spl99_37
| ~ spl99_45 ),
inference(trivial_inequality_removal,[],[f16463]) ).
thf(f16473,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_62 ),
inference(constrained_superposition,[],[f4674,f16466]) ).
thf(f16476,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ X0 ) ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_62 ),
inference(trivial_inequality_removal,[],[f16473]) ).
thf(f16498,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62 ),
inference(constrained_superposition,[],[f16401,f16476]) ).
thf(f16499,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62 ),
inference(duplicate_literal_removal,[],[f16498]) ).
thf(f16500,plain,
( ( $false
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62 ),
inference(trivial_inequality_removal,[],[f16499]) ).
thf(f16552,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62
| ~ spl99_105 ),
inference(forward_demodulation,[],[f16500,f8396]) ).
thf(f16553,plain,
( ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62
| ~ spl99_105 ),
inference(trivial_inequality_removal,[],[f16552]) ).
thf(f16570,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62
| ~ spl99_105
| ~ spl99_112 ),
inference(forward_demodulation,[],[f16553,f14193]) ).
thf(f16571,plain,
( ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62
| ~ spl99_105
| ~ spl99_112 ),
inference(trivial_inequality_removal,[],[f16570]) ).
thf(f16574,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62
| ~ spl99_105
| ~ spl99_112 ),
inference(forward_demodulation,[],[f16571,f97]) ).
thf(f16575,plain,
( ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62
| ~ spl99_105
| ~ spl99_112 ),
inference(trivial_inequality_removal,[],[f16574]) ).
thf(f16585,plain,
( ( $true = $false )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62
| ~ spl99_105
| ~ spl99_106
| ~ spl99_112 ),
inference(constrained_superposition,[],[f16575,f8400]) ).
thf(f16589,plain,
( $false
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62
| ~ spl99_105
| ~ spl99_106
| ~ spl99_112 ),
inference(trivial_inequality_removal,[],[f16585]) ).
thf(f16590,plain,
( ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62
| ~ spl99_105
| ~ spl99_106
| ~ spl99_112 ),
inference(avatar_contradiction_clause,[],[f16589]) ).
thf(f16720,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) ) )
| ~ spl99_37
| ~ spl99_62 ),
inference(constrained_superposition,[],[f4674,f15701]) ).
thf(f16723,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ X0 ) ) ) )
| ~ spl99_37
| ~ spl99_62 ),
inference(trivial_inequality_removal,[],[f16720]) ).
thf(f16743,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_53
| ~ spl99_62 ),
inference(constrained_superposition,[],[f16296,f16723]) ).
thf(f16750,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_53
| ~ spl99_62 ),
inference(duplicate_literal_removal,[],[f16743]) ).
thf(f16751,plain,
( ( $true
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_53
| ~ spl99_62 ),
inference(trivial_inequality_removal,[],[f16750]) ).
thf(f16781,plain,
( ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_53
| ~ spl99_62
| spl99_105 ),
inference(forward_subsumption_resolution,[],[f16751,f8395]) ).
thf(f16783,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_53
| ~ spl99_62
| spl99_105
| ~ spl99_112 ),
inference(forward_demodulation,[],[f16781,f14193]) ).
thf(f16784,plain,
( ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_53
| ~ spl99_62
| spl99_105
| ~ spl99_112 ),
inference(trivial_inequality_removal,[],[f16783]) ).
thf(f16787,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_53
| ~ spl99_62
| spl99_105
| ~ spl99_112 ),
inference(forward_demodulation,[],[f16784,f97]) ).
thf(f16788,plain,
( ( $false
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_53
| ~ spl99_62
| spl99_105
| ~ spl99_112 ),
inference(trivial_inequality_removal,[],[f16787]) ).
thf(f16792,plain,
( ( $true = $false )
| ~ spl99_37
| ~ spl99_53
| ~ spl99_62
| spl99_105
| ~ spl99_106
| ~ spl99_112 ),
inference(constrained_superposition,[],[f16788,f8400]) ).
thf(f16796,plain,
( $false
| ~ spl99_37
| ~ spl99_53
| ~ spl99_62
| spl99_105
| ~ spl99_106
| ~ spl99_112 ),
inference(trivial_inequality_removal,[],[f16792]) ).
thf(f16797,plain,
( ~ spl99_37
| ~ spl99_53
| ~ spl99_62
| spl99_105
| ~ spl99_106
| ~ spl99_112 ),
inference(avatar_contradiction_clause,[],[f16796]) ).
thf(f16840,plain,
( spl99_53
| spl99_39
| spl99_49
| spl99_43 ),
inference(avatar_split_clause,[],[f314,f4521,f4558,f4509,f4595]) ).
thf(f16895,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) ) )
| ~ spl99_43 ),
inference(constrained_superposition,[],[f2438,f4522]) ).
thf(f16898,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) ) )
| ~ spl99_43 ),
inference(trivial_inequality_removal,[],[f16895]) ).
thf(f16990,plain,
( spl99_53
| spl99_39
| spl99_66
| spl99_59 ),
inference(avatar_split_clause,[],[f1644,f4613,f4685,f4509,f4595]) ).
thf(f17250,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) ) )
| ~ spl99_43
| ~ spl99_51 ),
inference(constrained_superposition,[],[f4522,f14988]) ).
thf(f17253,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) ) )
| ~ spl99_43
| ~ spl99_51 ),
inference(trivial_inequality_removal,[],[f17250]) ).
thf(f17388,plain,
( spl99_53
| spl99_39
| spl99_49
| spl99_59 ),
inference(avatar_split_clause,[],[f1380,f4613,f4558,f4509,f4595]) ).
thf(f17469,plain,
( spl99_53
| spl99_39
| spl99_66
| spl99_68 ),
inference(avatar_split_clause,[],[f2175,f4691,f4685,f4509,f4595]) ).
thf(f17571,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ X0 ) ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_68 ),
inference(constrained_superposition,[],[f17253,f4692]) ).
thf(f17572,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ X0 ) ) ) )
| ~ spl99_43
| ~ spl99_68 ),
inference(constrained_superposition,[],[f16898,f4692]) ).
thf(f17573,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ X0 ) ) ) )
| ~ spl99_51
| ~ spl99_68 ),
inference(constrained_superposition,[],[f14989,f4692]) ).
thf(f17574,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ X0 ) ) ) )
| ~ spl99_68 ),
inference(constrained_superposition,[],[f2432,f4692]) ).
thf(f17575,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) ) )
| ~ spl99_68 ),
inference(trivial_inequality_removal,[],[f17574]) ).
thf(f17576,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ X0 ) ) ) )
| ~ spl99_51
| ~ spl99_68 ),
inference(trivial_inequality_removal,[],[f17573]) ).
thf(f17577,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ X0 ) ) ) )
| ~ spl99_43
| ~ spl99_68 ),
inference(trivial_inequality_removal,[],[f17572]) ).
thf(f17578,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ X0 ) ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_68 ),
inference(trivial_inequality_removal,[],[f17571]) ).
thf(f17653,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_59 ),
inference(constrained_superposition,[],[f2431,f4614]) ).
thf(f17655,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_59 ),
inference(constrained_superposition,[],[f2437,f4614]) ).
thf(f17658,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_59 ),
inference(trivial_inequality_removal,[],[f17655]) ).
thf(f17660,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_59 ),
inference(trivial_inequality_removal,[],[f17653]) ).
thf(f17710,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_59
| ~ spl99_68 ),
inference(constrained_superposition,[],[f4692,f17660]) ).
thf(f17713,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ X0 ) ) ) )
| ~ spl99_59
| ~ spl99_68 ),
inference(trivial_inequality_removal,[],[f17710]) ).
thf(f17768,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_59
| ~ spl99_68 ),
inference(constrained_superposition,[],[f17575,f17713]) ).
thf(f17782,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ~ spl99_59
| ~ spl99_68 ),
inference(duplicate_literal_removal,[],[f17768]) ).
thf(f17783,plain,
( ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ~ spl99_59
| ~ spl99_68 ),
inference(trivial_inequality_removal,[],[f17782]) ).
thf(f17786,plain,
( ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ~ spl99_59
| ~ spl99_68
| spl99_99 ),
inference(forward_subsumption_resolution,[],[f17783,f7174]) ).
thf(f17788,plain,
( ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_59
| ~ spl99_68
| spl99_99
| spl99_114 ),
inference(forward_subsumption_resolution,[],[f17786,f15118]) ).
thf(f17791,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_59
| ~ spl99_68
| ~ spl99_98
| spl99_99
| spl99_114 ),
inference(forward_demodulation,[],[f17788,f7171]) ).
thf(f17792,plain,
( ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_59
| ~ spl99_68
| ~ spl99_98
| spl99_99
| spl99_114 ),
inference(trivial_inequality_removal,[],[f17791]) ).
thf(f17793,plain,
( ( $true = $false )
| ~ spl99_59
| ~ spl99_68
| ~ spl99_98
| spl99_99
| spl99_114 ),
inference(forward_demodulation,[],[f17792,f97]) ).
thf(f17794,plain,
( $false
| ~ spl99_59
| ~ spl99_68
| ~ spl99_98
| spl99_99
| spl99_114 ),
inference(trivial_inequality_removal,[],[f17793]) ).
thf(f17795,plain,
( ~ spl99_59
| ~ spl99_68
| ~ spl99_98
| spl99_99
| spl99_114 ),
inference(avatar_contradiction_clause,[],[f17794]) ).
thf(f17887,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_43
| ~ spl99_59 ),
inference(constrained_superposition,[],[f4522,f17658]) ).
thf(f17890,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_43
| ~ spl99_59 ),
inference(trivial_inequality_removal,[],[f17887]) ).
thf(f17897,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_43
| ~ spl99_59
| ~ spl99_68 ),
inference(constrained_superposition,[],[f4692,f17890]) ).
thf(f17900,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ X0 ) ) ) )
| ~ spl99_43
| ~ spl99_59
| ~ spl99_68 ),
inference(trivial_inequality_removal,[],[f17897]) ).
thf(f17918,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_59
| ~ spl99_68 ),
inference(constrained_superposition,[],[f17577,f17900]) ).
thf(f17919,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_59
| ~ spl99_68 ),
inference(duplicate_literal_removal,[],[f17918]) ).
thf(f17920,plain,
( ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_59
| ~ spl99_68 ),
inference(trivial_inequality_removal,[],[f17919]) ).
thf(f17946,plain,
( ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_59
| ~ spl99_68
| spl99_99 ),
inference(forward_subsumption_resolution,[],[f17920,f7174]) ).
thf(f17948,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_59
| ~ spl99_68
| spl99_99
| ~ spl99_114 ),
inference(forward_demodulation,[],[f17946,f15119]) ).
thf(f17949,plain,
( ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_59
| ~ spl99_68
| spl99_99
| ~ spl99_114 ),
inference(trivial_inequality_removal,[],[f17948]) ).
thf(f17952,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_59
| ~ spl99_68
| spl99_99
| ~ spl99_114 ),
inference(forward_demodulation,[],[f17949,f97]) ).
thf(f17953,plain,
( ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_59
| ~ spl99_68
| spl99_99
| ~ spl99_114 ),
inference(trivial_inequality_removal,[],[f17952]) ).
thf(f17957,plain,
( ( $true = $false )
| ~ spl99_43
| ~ spl99_59
| ~ spl99_68
| ~ spl99_98
| spl99_99
| ~ spl99_114 ),
inference(constrained_superposition,[],[f17953,f7171]) ).
thf(f17961,plain,
( $false
| ~ spl99_43
| ~ spl99_59
| ~ spl99_68
| ~ spl99_98
| spl99_99
| ~ spl99_114 ),
inference(trivial_inequality_removal,[],[f17957]) ).
thf(f17962,plain,
( ~ spl99_43
| ~ spl99_59
| ~ spl99_68
| ~ spl99_98
| spl99_99
| ~ spl99_114 ),
inference(avatar_contradiction_clause,[],[f17961]) ).
thf(f17998,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_53 ),
inference(constrained_superposition,[],[f2381,f4596]) ).
thf(f18000,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_53 ),
inference(constrained_superposition,[],[f2387,f4596]) ).
thf(f18009,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_53 ),
inference(trivial_inequality_removal,[],[f18000]) ).
thf(f18011,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sK11 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) ) )
| ~ spl99_53 ),
inference(trivial_inequality_removal,[],[f17998]) ).
thf(f18147,plain,
( spl99_37
| spl99_39
| spl99_66
| spl99_59 ),
inference(avatar_split_clause,[],[f1628,f4613,f4685,f4509,f4503]) ).
thf(f18252,plain,
( spl99_45
| spl99_39
| spl99_66
| spl99_59 ),
inference(avatar_split_clause,[],[f1636,f4613,f4685,f4509,f4546]) ).
thf(f18374,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) ) )
| ~ spl99_45 ),
inference(constrained_superposition,[],[f2382,f4547]) ).
thf(f18375,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) ) )
| ~ spl99_45 ),
inference(constrained_superposition,[],[f2388,f4547]) ).
thf(f18380,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) ) )
| ~ spl99_45
| ~ spl99_53 ),
inference(constrained_superposition,[],[f18009,f4547]) ).
thf(f18381,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) ) )
| ~ spl99_45
| ~ spl99_53 ),
inference(constrained_superposition,[],[f18011,f4547]) ).
thf(f18382,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) ) )
| ~ spl99_45
| ~ spl99_53 ),
inference(trivial_inequality_removal,[],[f18381]) ).
thf(f18383,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) ) )
| ~ spl99_45
| ~ spl99_53 ),
inference(trivial_inequality_removal,[],[f18380]) ).
thf(f18388,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sK10 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) ) )
| ~ spl99_45 ),
inference(trivial_inequality_removal,[],[f18375]) ).
thf(f18389,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $true
= ( mrel @ X0 @ ( sK10 @ X0 ) ) ) )
| ~ spl99_45 ),
inference(trivial_inequality_removal,[],[f18374]) ).
thf(f18546,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53 ),
inference(constrained_superposition,[],[f4504,f18383]) ).
thf(f18549,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53 ),
inference(trivial_inequality_removal,[],[f18546]) ).
thf(f18594,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) ) )
| ~ spl99_37
| ~ spl99_45 ),
inference(constrained_superposition,[],[f4504,f18388]) ).
thf(f18597,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK9 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ X0 ) ) ) )
| ~ spl99_37
| ~ spl99_45 ),
inference(trivial_inequality_removal,[],[f18594]) ).
thf(f18602,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53 ),
inference(constrained_superposition,[],[f18597,f18549]) ).
thf(f18622,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53 ),
inference(duplicate_literal_removal,[],[f18602]) ).
thf(f18623,plain,
( ( $false
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53 ),
inference(trivial_inequality_removal,[],[f18622]) ).
thf(f18626,plain,
( ( $false
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| spl99_106 ),
inference(forward_subsumption_resolution,[],[f18623,f8399]) ).
thf(f18641,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_105
| spl99_106 ),
inference(forward_demodulation,[],[f18626,f8396]) ).
thf(f18642,plain,
( ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_105
| spl99_106 ),
inference(trivial_inequality_removal,[],[f18641]) ).
thf(f18643,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_105
| spl99_106 ),
inference(forward_demodulation,[],[f18642,f97]) ).
thf(f18644,plain,
( ( $false
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_105
| spl99_106 ),
inference(trivial_inequality_removal,[],[f18643]) ).
thf(f18762,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ~ spl99_45
| ~ spl99_53 ),
inference(constrained_superposition,[],[f18389,f18382]) ).
thf(f18788,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_45
| ~ spl99_53 ),
inference(duplicate_literal_removal,[],[f18762]) ).
thf(f18789,plain,
( ( $false
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK9 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_45
| ~ spl99_53 ),
inference(trivial_inequality_removal,[],[f18788]) ).
thf(f18792,plain,
( ( $false
= ( mrel @ sK0 @ ( sK11 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_45
| ~ spl99_53
| spl99_106 ),
inference(forward_subsumption_resolution,[],[f18789,f8399]) ).
thf(f18795,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_45
| ~ spl99_53
| ~ spl99_105
| spl99_106 ),
inference(forward_demodulation,[],[f18792,f8396]) ).
thf(f18796,plain,
( ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_45
| ~ spl99_53
| ~ spl99_105
| spl99_106 ),
inference(trivial_inequality_removal,[],[f18795]) ).
thf(f18799,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_45
| ~ spl99_53
| ~ spl99_105
| spl99_106 ),
inference(forward_demodulation,[],[f18796,f97]) ).
thf(f18800,plain,
( ( $true
= ( mrel @ sK0 @ ( sK10 @ sK0 ) ) )
| ~ spl99_45
| ~ spl99_53
| ~ spl99_105
| spl99_106 ),
inference(trivial_inequality_removal,[],[f18799]) ).
thf(f18801,plain,
( ( $true = $false )
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_105
| spl99_106 ),
inference(forward_demodulation,[],[f18800,f18644]) ).
thf(f18802,plain,
( $false
| ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_105
| spl99_106 ),
inference(trivial_inequality_removal,[],[f18801]) ).
thf(f18803,plain,
( ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_105
| spl99_106 ),
inference(avatar_contradiction_clause,[],[f18802]) ).
thf(f18836,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_59 ),
inference(constrained_superposition,[],[f2417,f4614]) ).
thf(f18837,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_59 ),
inference(constrained_superposition,[],[f2419,f4614]) ).
thf(f18838,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_59 ),
inference(constrained_superposition,[],[f2423,f4614]) ).
thf(f18839,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_59 ),
inference(constrained_superposition,[],[f2425,f4614]) ).
thf(f18841,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_59 ),
inference(constrained_superposition,[],[f2433,f4614]) ).
thf(f18843,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_59 ),
inference(constrained_superposition,[],[f2439,f4614]) ).
thf(f18844,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_59 ),
inference(trivial_inequality_removal,[],[f18843]) ).
thf(f18846,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_59 ),
inference(trivial_inequality_removal,[],[f18841]) ).
thf(f18848,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_59 ),
inference(trivial_inequality_removal,[],[f18839]) ).
thf(f18849,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_59 ),
inference(trivial_inequality_removal,[],[f18838]) ).
thf(f18850,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sK15 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_59 ),
inference(trivial_inequality_removal,[],[f18837]) ).
thf(f18851,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) ) )
| ~ spl99_59 ),
inference(trivial_inequality_removal,[],[f18836]) ).
thf(f18985,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_51
| ~ spl99_59 ),
inference(constrained_superposition,[],[f4565,f18846]) ).
thf(f18988,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_51
| ~ spl99_59 ),
inference(trivial_inequality_removal,[],[f18985]) ).
thf(f18995,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68 ),
inference(constrained_superposition,[],[f4692,f18988]) ).
thf(f18998,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ X0 ) ) ) )
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68 ),
inference(trivial_inequality_removal,[],[f18995]) ).
thf(f19074,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68 ),
inference(constrained_superposition,[],[f18998,f17576]) ).
thf(f19081,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68 ),
inference(duplicate_literal_removal,[],[f19074]) ).
thf(f19082,plain,
( ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68 ),
inference(trivial_inequality_removal,[],[f19081]) ).
thf(f19092,plain,
( ( $false
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68
| spl99_114 ),
inference(forward_subsumption_resolution,[],[f19082,f15118]) ).
thf(f19142,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68
| ~ spl99_99
| spl99_114 ),
inference(forward_demodulation,[],[f19092,f7175]) ).
thf(f19143,plain,
( ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68
| ~ spl99_99
| spl99_114 ),
inference(trivial_inequality_removal,[],[f19142]) ).
thf(f19150,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68
| ~ spl99_99
| spl99_114 ),
inference(forward_demodulation,[],[f19143,f97]) ).
thf(f19151,plain,
( ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68
| ~ spl99_99
| spl99_114 ),
inference(trivial_inequality_removal,[],[f19150]) ).
thf(f19159,plain,
( ( $true = $false )
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68
| ~ spl99_98
| ~ spl99_99
| spl99_114 ),
inference(constrained_superposition,[],[f19151,f7171]) ).
thf(f19163,plain,
( $false
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68
| ~ spl99_98
| ~ spl99_99
| spl99_114 ),
inference(trivial_inequality_removal,[],[f19159]) ).
thf(f19164,plain,
( ~ spl99_51
| ~ spl99_59
| ~ spl99_68
| ~ spl99_98
| ~ spl99_99
| spl99_114 ),
inference(avatar_contradiction_clause,[],[f19163]) ).
thf(f19192,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_59 ),
inference(constrained_superposition,[],[f18851,f2418]) ).
thf(f19238,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ~ spl99_59 ),
inference(duplicate_literal_removal,[],[f19192]) ).
thf(f19239,plain,
( ( $true
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ~ spl99_59 ),
inference(trivial_inequality_removal,[],[f19238]) ).
thf(f19440,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_51
| ~ spl99_59 ),
inference(constrained_superposition,[],[f4565,f18844]) ).
thf(f19441,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_51
| ~ spl99_59 ),
inference(trivial_inequality_removal,[],[f19440]) ).
thf(f19446,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59 ),
inference(constrained_superposition,[],[f4522,f19441]) ).
thf(f19447,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59 ),
inference(trivial_inequality_removal,[],[f19446]) ).
thf(f19452,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68 ),
inference(constrained_superposition,[],[f4692,f19447]) ).
thf(f19453,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ X0 ) ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68 ),
inference(trivial_inequality_removal,[],[f19452]) ).
thf(f19554,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68 ),
inference(constrained_superposition,[],[f19453,f17578]) ).
thf(f19555,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68 ),
inference(duplicate_literal_removal,[],[f19554]) ).
thf(f19556,plain,
( ( $false
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68 ),
inference(trivial_inequality_removal,[],[f19555]) ).
thf(f19630,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68
| ~ spl99_99 ),
inference(forward_demodulation,[],[f19556,f7175]) ).
thf(f19631,plain,
( ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68
| ~ spl99_99 ),
inference(trivial_inequality_removal,[],[f19630]) ).
thf(f19634,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68
| ~ spl99_99
| ~ spl99_114 ),
inference(forward_demodulation,[],[f19631,f15119]) ).
thf(f19635,plain,
( ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68
| ~ spl99_99
| ~ spl99_114 ),
inference(trivial_inequality_removal,[],[f19634]) ).
thf(f19638,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68
| ~ spl99_99
| ~ spl99_114 ),
inference(forward_demodulation,[],[f19635,f97]) ).
thf(f19639,plain,
( ( $false
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68
| ~ spl99_99
| ~ spl99_114 ),
inference(trivial_inequality_removal,[],[f19638]) ).
thf(f19643,plain,
( ( $true = $false )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68
| ~ spl99_98
| ~ spl99_99
| ~ spl99_114 ),
inference(constrained_superposition,[],[f19639,f7171]) ).
thf(f19647,plain,
( $false
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68
| ~ spl99_98
| ~ spl99_99
| ~ spl99_114 ),
inference(trivial_inequality_removal,[],[f19643]) ).
thf(f19648,plain,
( ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68
| ~ spl99_98
| ~ spl99_99
| ~ spl99_114 ),
inference(avatar_contradiction_clause,[],[f19647]) ).
thf(f19650,plain,
( spl99_45
| spl99_39
| spl99_66
| spl99_51 ),
inference(avatar_split_clause,[],[f1103,f4564,f4685,f4509,f4546]) ).
thf(f20096,plain,
( spl99_37
| spl99_39
| spl99_66
| spl99_51 ),
inference(avatar_split_clause,[],[f1095,f4564,f4685,f4509,f4503]) ).
thf(f20119,plain,
( spl99_53
| spl99_39
| spl99_66
| spl99_51 ),
inference(avatar_split_clause,[],[f1111,f4564,f4685,f4509,f4595]) ).
thf(f20137,plain,
( spl99_53
| spl99_39
| spl99_49
| spl99_51 ),
inference(avatar_split_clause,[],[f847,f4564,f4558,f4509,f4595]) ).
thf(f20182,plain,
( spl99_53
| spl99_64
| spl99_66
| spl99_51 ),
inference(avatar_split_clause,[],[f1208,f4564,f4685,f4679,f4595]) ).
thf(f20241,plain,
( spl99_53
| spl99_55
| spl99_66
| spl99_51 ),
inference(avatar_split_clause,[],[f1177,f4564,f4685,f4601,f4595]) ).
thf(f20320,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ X0 ) ) ) )
| ~ spl99_47
| ~ spl99_64 ),
inference(constrained_superposition,[],[f11362,f4680]) ).
thf(f20323,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ X0 ) ) ) )
| ~ spl99_47
| ~ spl99_64 ),
inference(trivial_inequality_removal,[],[f20320]) ).
thf(f20376,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) ) )
| ~ spl99_39
| ~ spl99_47 ),
inference(constrained_superposition,[],[f11274,f4510]) ).
thf(f20377,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) ) )
| ~ spl99_39
| ~ spl99_47 ),
inference(constrained_superposition,[],[f11626,f4510]) ).
thf(f20378,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) ) )
| ~ spl99_39
| ~ spl99_47 ),
inference(trivial_inequality_removal,[],[f20377]) ).
thf(f20379,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) ) )
| ~ spl99_39
| ~ spl99_47 ),
inference(trivial_inequality_removal,[],[f20376]) ).
thf(f20474,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) ) )
| ~ spl99_55 ),
inference(constrained_superposition,[],[f2341,f4602]) ).
thf(f20478,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) ) )
| ~ spl99_55 ),
inference(constrained_superposition,[],[f2361,f4602]) ).
thf(f20479,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) ) )
| ~ spl99_55 ),
inference(trivial_inequality_removal,[],[f20478]) ).
thf(f20483,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) ) )
| ~ spl99_55 ),
inference(trivial_inequality_removal,[],[f20474]) ).
thf(f20494,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) ) )
| ~ spl99_47
| ~ spl99_55 ),
inference(constrained_superposition,[],[f4553,f20483]) ).
thf(f20497,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) ) )
| ~ spl99_47
| ~ spl99_55 ),
inference(trivial_inequality_removal,[],[f20494]) ).
thf(f20509,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ~ spl99_47
| ~ spl99_55 ),
inference(constrained_superposition,[],[f10715,f20497]) ).
thf(f20510,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_47
| ~ spl99_55 ),
inference(duplicate_literal_removal,[],[f20509]) ).
thf(f20511,plain,
( ( $false
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_47
| ~ spl99_55 ),
inference(trivial_inequality_removal,[],[f20510]) ).
thf(f20526,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_55 ),
inference(constrained_superposition,[],[f4602,f2347]) ).
thf(f20529,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_55 ),
inference(trivial_inequality_removal,[],[f20526]) ).
thf(f20536,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_47
| ~ spl99_55 ),
inference(constrained_superposition,[],[f4553,f20529]) ).
thf(f20539,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_47
| ~ spl99_55 ),
inference(trivial_inequality_removal,[],[f20536]) ).
thf(f20546,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55 ),
inference(constrained_superposition,[],[f4510,f20539]) ).
thf(f20549,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55 ),
inference(trivial_inequality_removal,[],[f20546]) ).
thf(f20578,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_55 ),
inference(constrained_superposition,[],[f4602,f2355]) ).
thf(f20581,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sK7 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_55 ),
inference(trivial_inequality_removal,[],[f20578]) ).
thf(f20588,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_47
| ~ spl99_55 ),
inference(constrained_superposition,[],[f4553,f20581]) ).
thf(f20591,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_47
| ~ spl99_55 ),
inference(trivial_inequality_removal,[],[f20588]) ).
thf(f20598,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64 ),
inference(constrained_superposition,[],[f4680,f20591]) ).
thf(f20601,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64 ),
inference(trivial_inequality_removal,[],[f20598]) ).
thf(f20642,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) ) )
| ~ spl99_47
| ~ spl99_55 ),
inference(constrained_superposition,[],[f4553,f20479]) ).
thf(f20643,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sK6 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) ) )
| ~ spl99_47
| ~ spl99_55 ),
inference(trivial_inequality_removal,[],[f20642]) ).
thf(f20648,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55 ),
inference(constrained_superposition,[],[f4510,f20643]) ).
thf(f20649,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55 ),
inference(trivial_inequality_removal,[],[f20648]) ).
thf(f20654,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64 ),
inference(constrained_superposition,[],[f4680,f20649]) ).
thf(f20655,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ sK0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ X0 ) ) ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64 ),
inference(trivial_inequality_removal,[],[f20654]) ).
thf(f20706,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_64 ),
inference(constrained_superposition,[],[f4680,f20379]) ).
thf(f20709,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK8 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ X0 ) ) ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_64 ),
inference(trivial_inequality_removal,[],[f20706]) ).
thf(f20714,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64 ),
inference(constrained_superposition,[],[f20709,f20655]) ).
thf(f20740,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64 ),
inference(duplicate_literal_removal,[],[f20714]) ).
thf(f20741,plain,
( ( $false
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64 ),
inference(trivial_inequality_removal,[],[f20740]) ).
thf(f20744,plain,
( ( $false
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64
| spl99_107 ),
inference(forward_subsumption_resolution,[],[f20741,f12086]) ).
thf(f20766,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64
| ~ spl99_75
| spl99_107 ),
inference(forward_demodulation,[],[f20744,f5348]) ).
thf(f20767,plain,
( ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64
| ~ spl99_75
| spl99_107 ),
inference(trivial_inequality_removal,[],[f20766]) ).
thf(f20770,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64
| ~ spl99_75
| ~ spl99_76
| spl99_107 ),
inference(forward_demodulation,[],[f20767,f5352]) ).
thf(f20771,plain,
( ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64
| ~ spl99_75
| ~ spl99_76
| spl99_107 ),
inference(trivial_inequality_removal,[],[f20770]) ).
thf(f20772,plain,
( ( $true = $false )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64
| ~ spl99_75
| ~ spl99_76
| spl99_107 ),
inference(forward_demodulation,[],[f20771,f97]) ).
thf(f20773,plain,
( $false
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64
| ~ spl99_75
| ~ spl99_76
| spl99_107 ),
inference(trivial_inequality_removal,[],[f20772]) ).
thf(f20774,plain,
( ~ spl99_39
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64
| ~ spl99_75
| ~ spl99_76
| spl99_107 ),
inference(avatar_contradiction_clause,[],[f20773]) ).
thf(f20822,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55 ),
inference(constrained_superposition,[],[f20378,f20549]) ).
thf(f20842,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55 ),
inference(duplicate_literal_removal,[],[f20822]) ).
thf(f20843,plain,
( ( $false
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55 ),
inference(trivial_inequality_removal,[],[f20842]) ).
thf(f20857,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64 ),
inference(constrained_superposition,[],[f20601,f20323]) ).
thf(f20864,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64 ),
inference(duplicate_literal_removal,[],[f20857]) ).
thf(f20865,plain,
( ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64 ),
inference(trivial_inequality_removal,[],[f20864]) ).
thf(f20879,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64
| ~ spl99_107 ),
inference(forward_demodulation,[],[f20865,f12087]) ).
thf(f20880,plain,
( ( $false
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64
| ~ spl99_107 ),
inference(trivial_inequality_removal,[],[f20879]) ).
thf(f20883,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64
| ~ spl99_75
| ~ spl99_107 ),
inference(forward_demodulation,[],[f20880,f5348]) ).
thf(f20884,plain,
( ( $false
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64
| ~ spl99_75
| ~ spl99_107 ),
inference(trivial_inequality_removal,[],[f20883]) ).
thf(f20887,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64
| ~ spl99_75
| ~ spl99_76
| ~ spl99_107 ),
inference(forward_demodulation,[],[f20884,f5352]) ).
thf(f20888,plain,
( ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64
| ~ spl99_75
| ~ spl99_76
| ~ spl99_107 ),
inference(trivial_inequality_removal,[],[f20887]) ).
thf(f20891,plain,
( ( $true = $false )
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64
| ~ spl99_75
| ~ spl99_76
| ~ spl99_107 ),
inference(forward_demodulation,[],[f20888,f97]) ).
thf(f20892,plain,
( $false
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64
| ~ spl99_75
| ~ spl99_76
| ~ spl99_107 ),
inference(trivial_inequality_removal,[],[f20891]) ).
thf(f20893,plain,
( ~ spl99_47
| ~ spl99_55
| ~ spl99_64
| ~ spl99_75
| ~ spl99_76
| ~ spl99_107 ),
inference(avatar_contradiction_clause,[],[f20892]) ).
thf(f20894,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_47
| ~ spl99_55
| ~ spl99_75 ),
inference(forward_demodulation,[],[f20511,f5348]) ).
thf(f20895,plain,
( ( $true
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_47
| ~ spl99_55
| ~ spl99_75 ),
inference(trivial_inequality_removal,[],[f20894]) ).
thf(f20900,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_47
| ~ spl99_55
| ~ spl99_75
| ~ spl99_107 ),
inference(forward_demodulation,[],[f20895,f12087]) ).
thf(f20901,plain,
( ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_47
| ~ spl99_55
| ~ spl99_75
| ~ spl99_107 ),
inference(trivial_inequality_removal,[],[f20900]) ).
thf(f20904,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ~ spl99_47
| ~ spl99_55
| ~ spl99_75
| ~ spl99_107 ),
inference(forward_demodulation,[],[f20901,f97]) ).
thf(f20905,plain,
( ( $true
= ( mrel @ sK0 @ ( sK5 @ sK0 ) ) )
| ~ spl99_47
| ~ spl99_55
| ~ spl99_75
| ~ spl99_107 ),
inference(trivial_inequality_removal,[],[f20904]) ).
thf(f20969,plain,
( $false
| ~ spl99_47
| ~ spl99_55
| ~ spl99_75
| spl99_76
| ~ spl99_107 ),
inference(forward_subsumption_resolution,[],[f20905,f5351]) ).
thf(f20970,plain,
( ~ spl99_47
| ~ spl99_55
| ~ spl99_75
| spl99_76
| ~ spl99_107 ),
inference(avatar_contradiction_clause,[],[f20969]) ).
thf(f20979,plain,
( ( $false
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK6 @ sK0 ) ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55
| spl99_76 ),
inference(forward_subsumption_resolution,[],[f20843,f5351]) ).
thf(f21005,plain,
( ( $false
= ( mrel @ sK0 @ ( sK7 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55
| spl99_76
| spl99_107 ),
inference(forward_subsumption_resolution,[],[f20979,f12086]) ).
thf(f21008,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55
| ~ spl99_75
| spl99_76
| spl99_107 ),
inference(forward_demodulation,[],[f21005,f5348]) ).
thf(f21009,plain,
( ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55
| ~ spl99_75
| spl99_76
| spl99_107 ),
inference(trivial_inequality_removal,[],[f21008]) ).
thf(f21013,plain,
( ( $true = $false )
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55
| ~ spl99_75
| spl99_76
| spl99_107 ),
inference(forward_demodulation,[],[f21009,f97]) ).
thf(f21014,plain,
( $false
| ~ spl99_39
| ~ spl99_47
| ~ spl99_55
| ~ spl99_75
| spl99_76
| spl99_107 ),
inference(trivial_inequality_removal,[],[f21013]) ).
thf(f21015,plain,
( ~ spl99_39
| ~ spl99_47
| ~ spl99_55
| ~ spl99_75
| spl99_76
| spl99_107 ),
inference(avatar_contradiction_clause,[],[f21014]) ).
thf(f21198,plain,
( spl99_53
| spl99_47
| spl99_66
| spl99_51 ),
inference(avatar_split_clause,[],[f1144,f4564,f4685,f4552,f4595]) ).
thf(f21245,plain,
( spl99_53
| spl99_55
| spl99_49
| spl99_51 ),
inference(avatar_split_clause,[],[f913,f4564,f4558,f4601,f4595]) ).
thf(f21456,plain,
( spl99_53
| spl99_47
| spl99_57
| spl99_51 ),
inference(avatar_split_clause,[],[f1013,f4564,f4607,f4552,f4595]) ).
thf(f21575,plain,
( spl99_53
| spl99_55
| spl99_57
| spl99_51 ),
inference(avatar_split_clause,[],[f1046,f4564,f4607,f4601,f4595]) ).
thf(f21724,plain,
( spl99_53
| spl99_64
| spl99_49
| spl99_51 ),
inference(avatar_split_clause,[],[f944,f4564,f4558,f4679,f4595]) ).
thf(f21851,plain,
( spl99_53
| spl99_64
| spl99_57
| spl99_51 ),
inference(avatar_split_clause,[],[f1077,f4564,f4607,f4679,f4595]) ).
thf(f21929,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) ) )
| ~ spl99_49 ),
inference(constrained_superposition,[],[f2302,f4559]) ).
thf(f21930,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) ) )
| ~ spl99_49 ),
inference(constrained_superposition,[],[f2316,f4559]) ).
thf(f21931,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) ) )
| ~ spl99_49 ),
inference(trivial_inequality_removal,[],[f21930]) ).
thf(f21932,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) ) )
| ~ spl99_49 ),
inference(trivial_inequality_removal,[],[f21929]) ).
thf(f21979,plain,
( spl99_53
| spl99_64
| spl99_41
| spl99_51 ),
inference(avatar_split_clause,[],[f811,f4564,f4515,f4679,f4595]) ).
thf(f21998,plain,
( spl99_53
| spl99_55
| spl99_41
| spl99_51 ),
inference(avatar_split_clause,[],[f780,f4564,f4515,f4601,f4595]) ).
thf(f22124,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) ) )
| ~ spl99_57 ),
inference(constrained_superposition,[],[f2315,f4608]) ).
thf(f22125,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) ) )
| ~ spl99_57 ),
inference(constrained_superposition,[],[f2313,f4608]) ).
thf(f22126,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) ) )
| ~ spl99_57 ),
inference(constrained_superposition,[],[f2299,f4608]) ).
thf(f22127,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) ) )
| ~ spl99_57 ),
inference(constrained_superposition,[],[f2301,f4608]) ).
thf(f22128,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) ) )
| ~ spl99_57 ),
inference(trivial_inequality_removal,[],[f22127]) ).
thf(f22129,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) ) )
| ~ spl99_57 ),
inference(trivial_inequality_removal,[],[f22126]) ).
thf(f22130,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) ) )
| ~ spl99_57 ),
inference(trivial_inequality_removal,[],[f22125]) ).
thf(f22131,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) ) )
| ~ spl99_57 ),
inference(trivial_inequality_removal,[],[f22124]) ).
thf(f22512,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ X0 ) ) ) )
| ~ spl99_66 ),
inference(constrained_superposition,[],[f2314,f4686]) ).
thf(f22513,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) ) )
| ~ spl99_66 ),
inference(trivial_inequality_removal,[],[f22512]) ).
thf(f22524,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) ) )
| ~ spl99_49
| ~ spl99_66 ),
inference(constrained_superposition,[],[f4686,f21931]) ).
thf(f22527,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ X0 ) ) ) )
| ~ spl99_49
| ~ spl99_66 ),
inference(trivial_inequality_removal,[],[f22524]) ).
thf(f22540,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) ) )
| ~ spl99_57
| ~ spl99_66 ),
inference(constrained_superposition,[],[f4686,f22130]) ).
thf(f22543,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ X0 ) ) ) )
| ~ spl99_57
| ~ spl99_66 ),
inference(trivial_inequality_removal,[],[f22540]) ).
thf(f22554,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ~ spl99_57
| ~ spl99_66 ),
inference(constrained_superposition,[],[f22513,f22543]) ).
thf(f22558,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl99_57
| ~ spl99_66 ),
inference(duplicate_literal_removal,[],[f22554]) ).
thf(f22559,plain,
( ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl99_57
| ~ spl99_66 ),
inference(trivial_inequality_removal,[],[f22558]) ).
thf(f22574,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41 ),
inference(constrained_superposition,[],[f4516,f2320]) ).
thf(f22577,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41 ),
inference(trivial_inequality_removal,[],[f22574]) ).
thf(f22584,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41
| ~ spl99_66 ),
inference(constrained_superposition,[],[f4686,f22577]) ).
thf(f22587,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41
| ~ spl99_66 ),
inference(trivial_inequality_removal,[],[f22584]) ).
thf(f22606,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) ) )
| ~ spl99_49
| ~ spl99_57 ),
inference(constrained_superposition,[],[f4559,f22131]) ).
thf(f22609,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) ) )
| ~ spl99_49
| ~ spl99_57 ),
inference(trivial_inequality_removal,[],[f22606]) ).
thf(f22616,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) ) )
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66 ),
inference(constrained_superposition,[],[f4686,f22609]) ).
thf(f22619,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ X0 ) ) ) )
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66 ),
inference(trivial_inequality_removal,[],[f22616]) ).
thf(f22632,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66 ),
inference(constrained_superposition,[],[f22527,f22619]) ).
thf(f22636,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66 ),
inference(duplicate_literal_removal,[],[f22632]) ).
thf(f22637,plain,
( ( $false
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66 ),
inference(trivial_inequality_removal,[],[f22636]) ).
thf(f22653,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66
| ~ spl99_110 ),
inference(forward_demodulation,[],[f22637,f13050]) ).
thf(f22654,plain,
( ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66
| ~ spl99_110 ),
inference(trivial_inequality_removal,[],[f22653]) ).
thf(f22657,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66
| ~ spl99_110 ),
inference(forward_demodulation,[],[f22654,f97]) ).
thf(f22658,plain,
( ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66
| ~ spl99_110 ),
inference(trivial_inequality_removal,[],[f22657]) ).
thf(f22668,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_57 ),
inference(constrained_superposition,[],[f4608,f2319]) ).
thf(f22671,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_57 ),
inference(trivial_inequality_removal,[],[f22668]) ).
thf(f22678,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41
| ~ spl99_57 ),
inference(constrained_superposition,[],[f4516,f22671]) ).
thf(f22681,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41
| ~ spl99_57 ),
inference(trivial_inequality_removal,[],[f22678]) ).
thf(f22688,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41
| ~ spl99_57
| ~ spl99_66 ),
inference(constrained_superposition,[],[f4686,f22681]) ).
thf(f22691,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41
| ~ spl99_57
| ~ spl99_66 ),
inference(trivial_inequality_removal,[],[f22688]) ).
thf(f22705,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_57
| ~ spl99_66 ),
inference(constrained_superposition,[],[f22587,f22691]) ).
thf(f22706,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_57
| ~ spl99_66 ),
inference(duplicate_literal_removal,[],[f22705]) ).
thf(f22707,plain,
( ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_57
| ~ spl99_66 ),
inference(trivial_inequality_removal,[],[f22706]) ).
thf(f22728,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_49 ),
inference(constrained_superposition,[],[f4559,f2322]) ).
thf(f22731,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_49 ),
inference(trivial_inequality_removal,[],[f22728]) ).
thf(f22738,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41
| ~ spl99_49 ),
inference(constrained_superposition,[],[f4516,f22731]) ).
thf(f22741,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41
| ~ spl99_49 ),
inference(trivial_inequality_removal,[],[f22738]) ).
thf(f22748,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_66 ),
inference(constrained_superposition,[],[f4686,f22741]) ).
thf(f22751,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_66 ),
inference(trivial_inequality_removal,[],[f22748]) ).
thf(f22781,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_57 ),
inference(constrained_superposition,[],[f4608,f2321]) ).
thf(f22782,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_57 ),
inference(trivial_inequality_removal,[],[f22781]) ).
thf(f22787,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_49
| ~ spl99_57 ),
inference(constrained_superposition,[],[f4559,f22782]) ).
thf(f22788,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_49
| ~ spl99_57 ),
inference(trivial_inequality_removal,[],[f22787]) ).
thf(f22793,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57 ),
inference(constrained_superposition,[],[f4516,f22788]) ).
thf(f22794,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57 ),
inference(trivial_inequality_removal,[],[f22793]) ).
thf(f22799,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66 ),
inference(constrained_superposition,[],[f4686,f22794]) ).
thf(f22800,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66 ),
inference(trivial_inequality_removal,[],[f22799]) ).
thf(f22813,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66 ),
inference(constrained_superposition,[],[f22751,f22800]) ).
thf(f22814,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66 ),
inference(duplicate_literal_removal,[],[f22813]) ).
thf(f22815,plain,
( ( $false
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66 ),
inference(trivial_inequality_removal,[],[f22814]) ).
thf(f22835,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66
| ~ spl99_110 ),
inference(forward_demodulation,[],[f22815,f13050]) ).
thf(f22836,plain,
( ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66
| ~ spl99_110 ),
inference(trivial_inequality_removal,[],[f22835]) ).
thf(f22853,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66
| ~ spl99_110
| ~ spl99_111 ),
inference(forward_demodulation,[],[f22658,f13054]) ).
thf(f22854,plain,
( ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66
| ~ spl99_110
| ~ spl99_111 ),
inference(trivial_inequality_removal,[],[f22853]) ).
thf(f22859,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66
| ~ spl99_110
| ~ spl99_111 ),
inference(forward_demodulation,[],[f22836,f13054]) ).
thf(f22860,plain,
( ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66
| ~ spl99_110
| ~ spl99_111 ),
inference(trivial_inequality_removal,[],[f22859]) ).
thf(f22863,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66
| ~ spl99_110
| ~ spl99_111 ),
inference(forward_demodulation,[],[f22860,f97]) ).
thf(f22864,plain,
( ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66
| ~ spl99_110
| ~ spl99_111 ),
inference(trivial_inequality_removal,[],[f22863]) ).
thf(f22939,plain,
( ( $true = $false )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66
| ~ spl99_110
| ~ spl99_111 ),
inference(constrained_superposition,[],[f22864,f22854]) ).
thf(f22943,plain,
( $false
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66
| ~ spl99_110
| ~ spl99_111 ),
inference(trivial_inequality_removal,[],[f22939]) ).
thf(f22944,plain,
( ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66
| ~ spl99_110
| ~ spl99_111 ),
inference(avatar_contradiction_clause,[],[f22943]) ).
thf(f22994,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl99_57 ),
inference(constrained_superposition,[],[f2300,f22129]) ).
thf(f23010,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_57 ),
inference(duplicate_literal_removal,[],[f22994]) ).
thf(f23011,plain,
( ( $true
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_57 ),
inference(trivial_inequality_removal,[],[f23010]) ).
thf(f23030,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41 ),
inference(constrained_superposition,[],[f4516,f2306]) ).
thf(f23033,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41 ),
inference(trivial_inequality_removal,[],[f23030]) ).
thf(f23076,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) ) )
| ~ spl99_49
| ~ spl99_57 ),
inference(constrained_superposition,[],[f4559,f22128]) ).
thf(f23079,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) ) )
| ~ spl99_49
| ~ spl99_57 ),
inference(trivial_inequality_removal,[],[f23076]) ).
thf(f23094,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ~ spl99_49
| ~ spl99_57 ),
inference(constrained_superposition,[],[f21932,f23079]) ).
thf(f23110,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl99_49
| ~ spl99_57 ),
inference(duplicate_literal_removal,[],[f23094]) ).
thf(f23111,plain,
( ( $false
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl99_49
| ~ spl99_57 ),
inference(trivial_inequality_removal,[],[f23110]) ).
thf(f23131,plain,
( ( $false
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl99_49
| ~ spl99_57
| spl99_111 ),
inference(forward_subsumption_resolution,[],[f23111,f13053]) ).
thf(f23133,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl99_49
| ~ spl99_57
| ~ spl99_110
| spl99_111 ),
inference(forward_demodulation,[],[f23131,f13050]) ).
thf(f23134,plain,
( ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl99_49
| ~ spl99_57
| ~ spl99_110
| spl99_111 ),
inference(trivial_inequality_removal,[],[f23133]) ).
thf(f23137,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl99_49
| ~ spl99_57
| ~ spl99_110
| spl99_111 ),
inference(forward_demodulation,[],[f23134,f97]) ).
thf(f23138,plain,
( ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl99_49
| ~ spl99_57
| ~ spl99_110
| spl99_111 ),
inference(trivial_inequality_removal,[],[f23137]) ).
thf(f23144,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_57 ),
inference(constrained_superposition,[],[f4608,f2305]) ).
thf(f23147,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_57 ),
inference(trivial_inequality_removal,[],[f23144]) ).
thf(f23154,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41
| ~ spl99_57 ),
inference(constrained_superposition,[],[f4516,f23147]) ).
thf(f23157,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41
| ~ spl99_57 ),
inference(trivial_inequality_removal,[],[f23154]) ).
thf(f23177,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_57 ),
inference(constrained_superposition,[],[f23033,f23157]) ).
thf(f23178,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_57 ),
inference(duplicate_literal_removal,[],[f23177]) ).
thf(f23179,plain,
( ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_57 ),
inference(trivial_inequality_removal,[],[f23178]) ).
thf(f23212,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_49 ),
inference(constrained_superposition,[],[f4559,f2308]) ).
thf(f23215,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_49 ),
inference(trivial_inequality_removal,[],[f23212]) ).
thf(f23222,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41
| ~ spl99_49 ),
inference(constrained_superposition,[],[f4516,f23215]) ).
thf(f23225,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41
| ~ spl99_49 ),
inference(trivial_inequality_removal,[],[f23222]) ).
thf(f23280,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_57 ),
inference(constrained_superposition,[],[f4608,f2307]) ).
thf(f23283,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sK3 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_57 ),
inference(trivial_inequality_removal,[],[f23280]) ).
thf(f23290,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_49
| ~ spl99_57 ),
inference(constrained_superposition,[],[f4559,f23283]) ).
thf(f23293,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_49
| ~ spl99_57 ),
inference(trivial_inequality_removal,[],[f23290]) ).
thf(f23300,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57 ),
inference(constrained_superposition,[],[f4516,f23293]) ).
thf(f23303,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK1 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK4 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57 ),
inference(trivial_inequality_removal,[],[f23300]) ).
thf(f23316,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57 ),
inference(constrained_superposition,[],[f23303,f23225]) ).
thf(f23343,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57 ),
inference(duplicate_literal_removal,[],[f23316]) ).
thf(f23344,plain,
( ( $true
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57 ),
inference(trivial_inequality_removal,[],[f23343]) ).
thf(f23362,plain,
( ( $false
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| spl99_111 ),
inference(forward_subsumption_resolution,[],[f23344,f13053]) ).
thf(f23365,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_110
| spl99_111 ),
inference(forward_demodulation,[],[f23362,f13050]) ).
thf(f23366,plain,
( ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_110
| spl99_111 ),
inference(trivial_inequality_removal,[],[f23365]) ).
thf(f23369,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_110
| spl99_111 ),
inference(forward_demodulation,[],[f23366,f23138]) ).
thf(f23370,plain,
( ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_110
| spl99_111 ),
inference(trivial_inequality_removal,[],[f23369]) ).
thf(f23374,plain,
( ( $true = $false )
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_110
| spl99_111 ),
inference(forward_demodulation,[],[f23370,f97]) ).
thf(f23375,plain,
( $false
| ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_110
| spl99_111 ),
inference(trivial_inequality_removal,[],[f23374]) ).
thf(f23376,plain,
( ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_110
| spl99_111 ),
inference(avatar_contradiction_clause,[],[f23375]) ).
thf(f23377,plain,
( ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_57
| spl99_111 ),
inference(forward_subsumption_resolution,[],[f23011,f13053]) ).
thf(f23381,plain,
( ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_57
| spl99_111 ),
inference(forward_subsumption_resolution,[],[f23179,f13053]) ).
thf(f23387,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ~ spl99_57
| spl99_111 ),
inference(forward_demodulation,[],[f23377,f97]) ).
thf(f23388,plain,
( ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ~ spl99_57
| spl99_111 ),
inference(trivial_inequality_removal,[],[f23387]) ).
thf(f23391,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ~ spl99_41
| ~ spl99_57
| spl99_111 ),
inference(forward_demodulation,[],[f23381,f97]) ).
thf(f23392,plain,
( ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK3 @ sK0 ) ) )
| ~ spl99_41
| ~ spl99_57
| spl99_111 ),
inference(trivial_inequality_removal,[],[f23391]) ).
thf(f23507,plain,
( ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl99_57
| spl99_110
| spl99_111 ),
inference(forward_subsumption_resolution,[],[f23388,f13049]) ).
thf(f23508,plain,
( ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl99_41
| ~ spl99_57
| spl99_110
| spl99_111 ),
inference(forward_subsumption_resolution,[],[f23392,f13049]) ).
thf(f23510,plain,
( ( $true = $false )
| ~ spl99_41
| ~ spl99_57
| spl99_110
| spl99_111 ),
inference(constrained_superposition,[],[f23508,f23507]) ).
thf(f23514,plain,
( $false
| ~ spl99_41
| ~ spl99_57
| spl99_110
| spl99_111 ),
inference(trivial_inequality_removal,[],[f23510]) ).
thf(f23515,plain,
( ~ spl99_41
| ~ spl99_57
| spl99_110
| spl99_111 ),
inference(avatar_contradiction_clause,[],[f23514]) ).
thf(f23517,plain,
( ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl99_57
| ~ spl99_66
| spl99_110 ),
inference(forward_subsumption_resolution,[],[f22559,f13049]) ).
thf(f23519,plain,
( ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_41
| ~ spl99_57
| ~ spl99_66
| spl99_110 ),
inference(forward_subsumption_resolution,[],[f22707,f13049]) ).
thf(f23525,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl99_57
| ~ spl99_66
| spl99_110 ),
inference(forward_demodulation,[],[f23517,f97]) ).
thf(f23526,plain,
( ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl99_57
| ~ spl99_66
| spl99_110 ),
inference(trivial_inequality_removal,[],[f23525]) ).
thf(f23529,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ~ spl99_41
| ~ spl99_57
| ~ spl99_66
| spl99_110 ),
inference(forward_demodulation,[],[f23519,f97]) ).
thf(f23530,plain,
( ( $false
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ~ spl99_41
| ~ spl99_57
| ~ spl99_66
| spl99_110 ),
inference(trivial_inequality_removal,[],[f23529]) ).
thf(f23541,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl99_57
| ~ spl99_66
| spl99_110
| ~ spl99_111 ),
inference(forward_demodulation,[],[f23526,f13054]) ).
thf(f23542,plain,
( ( $true
= ( mrel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl99_57
| ~ spl99_66
| spl99_110
| ~ spl99_111 ),
inference(trivial_inequality_removal,[],[f23541]) ).
thf(f23543,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ~ spl99_41
| ~ spl99_57
| ~ spl99_66
| spl99_110
| ~ spl99_111 ),
inference(forward_demodulation,[],[f23530,f23542]) ).
thf(f23544,plain,
( ( $false
= ( mrel @ sK0 @ ( sK1 @ sK0 ) ) )
| ~ spl99_41
| ~ spl99_57
| ~ spl99_66
| spl99_110
| ~ spl99_111 ),
inference(trivial_inequality_removal,[],[f23543]) ).
thf(f23546,plain,
( ( $true = $false )
| ~ spl99_41
| ~ spl99_57
| ~ spl99_66
| spl99_110
| ~ spl99_111 ),
inference(constrained_superposition,[],[f23544,f13054]) ).
thf(f23550,plain,
( $false
| ~ spl99_41
| ~ spl99_57
| ~ spl99_66
| spl99_110
| ~ spl99_111 ),
inference(trivial_inequality_removal,[],[f23546]) ).
thf(f23551,plain,
( ~ spl99_41
| ~ spl99_57
| ~ spl99_66
| spl99_110
| ~ spl99_111 ),
inference(avatar_contradiction_clause,[],[f23550]) ).
thf(f23579,plain,
( spl99_53
| spl99_47
| spl99_49
| spl99_51 ),
inference(avatar_split_clause,[],[f880,f4564,f4558,f4552,f4595]) ).
thf(f23726,plain,
( spl99_53
| spl99_47
| spl99_49
| spl99_43 ),
inference(avatar_split_clause,[],[f347,f4521,f4558,f4552,f4595]) ).
thf(f24251,plain,
( spl99_53
| spl99_47
| spl99_49
| spl99_68 ),
inference(avatar_split_clause,[],[f1944,f4691,f4558,f4552,f4595]) ).
thf(f24364,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) ) )
| ~ spl99_51 ),
inference(constrained_superposition,[],[f2420,f4565]) ).
thf(f24365,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) ) )
| ~ spl99_51 ),
inference(constrained_superposition,[],[f2426,f4565]) ).
thf(f24370,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) ) )
| ~ spl99_51
| ~ spl99_59 ),
inference(constrained_superposition,[],[f18848,f4565]) ).
thf(f24371,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) ) )
| ~ spl99_51
| ~ spl99_59 ),
inference(constrained_superposition,[],[f18850,f4565]) ).
thf(f24372,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) ) )
| ~ spl99_51
| ~ spl99_59 ),
inference(trivial_inequality_removal,[],[f24371]) ).
thf(f24373,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) ) )
| ~ spl99_51
| ~ spl99_59 ),
inference(trivial_inequality_removal,[],[f24370]) ).
thf(f24378,plain,
( ! [X0: mworld] :
( ( $false
= ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sK14 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) ) )
| ~ spl99_51 ),
inference(trivial_inequality_removal,[],[f24365]) ).
thf(f24379,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $true
= ( mrel @ X0 @ ( sK14 @ X0 ) ) ) )
| ~ spl99_51 ),
inference(trivial_inequality_removal,[],[f24364]) ).
thf(f24420,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) ) )
| ~ spl99_43 ),
inference(constrained_superposition,[],[f2424,f4522]) ).
thf(f24423,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) ) )
| ~ spl99_43
| ~ spl99_59 ),
inference(constrained_superposition,[],[f18849,f4522]) ).
thf(f24424,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) ) )
| ~ spl99_43
| ~ spl99_59 ),
inference(trivial_inequality_removal,[],[f24423]) ).
thf(f24427,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) ) )
| ~ spl99_43 ),
inference(trivial_inequality_removal,[],[f24420]) ).
thf(f24491,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ~ spl99_51
| ~ spl99_59 ),
inference(constrained_superposition,[],[f24379,f24372]) ).
thf(f24495,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ~ spl99_51
| ~ spl99_59 ),
inference(duplicate_literal_removal,[],[f24491]) ).
thf(f24496,plain,
( ( $false
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ~ spl99_51
| ~ spl99_59 ),
inference(trivial_inequality_removal,[],[f24495]) ).
thf(f24516,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_59 ),
inference(constrained_superposition,[],[f24427,f24424]) ).
thf(f24517,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_59 ),
inference(duplicate_literal_removal,[],[f24516]) ).
thf(f24518,plain,
( ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_59 ),
inference(trivial_inequality_removal,[],[f24517]) ).
thf(f24532,plain,
( ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_59
| spl99_99 ),
inference(forward_subsumption_resolution,[],[f24518,f7174]) ).
thf(f24534,plain,
( ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_43
| ~ spl99_59
| spl99_98
| spl99_99 ),
inference(forward_subsumption_resolution,[],[f24532,f7170]) ).
thf(f24536,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_43
| ~ spl99_59
| spl99_98
| spl99_99
| ~ spl99_114 ),
inference(forward_demodulation,[],[f24534,f15119]) ).
thf(f24537,plain,
( ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_43
| ~ spl99_59
| spl99_98
| spl99_99
| ~ spl99_114 ),
inference(trivial_inequality_removal,[],[f24536]) ).
thf(f24540,plain,
( ( $true = $false )
| ~ spl99_43
| ~ spl99_59
| spl99_98
| spl99_99
| ~ spl99_114 ),
inference(forward_demodulation,[],[f24537,f97]) ).
thf(f24541,plain,
( $false
| ~ spl99_43
| ~ spl99_59
| spl99_98
| spl99_99
| ~ spl99_114 ),
inference(trivial_inequality_removal,[],[f24540]) ).
thf(f24542,plain,
( ~ spl99_43
| ~ spl99_59
| spl99_98
| spl99_99
| ~ spl99_114 ),
inference(avatar_contradiction_clause,[],[f24541]) ).
thf(f24543,plain,
( ( $true
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ~ spl99_59
| spl99_99 ),
inference(forward_subsumption_resolution,[],[f19239,f7174]) ).
thf(f24547,plain,
( ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ~ spl99_59
| spl99_98
| spl99_99 ),
inference(forward_subsumption_resolution,[],[f24543,f7170]) ).
thf(f24549,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ~ spl99_59
| spl99_98
| spl99_99 ),
inference(forward_demodulation,[],[f24547,f97]) ).
thf(f24550,plain,
( ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ~ spl99_59
| spl99_98
| spl99_99 ),
inference(trivial_inequality_removal,[],[f24549]) ).
thf(f24594,plain,
( $false
| ~ spl99_59
| spl99_98
| spl99_99
| spl99_114 ),
inference(forward_subsumption_resolution,[],[f24550,f15118]) ).
thf(f24595,plain,
( ~ spl99_59
| spl99_98
| spl99_99
| spl99_114 ),
inference(avatar_contradiction_clause,[],[f24594]) ).
thf(f24596,plain,
( ( $false
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $true
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ~ spl99_51
| ~ spl99_59
| spl99_98 ),
inference(forward_subsumption_resolution,[],[f24496,f7170]) ).
thf(f24602,plain,
( ( $false
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ~ spl99_51
| ~ spl99_59
| spl99_98
| spl99_114 ),
inference(forward_subsumption_resolution,[],[f24596,f15118]) ).
thf(f24611,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ~ spl99_51
| ~ spl99_59
| spl99_98
| spl99_114 ),
inference(forward_demodulation,[],[f24602,f97]) ).
thf(f24612,plain,
( ( $false
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ~ spl99_51
| ~ spl99_59
| spl99_98
| spl99_114 ),
inference(trivial_inequality_removal,[],[f24611]) ).
thf(f24621,plain,
( ( $true = $false )
| ~ spl99_51
| ~ spl99_59
| spl99_98
| ~ spl99_99
| spl99_114 ),
inference(constrained_superposition,[],[f24612,f7175]) ).
thf(f24625,plain,
( $false
| ~ spl99_51
| ~ spl99_59
| spl99_98
| ~ spl99_99
| spl99_114 ),
inference(trivial_inequality_removal,[],[f24621]) ).
thf(f24626,plain,
( ~ spl99_51
| ~ spl99_59
| spl99_98
| ~ spl99_99
| spl99_114 ),
inference(avatar_contradiction_clause,[],[f24625]) ).
thf(f24733,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) ) )
| ~ spl99_43
| ~ spl99_51 ),
inference(constrained_superposition,[],[f4522,f24378]) ).
thf(f24736,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) ) )
| ~ spl99_43
| ~ spl99_51 ),
inference(trivial_inequality_removal,[],[f24733]) ).
thf(f24767,plain,
( ! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) )
| ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59 ),
inference(constrained_superposition,[],[f4522,f24373]) ).
thf(f24770,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ X0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ X0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ X0 ) ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59 ),
inference(trivial_inequality_removal,[],[f24767]) ).
thf(f24784,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59 ),
inference(constrained_superposition,[],[f24736,f24770]) ).
thf(f24785,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59 ),
inference(duplicate_literal_removal,[],[f24784]) ).
thf(f24786,plain,
( ( $false
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $true
= ( mrel @ sK0 @ ( sK13 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59 ),
inference(trivial_inequality_removal,[],[f24785]) ).
thf(f24804,plain,
( ( $false
= ( mrel @ sK0 @ ( sK15 @ sK0 ) ) )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| spl99_98 ),
inference(forward_subsumption_resolution,[],[f24786,f7170]) ).
thf(f24806,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| spl99_98
| ~ spl99_99 ),
inference(forward_demodulation,[],[f24804,f7175]) ).
thf(f24807,plain,
( ( $false
= ( mrel @ sK0 @ sK0 ) )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| spl99_98
| ~ spl99_99 ),
inference(trivial_inequality_removal,[],[f24806]) ).
thf(f24810,plain,
( ( $true = $false )
| ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| spl99_98
| ~ spl99_99 ),
inference(forward_demodulation,[],[f24807,f97]) ).
thf(f24811,plain,
( ( $false
= ( mrel @ sK0 @ ( sK14 @ sK0 ) ) )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| spl99_98
| ~ spl99_99 ),
inference(trivial_inequality_removal,[],[f24810]) ).
thf(f24815,plain,
( ( $true = $false )
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| spl99_98
| ~ spl99_99
| ~ spl99_114 ),
inference(constrained_superposition,[],[f24811,f15119]) ).
thf(f24819,plain,
( $false
| ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| spl99_98
| ~ spl99_99
| ~ spl99_114 ),
inference(trivial_inequality_removal,[],[f24815]) ).
thf(f24820,plain,
( ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| spl99_98
| ~ spl99_99
| ~ spl99_114 ),
inference(avatar_contradiction_clause,[],[f24819]) ).
thf(f24826,plain,
( spl99_53
| spl99_47
| spl99_49
| spl99_59 ),
inference(avatar_split_clause,[],[f1413,f4613,f4558,f4552,f4595]) ).
thf(f25019,plain,
( spl99_53
| spl99_64
| spl99_49
| spl99_68 ),
inference(avatar_split_clause,[],[f2008,f4691,f4558,f4679,f4595]) ).
thf(f25079,plain,
( spl99_53
| spl99_55
| spl99_49
| spl99_68 ),
inference(avatar_split_clause,[],[f1977,f4691,f4558,f4601,f4595]) ).
thf(f25158,plain,
( spl99_53
| spl99_64
| spl99_49
| spl99_43 ),
inference(avatar_split_clause,[],[f411,f4521,f4558,f4679,f4595]) ).
thf(f25179,plain,
( spl99_53
| spl99_55
| spl99_49
| spl99_43 ),
inference(avatar_split_clause,[],[f380,f4521,f4558,f4601,f4595]) ).
thf(f25352,plain,
( spl99_53
| spl99_64
| spl99_49
| spl99_59 ),
inference(avatar_split_clause,[],[f1477,f4613,f4558,f4679,f4595]) ).
thf(f25369,plain,
( spl99_53
| spl99_55
| spl99_49
| spl99_59 ),
inference(avatar_split_clause,[],[f1446,f4613,f4558,f4601,f4595]) ).
thf(f25545,plain,
( spl99_53
| spl99_39
| spl99_49
| spl99_68 ),
inference(avatar_split_clause,[],[f1911,f4691,f4558,f4509,f4595]) ).
thf(f25564,plain,
( spl99_53
| spl99_39
| spl99_57
| spl99_68 ),
inference(avatar_split_clause,[],[f2044,f4691,f4607,f4509,f4595]) ).
thf(f25733,plain,
( spl99_53
| spl99_39
| spl99_41
| spl99_68 ),
inference(avatar_split_clause,[],[f1778,f4691,f4515,f4509,f4595]) ).
thf(f25818,plain,
( spl99_53
| spl99_39
| spl99_41
| spl99_59 ),
inference(avatar_split_clause,[],[f1247,f4613,f4515,f4509,f4595]) ).
thf(f25831,plain,
( spl99_53
| spl99_39
| spl99_57
| spl99_59 ),
inference(avatar_split_clause,[],[f1513,f4613,f4607,f4509,f4595]) ).
thf(f25946,plain,
( spl99_53
| spl99_39
| spl99_57
| spl99_43 ),
inference(avatar_split_clause,[],[f447,f4521,f4607,f4509,f4595]) ).
thf(f26009,plain,
( spl99_53
| spl99_39
| spl99_41
| spl99_43 ),
inference(avatar_split_clause,[],[f181,f4521,f4515,f4509,f4595]) ).
thf(f26020,plain,
( spl99_53
| spl99_39
| spl99_41
| spl99_51 ),
inference(avatar_split_clause,[],[f714,f4564,f4515,f4509,f4595]) ).
thf(f26277,plain,
( spl99_53
| spl99_39
| spl99_57
| spl99_51 ),
inference(avatar_split_clause,[],[f980,f4564,f4607,f4509,f4595]) ).
thf(f26376,plain,
( spl99_53
| spl99_47
| spl99_41
| spl99_51 ),
inference(avatar_split_clause,[],[f747,f4564,f4515,f4552,f4595]) ).
thf(f26423,plain,
( spl99_53
| spl99_47
| spl99_41
| spl99_59 ),
inference(avatar_split_clause,[],[f1280,f4613,f4515,f4552,f4595]) ).
thf(f26542,plain,
( spl99_53
| spl99_47
| spl99_41
| spl99_43 ),
inference(avatar_split_clause,[],[f214,f4521,f4515,f4552,f4595]) ).
thf(f26607,plain,
( spl99_53
| spl99_64
| spl99_41
| spl99_59 ),
inference(avatar_split_clause,[],[f1344,f4613,f4515,f4679,f4595]) ).
thf(f26624,plain,
( spl99_53
| spl99_55
| spl99_41
| spl99_59 ),
inference(avatar_split_clause,[],[f1313,f4613,f4515,f4601,f4595]) ).
thf(f26814,plain,
( spl99_53
| spl99_64
| spl99_41
| spl99_43 ),
inference(avatar_split_clause,[],[f278,f4521,f4515,f4679,f4595]) ).
thf(f26909,plain,
( spl99_53
| spl99_55
| spl99_41
| spl99_43 ),
inference(avatar_split_clause,[],[f247,f4521,f4515,f4601,f4595]) ).
thf(f27046,plain,
( spl99_53
| spl99_47
| spl99_66
| spl99_43 ),
inference(avatar_split_clause,[],[f611,f4521,f4685,f4552,f4595]) ).
thf(f27053,plain,
( spl99_53
| spl99_47
| spl99_57
| spl99_43 ),
inference(avatar_split_clause,[],[f480,f4521,f4607,f4552,f4595]) ).
thf(f27114,plain,
( spl99_53
| spl99_47
| spl99_66
| spl99_68 ),
inference(avatar_split_clause,[],[f2208,f4691,f4685,f4552,f4595]) ).
thf(f27121,plain,
( spl99_53
| spl99_47
| spl99_57
| spl99_68 ),
inference(avatar_split_clause,[],[f2077,f4691,f4607,f4552,f4595]) ).
thf(f27260,plain,
( spl99_53
| spl99_55
| spl99_66
| spl99_59 ),
inference(avatar_split_clause,[],[f1710,f4613,f4685,f4601,f4595]) ).
thf(f27375,plain,
( spl99_53
| spl99_47
| spl99_66
| spl99_59 ),
inference(avatar_split_clause,[],[f1677,f4613,f4685,f4552,f4595]) ).
thf(f27380,plain,
( spl99_53
| spl99_47
| spl99_57
| spl99_59 ),
inference(avatar_split_clause,[],[f1546,f4613,f4607,f4552,f4595]) ).
thf(f27455,plain,
( spl99_53
| spl99_64
| spl99_66
| spl99_59 ),
inference(avatar_split_clause,[],[f1741,f4613,f4685,f4679,f4595]) ).
thf(f27462,plain,
( spl99_53
| spl99_64
| spl99_57
| spl99_59 ),
inference(avatar_split_clause,[],[f1610,f4613,f4607,f4679,f4595]) ).
thf(f27553,plain,
( spl99_53
| spl99_64
| spl99_57
| spl99_43 ),
inference(avatar_split_clause,[],[f544,f4521,f4607,f4679,f4595]) ).
thf(f27568,plain,
( spl99_53
| spl99_55
| spl99_57
| spl99_43 ),
inference(avatar_split_clause,[],[f513,f4521,f4607,f4601,f4595]) ).
thf(f27635,plain,
( spl99_53
| spl99_64
| spl99_57
| spl99_68 ),
inference(avatar_split_clause,[],[f2141,f4691,f4607,f4679,f4595]) ).
thf(f27738,plain,
( spl99_53
| spl99_55
| spl99_57
| spl99_68 ),
inference(avatar_split_clause,[],[f2110,f4691,f4607,f4601,f4595]) ).
thf(f27883,plain,
( spl99_53
| spl99_55
| spl99_66
| spl99_68 ),
inference(avatar_split_clause,[],[f2241,f4691,f4685,f4601,f4595]) ).
thf(f28032,plain,
( spl99_53
| spl99_64
| spl99_66
| spl99_68 ),
inference(avatar_split_clause,[],[f2272,f4691,f4685,f4679,f4595]) ).
thf(f28043,plain,
( spl99_53
| spl99_64
| spl99_66
| spl99_43 ),
inference(avatar_split_clause,[],[f675,f4521,f4685,f4679,f4595]) ).
thf(f28058,plain,
( spl99_53
| spl99_55
| spl99_66
| spl99_43 ),
inference(avatar_split_clause,[],[f644,f4521,f4685,f4601,f4595]) ).
thf(f28149,plain,
( spl99_37
| spl99_47
| spl99_66
| spl99_43 ),
inference(avatar_split_clause,[],[f595,f4521,f4685,f4552,f4503]) ).
thf(f28170,plain,
( spl99_45
| spl99_47
| spl99_66
| spl99_43 ),
inference(avatar_split_clause,[],[f603,f4521,f4685,f4552,f4546]) ).
thf(f28199,plain,
( spl99_62
| spl99_47
| spl99_66
| spl99_43 ),
inference(avatar_split_clause,[],[f617,f4521,f4685,f4552,f4673]) ).
thf(f28391,plain,
( spl99_37
| spl99_55
| spl99_66
| spl99_68 ),
inference(avatar_split_clause,[],[f2225,f4691,f4685,f4601,f4503]) ).
thf(f28438,plain,
( spl99_37
| spl99_47
| spl99_66
| spl99_68 ),
inference(avatar_split_clause,[],[f2192,f4691,f4685,f4552,f4503]) ).
thf(f28457,plain,
( spl99_45
| spl99_47
| spl99_66
| spl99_68 ),
inference(avatar_split_clause,[],[f2200,f4691,f4685,f4552,f4546]) ).
thf(f28486,plain,
( spl99_62
| spl99_47
| spl99_66
| spl99_68 ),
inference(avatar_split_clause,[],[f2214,f4691,f4685,f4552,f4673]) ).
thf(f28631,plain,
( spl99_62
| spl99_47
| spl99_66
| spl99_59 ),
inference(avatar_split_clause,[],[f1683,f4613,f4685,f4552,f4673]) ).
thf(f28644,plain,
( spl99_37
| spl99_47
| spl99_66
| spl99_59 ),
inference(avatar_split_clause,[],[f1661,f4613,f4685,f4552,f4503]) ).
thf(f28733,plain,
( spl99_45
| spl99_47
| spl99_66
| spl99_59 ),
inference(avatar_split_clause,[],[f1669,f4613,f4685,f4552,f4546]) ).
thf(f28882,plain,
( spl99_37
| spl99_47
| spl99_57
| spl99_59 ),
inference(avatar_split_clause,[],[f1530,f4613,f4607,f4552,f4503]) ).
thf(f28905,plain,
( spl99_62
| spl99_47
| spl99_57
| spl99_59 ),
inference(avatar_split_clause,[],[f1552,f4613,f4607,f4552,f4673]) ).
thf(f29029,plain,
( spl99_37
| spl99_47
| spl99_57
| spl99_43 ),
inference(avatar_split_clause,[],[f464,f4521,f4607,f4552,f4503]) ).
thf(f29038,plain,
( spl99_45
| spl99_47
| spl99_57
| spl99_43 ),
inference(avatar_split_clause,[],[f472,f4521,f4607,f4552,f4546]) ).
thf(f29065,plain,
( spl99_62
| spl99_47
| spl99_57
| spl99_43 ),
inference(avatar_split_clause,[],[f486,f4521,f4607,f4552,f4673]) ).
thf(f29128,plain,
( spl99_37
| spl99_47
| spl99_49
| spl99_43 ),
inference(avatar_split_clause,[],[f331,f4521,f4558,f4552,f4503]) ).
thf(f29183,plain,
( spl99_45
| spl99_47
| spl99_49
| spl99_43 ),
inference(avatar_split_clause,[],[f339,f4521,f4558,f4552,f4546]) ).
thf(f29228,plain,
( spl99_37
| spl99_47
| spl99_49
| spl99_68 ),
inference(avatar_split_clause,[],[f1928,f4691,f4558,f4552,f4503]) ).
thf(f29289,plain,
( spl99_45
| spl99_47
| spl99_49
| spl99_68 ),
inference(avatar_split_clause,[],[f1936,f4691,f4558,f4552,f4546]) ).
thf(f29316,plain,
( spl99_62
| spl99_47
| spl99_49
| spl99_68 ),
inference(avatar_split_clause,[],[f1950,f4691,f4558,f4552,f4673]) ).
thf(f29347,plain,
( spl99_37
| spl99_47
| spl99_49
| spl99_59 ),
inference(avatar_split_clause,[],[f1397,f4613,f4558,f4552,f4503]) ).
thf(f29396,plain,
( spl99_62
| spl99_47
| spl99_49
| spl99_59 ),
inference(avatar_split_clause,[],[f1419,f4613,f4558,f4552,f4673]) ).
thf(f29405,plain,
( spl99_45
| spl99_47
| spl99_49
| spl99_59 ),
inference(avatar_split_clause,[],[f1405,f4613,f4558,f4552,f4546]) ).
thf(f29474,plain,
( spl99_37
| spl99_47
| spl99_49
| spl99_51 ),
inference(avatar_split_clause,[],[f864,f4564,f4558,f4552,f4503]) ).
thf(f29493,plain,
( spl99_62
| spl99_47
| spl99_49
| spl99_51 ),
inference(avatar_split_clause,[],[f886,f4564,f4558,f4552,f4673]) ).
thf(f29540,plain,
( spl99_37
| spl99_47
| spl99_41
| spl99_51 ),
inference(avatar_split_clause,[],[f731,f4564,f4515,f4552,f4503]) ).
thf(f29565,plain,
( spl99_37
| spl99_47
| spl99_41
| spl99_43 ),
inference(avatar_split_clause,[],[f198,f4521,f4515,f4552,f4503]) ).
thf(f29576,plain,
( spl99_45
| spl99_47
| spl99_41
| spl99_43 ),
inference(avatar_split_clause,[],[f206,f4521,f4515,f4552,f4546]) ).
thf(f29611,plain,
( spl99_37
| spl99_47
| spl99_41
| spl99_59 ),
inference(avatar_split_clause,[],[f1264,f4613,f4515,f4552,f4503]) ).
thf(f29670,plain,
( spl99_37
| spl99_47
| spl99_57
| spl99_68 ),
inference(avatar_split_clause,[],[f2061,f4691,f4607,f4552,f4503]) ).
thf(f29763,plain,
( spl99_37
| spl99_47
| spl99_57
| spl99_51 ),
inference(avatar_split_clause,[],[f997,f4564,f4607,f4552,f4503]) ).
thf(f29808,plain,
( spl99_37
| spl99_47
| spl99_66
| spl99_51 ),
inference(avatar_split_clause,[],[f1128,f4564,f4685,f4552,f4503]) ).
thf(f29951,plain,
( spl99_45
| spl99_47
| spl99_57
| spl99_51 ),
inference(avatar_split_clause,[],[f1005,f4564,f4607,f4552,f4546]) ).
thf(f29978,plain,
( spl99_62
| spl99_47
| spl99_57
| spl99_51 ),
inference(avatar_split_clause,[],[f1019,f4564,f4607,f4552,f4673]) ).
thf(f30025,plain,
( spl99_45
| spl99_47
| spl99_66
| spl99_51 ),
inference(avatar_split_clause,[],[f1136,f4564,f4685,f4552,f4546]) ).
thf(f30150,plain,
( spl99_62
| spl99_47
| spl99_66
| spl99_51 ),
inference(avatar_split_clause,[],[f1150,f4564,f4685,f4552,f4673]) ).
thf(f30167,plain,
( spl99_45
| spl99_47
| spl99_41
| spl99_51 ),
inference(avatar_split_clause,[],[f739,f4564,f4515,f4552,f4546]) ).
thf(f30332,plain,
( spl99_45
| spl99_47
| spl99_41
| spl99_59 ),
inference(avatar_split_clause,[],[f1272,f4613,f4515,f4552,f4546]) ).
thf(f30423,plain,
( spl99_62
| spl99_47
| spl99_57
| spl99_68 ),
inference(avatar_split_clause,[],[f2083,f4691,f4607,f4552,f4673]) ).
thf(f30430,plain,
( spl99_45
| spl99_47
| spl99_57
| spl99_68 ),
inference(avatar_split_clause,[],[f2069,f4691,f4607,f4552,f4546]) ).
thf(f30497,plain,
( spl99_37
| spl99_64
| spl99_57
| spl99_43 ),
inference(avatar_split_clause,[],[f528,f4521,f4607,f4679,f4503]) ).
thf(f30535,plain,
( spl99_37
| spl99_55
| spl99_57
| spl99_68 ),
inference(avatar_split_clause,[],[f2094,f4691,f4607,f4601,f4503]) ).
thf(f30708,plain,
( spl99_37
| spl99_39
| spl99_57
| spl99_43 ),
inference(avatar_split_clause,[],[f431,f4521,f4607,f4509,f4503]) ).
thf(f30723,plain,
( spl99_37
| spl99_55
| spl99_57
| spl99_43 ),
inference(avatar_split_clause,[],[f497,f4521,f4607,f4601,f4503]) ).
thf(f30808,plain,
( spl99_37
| spl99_64
| spl99_49
| spl99_43 ),
inference(avatar_split_clause,[],[f395,f4521,f4558,f4679,f4503]) ).
thf(f30815,plain,
( spl99_37
| spl99_55
| spl99_49
| spl99_43 ),
inference(avatar_split_clause,[],[f364,f4521,f4558,f4601,f4503]) ).
thf(f30996,plain,
( spl99_37
| spl99_39
| spl99_49
| spl99_43 ),
inference(avatar_split_clause,[],[f298,f4521,f4558,f4509,f4503]) ).
thf(f31029,plain,
( spl99_37
| spl99_55
| spl99_66
| spl99_43 ),
inference(avatar_split_clause,[],[f628,f4521,f4685,f4601,f4503]) ).
thf(f31094,plain,
( spl99_37
| spl99_64
| spl99_41
| spl99_51 ),
inference(avatar_split_clause,[],[f795,f4564,f4515,f4679,f4503]) ).
thf(f31099,plain,
( spl99_37
| spl99_55
| spl99_41
| spl99_51 ),
inference(avatar_split_clause,[],[f764,f4564,f4515,f4601,f4503]) ).
thf(f31170,plain,
( spl99_37
| spl99_64
| spl99_41
| spl99_43 ),
inference(avatar_split_clause,[],[f262,f4521,f4515,f4679,f4503]) ).
thf(f31177,plain,
( spl99_37
| spl99_55
| spl99_41
| spl99_43 ),
inference(avatar_split_clause,[],[f231,f4521,f4515,f4601,f4503]) ).
thf(f31236,plain,
( spl99_37
| spl99_64
| spl99_66
| spl99_43 ),
inference(avatar_split_clause,[],[f659,f4521,f4685,f4679,f4503]) ).
thf(f31255,plain,
( spl99_37
| spl99_64
| spl99_66
| spl99_68 ),
inference(avatar_split_clause,[],[f2256,f4691,f4685,f4679,f4503]) ).
thf(f31268,plain,
( spl99_37
| spl99_64
| spl99_66
| spl99_59 ),
inference(avatar_split_clause,[],[f1725,f4613,f4685,f4679,f4503]) ).
thf(f31273,plain,
( spl99_37
| spl99_55
| spl99_66
| spl99_59 ),
inference(avatar_split_clause,[],[f1694,f4613,f4685,f4601,f4503]) ).
thf(f31360,plain,
( spl99_37
| spl99_39
| spl99_66
| spl99_68 ),
inference(avatar_split_clause,[],[f2159,f4691,f4685,f4509,f4503]) ).
thf(f31469,plain,
( spl99_37
| spl99_39
| spl99_57
| spl99_68 ),
inference(avatar_split_clause,[],[f2028,f4691,f4607,f4509,f4503]) ).
thf(f31514,plain,
( spl99_37
| spl99_39
| spl99_49
| spl99_68 ),
inference(avatar_split_clause,[],[f1895,f4691,f4558,f4509,f4503]) ).
thf(f31539,plain,
( spl99_37
| spl99_39
| spl99_57
| spl99_59 ),
inference(avatar_split_clause,[],[f1497,f4613,f4607,f4509,f4503]) ).
thf(f31582,plain,
( spl99_37
| spl99_39
| spl99_49
| spl99_59 ),
inference(avatar_split_clause,[],[f1364,f4613,f4558,f4509,f4503]) ).
thf(f31615,plain,
( spl99_37
| spl99_64
| spl99_57
| spl99_59 ),
inference(avatar_split_clause,[],[f1594,f4613,f4607,f4679,f4503]) ).
thf(f31628,plain,
( spl99_37
| spl99_55
| spl99_57
| spl99_59 ),
inference(avatar_split_clause,[],[f1563,f4613,f4607,f4601,f4503]) ).
thf(f31715,plain,
( spl99_37
| spl99_64
| spl99_49
| spl99_59 ),
inference(avatar_split_clause,[],[f1461,f4613,f4558,f4679,f4503]) ).
thf(f31726,plain,
( spl99_37
| spl99_55
| spl99_49
| spl99_59 ),
inference(avatar_split_clause,[],[f1430,f4613,f4558,f4601,f4503]) ).
thf(f31873,plain,
( spl99_37
| spl99_64
| spl99_49
| spl99_68 ),
inference(avatar_split_clause,[],[f1992,f4691,f4558,f4679,f4503]) ).
thf(f31884,plain,
( spl99_37
| spl99_55
| spl99_49
| spl99_68 ),
inference(avatar_split_clause,[],[f1961,f4691,f4558,f4601,f4503]) ).
thf(f31945,plain,
( spl99_37
| spl99_64
| spl99_57
| spl99_68 ),
inference(avatar_split_clause,[],[f2125,f4691,f4607,f4679,f4503]) ).
thf(f31992,plain,
( spl99_37
| spl99_64
| spl99_41
| spl99_68 ),
inference(avatar_split_clause,[],[f1859,f4691,f4515,f4679,f4503]) ).
thf(f32011,plain,
( spl99_37
| spl99_64
| spl99_41
| spl99_59 ),
inference(avatar_split_clause,[],[f1328,f4613,f4515,f4679,f4503]) ).
thf(f32024,plain,
( spl99_37
| spl99_55
| spl99_41
| spl99_59 ),
inference(avatar_split_clause,[],[f1297,f4613,f4515,f4601,f4503]) ).
thf(f32105,plain,
( spl99_37
| spl99_55
| spl99_41
| spl99_68 ),
inference(avatar_split_clause,[],[f1828,f4691,f4515,f4601,f4503]) ).
thf(f32124,plain,
( spl99_37
| spl99_55
| spl99_57
| spl99_51 ),
inference(avatar_split_clause,[],[f1030,f4564,f4607,f4601,f4503]) ).
thf(f32167,plain,
( spl99_37
| spl99_55
| spl99_49
| spl99_51 ),
inference(avatar_split_clause,[],[f897,f4564,f4558,f4601,f4503]) ).
thf(f32228,plain,
( spl99_37
| spl99_64
| spl99_57
| spl99_51 ),
inference(avatar_split_clause,[],[f1061,f4564,f4607,f4679,f4503]) ).
thf(f32273,plain,
( spl99_37
| spl99_64
| spl99_49
| spl99_51 ),
inference(avatar_split_clause,[],[f928,f4564,f4558,f4679,f4503]) ).
thf(f32306,plain,
( spl99_37
| spl99_55
| spl99_66
| spl99_51 ),
inference(avatar_split_clause,[],[f1161,f4564,f4685,f4601,f4503]) ).
thf(f32395,plain,
( spl99_37
| spl99_39
| spl99_41
| spl99_68 ),
inference(avatar_split_clause,[],[f1762,f4691,f4515,f4509,f4503]) ).
thf(f32410,plain,
( spl99_37
| spl99_39
| spl99_41
| spl99_59 ),
inference(avatar_split_clause,[],[f1231,f4613,f4515,f4509,f4503]) ).
thf(f32549,plain,
( spl99_37
| spl99_39
| spl99_41
| spl99_51 ),
inference(avatar_split_clause,[],[f698,f4564,f4515,f4509,f4503]) ).
thf(f32725,plain,
( spl99_37
| spl99_39
| spl99_57
| spl99_51 ),
inference(avatar_split_clause,[],[f964,f4564,f4607,f4509,f4503]) ).
thf(f32768,plain,
( spl99_37
| spl99_39
| spl99_49
| spl99_51 ),
inference(avatar_split_clause,[],[f831,f4564,f4558,f4509,f4503]) ).
thf(f32801,plain,
( spl99_62
| spl99_39
| spl99_57
| spl99_51 ),
inference(avatar_split_clause,[],[f986,f4564,f4607,f4509,f4673]) ).
thf(f32914,plain,
( spl99_45
| spl99_39
| spl99_57
| spl99_51 ),
inference(avatar_split_clause,[],[f972,f4564,f4607,f4509,f4546]) ).
thf(f32989,plain,
( spl99_62
| spl99_39
| spl99_49
| spl99_51 ),
inference(avatar_split_clause,[],[f853,f4564,f4558,f4509,f4673]) ).
thf(f32996,plain,
( spl99_45
| spl99_39
| spl99_49
| spl99_51 ),
inference(avatar_split_clause,[],[f839,f4564,f4558,f4509,f4546]) ).
thf(f33053,plain,
( spl99_62
| spl99_39
| spl99_66
| spl99_51 ),
inference(avatar_split_clause,[],[f1117,f4564,f4685,f4509,f4673]) ).
thf(f33068,plain,
( spl99_62
| spl99_39
| spl99_41
| spl99_51 ),
inference(avatar_split_clause,[],[f720,f4564,f4515,f4509,f4673]) ).
thf(f33087,plain,
( spl99_62
| spl99_64
| spl99_41
| spl99_51 ),
inference(avatar_split_clause,[],[f817,f4564,f4515,f4679,f4673]) ).
thf(f33094,plain,
( spl99_45
| spl99_64
| spl99_41
| spl99_51 ),
inference(avatar_split_clause,[],[f803,f4564,f4515,f4679,f4546]) ).
thf(f33141,plain,
( spl99_62
| spl99_55
| spl99_41
| spl99_51 ),
inference(avatar_split_clause,[],[f786,f4564,f4515,f4601,f4673]) ).
thf(f33162,plain,
( spl99_62
| spl99_55
| spl99_57
| spl99_51 ),
inference(avatar_split_clause,[],[f1052,f4564,f4607,f4601,f4673]) ).
thf(f33167,plain,
( spl99_45
| spl99_55
| spl99_57
| spl99_51 ),
inference(avatar_split_clause,[],[f1038,f4564,f4607,f4601,f4546]) ).
thf(f33244,plain,
( spl99_62
| spl99_64
| spl99_57
| spl99_51 ),
inference(avatar_split_clause,[],[f1083,f4564,f4607,f4679,f4673]) ).
thf(f33291,plain,
( spl99_62
| spl99_64
| spl99_49
| spl99_51 ),
inference(avatar_split_clause,[],[f950,f4564,f4558,f4679,f4673]) ).
thf(f33316,plain,
( spl99_62
| spl99_64
| spl99_66
| spl99_51 ),
inference(avatar_split_clause,[],[f1214,f4564,f4685,f4679,f4673]) ).
thf(f33445,plain,
( spl99_62
| spl99_55
| spl99_66
| spl99_51 ),
inference(avatar_split_clause,[],[f1183,f4564,f4685,f4601,f4673]) ).
thf(f33462,plain,
( spl99_45
| spl99_55
| spl99_66
| spl99_51 ),
inference(avatar_split_clause,[],[f1169,f4564,f4685,f4601,f4546]) ).
thf(f33507,plain,
( spl99_62
| spl99_55
| spl99_49
| spl99_51 ),
inference(avatar_split_clause,[],[f919,f4564,f4558,f4601,f4673]) ).
thf(f33518,plain,
( spl99_45
| spl99_55
| spl99_49
| spl99_51 ),
inference(avatar_split_clause,[],[f905,f4564,f4558,f4601,f4546]) ).
thf(f33583,plain,
( spl99_62
| spl99_55
| spl99_49
| spl99_68 ),
inference(avatar_split_clause,[],[f1983,f4691,f4558,f4601,f4673]) ).
thf(f33598,plain,
( spl99_62
| spl99_55
| spl99_49
| spl99_59 ),
inference(avatar_split_clause,[],[f1452,f4613,f4558,f4601,f4673]) ).
thf(f33641,plain,
( spl99_62
| spl99_55
| spl99_49
| spl99_43 ),
inference(avatar_split_clause,[],[f386,f4521,f4558,f4601,f4673]) ).
thf(f33678,plain,
( spl99_62
| spl99_55
| spl99_57
| spl99_68 ),
inference(avatar_split_clause,[],[f2116,f4691,f4607,f4601,f4673]) ).
thf(f33683,plain,
( spl99_62
| spl99_55
| spl99_57
| spl99_59 ),
inference(avatar_split_clause,[],[f1585,f4613,f4607,f4601,f4673]) ).
thf(f33726,plain,
( spl99_62
| spl99_55
| spl99_57
| spl99_43 ),
inference(avatar_split_clause,[],[f519,f4521,f4607,f4601,f4673]) ).
thf(f33791,plain,
( spl99_62
| spl99_55
| spl99_41
| spl99_68 ),
inference(avatar_split_clause,[],[f1850,f4691,f4515,f4601,f4673]) ).
thf(f33804,plain,
( spl99_62
| spl99_55
| spl99_41
| spl99_43 ),
inference(avatar_split_clause,[],[f253,f4521,f4515,f4601,f4673]) ).
thf(f33845,plain,
( spl99_62
| spl99_55
| spl99_66
| spl99_68 ),
inference(avatar_split_clause,[],[f2247,f4691,f4685,f4601,f4673]) ).
thf(f33852,plain,
( spl99_62
| spl99_55
| spl99_66
| spl99_59 ),
inference(avatar_split_clause,[],[f1716,f4613,f4685,f4601,f4673]) ).
thf(f33895,plain,
( spl99_62
| spl99_55
| spl99_66
| spl99_43 ),
inference(avatar_split_clause,[],[f650,f4521,f4685,f4601,f4673]) ).
thf(f33952,plain,
( spl99_62
| spl99_64
| spl99_66
| spl99_59 ),
inference(avatar_split_clause,[],[f1747,f4613,f4685,f4679,f4673]) ).
thf(f33997,plain,
( spl99_62
| spl99_64
| spl99_66
| spl99_43 ),
inference(avatar_split_clause,[],[f681,f4521,f4685,f4679,f4673]) ).
thf(f34062,plain,
( spl99_62
| spl99_64
| spl99_57
| spl99_43 ),
inference(avatar_split_clause,[],[f550,f4521,f4607,f4679,f4673]) ).
thf(f34085,plain,
( spl99_62
| spl99_64
| spl99_57
| spl99_68 ),
inference(avatar_split_clause,[],[f2147,f4691,f4607,f4679,f4673]) ).
thf(f34098,plain,
( spl99_62
| spl99_64
| spl99_57
| spl99_59 ),
inference(avatar_split_clause,[],[f1616,f4613,f4607,f4679,f4673]) ).
thf(f34185,plain,
( spl99_62
| spl99_64
| spl99_49
| spl99_68 ),
inference(avatar_split_clause,[],[f2014,f4691,f4558,f4679,f4673]) ).
thf(f34212,plain,
( spl99_62
| spl99_64
| spl99_41
| spl99_68 ),
inference(avatar_split_clause,[],[f1881,f4691,f4515,f4679,f4673]) ).
thf(f34223,plain,
( spl99_62
| spl99_64
| spl99_41
| spl99_59 ),
inference(avatar_split_clause,[],[f1350,f4613,f4515,f4679,f4673]) ).
thf(f34236,plain,
( spl99_62
| spl99_64
| spl99_49
| spl99_59 ),
inference(avatar_split_clause,[],[f1483,f4613,f4558,f4679,f4673]) ).
thf(f34469,plain,
( spl99_62
| spl99_64
| spl99_49
| spl99_43 ),
inference(avatar_split_clause,[],[f417,f4521,f4558,f4679,f4673]) ).
thf(f34496,plain,
( spl99_62
| spl99_64
| spl99_41
| spl99_43 ),
inference(avatar_split_clause,[],[f284,f4521,f4515,f4679,f4673]) ).
thf(f34657,plain,
( spl99_62
| spl99_39
| spl99_41
| spl99_59 ),
inference(avatar_split_clause,[],[f1253,f4613,f4515,f4509,f4673]) ).
thf(f34682,plain,
( spl99_62
| spl99_39
| spl99_66
| spl99_59 ),
inference(avatar_split_clause,[],[f1650,f4613,f4685,f4509,f4673]) ).
thf(f34777,plain,
( spl99_62
| spl99_39
| spl99_41
| spl99_43 ),
inference(avatar_split_clause,[],[f187,f4521,f4515,f4509,f4673]) ).
thf(f34796,plain,
( spl99_62
| spl99_39
| spl99_41
| spl99_68 ),
inference(avatar_split_clause,[],[f1784,f4691,f4515,f4509,f4673]) ).
thf(f34815,plain,
( spl99_62
| spl99_39
| spl99_66
| spl99_43 ),
inference(avatar_split_clause,[],[f584,f4521,f4685,f4509,f4673]) ).
thf(f34820,plain,
( spl99_62
| spl99_39
| spl99_57
| spl99_43 ),
inference(avatar_split_clause,[],[f453,f4521,f4607,f4509,f4673]) ).
thf(f34863,plain,
( spl99_62
| spl99_39
| spl99_49
| spl99_43 ),
inference(avatar_split_clause,[],[f320,f4521,f4558,f4509,f4673]) ).
thf(f34906,plain,
( spl99_62
| spl99_39
| spl99_66
| spl99_68 ),
inference(avatar_split_clause,[],[f2181,f4691,f4685,f4509,f4673]) ).
thf(f34913,plain,
( spl99_62
| spl99_39
| spl99_57
| spl99_68 ),
inference(avatar_split_clause,[],[f2050,f4691,f4607,f4509,f4673]) ).
thf(f34956,plain,
( spl99_62
| spl99_39
| spl99_49
| spl99_68 ),
inference(avatar_split_clause,[],[f1917,f4691,f4558,f4509,f4673]) ).
thf(f34987,plain,
( spl99_62
| spl99_39
| spl99_57
| spl99_59 ),
inference(avatar_split_clause,[],[f1519,f4613,f4607,f4509,f4673]) ).
thf(f35034,plain,
( spl99_62
| spl99_39
| spl99_49
| spl99_59 ),
inference(avatar_split_clause,[],[f1386,f4613,f4558,f4509,f4673]) ).
thf(f35111,plain,
( spl99_45
| spl99_39
| spl99_41
| spl99_43 ),
inference(avatar_split_clause,[],[f173,f4521,f4515,f4509,f4546]) ).
thf(f35158,plain,
( spl99_45
| spl99_39
| spl99_66
| spl99_68 ),
inference(avatar_split_clause,[],[f2167,f4691,f4685,f4509,f4546]) ).
thf(f35191,plain,
( spl99_45
| spl99_55
| spl99_66
| spl99_68 ),
inference(avatar_split_clause,[],[f2233,f4691,f4685,f4601,f4546]) ).
thf(f35222,plain,
( spl99_45
| spl99_55
| spl99_41
| spl99_43 ),
inference(avatar_split_clause,[],[f239,f4521,f4515,f4601,f4546]) ).
thf(f35265,plain,
( spl99_45
| spl99_64
| spl99_41
| spl99_43 ),
inference(avatar_split_clause,[],[f270,f4521,f4515,f4679,f4546]) ).
thf(f35286,plain,
( spl99_45
| spl99_55
| spl99_41
| spl99_59 ),
inference(avatar_split_clause,[],[f1305,f4613,f4515,f4601,f4546]) ).
thf(f35331,plain,
( spl99_45
| spl99_64
| spl99_41
| spl99_59 ),
inference(avatar_split_clause,[],[f1336,f4613,f4515,f4679,f4546]) ).
thf(f35452,plain,
( spl99_45
| spl99_55
| spl99_57
| spl99_68 ),
inference(avatar_split_clause,[],[f2102,f4691,f4607,f4601,f4546]) ).
thf(f35499,plain,
( spl99_45
| spl99_55
| spl99_49
| spl99_43 ),
inference(avatar_split_clause,[],[f372,f4521,f4558,f4601,f4546]) ).
thf(f35546,plain,
( spl99_45
| spl99_64
| spl99_49
| spl99_43 ),
inference(avatar_split_clause,[],[f403,f4521,f4558,f4679,f4546]) ).
thf(f35579,plain,
( spl99_45
| spl99_55
| spl99_66
| spl99_43 ),
inference(avatar_split_clause,[],[f636,f4521,f4685,f4601,f4546]) ).
thf(f35584,plain,
( spl99_45
| spl99_55
| spl99_57
| spl99_43 ),
inference(avatar_split_clause,[],[f505,f4521,f4607,f4601,f4546]) ).
thf(f35649,plain,
( spl99_45
| spl99_55
| spl99_66
| spl99_59 ),
inference(avatar_split_clause,[],[f1702,f4613,f4685,f4601,f4546]) ).
thf(f35700,plain,
( spl99_45
| spl99_64
| spl99_66
| spl99_59 ),
inference(avatar_split_clause,[],[f1733,f4613,f4685,f4679,f4546]) ).
thf(f35751,plain,
( spl99_45
| spl99_64
| spl99_57
| spl99_43 ),
inference(avatar_split_clause,[],[f536,f4521,f4607,f4679,f4546]) ).
thf(f35806,plain,
( spl99_45
| spl99_64
| spl99_49
| spl99_59 ),
inference(avatar_split_clause,[],[f1469,f4613,f4558,f4679,f4546]) ).
thf(f35881,plain,
( spl99_45
| spl99_39
| spl99_57
| spl99_68 ),
inference(avatar_split_clause,[],[f2036,f4691,f4607,f4509,f4546]) ).
thf(f35898,plain,
( spl99_45
| spl99_39
| spl99_57
| spl99_43 ),
inference(avatar_split_clause,[],[f439,f4521,f4607,f4509,f4546]) ).
thf(f35911,plain,
( spl99_45
| spl99_39
| spl99_57
| spl99_59 ),
inference(avatar_split_clause,[],[f1505,f4613,f4607,f4509,f4546]) ).
thf(f35952,plain,
( spl99_45
| spl99_39
| spl99_41
| spl99_59 ),
inference(avatar_split_clause,[],[f1239,f4613,f4515,f4509,f4546]) ).
thf(f36017,plain,
( spl99_45
| spl99_39
| spl99_49
| spl99_68 ),
inference(avatar_split_clause,[],[f1903,f4691,f4558,f4509,f4546]) ).
thf(f36034,plain,
( spl99_45
| spl99_39
| spl99_49
| spl99_43 ),
inference(avatar_split_clause,[],[f306,f4521,f4558,f4509,f4546]) ).
cnf(s752,plain,
( spl99_37
| spl99_39
| spl99_41
| spl99_43 ),
inference(sat_conversion,[],[f4523]) ).
cnf(s769,plain,
( spl99_45
| spl99_47
| spl99_49
| spl99_51 ),
inference(sat_conversion,[],[f4566]) ).
cnf(s788,plain,
( spl99_53
| spl99_55
| spl99_57
| spl99_59 ),
inference(sat_conversion,[],[f4615]) ).
cnf(s811,plain,
( spl99_62
| spl99_64
| spl99_66
| spl99_68 ),
inference(sat_conversion,[],[f4693]) ).
cnf(s945,plain,
( spl99_39
| spl99_41
| spl99_45
| spl99_51 ),
inference(sat_conversion,[],[f5040]) ).
cnf(s969,plain,
( spl99_39
| spl99_45
| spl99_49
| spl99_59 ),
inference(sat_conversion,[],[f5079]) ).
cnf(s993,plain,
( spl99_45
| spl99_49
| spl99_55
| spl99_59 ),
inference(sat_conversion,[],[f5127]) ).
cnf(s1021,plain,
( spl99_45
| spl99_55
| spl99_57
| spl99_59 ),
inference(sat_conversion,[],[f5190]) ).
cnf(s1048,plain,
( spl99_45
| spl99_57
| spl99_59
| spl99_64 ),
inference(sat_conversion,[],[f5270]) ).
cnf(s1116,plain,
( spl99_45
| spl99_47
| spl99_57
| spl99_59 ),
inference(sat_conversion,[],[f5433]) ).
cnf(s1193,plain,
( spl99_41
| spl99_43
| spl99_47
| spl99_62 ),
inference(sat_conversion,[],[f5622]) ).
cnf(s1285,plain,
( spl99_43
| spl99_47
| spl99_49
| spl99_62 ),
inference(sat_conversion,[],[f5823]) ).
cnf(s1292,plain,
( spl99_41
| spl99_47
| spl99_51
| spl99_62 ),
inference(sat_conversion,[],[f5824]) ).
cnf(s1297,plain,
( spl99_41
| spl99_47
| spl99_62
| spl99_68 ),
inference(sat_conversion,[],[f5825]) ).
cnf(s1331,plain,
( spl99_41
| spl99_55
| spl99_59
| spl99_62 ),
inference(sat_conversion,[],[f5854]) ).
cnf(s1455,plain,
( spl99_41
| spl99_47
| spl99_59
| spl99_62 ),
inference(sat_conversion,[],[f6240]) ).
cnf(s1865,plain,
( spl99_37
| spl99_41
| spl99_47
| spl99_68 ),
inference(sat_conversion,[],[f7472]) ).
cnf(s1984,plain,
( spl99_41
| spl99_45
| spl99_51
| spl99_55 ),
inference(sat_conversion,[],[f7733]) ).
cnf(s2083,plain,
( spl99_39
| spl99_41
| spl99_45
| spl99_68 ),
inference(sat_conversion,[],[f8032]) ).
cnf(s2201,plain,
( spl99_41
| spl99_45
| spl99_55
| spl99_68 ),
inference(sat_conversion,[],[f8371]) ).
cnf(s2256,plain,
( spl99_41
| spl99_45
| spl99_64
| spl99_68 ),
inference(sat_conversion,[],[f8532]) ).
cnf(s2344,plain,
( spl99_41
| spl99_53
| spl99_64
| spl99_68 ),
inference(sat_conversion,[],[f8902]) ).
cnf(s2393,plain,
( spl99_41
| spl99_53
| spl99_55
| spl99_68 ),
inference(sat_conversion,[],[f9018]) ).
cnf(s2467,plain,
( spl99_41
| spl99_45
| spl99_47
| spl99_68 ),
inference(sat_conversion,[],[f9300]) ).
cnf(s2646,plain,
( spl99_41
| spl99_47
| spl99_53
| spl99_68 ),
inference(sat_conversion,[],[f9872]) ).
cnf(s2720,plain,
( ~ spl99_37
| ~ spl99_53
| spl99_105
| spl99_106 ),
inference(sat_conversion,[],[f10183]) ).
cnf(s2938,plain,
( ~ spl99_39
| ~ spl99_55
| spl99_75
| spl99_76 ),
inference(sat_conversion,[],[f11033]) ).
cnf(s3124,plain,
( ~ spl99_39
| ~ spl99_55
| ~ spl99_64
| spl99_75
| ~ spl99_76 ),
inference(sat_conversion,[],[f11868]) ).
cnf(s3250,plain,
( spl99_45
| spl99_49
| spl99_55
| spl99_68 ),
inference(sat_conversion,[],[f12127]) ).
cnf(s3317,plain,
( spl99_45
| spl99_49
| spl99_64
| spl99_68 ),
inference(sat_conversion,[],[f12348]) ).
cnf(s3348,plain,
( spl99_45
| spl99_64
| spl99_66
| spl99_68 ),
inference(sat_conversion,[],[f12463]) ).
cnf(s3360,plain,
( spl99_45
| spl99_57
| spl99_64
| spl99_68 ),
inference(sat_conversion,[],[f12478]) ).
cnf(s3658,plain,
( spl99_45
| spl99_51
| spl99_64
| spl99_66 ),
inference(sat_conversion,[],[f13543]) ).
cnf(s3771,plain,
( spl99_37
| spl99_51
| spl99_64
| spl99_66 ),
inference(sat_conversion,[],[f14142]) ).
cnf(s3811,plain,
( ~ spl99_53
| ~ spl99_62
| spl99_105
| ~ spl99_106
| spl99_112 ),
inference(sat_conversion,[],[f14194]) ).
cnf(s3844,plain,
( spl99_45
| spl99_51
| spl99_57
| spl99_64 ),
inference(sat_conversion,[],[f14378]) ).
cnf(s3973,plain,
( spl99_45
| spl99_49
| spl99_51
| spl99_64 ),
inference(sat_conversion,[],[f14888]) ).
cnf(s4050,plain,
( spl99_43
| spl99_45
| spl99_64
| spl99_66 ),
inference(sat_conversion,[],[f15124]) ).
cnf(s4164,plain,
( spl99_39
| spl99_43
| spl99_45
| spl99_66 ),
inference(sat_conversion,[],[f15491]) ).
cnf(s4229,plain,
( spl99_37
| spl99_39
| spl99_43
| spl99_66 ),
inference(sat_conversion,[],[f15678]) ).
cnf(s4256,plain,
( spl99_39
| spl99_43
| spl99_53
| spl99_66 ),
inference(sat_conversion,[],[f15756]) ).
cnf(s4346,plain,
( ~ spl99_45
| ~ spl99_53
| ~ spl99_62
| ~ spl99_105
| ~ spl99_106
| spl99_112 ),
inference(sat_conversion,[],[f16112]) ).
cnf(s4446,plain,
( ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_62
| ~ spl99_105
| ~ spl99_106
| ~ spl99_112 ),
inference(sat_conversion,[],[f16590]) ).
cnf(s4463,plain,
( ~ spl99_37
| ~ spl99_53
| ~ spl99_62
| spl99_105
| ~ spl99_106
| ~ spl99_112 ),
inference(sat_conversion,[],[f16797]) ).
cnf(s4480,plain,
( spl99_39
| spl99_43
| spl99_49
| spl99_53 ),
inference(sat_conversion,[],[f16840]) ).
cnf(s4537,plain,
( spl99_39
| spl99_53
| spl99_59
| spl99_66 ),
inference(sat_conversion,[],[f16990]) ).
cnf(s4662,plain,
( spl99_39
| spl99_49
| spl99_53
| spl99_59 ),
inference(sat_conversion,[],[f17388]) ).
cnf(s4684,plain,
( spl99_39
| spl99_53
| spl99_66
| spl99_68 ),
inference(sat_conversion,[],[f17469]) ).
cnf(s4749,plain,
( ~ spl99_59
| ~ spl99_68
| ~ spl99_98
| spl99_99
| spl99_114 ),
inference(sat_conversion,[],[f17795]) ).
cnf(s4781,plain,
( ~ spl99_43
| ~ spl99_59
| ~ spl99_68
| ~ spl99_98
| spl99_99
| ~ spl99_114 ),
inference(sat_conversion,[],[f17962]) ).
cnf(s4828,plain,
( spl99_37
| spl99_39
| spl99_59
| spl99_66 ),
inference(sat_conversion,[],[f18147]) ).
cnf(s4861,plain,
( spl99_39
| spl99_45
| spl99_59
| spl99_66 ),
inference(sat_conversion,[],[f18252]) ).
cnf(s4983,plain,
( ~ spl99_37
| ~ spl99_45
| ~ spl99_53
| ~ spl99_105
| spl99_106 ),
inference(sat_conversion,[],[f18803]) ).
cnf(s5059,plain,
( ~ spl99_51
| ~ spl99_59
| ~ spl99_68
| ~ spl99_98
| ~ spl99_99
| spl99_114 ),
inference(sat_conversion,[],[f19164]) ).
cnf(s5122,plain,
( ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| ~ spl99_68
| ~ spl99_98
| ~ spl99_99
| ~ spl99_114 ),
inference(sat_conversion,[],[f19648]) ).
cnf(s5125,plain,
( spl99_39
| spl99_45
| spl99_51
| spl99_66 ),
inference(sat_conversion,[],[f19650]) ).
cnf(s5242,plain,
( spl99_37
| spl99_39
| spl99_51
| spl99_66 ),
inference(sat_conversion,[],[f20096]) ).
cnf(s5254,plain,
( spl99_39
| spl99_51
| spl99_53
| spl99_66 ),
inference(sat_conversion,[],[f20119]) ).
cnf(s5267,plain,
( spl99_39
| spl99_49
| spl99_51
| spl99_53 ),
inference(sat_conversion,[],[f20137]) ).
cnf(s5281,plain,
( spl99_51
| spl99_53
| spl99_64
| spl99_66 ),
inference(sat_conversion,[],[f20182]) ).
cnf(s5300,plain,
( spl99_51
| spl99_53
| spl99_55
| spl99_66 ),
inference(sat_conversion,[],[f20241]) ).
cnf(s5443,plain,
( ~ spl99_39
| ~ spl99_47
| ~ spl99_55
| ~ spl99_64
| ~ spl99_75
| ~ spl99_76
| spl99_107 ),
inference(sat_conversion,[],[f20774]) ).
cnf(s5459,plain,
( ~ spl99_47
| ~ spl99_55
| ~ spl99_64
| ~ spl99_75
| ~ spl99_76
| ~ spl99_107 ),
inference(sat_conversion,[],[f20893]) ).
cnf(s5478,plain,
( ~ spl99_47
| ~ spl99_55
| ~ spl99_75
| spl99_76
| ~ spl99_107 ),
inference(sat_conversion,[],[f20970]) ).
cnf(s5493,plain,
( ~ spl99_39
| ~ spl99_47
| ~ spl99_55
| ~ spl99_75
| spl99_76
| spl99_107 ),
inference(sat_conversion,[],[f21015]) ).
cnf(s5517,plain,
( spl99_47
| spl99_51
| spl99_53
| spl99_66 ),
inference(sat_conversion,[],[f21198]) ).
cnf(s5536,plain,
( spl99_49
| spl99_51
| spl99_53
| spl99_55 ),
inference(sat_conversion,[],[f21245]) ).
cnf(s5600,plain,
( spl99_47
| spl99_51
| spl99_53
| spl99_57 ),
inference(sat_conversion,[],[f21456]) ).
cnf(s5628,plain,
( spl99_51
| spl99_53
| spl99_55
| spl99_57 ),
inference(sat_conversion,[],[f21575]) ).
cnf(s5674,plain,
( spl99_49
| spl99_51
| spl99_53
| spl99_64 ),
inference(sat_conversion,[],[f21724]) ).
cnf(s5704,plain,
( spl99_51
| spl99_53
| spl99_57
| spl99_64 ),
inference(sat_conversion,[],[f21851]) ).
cnf(s5745,plain,
( spl99_41
| spl99_51
| spl99_53
| spl99_64 ),
inference(sat_conversion,[],[f21979]) ).
cnf(s5754,plain,
( spl99_41
| spl99_51
| spl99_53
| spl99_55 ),
inference(sat_conversion,[],[f21998]) ).
cnf(s5991,plain,
( ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_66
| ~ spl99_110
| ~ spl99_111 ),
inference(sat_conversion,[],[f22944]) ).
cnf(s6038,plain,
( ~ spl99_41
| ~ spl99_49
| ~ spl99_57
| ~ spl99_110
| spl99_111 ),
inference(sat_conversion,[],[f23376]) ).
cnf(s6083,plain,
( ~ spl99_41
| ~ spl99_57
| spl99_110
| spl99_111 ),
inference(sat_conversion,[],[f23515]) ).
cnf(s6099,plain,
( ~ spl99_41
| ~ spl99_57
| ~ spl99_66
| spl99_110
| ~ spl99_111 ),
inference(sat_conversion,[],[f23551]) ).
cnf(s6111,plain,
( spl99_47
| spl99_49
| spl99_51
| spl99_53 ),
inference(sat_conversion,[],[f23579]) ).
cnf(s6150,plain,
( spl99_43
| spl99_47
| spl99_49
| spl99_53 ),
inference(sat_conversion,[],[f23726]) ).
cnf(s6235,plain,
( spl99_47
| spl99_49
| spl99_53
| spl99_68 ),
inference(sat_conversion,[],[f24251]) ).
cnf(s6292,plain,
( ~ spl99_43
| ~ spl99_59
| spl99_98
| spl99_99
| ~ spl99_114 ),
inference(sat_conversion,[],[f24542]) ).
cnf(s6308,plain,
( ~ spl99_59
| spl99_98
| spl99_99
| spl99_114 ),
inference(sat_conversion,[],[f24595]) ).
cnf(s6320,plain,
( ~ spl99_51
| ~ spl99_59
| spl99_98
| ~ spl99_99
| spl99_114 ),
inference(sat_conversion,[],[f24626]) ).
cnf(s6371,plain,
( ~ spl99_43
| ~ spl99_51
| ~ spl99_59
| spl99_98
| ~ spl99_99
| ~ spl99_114 ),
inference(sat_conversion,[],[f24820]) ).
cnf(s6376,plain,
( spl99_47
| spl99_49
| spl99_53
| spl99_59 ),
inference(sat_conversion,[],[f24826]) ).
cnf(s6429,plain,
( spl99_49
| spl99_53
| spl99_64
| spl99_68 ),
inference(sat_conversion,[],[f25019]) ).
cnf(s6454,plain,
( spl99_49
| spl99_53
| spl99_55
| spl99_68 ),
inference(sat_conversion,[],[f25079]) ).
cnf(s6475,plain,
( spl99_43
| spl99_49
| spl99_53
| spl99_64 ),
inference(sat_conversion,[],[f25158]) ).
cnf(s6483,plain,
( spl99_43
| spl99_49
| spl99_53
| spl99_55 ),
inference(sat_conversion,[],[f25179]) ).
cnf(s6521,plain,
( spl99_49
| spl99_53
| spl99_59
| spl99_64 ),
inference(sat_conversion,[],[f25352]) ).
cnf(s6527,plain,
( spl99_49
| spl99_53
| spl99_55
| spl99_59 ),
inference(sat_conversion,[],[f25369]) ).
cnf(s6575,plain,
( spl99_39
| spl99_49
| spl99_53
| spl99_68 ),
inference(sat_conversion,[],[f25545]) ).
cnf(s6583,plain,
( spl99_39
| spl99_53
| spl99_57
| spl99_68 ),
inference(sat_conversion,[],[f25564]) ).
cnf(s6619,plain,
( spl99_39
| spl99_41
| spl99_53
| spl99_68 ),
inference(sat_conversion,[],[f25733]) ).
cnf(s6651,plain,
( spl99_39
| spl99_41
| spl99_53
| spl99_59 ),
inference(sat_conversion,[],[f25818]) ).
cnf(s6655,plain,
( spl99_39
| spl99_53
| spl99_57
| spl99_59 ),
inference(sat_conversion,[],[f25831]) ).
cnf(s6688,plain,
( spl99_39
| spl99_43
| spl99_53
| spl99_57 ),
inference(sat_conversion,[],[f25946]) ).
cnf(s6708,plain,
( spl99_39
| spl99_41
| spl99_43
| spl99_53 ),
inference(sat_conversion,[],[f26009]) ).
cnf(s6717,plain,
( spl99_39
| spl99_41
| spl99_51
| spl99_53 ),
inference(sat_conversion,[],[f26020]) ).
cnf(s6784,plain,
( spl99_39
| spl99_51
| spl99_53
| spl99_57 ),
inference(sat_conversion,[],[f26277]) ).
cnf(s6809,plain,
( spl99_41
| spl99_47
| spl99_51
| spl99_53 ),
inference(sat_conversion,[],[f26376]) ).
cnf(s6826,plain,
( spl99_41
| spl99_47
| spl99_53
| spl99_59 ),
inference(sat_conversion,[],[f26423]) ).
cnf(s6858,plain,
( spl99_41
| spl99_43
| spl99_47
| spl99_53 ),
inference(sat_conversion,[],[f26542]) ).
cnf(s6879,plain,
( spl99_41
| spl99_53
| spl99_59
| spl99_64 ),
inference(sat_conversion,[],[f26607]) ).
cnf(s6889,plain,
( spl99_41
| spl99_53
| spl99_55
| spl99_59 ),
inference(sat_conversion,[],[f26624]) ).
cnf(s6931,plain,
( spl99_41
| spl99_43
| spl99_53
| spl99_64 ),
inference(sat_conversion,[],[f26814]) ).
cnf(s6958,plain,
( spl99_41
| spl99_43
| spl99_53
| spl99_55 ),
inference(sat_conversion,[],[f26909]) ).
cnf(s6999,plain,
( spl99_43
| spl99_47
| spl99_53
| spl99_66 ),
inference(sat_conversion,[],[f27046]) ).
cnf(s7007,plain,
( spl99_43
| spl99_47
| spl99_53
| spl99_57 ),
inference(sat_conversion,[],[f27053]) ).
cnf(s7024,plain,
( spl99_47
| spl99_53
| spl99_66
| spl99_68 ),
inference(sat_conversion,[],[f27114]) ).
cnf(s7032,plain,
( spl99_47
| spl99_53
| spl99_57
| spl99_68 ),
inference(sat_conversion,[],[f27121]) ).
cnf(s7079,plain,
( spl99_53
| spl99_55
| spl99_59
| spl99_66 ),
inference(sat_conversion,[],[f27260]) ).
cnf(s7112,plain,
( spl99_47
| spl99_53
| spl99_59
| spl99_66 ),
inference(sat_conversion,[],[f27375]) ).
cnf(s7118,plain,
( spl99_47
| spl99_53
| spl99_57
| spl99_59 ),
inference(sat_conversion,[],[f27380]) ).
cnf(s7137,plain,
( spl99_53
| spl99_59
| spl99_64
| spl99_66 ),
inference(sat_conversion,[],[f27455]) ).
cnf(s7145,plain,
( spl99_53
| spl99_57
| spl99_59
| spl99_64 ),
inference(sat_conversion,[],[f27462]) ).
cnf(s7164,plain,
( spl99_43
| spl99_53
| spl99_57
| spl99_64 ),
inference(sat_conversion,[],[f27553]) ).
cnf(s7173,plain,
( spl99_43
| spl99_53
| spl99_55
| spl99_57 ),
inference(sat_conversion,[],[f27568]) ).
cnf(s7191,plain,
( spl99_53
| spl99_57
| spl99_64
| spl99_68 ),
inference(sat_conversion,[],[f27635]) ).
cnf(s7231,plain,
( spl99_53
| spl99_55
| spl99_57
| spl99_68 ),
inference(sat_conversion,[],[f27738]) ).
cnf(s7267,plain,
( spl99_53
| spl99_55
| spl99_66
| spl99_68 ),
inference(sat_conversion,[],[f27883]) ).
cnf(s7300,plain,
( spl99_53
| spl99_64
| spl99_66
| spl99_68 ),
inference(sat_conversion,[],[f28032]) ).
cnf(s7308,plain,
( spl99_43
| spl99_53
| spl99_64
| spl99_66 ),
inference(sat_conversion,[],[f28043]) ).
cnf(s7317,plain,
( spl99_43
| spl99_53
| spl99_55
| spl99_66 ),
inference(sat_conversion,[],[f28058]) ).
cnf(s7337,plain,
( spl99_37
| spl99_43
| spl99_47
| spl99_66 ),
inference(sat_conversion,[],[f28149]) ).
cnf(s7350,plain,
( spl99_43
| spl99_45
| spl99_47
| spl99_66 ),
inference(sat_conversion,[],[f28170]) ).
cnf(s7361,plain,
( spl99_43
| spl99_47
| spl99_62
| spl99_66 ),
inference(sat_conversion,[],[f28199]) ).
cnf(s7431,plain,
( spl99_37
| spl99_55
| spl99_66
| spl99_68 ),
inference(sat_conversion,[],[f28391]) ).
cnf(s7448,plain,
( spl99_37
| spl99_47
| spl99_66
| spl99_68 ),
inference(sat_conversion,[],[f28438]) ).
cnf(s7456,plain,
( spl99_45
| spl99_47
| spl99_66
| spl99_68 ),
inference(sat_conversion,[],[f28457]) ).
cnf(s7465,plain,
( spl99_47
| spl99_62
| spl99_66
| spl99_68 ),
inference(sat_conversion,[],[f28486]) ).
cnf(s7505,plain,
( spl99_47
| spl99_59
| spl99_62
| spl99_66 ),
inference(sat_conversion,[],[f28631]) ).
cnf(s7517,plain,
( spl99_37
| spl99_47
| spl99_59
| spl99_66 ),
inference(sat_conversion,[],[f28644]) ).
cnf(s7538,plain,
( spl99_45
| spl99_47
| spl99_59
| spl99_66 ),
inference(sat_conversion,[],[f28733]) ).
cnf(s7589,plain,
( spl99_37
| spl99_47
| spl99_57
| spl99_59 ),
inference(sat_conversion,[],[f28882]) ).
cnf(s7600,plain,
( spl99_47
| spl99_57
| spl99_59
| spl99_62 ),
inference(sat_conversion,[],[f28905]) ).
cnf(s7628,plain,
( spl99_37
| spl99_43
| spl99_47
| spl99_57 ),
inference(sat_conversion,[],[f29029]) ).
cnf(s7634,plain,
( spl99_43
| spl99_45
| spl99_47
| spl99_57 ),
inference(sat_conversion,[],[f29038]) ).
cnf(s7643,plain,
( spl99_43
| spl99_47
| spl99_57
| spl99_62 ),
inference(sat_conversion,[],[f29065]) ).
cnf(s7662,plain,
( spl99_37
| spl99_43
| spl99_47
| spl99_49 ),
inference(sat_conversion,[],[f29128]) ).
cnf(s7683,plain,
( spl99_43
| spl99_45
| spl99_47
| spl99_49 ),
inference(sat_conversion,[],[f29183]) ).
cnf(s7700,plain,
( spl99_37
| spl99_47
| spl99_49
| spl99_68 ),
inference(sat_conversion,[],[f29228]) ).
cnf(s7725,plain,
( spl99_45
| spl99_47
| spl99_49
| spl99_68 ),
inference(sat_conversion,[],[f29289]) ).
cnf(s7733,plain,
( spl99_47
| spl99_49
| spl99_62
| spl99_68 ),
inference(sat_conversion,[],[f29316]) ).
cnf(s7749,plain,
( spl99_37
| spl99_47
| spl99_49
| spl99_59 ),
inference(sat_conversion,[],[f29347]) ).
cnf(s7767,plain,
( spl99_47
| spl99_49
| spl99_59
| spl99_62 ),
inference(sat_conversion,[],[f29396]) ).
cnf(s7775,plain,
( spl99_45
| spl99_47
| spl99_49
| spl99_59 ),
inference(sat_conversion,[],[f29405]) ).
cnf(s7790,plain,
( spl99_37
| spl99_47
| spl99_49
| spl99_51 ),
inference(sat_conversion,[],[f29474]) ).
cnf(s7802,plain,
( spl99_47
| spl99_49
| spl99_51
| spl99_62 ),
inference(sat_conversion,[],[f29493]) ).
cnf(s7823,plain,
( spl99_37
| spl99_41
| spl99_47
| spl99_51 ),
inference(sat_conversion,[],[f29540]) ).
cnf(s7836,plain,
( spl99_37
| spl99_41
| spl99_43
| spl99_47 ),
inference(sat_conversion,[],[f29565]) ).
cnf(s7843,plain,
( spl99_41
| spl99_43
| spl99_45
| spl99_47 ),
inference(sat_conversion,[],[f29576]) ).
cnf(s7855,plain,
( spl99_37
| spl99_41
| spl99_47
| spl99_59 ),
inference(sat_conversion,[],[f29611]) ).
cnf(s7870,plain,
( spl99_37
| spl99_47
| spl99_57
| spl99_68 ),
inference(sat_conversion,[],[f29670]) ).
cnf(s7903,plain,
( spl99_37
| spl99_47
| spl99_51
| spl99_57 ),
inference(sat_conversion,[],[f29763]) ).
cnf(s7914,plain,
( spl99_37
| spl99_47
| spl99_51
| spl99_66 ),
inference(sat_conversion,[],[f29808]) ).
cnf(s7952,plain,
( spl99_45
| spl99_47
| spl99_51
| spl99_57 ),
inference(sat_conversion,[],[f29951]) ).
cnf(s7961,plain,
( spl99_47
| spl99_51
| spl99_57
| spl99_62 ),
inference(sat_conversion,[],[f29978]) ).
cnf(s7973,plain,
( spl99_45
| spl99_47
| spl99_51
| spl99_66 ),
inference(sat_conversion,[],[f30025]) ).
cnf(s8010,plain,
( spl99_47
| spl99_51
| spl99_62
| spl99_66 ),
inference(sat_conversion,[],[f30150]) ).
cnf(s8022,plain,
( spl99_41
| spl99_45
| spl99_47
| spl99_51 ),
inference(sat_conversion,[],[f30167]) ).
cnf(s8078,plain,
( spl99_41
| spl99_45
| spl99_47
| spl99_59 ),
inference(sat_conversion,[],[f30332]) ).
cnf(s8103,plain,
( spl99_47
| spl99_57
| spl99_62
| spl99_68 ),
inference(sat_conversion,[],[f30423]) ).
cnf(s8111,plain,
( spl99_45
| spl99_47
| spl99_57
| spl99_68 ),
inference(sat_conversion,[],[f30430]) ).
cnf(s8133,plain,
( spl99_37
| spl99_43
| spl99_57
| spl99_64 ),
inference(sat_conversion,[],[f30497]) ).
cnf(s8153,plain,
( spl99_37
| spl99_55
| spl99_57
| spl99_68 ),
inference(sat_conversion,[],[f30535]) ).
cnf(s8186,plain,
( spl99_37
| spl99_39
| spl99_43
| spl99_57 ),
inference(sat_conversion,[],[f30708]) ).
cnf(s8194,plain,
( spl99_37
| spl99_43
| spl99_55
| spl99_57 ),
inference(sat_conversion,[],[f30723]) ).
cnf(s8209,plain,
( spl99_37
| spl99_43
| spl99_49
| spl99_64 ),
inference(sat_conversion,[],[f30808]) ).
cnf(s8217,plain,
( spl99_37
| spl99_43
| spl99_49
| spl99_55 ),
inference(sat_conversion,[],[f30815]) ).
cnf(s8269,plain,
( spl99_37
| spl99_39
| spl99_43
| spl99_49 ),
inference(sat_conversion,[],[f30996]) ).
cnf(s8282,plain,
( spl99_37
| spl99_43
| spl99_55
| spl99_66 ),
inference(sat_conversion,[],[f31029]) ).
cnf(s8305,plain,
( spl99_37
| spl99_41
| spl99_51
| spl99_64 ),
inference(sat_conversion,[],[f31094]) ).
cnf(s8311,plain,
( spl99_37
| spl99_41
| spl99_51
| spl99_55 ),
inference(sat_conversion,[],[f31099]) ).
cnf(s8329,plain,
( spl99_37
| spl99_41
| spl99_43
| spl99_64 ),
inference(sat_conversion,[],[f31170]) ).
cnf(s8338,plain,
( spl99_37
| spl99_41
| spl99_43
| spl99_55 ),
inference(sat_conversion,[],[f31177]) ).
cnf(s8353,plain,
( spl99_37
| spl99_43
| spl99_64
| spl99_66 ),
inference(sat_conversion,[],[f31236]) ).
cnf(s8365,plain,
( spl99_37
| spl99_64
| spl99_66
| spl99_68 ),
inference(sat_conversion,[],[f31255]) ).
cnf(s8373,plain,
( spl99_37
| spl99_59
| spl99_64
| spl99_66 ),
inference(sat_conversion,[],[f31268]) ).
cnf(s8379,plain,
( spl99_37
| spl99_55
| spl99_59
| spl99_66 ),
inference(sat_conversion,[],[f31273]) ).
cnf(s8397,plain,
( spl99_37
| spl99_39
| spl99_66
| spl99_68 ),
inference(sat_conversion,[],[f31360]) ).
cnf(s8427,plain,
( spl99_37
| spl99_39
| spl99_57
| spl99_68 ),
inference(sat_conversion,[],[f31469]) ).
cnf(s8438,plain,
( spl99_37
| spl99_39
| spl99_49
| spl99_68 ),
inference(sat_conversion,[],[f31514]) ).
cnf(s8447,plain,
( spl99_37
| spl99_39
| spl99_57
| spl99_59 ),
inference(sat_conversion,[],[f31539]) ).
cnf(s8456,plain,
( spl99_37
| spl99_39
| spl99_49
| spl99_59 ),
inference(sat_conversion,[],[f31582]) ).
cnf(s8469,plain,
( spl99_37
| spl99_57
| spl99_59
| spl99_64 ),
inference(sat_conversion,[],[f31615]) ).
cnf(s8477,plain,
( spl99_37
| spl99_55
| spl99_57
| spl99_59 ),
inference(sat_conversion,[],[f31628]) ).
cnf(s8495,plain,
( spl99_37
| spl99_49
| spl99_59
| spl99_64 ),
inference(sat_conversion,[],[f31715]) ).
cnf(s8503,plain,
( spl99_37
| spl99_49
| spl99_55
| spl99_59 ),
inference(sat_conversion,[],[f31726]) ).
cnf(s8536,plain,
( spl99_37
| spl99_49
| spl99_64
| spl99_68 ),
inference(sat_conversion,[],[f31873]) ).
cnf(s8544,plain,
( spl99_37
| spl99_49
| spl99_55
| spl99_68 ),
inference(sat_conversion,[],[f31884]) ).
cnf(s8559,plain,
( spl99_37
| spl99_57
| spl99_64
| spl99_68 ),
inference(sat_conversion,[],[f31945]) ).
cnf(s8570,plain,
( spl99_37
| spl99_41
| spl99_64
| spl99_68 ),
inference(sat_conversion,[],[f31992]) ).
cnf(s8581,plain,
( spl99_37
| spl99_41
| spl99_59
| spl99_64 ),
inference(sat_conversion,[],[f32011]) ).
cnf(s8589,plain,
( spl99_37
| spl99_41
| spl99_55
| spl99_59 ),
inference(sat_conversion,[],[f32024]) ).
cnf(s8606,plain,
( spl99_37
| spl99_41
| spl99_55
| spl99_68 ),
inference(sat_conversion,[],[f32105]) ).
cnf(s8616,plain,
( spl99_37
| spl99_51
| spl99_55
| spl99_57 ),
inference(sat_conversion,[],[f32124]) ).
cnf(s8625,plain,
( spl99_37
| spl99_49
| spl99_51
| spl99_55 ),
inference(sat_conversion,[],[f32167]) ).
cnf(s8640,plain,
( spl99_37
| spl99_51
| spl99_57
| spl99_64 ),
inference(sat_conversion,[],[f32228]) ).
cnf(s8651,plain,
( spl99_37
| spl99_49
| spl99_51
| spl99_64 ),
inference(sat_conversion,[],[f32273]) ).
cnf(s8664,plain,
( spl99_37
| spl99_51
| spl99_55
| spl99_66 ),
inference(sat_conversion,[],[f32306]) ).
cnf(s8690,plain,
( spl99_37
| spl99_39
| spl99_41
| spl99_68 ),
inference(sat_conversion,[],[f32395]) ).
cnf(s8700,plain,
( spl99_37
| spl99_39
| spl99_41
| spl99_59 ),
inference(sat_conversion,[],[f32410]) ).
cnf(s8735,plain,
( spl99_37
| spl99_39
| spl99_41
| spl99_51 ),
inference(sat_conversion,[],[f32549]) ).
cnf(s8776,plain,
( spl99_37
| spl99_39
| spl99_51
| spl99_57 ),
inference(sat_conversion,[],[f32725]) ).
cnf(s8785,plain,
( spl99_37
| spl99_39
| spl99_49
| spl99_51 ),
inference(sat_conversion,[],[f32768]) ).
cnf(s8798,plain,
( spl99_39
| spl99_51
| spl99_57
| spl99_62 ),
inference(sat_conversion,[],[f32801]) ).
cnf(s8835,plain,
( spl99_39
| spl99_45
| spl99_51
| spl99_57 ),
inference(sat_conversion,[],[f32914]) ).
cnf(s8853,plain,
( spl99_39
| spl99_49
| spl99_51
| spl99_62 ),
inference(sat_conversion,[],[f32989]) ).
cnf(s8861,plain,
( spl99_39
| spl99_45
| spl99_49
| spl99_51 ),
inference(sat_conversion,[],[f32996]) ).
cnf(s8880,plain,
( spl99_39
| spl99_51
| spl99_62
| spl99_66 ),
inference(sat_conversion,[],[f33053]) ).
cnf(s8890,plain,
( spl99_39
| spl99_41
| spl99_51
| spl99_62 ),
inference(sat_conversion,[],[f33068]) ).
cnf(s8899,plain,
( spl99_41
| spl99_51
| spl99_62
| spl99_64 ),
inference(sat_conversion,[],[f33087]) ).
cnf(s8907,plain,
( spl99_41
| spl99_45
| spl99_51
| spl99_64 ),
inference(sat_conversion,[],[f33094]) ).
cnf(s8925,plain,
( spl99_41
| spl99_51
| spl99_55
| spl99_62 ),
inference(sat_conversion,[],[f33141]) ).
cnf(s8936,plain,
( spl99_51
| spl99_55
| spl99_57
| spl99_62 ),
inference(sat_conversion,[],[f33162]) ).
cnf(s8942,plain,
( spl99_45
| spl99_51
| spl99_55
| spl99_57 ),
inference(sat_conversion,[],[f33167]) ).
cnf(s8963,plain,
( spl99_51
| spl99_57
| spl99_62
| spl99_64 ),
inference(sat_conversion,[],[f33244]) ).
cnf(s8976,plain,
( spl99_49
| spl99_51
| spl99_62
| spl99_64 ),
inference(sat_conversion,[],[f33291]) ).
cnf(s8986,plain,
( spl99_51
| spl99_62
| spl99_64
| spl99_66 ),
inference(sat_conversion,[],[f33316]) ).
cnf(s9035,plain,
( spl99_51
| spl99_55
| spl99_62
| spl99_66 ),
inference(sat_conversion,[],[f33445]) ).
cnf(s9045,plain,
( spl99_45
| spl99_51
| spl99_55
| spl99_66 ),
inference(sat_conversion,[],[f33462]) ).
cnf(s9064,plain,
( spl99_49
| spl99_51
| spl99_55
| spl99_62 ),
inference(sat_conversion,[],[f33507]) ).
cnf(s9072,plain,
( spl99_45
| spl99_49
| spl99_51
| spl99_55 ),
inference(sat_conversion,[],[f33518]) ).
cnf(s9093,plain,
( spl99_49
| spl99_55
| spl99_62
| spl99_68 ),
inference(sat_conversion,[],[f33583]) ).
cnf(s9103,plain,
( spl99_49
| spl99_55
| spl99_59
| spl99_62 ),
inference(sat_conversion,[],[f33598]) ).
cnf(s9112,plain,
( spl99_43
| spl99_49
| spl99_55
| spl99_62 ),
inference(sat_conversion,[],[f33641]) ).
cnf(s9125,plain,
( spl99_55
| spl99_57
| spl99_62
| spl99_68 ),
inference(sat_conversion,[],[f33678]) ).
cnf(s9131,plain,
( spl99_55
| spl99_57
| spl99_59
| spl99_62 ),
inference(sat_conversion,[],[f33683]) ).
cnf(s9140,plain,
( spl99_43
| spl99_55
| spl99_57
| spl99_62 ),
inference(sat_conversion,[],[f33726]) ).
cnf(s9156,plain,
( spl99_41
| spl99_55
| spl99_62
| spl99_68 ),
inference(sat_conversion,[],[f33791]) ).
cnf(s9168,plain,
( spl99_41
| spl99_43
| spl99_55
| spl99_62 ),
inference(sat_conversion,[],[f33804]) ).
cnf(s9184,plain,
( spl99_55
| spl99_62
| spl99_66
| spl99_68 ),
inference(sat_conversion,[],[f33845]) ).
cnf(s9192,plain,
( spl99_55
| spl99_59
| spl99_62
| spl99_66 ),
inference(sat_conversion,[],[f33852]) ).
cnf(s9201,plain,
( spl99_43
| spl99_55
| spl99_62
| spl99_66 ),
inference(sat_conversion,[],[f33895]) ).
cnf(s9216,plain,
( spl99_59
| spl99_62
| spl99_64
| spl99_66 ),
inference(sat_conversion,[],[f33952]) ).
cnf(s9227,plain,
( spl99_43
| spl99_62
| spl99_64
| spl99_66 ),
inference(sat_conversion,[],[f33997]) ).
cnf(s9244,plain,
( spl99_43
| spl99_57
| spl99_62
| spl99_64 ),
inference(sat_conversion,[],[f34062]) ).
cnf(s9258,plain,
( spl99_57
| spl99_62
| spl99_64
| spl99_68 ),
inference(sat_conversion,[],[f34085]) ).
cnf(s9266,plain,
( spl99_57
| spl99_59
| spl99_62
| spl99_64 ),
inference(sat_conversion,[],[f34098]) ).
cnf(s9284,plain,
( spl99_49
| spl99_62
| spl99_64
| spl99_68 ),
inference(sat_conversion,[],[f34185]) ).
cnf(s9294,plain,
( spl99_41
| spl99_62
| spl99_64
| spl99_68 ),
inference(sat_conversion,[],[f34212]) ).
cnf(s9303,plain,
( spl99_41
| spl99_59
| spl99_62
| spl99_64 ),
inference(sat_conversion,[],[f34223]) ).
cnf(s9307,plain,
( spl99_49
| spl99_59
| spl99_62
| spl99_64 ),
inference(sat_conversion,[],[f34236]) ).
cnf(s9369,plain,
( spl99_43
| spl99_49
| spl99_62
| spl99_64 ),
inference(sat_conversion,[],[f34469]) ).
cnf(s9380,plain,
( spl99_41
| spl99_43
| spl99_62
| spl99_64 ),
inference(sat_conversion,[],[f34496]) ).
cnf(s9429,plain,
( spl99_39
| spl99_41
| spl99_59
| spl99_62 ),
inference(sat_conversion,[],[f34657]) ).
cnf(s9439,plain,
( spl99_39
| spl99_59
| spl99_62
| spl99_66 ),
inference(sat_conversion,[],[f34682]) ).
cnf(s9463,plain,
( spl99_39
| spl99_41
| spl99_43
| spl99_62 ),
inference(sat_conversion,[],[f34777]) ).
cnf(s9472,plain,
( spl99_39
| spl99_41
| spl99_62
| spl99_68 ),
inference(sat_conversion,[],[f34796]) ).
cnf(s9482,plain,
( spl99_39
| spl99_43
| spl99_62
| spl99_66 ),
inference(sat_conversion,[],[f34815]) ).
cnf(s9488,plain,
( spl99_39
| spl99_43
| spl99_57
| spl99_62 ),
inference(sat_conversion,[],[f34820]) ).
cnf(s9497,plain,
( spl99_39
| spl99_43
| spl99_49
| spl99_62 ),
inference(sat_conversion,[],[f34863]) ).
cnf(s9512,plain,
( spl99_39
| spl99_62
| spl99_66
| spl99_68 ),
inference(sat_conversion,[],[f34906]) ).
cnf(s9520,plain,
( spl99_39
| spl99_57
| spl99_62
| spl99_68 ),
inference(sat_conversion,[],[f34913]) ).
cnf(s9529,plain,
( spl99_39
| spl99_49
| spl99_62
| spl99_68 ),
inference(sat_conversion,[],[f34956]) ).
cnf(s9541,plain,
( spl99_39
| spl99_57
| spl99_59
| spl99_62 ),
inference(sat_conversion,[],[f34987]) ).
cnf(s9552,plain,
( spl99_39
| spl99_49
| spl99_59
| spl99_62 ),
inference(sat_conversion,[],[f35034]) ).
cnf(s9573,plain,
( spl99_39
| spl99_41
| spl99_43
| spl99_45 ),
inference(sat_conversion,[],[f35111]) ).
cnf(s9593,plain,
( spl99_39
| spl99_45
| spl99_66
| spl99_68 ),
inference(sat_conversion,[],[f35158]) ).
cnf(s9609,plain,
( spl99_45
| spl99_55
| spl99_66
| spl99_68 ),
inference(sat_conversion,[],[f35191]) ).
cnf(s9630,plain,
( spl99_41
| spl99_43
| spl99_45
| spl99_55 ),
inference(sat_conversion,[],[f35222]) ).
cnf(s9642,plain,
( spl99_41
| spl99_43
| spl99_45
| spl99_64 ),
inference(sat_conversion,[],[f35265]) ).
cnf(s9651,plain,
( spl99_41
| spl99_45
| spl99_55
| spl99_59 ),
inference(sat_conversion,[],[f35286]) ).
cnf(s9662,plain,
( spl99_41
| spl99_45
| spl99_59
| spl99_64 ),
inference(sat_conversion,[],[f35331]) ).
cnf(s9696,plain,
( spl99_45
| spl99_55
| spl99_57
| spl99_68 ),
inference(sat_conversion,[],[f35452]) ).
cnf(s9708,plain,
( spl99_43
| spl99_45
| spl99_49
| spl99_55 ),
inference(sat_conversion,[],[f35499]) ).
cnf(s9722,plain,
( spl99_43
| spl99_45
| spl99_49
| spl99_64 ),
inference(sat_conversion,[],[f35546]) ).
cnf(s9735,plain,
( spl99_43
| spl99_45
| spl99_55
| spl99_66 ),
inference(sat_conversion,[],[f35579]) ).
cnf(s9741,plain,
( spl99_43
| spl99_45
| spl99_55
| spl99_57 ),
inference(sat_conversion,[],[f35584]) ).
cnf(s9756,plain,
( spl99_45
| spl99_55
| spl99_59
| spl99_66 ),
inference(sat_conversion,[],[f35649]) ).
cnf(s9772,plain,
( spl99_45
| spl99_59
| spl99_64
| spl99_66 ),
inference(sat_conversion,[],[f35700]) ).
cnf(s9789,plain,
( spl99_43
| spl99_45
| spl99_57
| spl99_64 ),
inference(sat_conversion,[],[f35751]) ).
cnf(s9801,plain,
( spl99_45
| spl99_49
| spl99_59
| spl99_64 ),
inference(sat_conversion,[],[f35806]) ).
cnf(s9827,plain,
( spl99_39
| spl99_45
| spl99_57
| spl99_68 ),
inference(sat_conversion,[],[f35881]) ).
cnf(s9842,plain,
( spl99_39
| spl99_43
| spl99_45
| spl99_57 ),
inference(sat_conversion,[],[f35898]) ).
cnf(s9848,plain,
( spl99_39
| spl99_45
| spl99_57
| spl99_59 ),
inference(sat_conversion,[],[f35911]) ).
cnf(s9856,plain,
( spl99_39
| spl99_41
| spl99_45
| spl99_59 ),
inference(sat_conversion,[],[f35952]) ).
cnf(s9875,plain,
( spl99_39
| spl99_45
| spl99_49
| spl99_68 ),
inference(sat_conversion,[],[f36017]) ).
cnf(s9890,plain,
( spl99_39
| spl99_43
| spl99_45
| spl99_49 ),
inference(sat_conversion,[],[f36034]) ).
cnf(s9893,plain,
( spl99_99
| spl99_98
| ~ spl99_59
| ~ spl99_43 ),
inference(rat,[],[s6308,s6292]) ).
cnf(s9894,plain,
( spl99_98
| ~ spl99_43
| ~ spl99_59
| ~ spl99_51 ),
inference(rat,[],[s6371,s6320,s9893]) ).
cnf(s9895,plain,
( spl99_99
| ~ spl99_98
| ~ spl99_68
| ~ spl99_59
| ~ spl99_43 ),
inference(rat,[],[s4749,s4781]) ).
cnf(s9896,plain,
( ~ spl99_99
| ~ spl99_59
| ~ spl99_98
| ~ spl99_68
| ~ spl99_43
| ~ spl99_51 ),
inference(rat,[],[s5059,s5122]) ).
cnf(s9897,plain,
( spl99_41
| spl99_39
| spl99_37 ),
inference(rat,[],[s9896,s9895,s9894,s752,s8690,s8700,s8735]) ).
cnf(s9898,plain,
( spl99_110
| ~ spl99_57
| ~ spl99_66
| ~ spl99_41 ),
inference(rat,[],[s6083,s6099]) ).
cnf(s9899,plain,
( spl99_51
| spl99_39
| spl99_37 ),
inference(rat,[],[s5991,s6038,s9898,s5242,s8776,s8785,s9897]) ).
cnf(s9900,plain,
( spl99_68
| spl99_39
| spl99_37 ),
inference(rat,[],[s5991,s6038,s9898,s8397,s8427,s8438,s9897]) ).
cnf(s9901,plain,
( ~ spl99_59
| ~ spl99_43
| ~ spl99_68
| ~ spl99_51 ),
inference(rat,[],[s9896,s9895,s9894]) ).
cnf(s9902,plain,
( spl99_59
| spl99_39
| spl99_37 ),
inference(rat,[],[s5991,s6038,s9898,s4828,s8447,s8456,s9897]) ).
cnf(s9903,plain,
( spl99_39
| spl99_37 ),
inference(rat,[],[s5991,s6038,s9898,s4229,s8186,s8269,s9901,s9902,s9900,s9899,s9897]) ).
cnf(s9904,plain,
( spl99_75
| ~ spl99_55
| ~ spl99_64
| ~ spl99_39 ),
inference(rat,[],[s3124,s2938]) ).
cnf(s9905,plain,
( spl99_76
| ~ spl99_75
| ~ spl99_39
| ~ spl99_55
| ~ spl99_47 ),
inference(rat,[],[s5478,s5493]) ).
cnf(s9906,plain,
( spl99_49
| spl99_51
| spl99_37 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s7790,s8625,s8651,s9903]) ).
cnf(s9907,plain,
( spl99_66
| spl99_51
| spl99_37 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s7914,s3771,s8664,s9903]) ).
cnf(s9908,plain,
( ~ spl99_57
| ~ spl99_41
| ~ spl99_66
| ~ spl99_49 ),
inference(rat,[],[s5991,s6038,s9898]) ).
cnf(s9909,plain,
( spl99_57
| spl99_51
| spl99_37 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s7903,s8616,s8640,s9903]) ).
cnf(s9910,plain,
( spl99_51
| spl99_37 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s7823,s8311,s8305,s9908,s9909,s9907,s9906,s9903]) ).
cnf(s9911,plain,
( spl99_66
| spl99_68
| spl99_37 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s7448,s8365,s7431,s9903]) ).
cnf(s9912,plain,
( spl99_49
| spl99_68
| spl99_37 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s7700,s8544,s8536,s9903]) ).
cnf(s9913,plain,
( spl99_57
| spl99_68
| spl99_37 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s7870,s8153,s8559,s9903]) ).
cnf(s9914,plain,
( spl99_68
| spl99_37 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s1865,s8570,s8606,s9908,s9913,s9912,s9911,s9903]) ).
cnf(s9915,plain,
( spl99_66
| spl99_59
| spl99_37 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s7517,s8373,s8379,s9903]) ).
cnf(s9916,plain,
( spl99_49
| spl99_59
| spl99_37 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s7749,s8503,s8495,s9903]) ).
cnf(s9917,plain,
( spl99_57
| spl99_59
| spl99_37 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s7589,s8477,s8469,s9903]) ).
cnf(s9918,plain,
( spl99_59
| spl99_37 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s7855,s8589,s8581,s9908,s9917,s9916,s9915,s9903]) ).
cnf(s9919,plain,
( spl99_66
| spl99_37 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s7337,s8353,s8282,s9903,s9901,s9918,s9914,s9910]) ).
cnf(s9920,plain,
( spl99_49
| spl99_37 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s7662,s8209,s8217,s9903,s9901,s9918,s9914,s9910]) ).
cnf(s9921,plain,
( spl99_57
| spl99_37 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s7628,s8194,s8133,s9903,s9901,s9918,s9914,s9910]) ).
cnf(s9922,plain,
spl99_37,
inference(rat,[],[s5443,s5459,s9905,s9904,s7836,s8338,s8329,s9908,s9921,s9920,s9919,s9901,s9918,s9914,s9910,s9903]) ).
cnf(s9923,plain,
( ~ spl99_106
| spl99_105
| ~ spl99_62
| ~ spl99_53 ),
inference(rat,[],[s3811,s4463,s9922]) ).
cnf(s9924,plain,
( spl99_105
| ~ spl99_53
| ~ spl99_62 ),
inference(rat,[],[s9923,s2720,s9922]) ).
cnf(s9925,plain,
( ~ spl99_105
| ~ spl99_45
| ~ spl99_62
| ~ spl99_53
| ~ spl99_106 ),
inference(rat,[],[s4446,s4346,s9922]) ).
cnf(s9926,plain,
( spl99_51
| spl99_66
| spl99_39 ),
inference(rat,[],[s9925,s4983,s9924,s5125,s5254,s8880,s9922]) ).
cnf(s9928,plain,
( spl99_59
| spl99_66
| spl99_39 ),
inference(rat,[],[s9925,s4983,s9924,s4537,s4861,s9439,s9922]) ).
cnf(s9929,plain,
( spl99_68
| spl99_66
| spl99_39 ),
inference(rat,[],[s9925,s4983,s9924,s4684,s9512,s9593,s9922]) ).
cnf(s9930,plain,
( spl99_43
| spl99_66
| spl99_39 ),
inference(rat,[],[s9925,s4983,s9924,s4164,s4256,s9482,s9922]) ).
cnf(s9931,plain,
( spl99_66
| spl99_39 ),
inference(rat,[],[s9930,s9901,s9929,s9928,s9926]) ).
cnf(s9932,plain,
( spl99_51
| spl99_49
| spl99_39 ),
inference(rat,[],[s9925,s4983,s9924,s8861,s5267,s8853,s9922]) ).
cnf(s9933,plain,
( spl99_68
| spl99_49
| spl99_39 ),
inference(rat,[],[s9925,s4983,s9924,s6575,s9529,s9875,s9922]) ).
cnf(s9934,plain,
( spl99_59
| spl99_49
| spl99_39 ),
inference(rat,[],[s9925,s4983,s9924,s969,s4662,s9552,s9922]) ).
cnf(s9935,plain,
( spl99_43
| spl99_49
| spl99_39 ),
inference(rat,[],[s9925,s4983,s9924,s9890,s4480,s9497,s9922]) ).
cnf(s9936,plain,
( spl99_49
| spl99_39 ),
inference(rat,[],[s9935,s9901,s9934,s9933,s9932]) ).
cnf(s9937,plain,
( spl99_51
| spl99_39
| spl99_57 ),
inference(rat,[],[s9925,s4983,s9924,s8835,s6784,s8798,s9922]) ).
cnf(s9938,plain,
( spl99_53
| ~ spl99_43
| spl99_57
| spl99_39 ),
inference(rat,[],[s9901,s6583,s6655,s9937]) ).
cnf(s9939,plain,
( spl99_68
| ~ spl99_53
| spl99_57
| spl99_39 ),
inference(rat,[],[s9925,s4983,s9924,s9520,s9827,s9922]) ).
cnf(s9940,plain,
( ~ spl99_43
| spl99_57
| spl99_39 ),
inference(rat,[],[s9925,s4983,s9924,s9848,s9541,s9901,s9939,s9938,s9937,s9922]) ).
cnf(s9941,plain,
( spl99_43
| spl99_39
| spl99_57 ),
inference(rat,[],[s9925,s4983,s9924,s9842,s6688,s9488,s9922]) ).
cnf(s9942,plain,
( spl99_57
| spl99_39 ),
inference(rat,[],[s9941,s9940]) ).
cnf(s9943,plain,
( spl99_39
| ~ spl99_41 ),
inference(rat,[],[s9942,s9908,s9936,s9931]) ).
cnf(s9944,plain,
( spl99_53
| spl99_51
| spl99_66
| ~ spl99_39 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s5517,s5281,s5300]) ).
cnf(s9945,plain,
( spl99_62
| spl99_51
| spl99_66
| ~ spl99_39 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s8986,s9035,s8010]) ).
cnf(s9946,plain,
( spl99_45
| spl99_51
| spl99_66
| ~ spl99_39 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s3658,s7973,s9045]) ).
cnf(s9947,plain,
( spl99_51
| spl99_66
| ~ spl99_39 ),
inference(rat,[],[s9925,s4983,s9946,s9924,s9945,s9944,s9922]) ).
cnf(s9949,plain,
( spl99_59
| spl99_53
| spl99_66
| ~ spl99_39 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s7079,s7112,s7137]) ).
cnf(s9950,plain,
( spl99_53
| ~ spl99_43
| spl99_66
| ~ spl99_39 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s7300,s7267,s7024,s9901,s9949,s9947]) ).
cnf(s9951,plain,
( spl99_68
| spl99_62
| spl99_66
| ~ spl99_39 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s811,s9184,s7465]) ).
cnf(s9952,plain,
( spl99_62
| ~ spl99_43
| spl99_66
| ~ spl99_39 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s7505,s9216,s9192,s9901,s9951,s9947]) ).
cnf(s9953,plain,
( ~ spl99_45
| ~ spl99_62
| ~ spl99_53 ),
inference(rat,[],[s9925,s4983,s9924,s9922]) ).
cnf(s9954,plain,
( spl99_68
| spl99_45
| spl99_66
| ~ spl99_39 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s7456,s3348,s9609]) ).
cnf(s9955,plain,
( ~ spl99_43
| spl99_66
| ~ spl99_39 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s7538,s9756,s9772,s9901,s9954,s9953,s9952,s9950,s9947]) ).
cnf(s9956,plain,
( spl99_62
| spl99_66
| ~ spl99_39 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s9227,s9201,s7361,s9955]) ).
cnf(s9957,plain,
( spl99_53
| spl99_66
| ~ spl99_39 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s6999,s7308,s7317,s9955]) ).
cnf(s9958,plain,
( spl99_66
| ~ spl99_39 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s4050,s7350,s9735,s9953,s9957,s9956,s9955]) ).
cnf(s9959,plain,
( spl99_51
| spl99_62
| spl99_49
| ~ spl99_39 ),
inference(rat,[],[s5443,s5459,s9905,s9904,s9064,s7802,s8976]) ).
cnf(s9960,plain,
( spl99_55
| ~ spl99_51
| spl99_62
| ~ spl99_43
| spl99_49 ),
inference(rat,[],[s9901,s9103,s9093]) ).
cnf(s9962,plain,
( spl99_47
| ~ spl99_51
| spl99_62
| ~ spl99_43
| spl99_49 ),
inference(rat,[],[s9901,s7767,s7733]) ).
cnf(s9963,plain,
( ~ spl99_64
| ~ spl99_47
| ~ spl99_55
| ~ spl99_39 ),
inference(rat,[],[s5443,s5459,s9905,s9904]) ).
cnf(s9964,plain,
( spl99_62
| ~ spl99_43
| spl99_49
| ~ spl99_39 ),
inference(rat,[],[s9901,s9284,s9307,s9963,s9962,s9960,s9959]) ).
cnf(s9965,plain,
( spl99_55
| spl99_51
| ~ spl99_62
| spl99_49 ),
inference(rat,[],[s9953,s9072,s5536]) ).
cnf(s9966,plain,
( spl99_64
| spl99_51
| ~ spl99_62
| spl99_49 ),
inference(rat,[],[s9953,s3973,s5674]) ).
cnf(s9967,plain,
( spl99_51
| ~ spl99_62
| spl99_49
| ~ spl99_39 ),
inference(rat,[],[s9953,s769,s6111,s9963,s9966,s9965]) ).
cnf(s9968,plain,
( spl99_53
| spl99_64
| ~ spl99_51
| ~ spl99_43
| spl99_49 ),
inference(rat,[],[s9901,s6521,s6429]) ).
cnf(s9969,plain,
( spl99_64
| ~ spl99_51
| ~ spl99_62
| ~ spl99_43
| spl99_49 ),
inference(rat,[],[s9901,s3317,s9801,s9953,s9968]) ).
cnf(s9970,plain,
( spl99_53
| spl99_55
| ~ spl99_51
| ~ spl99_43
| spl99_49 ),
inference(rat,[],[s9901,s6527,s6454]) ).
cnf(s9971,plain,
( spl99_55
| ~ spl99_51
| ~ spl99_62
| ~ spl99_43
| spl99_49 ),
inference(rat,[],[s9901,s993,s3250,s9953,s9970]) ).
cnf(s9972,plain,
( spl99_53
| spl99_47
| ~ spl99_51
| ~ spl99_43
| spl99_49 ),
inference(rat,[],[s9901,s6376,s6235]) ).
cnf(s9973,plain,
( ~ spl99_43
| spl99_49
| ~ spl99_39 ),
inference(rat,[],[s9901,s7775,s7725,s9953,s9972,s9963,s9971,s9969,s9967,s9964]) ).
cnf(s9974,plain,
( spl99_62
| spl99_49
| ~ spl99_39 ),
inference(rat,[],[s9963,s9112,s1285,s9369,s9973]) ).
cnf(s9975,plain,
( spl99_55
| ~ spl99_62
| spl99_43
| spl99_49 ),
inference(rat,[],[s9953,s6483,s9708]) ).
cnf(s9976,plain,
( spl99_53
| spl99_49
| ~ spl99_39 ),
inference(rat,[],[s9963,s6150,s6475,s9975,s9974,s9973]) ).
cnf(s9977,plain,
( spl99_49
| ~ spl99_39 ),
inference(rat,[],[s9963,s7683,s9722,s9953,s9976,s9975,s9974,s9973]) ).
cnf(s9978,plain,
( spl99_55
| spl99_62
| ~ spl99_43
| spl99_57 ),
inference(rat,[],[s9901,s9131,s9125,s8936]) ).
cnf(s9979,plain,
( spl99_51
| ~ spl99_55
| spl99_62
| ~ spl99_41 ),
inference(rat,[],[s9963,s7961,s8963,s9908,s9977,s9958,s9943]) ).
cnf(s9981,plain,
( spl99_47
| ~ spl99_51
| spl99_62
| ~ spl99_43
| spl99_57 ),
inference(rat,[],[s9901,s7600,s8103]) ).
cnf(s9982,plain,
( spl99_62
| ~ spl99_43
| ~ spl99_41 ),
inference(rat,[],[s9901,s9266,s9258,s9963,s9981,s9979,s9978,s9908,s9977,s9958,s9943]) ).
cnf(s9983,plain,
( spl99_51
| spl99_55
| ~ spl99_62
| spl99_57 ),
inference(rat,[],[s9953,s5628,s8942]) ).
cnf(s9984,plain,
( spl99_53
| ~ spl99_51
| spl99_55
| ~ spl99_43
| spl99_57 ),
inference(rat,[],[s9901,s7231,s788]) ).
cnf(s9985,plain,
( spl99_55
| ~ spl99_62
| ~ spl99_43
| spl99_57 ),
inference(rat,[],[s9901,s1021,s9696,s9953,s9984,s9983]) ).
cnf(s9986,plain,
( spl99_53
| spl99_51
| ~ spl99_55
| ~ spl99_41 ),
inference(rat,[],[s9963,s5600,s5704,s9908,s9977,s9958,s9943]) ).
cnf(s9987,plain,
( spl99_51
| ~ spl99_43
| ~ spl99_41 ),
inference(rat,[],[s9963,s3844,s7952,s9953,s9986,s9985,s9982,s9908,s9977,s9958,s9943]) ).
cnf(s9988,plain,
( spl99_64
| spl99_53
| ~ spl99_51
| ~ spl99_43
| spl99_57 ),
inference(rat,[],[s9901,s7191,s7145]) ).
cnf(s9989,plain,
( spl99_53
| ~ spl99_43
| ~ spl99_41 ),
inference(rat,[],[s9901,s7118,s7032,s9963,s9988,s9985,s9982,s9908,s9977,s9958,s9943,s9987]) ).
cnf(s9990,plain,
( spl99_64
| spl99_45
| ~ spl99_51
| ~ spl99_43
| spl99_57 ),
inference(rat,[],[s9901,s3360,s1048]) ).
cnf(s9991,plain,
( ~ spl99_43
| ~ spl99_41 ),
inference(rat,[],[s9901,s1116,s8111,s9963,s9990,s9953,s9989,s9987,s9985,s9982,s9908,s9977,s9958,s9943]) ).
cnf(s9994,plain,
( spl99_62
| ~ spl99_41 ),
inference(rat,[],[s9963,s9140,s7643,s9244,s9908,s9977,s9958,s9943,s9991]) ).
cnf(s9995,plain,
( spl99_55
| ~ spl99_41 ),
inference(rat,[],[s9953,s9741,s7173,s9908,s9977,s9958,s9943,s9991,s9994]) ).
cnf(s9996,plain,
( spl99_53
| ~ spl99_41 ),
inference(rat,[],[s9963,s7007,s7164,s9908,s9977,s9958,s9943,s9991,s9995]) ).
cnf(s9997,plain,
~ spl99_41,
inference(rat,[],[s9963,s7634,s9789,s9953,s9996,s9995,s9994,s9991,s9908,s9977,s9958,s9943]) ).
cnf(s9998,plain,
( spl99_62
| spl99_39
| ~ spl99_43 ),
inference(rat,[],[s9901,s8890,s9429,s9472,s9997]) ).
cnf(s9999,plain,
( spl99_51
| ~ spl99_62
| spl99_39 ),
inference(rat,[],[s9953,s945,s6717,s9997]) ).
cnf(s10000,plain,
( spl99_53
| spl99_39
| ~ spl99_43 ),
inference(rat,[],[s9901,s6619,s6651,s9999,s9998,s9997]) ).
cnf(s10001,plain,
( spl99_39
| ~ spl99_43 ),
inference(rat,[],[s9901,s2083,s9856,s9953,s10000,s9999,s9998,s9997]) ).
cnf(s10002,plain,
( spl99_51
| spl99_62
| ~ spl99_39 ),
inference(rat,[],[s9963,s1292,s8899,s8925,s9997]) ).
cnf(s10003,plain,
( spl99_55
| spl99_62
| ~ spl99_43 ),
inference(rat,[],[s9901,s1331,s9156,s10002,s10001,s9997]) ).
cnf(s10004,plain,
( spl99_64
| spl99_62
| ~ spl99_43 ),
inference(rat,[],[s9901,s9303,s9294,s10002,s10001,s9997]) ).
cnf(s10005,plain,
( spl99_62
| ~ spl99_43 ),
inference(rat,[],[s9901,s1297,s1455,s9963,s10004,s10003,s10002,s10001,s9997]) ).
cnf(s10006,plain,
( spl99_55
| spl99_51
| ~ spl99_62 ),
inference(rat,[],[s9953,s1984,s5754,s9997]) ).
cnf(s10007,plain,
( spl99_53
| ~ spl99_55
| spl99_51
| ~ spl99_39 ),
inference(rat,[],[s9963,s6809,s5745,s9997]) ).
cnf(s10008,plain,
( spl99_51
| ~ spl99_43 ),
inference(rat,[],[s9963,s8022,s8907,s9953,s10007,s10006,s10001,s10005,s9997]) ).
cnf(s10009,plain,
( spl99_53
| spl99_55
| ~ spl99_43 ),
inference(rat,[],[s9901,s2393,s6889,s10008,s9997]) ).
cnf(s10010,plain,
( spl99_55
| ~ spl99_43 ),
inference(rat,[],[s9901,s9651,s2201,s9953,s10009,s10005,s10008,s9997]) ).
cnf(s10011,plain,
( spl99_64
| spl99_53
| ~ spl99_43 ),
inference(rat,[],[s9901,s2344,s6879,s10008,s9997]) ).
cnf(s10012,plain,
( spl99_53
| ~ spl99_43 ),
inference(rat,[],[s9901,s6826,s2646,s9963,s10011,s10001,s10008,s10010,s9997]) ).
cnf(s10013,plain,
( spl99_64
| ~ spl99_43 ),
inference(rat,[],[s9901,s9662,s2256,s10008,s9953,s10012,s10005,s9997]) ).
cnf(s10014,plain,
~ spl99_43,
inference(rat,[],[s9901,s8078,s2467,s9963,s10013,s9953,s10012,s10010,s10008,s10005,s10001,s9997]) ).
cnf(s10018,plain,
spl99_62,
inference(rat,[],[s9963,s1193,s9168,s9380,s9463,s10014,s9997]) ).
cnf(s10019,plain,
spl99_39,
inference(rat,[],[s9953,s6708,s9573,s10018,s9997,s10014]) ).
cnf(s10022,plain,
spl99_55,
inference(rat,[],[s9953,s6958,s9630,s10018,s10014,s9997]) ).
cnf(s10023,plain,
spl99_53,
inference(rat,[],[s9963,s6858,s6931,s10022,s10019,s10014,s9997]) ).
cnf(s10025,plain,
~ spl99_45,
inference(rat,[],[s9953,s10018,s10023]) ).
cnf(s10027,plain,
spl99_64,
inference(rat,[],[s9642,s9997,s10014,s10025]) ).
cnf(s10028,plain,
spl99_47,
inference(rat,[],[s7843,s9997,s10014,s10025]) ).
cnf(s10030,plain,
$false,
inference(rat,[],[s9963,s10019,s10022,s10028,s10027]) ).
thf(f36035,plain,
$false,
inference(avatar_sat_refutation,[],[s10030]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL942^2 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 10:46:13 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.80/1.16 % (2354289)Will run a generic schedule for satisfiability detection.
% 5.80/1.16 % (2354296)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2453987582:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 5.80/1.16 % (2354295)% WARNING: option uhcvi not known.
% 5.80/1.16 % (2354295)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2894576840:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 5.80/1.16 % (2354294)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3415726494_2999 on theBenchmark for (2999ds/0Mi)
% 5.80/1.16 % (2354297)dis+10_1_sil=32000:sp=arity:random_seed=1622611498:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 5.80/1.16 % (2354298)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3355021638:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 5.80/1.16 % (2354300)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1162597246:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 5.80/1.16 % (2354299)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2327130685:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 5.80/1.16 % (2354295)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.80/1.16 % (2354298)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.80/1.16 % (2354297)Instruction limit reached!
% 5.80/1.16 % (2354297)------------------------------
% 5.80/1.16 % (2354297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.80/1.16 % (2354297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.80/1.16 % (2354297)CaDiCaL version: 2.1.3
% 5.80/1.16 % (2354297)Termination reason: Instruction limit
% 5.80/1.16 % (2354297)Termination phase: Property scanning
% 5.80/1.16 % (2354297)Time elapsed: 0.036 s
% 5.80/1.16 % (2354297)Peak memory usage: 10 MB
% 5.80/1.16 % (2354297)Instructions burned: 104 (million)
% 5.80/1.16 % (2354298)Instruction limit reached!
% 5.80/1.16 % (2354298)------------------------------
% 5.80/1.16 % (2354298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.80/1.16 % (2354298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.80/1.16 % (2354298)CaDiCaL version: 2.1.3
% 5.80/1.16 % (2354298)Termination reason: Instruction limit
% 5.80/1.16 % (2354298)Termination phase: Property scanning
% 5.80/1.16 % (2354298)Time elapsed: 0.041 s
% 5.80/1.16 % (2354298)Peak memory usage: 10 MB
% 5.80/1.16 % (2354298)Instructions burned: 116 (million)
% 5.80/1.16 % Exception at run slice level
% 5.80/1.16 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.80/1.16 % (2354295)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.80/1.16 % (2354308)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=35619895:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 5.80/1.16 % (2354299)Instruction limit reached!
% 5.80/1.16 % (2354299)------------------------------
% 5.80/1.16 % (2354299)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.80/1.16 % (2354299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.80/1.16 % (2354299)CaDiCaL version: 2.1.3
% 5.80/1.16 % (2354299)Termination reason: Instruction limit
% 5.80/1.16 % (2354299)Termination phase: Property scanning
% 5.80/1.16 % (2354299)Time elapsed: 0.054 s
% 5.80/1.16 % (2354299)Peak memory usage: 10 MB
% 5.80/1.16 % (2354299)Instructions burned: 132 (million)
% 5.80/1.16 % (2354309)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=223509124:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 5.80/1.16 % (2354310)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3031925236:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 5.80/1.16 % (2354300)Instruction limit reached!
% 5.80/1.16 % (2354300)------------------------------
% 5.80/1.16 % (2354300)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.80/1.16 % (2354300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.80/1.16 % (2354300)CaDiCaL version: 2.1.3
% 5.80/1.16 % (2354300)Termination reason: Instruction limit
% 5.80/1.16 % (2354300)Termination phase: Saturation
% 5.80/1.16 % (2354300)Time elapsed: 0.071 s
% 5.80/1.16 % (2354300)Peak memory usage: 11 MB
% 13.86/2.21 % (2354300)Instructions burned: 161 (million)
% 13.86/2.21 % (2354313)ott-21_1_sil=16000:fs=off:random_seed=3019257060:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 13.86/2.21 % (2354315)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2310606403:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 13.86/2.21 % (2354310)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 13.86/2.21 % (2354309)Instruction limit reached!
% 13.86/2.21 % (2354309)------------------------------
% 13.86/2.21 % (2354309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.86/2.21 % (2354309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.86/2.21 % (2354309)CaDiCaL version: 2.1.3
% 13.86/2.21 % (2354309)Termination reason: Instruction limit
% 13.86/2.21 % (2354309)Termination phase: Property scanning
% 13.86/2.21 % (2354309)Time elapsed: 0.047 s
% 13.86/2.21 % (2354309)Peak memory usage: 10 MB
% 13.86/2.21 % (2354309)Instructions burned: 131 (million)
% 13.86/2.21 % (2354310)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 13.86/2.21 % (2354318)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=127867883:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 13.86/2.21 % Exception at run slice level
% 13.86/2.21 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 13.86/2.21 % (2354313)Instruction limit reached!
% 13.86/2.21 % (2354313)------------------------------
% 13.86/2.21 % (2354313)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.86/2.21 % (2354313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.86/2.21 % (2354313)CaDiCaL version: 2.1.3
% 13.86/2.21 % (2354313)Termination reason: Instruction limit
% 13.86/2.21 % (2354313)Termination phase: Saturation
% 13.86/2.21 % (2354313)Time elapsed: 0.068 s
% 13.86/2.21 % (2354313)Peak memory usage: 11 MB
% 13.86/2.21 % (2354313)Instructions burned: 185 (million)
% 13.86/2.21 % (2354321)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=320761077:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 13.86/2.21 % (2354320)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1659408599:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 13.86/2.21 % Exception at run slice level
% 13.86/2.21 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 13.86/2.21 % (2354324)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=501866345:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 13.86/2.21 % Exception at run slice level
% 13.86/2.21 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 13.86/2.21 % (2354324)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 13.86/2.21 % (2354326)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=935785501:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 13.86/2.21 % (2354326)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 13.86/2.21 % (2354315)Instruction limit reached!
% 13.86/2.21 % (2354315)------------------------------
% 13.86/2.21 % (2354315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.86/2.21 % (2354315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.86/2.21 % (2354315)CaDiCaL version: 2.1.3
% 13.86/2.21 % (2354315)Termination reason: Instruction limit
% 13.86/2.21 % (2354315)Termination phase: Saturation
% 13.86/2.21 % (2354315)Time elapsed: 0.197 s
% 13.86/2.21 % (2354315)Peak memory usage: 15 MB
% 13.86/2.21 % (2354315)Instructions burned: 478 (million)
% 13.86/2.21 % (2354328)fmb+10_1_sil=64000:random_seed=3833087881:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 13.86/2.21 % (2354328)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 13.86/2.21 % (2354310)Instruction limit reached!
% 13.86/2.21 % (2354310)------------------------------
% 13.86/2.21 % (2354310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.86/2.21 % (2354310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.86/2.21 % (2354310)CaDiCaL version: 2.1.3
% 13.86/2.21 % (2354310)Termination reason: Instruction limit
% 13.86/2.21 % (2354310)Termination phase: Saturation
% 13.86/2.21 % (2354310)Time elapsed: 0.285 s
% 13.86/2.21 % (2354310)Peak memory usage: 16 MB
% 13.86/2.21 % (2354310)Instructions burned: 685 (million)
% 13.86/2.21 % Exception at run slice level
% 13.86/2.21 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 13.86/2.21 % (2354330)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=391598055:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 13.86/2.21 % (2354331)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3385256408:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 13.86/2.21 % Exception at run slice level
% 13.86/2.21 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 13.86/2.21 % Exception at run slice level
% 13.86/2.21 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 13.86/2.21 % (2354334)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=619049323:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 13.86/2.21 % (2354335)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=163895729:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 13.86/2.21 % (2354334)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 13.86/2.21 % (2354324)Instruction limit reached!
% 13.86/2.21 % (2354324)------------------------------
% 13.86/2.21 % (2354324)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.86/2.21 % (2354324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.86/2.21 % (2354324)CaDiCaL version: 2.1.3
% 13.86/2.21 % (2354324)Termination reason: Instruction limit
% 13.86/2.21 % (2354324)Termination phase: Saturation
% 13.86/2.21 % (2354324)Time elapsed: 0.273 s
% 13.86/2.21 % (2354324)Peak memory usage: 16 MB
% 13.86/2.21 % (2354324)Instructions burned: 693 (million)
% 13.86/2.21 % (2354335)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 13.86/2.21 % (2354335)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 13.86/2.21 % (2354338)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=983827894:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 13.86/2.21 % Exception at run slice level
% 13.86/2.21 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 13.86/2.21 % (2354340)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=880521577:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 13.86/2.21 % (2354326)Instruction limit reached!
% 13.86/2.21 % (2354326)------------------------------
% 13.86/2.21 % (2354326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.86/2.21 % (2354326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.86/2.21 % (2354326)CaDiCaL version: 2.1.3
% 13.86/2.21 % (2354326)Termination reason: Instruction limit
% 13.86/2.21 % (2354326)Termination phase: Saturation
% 13.86/2.21 % (2354326)Time elapsed: 0.373 s
% 13.86/2.21 % (2354326)Peak memory usage: 17 MB
% 13.86/2.21 % (2354326)Instructions burned: 881 (million)
% 13.86/2.21 % Exception at run slice level
% 13.86/2.21 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 13.86/2.21 % (2354342)ott-2_1_sil=16000:newcnf=on:random_seed=2892373221:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2993 on theBenchmark for (2993ds/869Mi)
% 13.86/2.21 % (2354343)ott+10_1_sil=32000:tgt=ground:random_seed=217141332:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 13.86/2.21 % (2354342)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 13.86/2.21 % (2354320)Instruction limit reached!
% 13.86/2.21 % (2354320)------------------------------
% 13.86/2.21 % (2354320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.86/2.21 % (2354320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.86/2.21 % (2354320)CaDiCaL version: 2.1.3
% 13.86/2.21 % (2354320)Termination reason: Instruction limit
% 13.86/2.21 % (2354320)Termination phase: Saturation
% 13.86/2.21 % (2354320)Time elapsed: 0.632 s
% 13.86/2.21 % (2354320)Peak memory usage: 21 MB
% 13.86/2.21 % (2354320)Instructions burned: 1180 (million)
% 13.86/2.21 % (2354346)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=2527226998:i=54282_2991 on theBenchmark for (2991ds/54282Mi)
% 13.86/2.21 % Exception at run slice level
% 13.86/2.21 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 13.86/2.21 % (2354348)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3017691106:i=3512:aac=none_2990 on theBenchmark for (2990ds/3512Mi)
% 13.86/2.21 % (2354348)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 13.86/2.21 % (2354342)Instruction limit reached!
% 13.86/2.21 % (2354342)------------------------------
% 13.86/2.21 % (2354342)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.86/2.21 % (2354342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.86/2.21 % (2354342)CaDiCaL version: 2.1.3
% 13.86/2.21 % (2354342)Termination reason: Instruction limit
% 13.86/2.21 % (2354342)Termination phase: Saturation
% 13.86/2.21 % (2354342)Time elapsed: 0.364 s
% 13.86/2.21 % (2354342)Peak memory usage: 16 MB
% 13.86/2.21 % (2354342)Instructions burned: 870 (million)
% 13.86/2.21 % (2354350)dis+21_1_sil=32000:sas=cadical:random_seed=2432586223:i=3773:amm=off_2989 on theBenchmark for (2989ds/3773Mi)
% 13.86/2.21 % (2354335)Instruction limit reached!
% 13.86/2.21 % (2354335)------------------------------
% 13.86/2.21 % (2354335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.86/2.21 % (2354335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.86/2.21 % (2354335)CaDiCaL version: 2.1.3
% 13.86/2.21 % (2354335)Termination reason: Instruction limit
% 13.86/2.21 % (2354335)Termination phase: Saturation
% 13.86/2.21 % (2354335)Time elapsed: 0.741 s
% 13.86/2.21 % (2354335)Peak memory usage: 22 MB
% 13.86/2.21 % (2354335)Instructions burned: 1472 (million)
% 13.86/2.21 % (2354352)ott+11_1_sil=16000:gs=on:random_seed=4074956555:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2987 on theBenchmark for (2987ds/2251Mi)
% 13.86/2.21 % (2354352)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 13.86/2.21 % (2354296) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2354289-2354296"...
% 13.86/2.21 % (2354296)...printing done.
% 13.86/2.21 % (2354296)Refutation found. Thanks to Tanya!
% 13.86/2.21 % SZS status Theorem for theBenchmark
% 13.86/2.21 % SZS output start Proof for theBenchmark
% See solution above
% 13.86/2.24 % (2354296)------------------------------
% 13.86/2.24 % (2354296)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.86/2.24 % (2354296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.86/2.24 % (2354296)CaDiCaL version: 2.1.3
% 13.86/2.24 % (2354296)Termination reason: Refutation
% 13.86/2.24 % (2354296)Time elapsed: 1.930 s
% 13.86/2.24 % (2354296)Peak memory usage: 21 MB
% 13.86/2.24 % (2354296)Instructions burned: 7758 (million)
% 13.86/2.24 % (2354289)Success in time 1.996 s
% 13.86/2.24 % Vampire exiting
%------------------------------------------------------------------------------