%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO068^4.020 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:48:53 AM UTC 2026
% Result : Theorem 0.20s 0.34s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 50
% Syntax : Number of formulae : 763 ( 189 unt; 0 typ; 20 def)
% Number of atoms : 7994 (1612 equ; 0 cnn)
% Maximal formula atoms : 9 ( 10 avg)
% Number of connectives : 11819 ( 637 ~;1488 |; 0 &;7818 @)
% ( 20 <=>;1046 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 493 ( 493 >; 0 *; 0 +; 0 <<)
% Number of symbols : 137 ( 133 usr; 24 con; 0-4 aty)
% ( 810 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 2739 ( 0 sgn1080 !; 0 ?;2739 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
irel: $i > $i > $o ).
thf(func_def_2,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
iatom: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
inot: ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
itrue: $i > $o ).
thf(func_def_10,type,
ifalse: $i > $o ).
thf(func_def_11,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_16,type,
ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
ivalid: ( $i > $o ) > $o ).
thf(func_def_18,type,
isatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
icountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_20,type,
iinvalid: ( $i > $o ) > $o ).
thf(func_def_21,type,
p0: $i > $o ).
thf(func_def_22,type,
p1: $i > $o ).
thf(func_def_23,type,
p10: $i > $o ).
thf(func_def_24,type,
p11: $i > $o ).
thf(func_def_25,type,
p12: $i > $o ).
thf(func_def_26,type,
p13: $i > $o ).
thf(func_def_27,type,
p14: $i > $o ).
thf(func_def_28,type,
p15: $i > $o ).
thf(func_def_29,type,
p16: $i > $o ).
thf(func_def_30,type,
p17: $i > $o ).
thf(func_def_31,type,
p18: $i > $o ).
thf(func_def_32,type,
p19: $i > $o ).
thf(func_def_33,type,
p2: $i > $o ).
thf(func_def_34,type,
p20: $i > $o ).
thf(func_def_35,type,
p3: $i > $o ).
thf(func_def_36,type,
p4: $i > $o ).
thf(func_def_37,type,
p5: $i > $o ).
thf(func_def_38,type,
p6: $i > $o ).
thf(func_def_39,type,
p7: $i > $o ).
thf(func_def_40,type,
p8: $i > $o ).
thf(func_def_41,type,
p9: $i > $o ).
thf(func_def_44,type,
vNOT: $o > $o ).
thf(func_def_45,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_48,type,
vOR: $o > $o > $o ).
thf(func_def_49,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vAND: $o > $o > $o ).
thf(func_def_51,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_52,type,
vIMP: $o > $o > $o ).
thf(func_def_53,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_55,type,
sK1: $i > $i ).
thf(func_def_56,type,
sK2: $i > $i ).
thf(func_def_57,type,
sK3: $i > $i ).
thf(func_def_58,type,
sK4: $i > $i ).
thf(func_def_59,type,
sK5: $i > $i ).
thf(func_def_60,type,
sK6: $i > $i ).
thf(func_def_61,type,
sK7: $i > $i ).
thf(func_def_62,type,
sK8: $i > $i ).
thf(func_def_63,type,
sK9: $i > $i ).
thf(func_def_64,type,
sK10: $i > $i ).
thf(func_def_65,type,
sK11: $i > $i ).
thf(func_def_66,type,
sK12: $i > $i ).
thf(func_def_67,type,
sK13: $i > $i ).
thf(func_def_68,type,
sK14: $i > $i ).
thf(func_def_69,type,
sK15: $i > $i ).
thf(func_def_70,type,
sK16: $i > $i ).
thf(func_def_71,type,
sK17: $i > $i ).
thf(func_def_72,type,
sK18: $i > $i ).
thf(func_def_73,type,
sK19: $i > $i ).
thf(func_def_74,type,
sK20: $i > $i ).
thf(func_def_75,type,
sK21: $i > $i ).
thf(func_def_76,type,
sK22: $i > $i ).
thf(func_def_77,type,
sK23: $i > $i ).
thf(func_def_78,type,
sK24: $i > $i ).
thf(func_def_79,type,
sK25: $i > $i ).
thf(func_def_80,type,
sK26: $i > $i ).
thf(func_def_81,type,
sK27: $i > $i ).
thf(func_def_82,type,
sK28: $i > $i ).
thf(func_def_83,type,
sK29: $i > $i ).
thf(func_def_84,type,
sK30: $i > $i ).
thf(func_def_85,type,
sK31: $i > $i ).
thf(func_def_86,type,
sK32: $i > $i ).
thf(func_def_87,type,
sK33: $i > $i ).
thf(func_def_88,type,
sK34: $i > $i ).
thf(func_def_89,type,
sK35: $i > $i ).
thf(func_def_90,type,
sK36: $i > $i ).
thf(func_def_91,type,
sK37: $i > $i ).
thf(func_def_92,type,
sK38: $i > $i ).
thf(func_def_93,type,
sK39: $i > $i ).
thf(func_def_94,type,
sK40: $i > $i ).
thf(func_def_95,type,
sK41: $i > $i ).
thf(func_def_96,type,
sK42: $i > $i ).
thf(func_def_97,type,
sK43: $i > $i ).
thf(func_def_98,type,
sK44: $i > $i ).
thf(func_def_99,type,
sK45: $i > $i ).
thf(func_def_100,type,
sK46: $i > $i ).
thf(func_def_101,type,
sK47: $i > $i ).
thf(func_def_102,type,
sK48: $i > $i ).
thf(func_def_103,type,
sK49: $i > $i ).
thf(func_def_104,type,
sK50: $i > $i ).
thf(func_def_105,type,
sK51: $i > $i ).
thf(func_def_106,type,
sK52: $i > $i ).
thf(func_def_107,type,
sK53: $i > $i ).
thf(func_def_108,type,
sK54: $i > $i ).
thf(func_def_109,type,
sK55: $i > $i ).
thf(func_def_110,type,
sK56: $i > $i ).
thf(func_def_111,type,
sK57: $i > $i ).
thf(func_def_112,type,
sK58: $i > $i ).
thf(func_def_113,type,
sK59: $i > $i ).
thf(func_def_114,type,
sK60: $i > $i ).
thf(f1,axiom,
! [X0: $i] : ( irel @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',refl_axiom) ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mimplies) ).
thf(f7,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).
thf(f8,axiom,
( iatom
= ( ^ [X0: $i > $o] : X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iatom) ).
thf(f14,axiom,
( iimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mimplies @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iimplies) ).
thf(f18,axiom,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,axiom,
ivalid @ ( iatom @ p20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1) ).
thf(f23,axiom,
ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2) ).
thf(f24,axiom,
ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom3) ).
thf(f25,axiom,
ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom4) ).
thf(f26,axiom,
ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom5) ).
thf(f27,axiom,
ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom6) ).
thf(f28,axiom,
ivalid @ ( iimplies @ ( iatom @ p6 ) @ ( iimplies @ ( iatom @ p6 ) @ ( iatom @ p5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom7) ).
thf(f29,axiom,
ivalid @ ( iimplies @ ( iatom @ p7 ) @ ( iimplies @ ( iatom @ p7 ) @ ( iatom @ p6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom8) ).
thf(f30,axiom,
ivalid @ ( iimplies @ ( iatom @ p8 ) @ ( iimplies @ ( iatom @ p8 ) @ ( iatom @ p7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom9) ).
thf(f31,axiom,
ivalid @ ( iimplies @ ( iatom @ p9 ) @ ( iimplies @ ( iatom @ p9 ) @ ( iatom @ p8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom10) ).
thf(f32,axiom,
ivalid @ ( iimplies @ ( iatom @ p10 ) @ ( iimplies @ ( iatom @ p10 ) @ ( iatom @ p9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom11) ).
thf(f33,axiom,
ivalid @ ( iimplies @ ( iatom @ p11 ) @ ( iimplies @ ( iatom @ p11 ) @ ( iatom @ p10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom12) ).
thf(f34,axiom,
ivalid @ ( iimplies @ ( iatom @ p12 ) @ ( iimplies @ ( iatom @ p12 ) @ ( iatom @ p11 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom13) ).
thf(f35,axiom,
ivalid @ ( iimplies @ ( iatom @ p13 ) @ ( iimplies @ ( iatom @ p13 ) @ ( iatom @ p12 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom14) ).
thf(f36,axiom,
ivalid @ ( iimplies @ ( iatom @ p14 ) @ ( iimplies @ ( iatom @ p14 ) @ ( iatom @ p13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom15) ).
thf(f37,axiom,
ivalid @ ( iimplies @ ( iatom @ p15 ) @ ( iimplies @ ( iatom @ p15 ) @ ( iatom @ p14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom16) ).
thf(f38,axiom,
ivalid @ ( iimplies @ ( iatom @ p16 ) @ ( iimplies @ ( iatom @ p16 ) @ ( iatom @ p15 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom17) ).
thf(f39,axiom,
ivalid @ ( iimplies @ ( iatom @ p17 ) @ ( iimplies @ ( iatom @ p17 ) @ ( iatom @ p16 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom18) ).
thf(f40,axiom,
ivalid @ ( iimplies @ ( iatom @ p18 ) @ ( iimplies @ ( iatom @ p18 ) @ ( iatom @ p17 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom19) ).
thf(f41,axiom,
ivalid @ ( iimplies @ ( iatom @ p19 ) @ ( iimplies @ ( iatom @ p19 ) @ ( iatom @ p18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom20) ).
thf(f42,axiom,
ivalid @ ( iimplies @ ( iatom @ p20 ) @ ( iimplies @ ( iatom @ p20 ) @ ( iatom @ p19 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom21) ).
thf(f43,conjecture,
ivalid @ ( iatom @ p0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f44,negated_conjecture,
~ ( ivalid @ ( iatom @ p0 ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
thf(f45,plain,
! [X0: $i] : ( irel @ X0 @ X0 ),
inference(rectify,[],[f1]) ).
thf(f46,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f45]) ).
thf(f49,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f50,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f51,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f52,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f55,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f56,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f57,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f58,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f63,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f67,plain,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f68,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f75,plain,
ivalid @ ( iatom @ p20 ),
inference(rectify,[],[f22]) ).
thf(f76,plain,
( ( ivalid @ ( iatom @ p20 ) )
= $true ),
inference(fool_elimination,[],[f75]) ).
thf(f77,plain,
ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ),
inference(rectify,[],[f23]) ).
thf(f78,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ) )
= $true ),
inference(fool_elimination,[],[f77]) ).
thf(f79,plain,
ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ),
inference(rectify,[],[f24]) ).
thf(f80,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ) )
= $true ),
inference(fool_elimination,[],[f79]) ).
thf(f81,plain,
ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ),
inference(rectify,[],[f25]) ).
thf(f82,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ) )
= $true ),
inference(fool_elimination,[],[f81]) ).
thf(f83,plain,
ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ),
inference(rectify,[],[f26]) ).
thf(f84,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ) )
= $true ),
inference(fool_elimination,[],[f83]) ).
thf(f85,plain,
ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ),
inference(rectify,[],[f27]) ).
thf(f86,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ) )
= $true ),
inference(fool_elimination,[],[f85]) ).
thf(f87,plain,
ivalid @ ( iimplies @ ( iatom @ p6 ) @ ( iimplies @ ( iatom @ p6 ) @ ( iatom @ p5 ) ) ),
inference(rectify,[],[f28]) ).
thf(f88,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p6 ) @ ( iimplies @ ( iatom @ p6 ) @ ( iatom @ p5 ) ) ) )
= $true ),
inference(fool_elimination,[],[f87]) ).
thf(f89,plain,
ivalid @ ( iimplies @ ( iatom @ p7 ) @ ( iimplies @ ( iatom @ p7 ) @ ( iatom @ p6 ) ) ),
inference(rectify,[],[f29]) ).
thf(f90,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p7 ) @ ( iimplies @ ( iatom @ p7 ) @ ( iatom @ p6 ) ) ) )
= $true ),
inference(fool_elimination,[],[f89]) ).
thf(f91,plain,
ivalid @ ( iimplies @ ( iatom @ p8 ) @ ( iimplies @ ( iatom @ p8 ) @ ( iatom @ p7 ) ) ),
inference(rectify,[],[f30]) ).
thf(f92,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p8 ) @ ( iimplies @ ( iatom @ p8 ) @ ( iatom @ p7 ) ) ) )
= $true ),
inference(fool_elimination,[],[f91]) ).
thf(f93,plain,
ivalid @ ( iimplies @ ( iatom @ p9 ) @ ( iimplies @ ( iatom @ p9 ) @ ( iatom @ p8 ) ) ),
inference(rectify,[],[f31]) ).
thf(f94,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p9 ) @ ( iimplies @ ( iatom @ p9 ) @ ( iatom @ p8 ) ) ) )
= $true ),
inference(fool_elimination,[],[f93]) ).
thf(f95,plain,
ivalid @ ( iimplies @ ( iatom @ p10 ) @ ( iimplies @ ( iatom @ p10 ) @ ( iatom @ p9 ) ) ),
inference(rectify,[],[f32]) ).
thf(f96,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p10 ) @ ( iimplies @ ( iatom @ p10 ) @ ( iatom @ p9 ) ) ) )
= $true ),
inference(fool_elimination,[],[f95]) ).
thf(f97,plain,
ivalid @ ( iimplies @ ( iatom @ p11 ) @ ( iimplies @ ( iatom @ p11 ) @ ( iatom @ p10 ) ) ),
inference(rectify,[],[f33]) ).
thf(f98,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p11 ) @ ( iimplies @ ( iatom @ p11 ) @ ( iatom @ p10 ) ) ) )
= $true ),
inference(fool_elimination,[],[f97]) ).
thf(f99,plain,
ivalid @ ( iimplies @ ( iatom @ p12 ) @ ( iimplies @ ( iatom @ p12 ) @ ( iatom @ p11 ) ) ),
inference(rectify,[],[f34]) ).
thf(f100,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p12 ) @ ( iimplies @ ( iatom @ p12 ) @ ( iatom @ p11 ) ) ) )
= $true ),
inference(fool_elimination,[],[f99]) ).
thf(f101,plain,
ivalid @ ( iimplies @ ( iatom @ p13 ) @ ( iimplies @ ( iatom @ p13 ) @ ( iatom @ p12 ) ) ),
inference(rectify,[],[f35]) ).
thf(f102,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p13 ) @ ( iimplies @ ( iatom @ p13 ) @ ( iatom @ p12 ) ) ) )
= $true ),
inference(fool_elimination,[],[f101]) ).
thf(f103,plain,
ivalid @ ( iimplies @ ( iatom @ p14 ) @ ( iimplies @ ( iatom @ p14 ) @ ( iatom @ p13 ) ) ),
inference(rectify,[],[f36]) ).
thf(f104,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p14 ) @ ( iimplies @ ( iatom @ p14 ) @ ( iatom @ p13 ) ) ) )
= $true ),
inference(fool_elimination,[],[f103]) ).
thf(f105,plain,
ivalid @ ( iimplies @ ( iatom @ p15 ) @ ( iimplies @ ( iatom @ p15 ) @ ( iatom @ p14 ) ) ),
inference(rectify,[],[f37]) ).
thf(f106,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p15 ) @ ( iimplies @ ( iatom @ p15 ) @ ( iatom @ p14 ) ) ) )
= $true ),
inference(fool_elimination,[],[f105]) ).
thf(f107,plain,
ivalid @ ( iimplies @ ( iatom @ p16 ) @ ( iimplies @ ( iatom @ p16 ) @ ( iatom @ p15 ) ) ),
inference(rectify,[],[f38]) ).
thf(f108,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p16 ) @ ( iimplies @ ( iatom @ p16 ) @ ( iatom @ p15 ) ) ) )
= $true ),
inference(fool_elimination,[],[f107]) ).
thf(f109,plain,
ivalid @ ( iimplies @ ( iatom @ p17 ) @ ( iimplies @ ( iatom @ p17 ) @ ( iatom @ p16 ) ) ),
inference(rectify,[],[f39]) ).
thf(f110,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p17 ) @ ( iimplies @ ( iatom @ p17 ) @ ( iatom @ p16 ) ) ) )
= $true ),
inference(fool_elimination,[],[f109]) ).
thf(f111,plain,
ivalid @ ( iimplies @ ( iatom @ p18 ) @ ( iimplies @ ( iatom @ p18 ) @ ( iatom @ p17 ) ) ),
inference(rectify,[],[f40]) ).
thf(f112,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p18 ) @ ( iimplies @ ( iatom @ p18 ) @ ( iatom @ p17 ) ) ) )
= $true ),
inference(fool_elimination,[],[f111]) ).
thf(f113,plain,
ivalid @ ( iimplies @ ( iatom @ p19 ) @ ( iimplies @ ( iatom @ p19 ) @ ( iatom @ p18 ) ) ),
inference(rectify,[],[f41]) ).
thf(f114,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p19 ) @ ( iimplies @ ( iatom @ p19 ) @ ( iatom @ p18 ) ) ) )
= $true ),
inference(fool_elimination,[],[f113]) ).
thf(f115,plain,
ivalid @ ( iimplies @ ( iatom @ p20 ) @ ( iimplies @ ( iatom @ p20 ) @ ( iatom @ p19 ) ) ),
inference(rectify,[],[f42]) ).
thf(f116,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p20 ) @ ( iimplies @ ( iatom @ p20 ) @ ( iatom @ p19 ) ) ) )
= $true ),
inference(fool_elimination,[],[f115]) ).
thf(f117,plain,
~ ( ivalid @ ( iatom @ p0 ) ),
inference(rectify,[],[f44]) ).
thf(f118,plain,
( ( ivalid @ ( iatom @ p0 ) )
!= $true ),
inference(fool_elimination,[],[f117]) ).
thf(f119,plain,
( ( ivalid @ ( iatom @ p0 ) )
!= $true ),
inference(flattening,[],[f118]) ).
thf(f122,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f46]) ).
thf(f124,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f125,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f127,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f128,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f129,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f135,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f139,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f143,plain,
( ( ivalid @ ( iatom @ p20 ) )
= $true ),
inference(cnf_transformation,[],[f76]) ).
thf(f144,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f78]) ).
thf(f145,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f80]) ).
thf(f146,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f82]) ).
thf(f147,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f84]) ).
thf(f148,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f86]) ).
thf(f149,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p6 ) @ ( iimplies @ ( iatom @ p6 ) @ ( iatom @ p5 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f88]) ).
thf(f150,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p7 ) @ ( iimplies @ ( iatom @ p7 ) @ ( iatom @ p6 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f90]) ).
thf(f151,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p8 ) @ ( iimplies @ ( iatom @ p8 ) @ ( iatom @ p7 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f92]) ).
thf(f152,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p9 ) @ ( iimplies @ ( iatom @ p9 ) @ ( iatom @ p8 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f94]) ).
thf(f153,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p10 ) @ ( iimplies @ ( iatom @ p10 ) @ ( iatom @ p9 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f96]) ).
thf(f154,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p11 ) @ ( iimplies @ ( iatom @ p11 ) @ ( iatom @ p10 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f155,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p12 ) @ ( iimplies @ ( iatom @ p12 ) @ ( iatom @ p11 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f100]) ).
thf(f156,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p13 ) @ ( iimplies @ ( iatom @ p13 ) @ ( iatom @ p12 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f102]) ).
thf(f157,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p14 ) @ ( iimplies @ ( iatom @ p14 ) @ ( iatom @ p13 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f104]) ).
thf(f158,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p15 ) @ ( iimplies @ ( iatom @ p15 ) @ ( iatom @ p14 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f106]) ).
thf(f159,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p16 ) @ ( iimplies @ ( iatom @ p16 ) @ ( iatom @ p15 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f108]) ).
thf(f160,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p17 ) @ ( iimplies @ ( iatom @ p17 ) @ ( iatom @ p16 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f110]) ).
thf(f161,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p18 ) @ ( iimplies @ ( iatom @ p18 ) @ ( iatom @ p17 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f112]) ).
thf(f162,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p19 ) @ ( iimplies @ ( iatom @ p19 ) @ ( iatom @ p18 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f114]) ).
thf(f163,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p20 ) @ ( iimplies @ ( iatom @ p20 ) @ ( iatom @ p19 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f116]) ).
thf(f164,plain,
( ( ivalid @ ( iatom @ p0 ) )
!= $true ),
inference(cnf_transformation,[],[f119]) ).
thf(f167,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f127,f125,f124]) ).
thf(f172,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f135,f167,f128,f128]) ).
thf(f176,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p20 ) ) ),
inference(definition_unfolding,[],[f143,f139,f129]) ).
thf(f177,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p1 )
@ ( ^ [Y0: $i > $o] : Y0
@ p0 ) ) ) ) ),
inference(definition_unfolding,[],[f144,f139,f172,f129,f172,f129,f129]) ).
thf(f178,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p2 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p2 )
@ ( ^ [Y0: $i > $o] : Y0
@ p1 ) ) ) ) ),
inference(definition_unfolding,[],[f145,f139,f172,f129,f172,f129,f129]) ).
thf(f179,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p3 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p3 )
@ ( ^ [Y0: $i > $o] : Y0
@ p2 ) ) ) ) ),
inference(definition_unfolding,[],[f146,f139,f172,f129,f172,f129,f129]) ).
thf(f180,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p4 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p4 )
@ ( ^ [Y0: $i > $o] : Y0
@ p3 ) ) ) ) ),
inference(definition_unfolding,[],[f147,f139,f172,f129,f172,f129,f129]) ).
thf(f181,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p5 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p5 )
@ ( ^ [Y0: $i > $o] : Y0
@ p4 ) ) ) ) ),
inference(definition_unfolding,[],[f148,f139,f172,f129,f172,f129,f129]) ).
thf(f182,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p6 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p6 )
@ ( ^ [Y0: $i > $o] : Y0
@ p5 ) ) ) ) ),
inference(definition_unfolding,[],[f149,f139,f172,f129,f172,f129,f129]) ).
thf(f183,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p7 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p7 )
@ ( ^ [Y0: $i > $o] : Y0
@ p6 ) ) ) ) ),
inference(definition_unfolding,[],[f150,f139,f172,f129,f172,f129,f129]) ).
thf(f184,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p8 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p8 )
@ ( ^ [Y0: $i > $o] : Y0
@ p7 ) ) ) ) ),
inference(definition_unfolding,[],[f151,f139,f172,f129,f172,f129,f129]) ).
thf(f185,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p9 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p9 )
@ ( ^ [Y0: $i > $o] : Y0
@ p8 ) ) ) ) ),
inference(definition_unfolding,[],[f152,f139,f172,f129,f172,f129,f129]) ).
thf(f186,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p10 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p10 )
@ ( ^ [Y0: $i > $o] : Y0
@ p9 ) ) ) ) ),
inference(definition_unfolding,[],[f153,f139,f172,f129,f172,f129,f129]) ).
thf(f187,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p11 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p11 )
@ ( ^ [Y0: $i > $o] : Y0
@ p10 ) ) ) ) ),
inference(definition_unfolding,[],[f154,f139,f172,f129,f172,f129,f129]) ).
thf(f188,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p12 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p12 )
@ ( ^ [Y0: $i > $o] : Y0
@ p11 ) ) ) ) ),
inference(definition_unfolding,[],[f155,f139,f172,f129,f172,f129,f129]) ).
thf(f189,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p13 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p13 )
@ ( ^ [Y0: $i > $o] : Y0
@ p12 ) ) ) ) ),
inference(definition_unfolding,[],[f156,f139,f172,f129,f172,f129,f129]) ).
thf(f190,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p14 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p14 )
@ ( ^ [Y0: $i > $o] : Y0
@ p13 ) ) ) ) ),
inference(definition_unfolding,[],[f157,f139,f172,f129,f172,f129,f129]) ).
thf(f191,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p15 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p15 )
@ ( ^ [Y0: $i > $o] : Y0
@ p14 ) ) ) ) ),
inference(definition_unfolding,[],[f158,f139,f172,f129,f172,f129,f129]) ).
thf(f192,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p16 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p16 )
@ ( ^ [Y0: $i > $o] : Y0
@ p15 ) ) ) ) ),
inference(definition_unfolding,[],[f159,f139,f172,f129,f172,f129,f129]) ).
thf(f193,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p17 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p17 )
@ ( ^ [Y0: $i > $o] : Y0
@ p16 ) ) ) ) ),
inference(definition_unfolding,[],[f160,f139,f172,f129,f172,f129,f129]) ).
thf(f194,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p18 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p18 )
@ ( ^ [Y0: $i > $o] : Y0
@ p17 ) ) ) ) ),
inference(definition_unfolding,[],[f161,f139,f172,f129,f172,f129,f129]) ).
thf(f195,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p19 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p19 )
@ ( ^ [Y0: $i > $o] : Y0
@ p18 ) ) ) ) ),
inference(definition_unfolding,[],[f162,f139,f172,f129,f172,f129,f129]) ).
thf(f196,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p20 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p20 )
@ ( ^ [Y0: $i > $o] : Y0
@ p19 ) ) ) ) ),
inference(definition_unfolding,[],[f163,f139,f172,f129,f172,f129,f129]) ).
thf(f197,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p0 ) ) ),
inference(definition_unfolding,[],[f164,f139,f129]) ).
thf(f198,plain,
( $true
!= ( !! @ $i @ p0 ) ),
inference(beta-eta_normalization,[],[f197]) ).
thf(f199,plain,
( $false
= ( p0 @ sK0 ) ),
inference(sigma_proxy_clausification,[],[f198]) ).
thf(f200,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p20 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p20 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p19 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f196]) ).
thf(f201,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p20 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p20 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p19 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p20 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p20 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f203,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p20 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p20 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p20 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p20 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p20 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p20 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p20 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p20 @ Y0 ) )
@ ( sK1 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p20 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK1 @ X1 ) )
=> ( p20 @ ( sK1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f206]) ).
thf(f208,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK1 @ X1 ) )
=> ( p20 @ ( sK1 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p20 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p20 @ ( sK1 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p20 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f208]) ).
thf(f219,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p20 @ ( sK1 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p20 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f209]) ).
thf(f220,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p20 @ ( sK1 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p20 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p20 @ ( sK1 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p20 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p20 @ ( sK1 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p20 @ Y0 ) )
@ ( sK3 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p20 @ ( sK1 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p19 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK3 @ X2 ) )
=> ( p20 @ ( sK3 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f222]) ).
thf(f224,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p20 @ ( sK1 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK3 @ X2 ) )
=> ( p20 @ ( sK3 @ X2 ) ) ) )
| ( $true
= ( p19 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p20 @ ( sK1 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p20 @ ( sK3 @ X2 ) ) )
| ( $true
= ( p19 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f224]) ).
thf(f227,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p19 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p18 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f195]) ).
thf(f228,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p19 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p18 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p19 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f228]) ).
thf(f230,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p19 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p19 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p19 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p19 @ Y0 ) )
@ ( sK4 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK4 @ X1 ) )
=> ( p19 @ ( sK4 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f233]) ).
thf(f235,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK4 @ X1 ) )
=> ( p19 @ ( sK4 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f234]) ).
thf(f236,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p19 @ ( sK4 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f235]) ).
thf(f246,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p19 @ ( sK4 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f236]) ).
thf(f247,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p19 @ ( sK4 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f246]) ).
thf(f248,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p19 @ ( sK4 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f247]) ).
thf(f249,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p19 @ ( sK4 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) )
@ ( sK6 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f248]) ).
thf(f250,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p19 @ ( sK4 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p18 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK6 @ X2 ) )
=> ( p19 @ ( sK6 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f249]) ).
thf(f251,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p19 @ ( sK4 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK6 @ X2 ) )
=> ( p19 @ ( sK6 @ X2 ) ) ) )
| ( $true
= ( p18 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f250]) ).
thf(f252,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p19 @ ( sK4 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p19 @ ( sK6 @ X2 ) ) )
| ( $true
= ( p18 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f251]) ).
thf(f254,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p18 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p17 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f194]) ).
thf(f255,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p18 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p17 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f254]) ).
thf(f256,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p18 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f255]) ).
thf(f257,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p18 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f256]) ).
thf(f258,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p18 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f257]) ).
thf(f259,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p18 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f258]) ).
thf(f260,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p18 @ Y0 ) )
@ ( sK7 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f259]) ).
thf(f261,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK7 @ X1 ) )
=> ( p18 @ ( sK7 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f260]) ).
thf(f262,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK7 @ X1 ) )
=> ( p18 @ ( sK7 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f261]) ).
thf(f263,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p18 @ ( sK7 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f262]) ).
thf(f273,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p18 @ ( sK7 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f263]) ).
thf(f274,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p18 @ ( sK7 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f273]) ).
thf(f275,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p18 @ ( sK7 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f274]) ).
thf(f276,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p18 @ ( sK7 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) )
@ ( sK9 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f275]) ).
thf(f277,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p18 @ ( sK7 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p17 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK9 @ X2 ) )
=> ( p18 @ ( sK9 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f276]) ).
thf(f278,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p18 @ ( sK7 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK9 @ X2 ) )
=> ( p18 @ ( sK9 @ X2 ) ) ) )
| ( $true
= ( p17 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f277]) ).
thf(f279,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p18 @ ( sK7 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p18 @ ( sK9 @ X2 ) ) )
| ( $true
= ( p17 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f278]) ).
thf(f281,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p17 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p16 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f193]) ).
thf(f282,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p17 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p16 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f281]) ).
thf(f283,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p17 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f282]) ).
thf(f284,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p17 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f283]) ).
thf(f285,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p17 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f284]) ).
thf(f286,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p17 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f285]) ).
thf(f287,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p17 @ Y0 ) )
@ ( sK10 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f286]) ).
thf(f288,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK10 @ X1 ) )
=> ( p17 @ ( sK10 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f287]) ).
thf(f289,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK10 @ X1 ) )
=> ( p17 @ ( sK10 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f288]) ).
thf(f290,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p17 @ ( sK10 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f289]) ).
thf(f300,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p17 @ ( sK10 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f290]) ).
thf(f301,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p17 @ ( sK10 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f300]) ).
thf(f302,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p17 @ ( sK10 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f301]) ).
thf(f303,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p17 @ ( sK10 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) )
@ ( sK12 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f302]) ).
thf(f304,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p17 @ ( sK10 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p16 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK12 @ X2 ) )
=> ( p17 @ ( sK12 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f303]) ).
thf(f305,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p17 @ ( sK10 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK12 @ X2 ) )
=> ( p17 @ ( sK12 @ X2 ) ) ) )
| ( $true
= ( p16 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f304]) ).
thf(f306,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p17 @ ( sK10 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p17 @ ( sK12 @ X2 ) ) )
| ( $true
= ( p16 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f305]) ).
thf(f308,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p16 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p15 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f309,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p16 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p15 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f308]) ).
thf(f310,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p16 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p15 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f309]) ).
thf(f311,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p15 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p16 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f310]) ).
thf(f312,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p15 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p16 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f311]) ).
thf(f313,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p15 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p16 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f312]) ).
thf(f314,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p15 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p16 @ Y0 ) )
@ ( sK13 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f313]) ).
thf(f315,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK13 @ X1 ) )
=> ( p16 @ ( sK13 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f314]) ).
thf(f316,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK13 @ X1 ) )
=> ( p16 @ ( sK13 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f315]) ).
thf(f317,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p16 @ ( sK13 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f316]) ).
thf(f327,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p16 @ ( sK13 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f317]) ).
thf(f328,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p16 @ ( sK13 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f327]) ).
thf(f329,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p16 @ ( sK13 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f328]) ).
thf(f330,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p16 @ ( sK13 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) )
@ ( sK15 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f329]) ).
thf(f331,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p16 @ ( sK13 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p15 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK15 @ X2 ) )
=> ( p16 @ ( sK15 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f330]) ).
thf(f332,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p16 @ ( sK13 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK15 @ X2 ) )
=> ( p16 @ ( sK15 @ X2 ) ) ) )
| ( $true
= ( p15 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f331]) ).
thf(f333,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p16 @ ( sK13 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p16 @ ( sK15 @ X2 ) ) )
| ( $true
= ( p15 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f332]) ).
thf(f335,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p15 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p15 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p14 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f336,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p15 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p15 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p14 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f335]) ).
thf(f337,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p15 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p15 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p14 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f336]) ).
thf(f338,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p15 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p14 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p15 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f337]) ).
thf(f339,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p15 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p14 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p15 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f338]) ).
thf(f340,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p15 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p14 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p15 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f339]) ).
thf(f341,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p15 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p14 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p15 @ Y0 ) )
@ ( sK16 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f340]) ).
thf(f342,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK16 @ X1 ) )
=> ( p15 @ ( sK16 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f341]) ).
thf(f343,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK16 @ X1 ) )
=> ( p15 @ ( sK16 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f342]) ).
thf(f344,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p15 @ ( sK16 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f343]) ).
thf(f354,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p15 @ ( sK16 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f344]) ).
thf(f355,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p15 @ ( sK16 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f354]) ).
thf(f356,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p15 @ ( sK16 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f355]) ).
thf(f357,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p15 @ ( sK16 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) )
@ ( sK18 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f356]) ).
thf(f358,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p15 @ ( sK16 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p14 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK18 @ X2 ) )
=> ( p15 @ ( sK18 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f357]) ).
thf(f359,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p15 @ ( sK16 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK18 @ X2 ) )
=> ( p15 @ ( sK18 @ X2 ) ) ) )
| ( $true
= ( p14 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f358]) ).
thf(f360,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p15 @ ( sK16 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p15 @ ( sK18 @ X2 ) ) )
| ( $true
= ( p14 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f359]) ).
thf(f362,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p14 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p14 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p13 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f190]) ).
thf(f363,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p14 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p14 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p13 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f362]) ).
thf(f364,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p14 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p14 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p13 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f363]) ).
thf(f365,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p14 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p13 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p14 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f364]) ).
thf(f366,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p14 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p13 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p14 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f365]) ).
thf(f367,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p14 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p13 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p14 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f366]) ).
thf(f368,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p14 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p13 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p14 @ Y0 ) )
@ ( sK19 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f367]) ).
thf(f369,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK19 @ X1 ) )
=> ( p14 @ ( sK19 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f368]) ).
thf(f370,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK19 @ X1 ) )
=> ( p14 @ ( sK19 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f369]) ).
thf(f371,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p14 @ ( sK19 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f370]) ).
thf(f381,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p14 @ ( sK19 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f371]) ).
thf(f382,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p14 @ ( sK19 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f381]) ).
thf(f383,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p14 @ ( sK19 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f382]) ).
thf(f384,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p14 @ ( sK19 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) )
@ ( sK21 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f383]) ).
thf(f385,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p14 @ ( sK19 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p13 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK21 @ X2 ) )
=> ( p14 @ ( sK21 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f384]) ).
thf(f386,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p14 @ ( sK19 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK21 @ X2 ) )
=> ( p14 @ ( sK21 @ X2 ) ) ) )
| ( $true
= ( p13 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f385]) ).
thf(f387,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p14 @ ( sK19 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p14 @ ( sK21 @ X2 ) ) )
| ( $true
= ( p13 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f386]) ).
thf(f389,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p13 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p13 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p12 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f189]) ).
thf(f390,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p13 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p13 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p12 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f389]) ).
thf(f391,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p13 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p13 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f390]) ).
thf(f392,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p13 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p13 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f391]) ).
thf(f393,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p13 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p13 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f392]) ).
thf(f394,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p13 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p13 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f393]) ).
thf(f395,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p13 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p13 @ Y0 ) )
@ ( sK22 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f394]) ).
thf(f396,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK22 @ X1 ) )
=> ( p13 @ ( sK22 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f395]) ).
thf(f397,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK22 @ X1 ) )
=> ( p13 @ ( sK22 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f396]) ).
thf(f398,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p13 @ ( sK22 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f397]) ).
thf(f408,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p13 @ ( sK22 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f398]) ).
thf(f409,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p13 @ ( sK22 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f408]) ).
thf(f410,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p13 @ ( sK22 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f409]) ).
thf(f411,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p13 @ ( sK22 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) )
@ ( sK24 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f410]) ).
thf(f412,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p13 @ ( sK22 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p12 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK24 @ X2 ) )
=> ( p13 @ ( sK24 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f411]) ).
thf(f413,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p13 @ ( sK22 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK24 @ X2 ) )
=> ( p13 @ ( sK24 @ X2 ) ) ) )
| ( $true
= ( p12 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f412]) ).
thf(f414,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p13 @ ( sK22 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p13 @ ( sK24 @ X2 ) ) )
| ( $true
= ( p12 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f413]) ).
thf(f416,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p12 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p11 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f188]) ).
thf(f417,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p12 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p11 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f416]) ).
thf(f418,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p12 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p11 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f417]) ).
thf(f419,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p11 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p12 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f418]) ).
thf(f420,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p11 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p12 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f419]) ).
thf(f421,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p11 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p12 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f420]) ).
thf(f422,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p11 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p12 @ Y0 ) )
@ ( sK25 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f421]) ).
thf(f423,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK25 @ X1 ) )
=> ( p12 @ ( sK25 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f422]) ).
thf(f424,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK25 @ X1 ) )
=> ( p12 @ ( sK25 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f423]) ).
thf(f425,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p12 @ ( sK25 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f424]) ).
thf(f435,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p12 @ ( sK25 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f425]) ).
thf(f436,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p12 @ ( sK25 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f435]) ).
thf(f437,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p12 @ ( sK25 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f436]) ).
thf(f438,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p12 @ ( sK25 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) )
@ ( sK27 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f437]) ).
thf(f439,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p12 @ ( sK25 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p11 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK27 @ X2 ) )
=> ( p12 @ ( sK27 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f438]) ).
thf(f440,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p12 @ ( sK25 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK27 @ X2 ) )
=> ( p12 @ ( sK27 @ X2 ) ) ) )
| ( $true
= ( p11 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f439]) ).
thf(f441,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p12 @ ( sK25 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p12 @ ( sK27 @ X2 ) ) )
| ( $true
= ( p11 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f440]) ).
thf(f443,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p11 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p11 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p10 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f444,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p11 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p11 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p10 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f443]) ).
thf(f445,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p11 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p11 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f444]) ).
thf(f446,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p11 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p11 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f445]) ).
thf(f447,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p11 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p11 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f446]) ).
thf(f448,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p11 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p11 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f447]) ).
thf(f449,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p11 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p11 @ Y0 ) )
@ ( sK28 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f448]) ).
thf(f450,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK28 @ X1 ) )
=> ( p11 @ ( sK28 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f449]) ).
thf(f451,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK28 @ X1 ) )
=> ( p11 @ ( sK28 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f450]) ).
thf(f452,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p11 @ ( sK28 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f451]) ).
thf(f462,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p11 @ ( sK28 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f452]) ).
thf(f463,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p11 @ ( sK28 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f462]) ).
thf(f464,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p11 @ ( sK28 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f463]) ).
thf(f465,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p11 @ ( sK28 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) )
@ ( sK30 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f464]) ).
thf(f466,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p11 @ ( sK28 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p10 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK30 @ X2 ) )
=> ( p11 @ ( sK30 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f465]) ).
thf(f467,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p11 @ ( sK28 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK30 @ X2 ) )
=> ( p11 @ ( sK30 @ X2 ) ) ) )
| ( $true
= ( p10 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f466]) ).
thf(f468,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p11 @ ( sK28 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p11 @ ( sK30 @ X2 ) ) )
| ( $true
= ( p10 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f467]) ).
thf(f470,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p10 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p9 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f471,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p10 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p9 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f470]) ).
thf(f472,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p10 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f471]) ).
thf(f473,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f472]) ).
thf(f474,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f473]) ).
thf(f475,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f474]) ).
thf(f476,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p10 @ Y0 ) )
@ ( sK31 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f475]) ).
thf(f477,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK31 @ X1 ) )
=> ( p10 @ ( sK31 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f476]) ).
thf(f478,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK31 @ X1 ) )
=> ( p10 @ ( sK31 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f477]) ).
thf(f479,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p10 @ ( sK31 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f478]) ).
thf(f489,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p10 @ ( sK31 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f479]) ).
thf(f490,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p10 @ ( sK31 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f489]) ).
thf(f491,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p10 @ ( sK31 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f490]) ).
thf(f492,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p10 @ ( sK31 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) )
@ ( sK33 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f491]) ).
thf(f493,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p10 @ ( sK31 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p9 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK33 @ X2 ) )
=> ( p10 @ ( sK33 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f492]) ).
thf(f494,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p10 @ ( sK31 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK33 @ X2 ) )
=> ( p10 @ ( sK33 @ X2 ) ) ) )
| ( $true
= ( p9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f493]) ).
thf(f495,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p10 @ ( sK31 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p10 @ ( sK33 @ X2 ) ) )
| ( $true
= ( p9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f494]) ).
thf(f497,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p9 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p8 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f498,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p9 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p8 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f497]) ).
thf(f499,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p9 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f498]) ).
thf(f500,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f499]) ).
thf(f501,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f500]) ).
thf(f502,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f501]) ).
thf(f503,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p9 @ Y0 ) )
@ ( sK34 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f502]) ).
thf(f504,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK34 @ X1 ) )
=> ( p9 @ ( sK34 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f503]) ).
thf(f505,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK34 @ X1 ) )
=> ( p9 @ ( sK34 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f504]) ).
thf(f506,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p9 @ ( sK34 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f505]) ).
thf(f516,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p9 @ ( sK34 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f506]) ).
thf(f517,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p9 @ ( sK34 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f516]) ).
thf(f518,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p9 @ ( sK34 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f517]) ).
thf(f519,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p9 @ ( sK34 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) )
@ ( sK36 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f518]) ).
thf(f520,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p9 @ ( sK34 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p8 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK36 @ X2 ) )
=> ( p9 @ ( sK36 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f519]) ).
thf(f521,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p9 @ ( sK34 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK36 @ X2 ) )
=> ( p9 @ ( sK36 @ X2 ) ) ) )
| ( $true
= ( p8 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f520]) ).
thf(f522,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p9 @ ( sK34 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p9 @ ( sK36 @ X2 ) ) )
| ( $true
= ( p8 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f521]) ).
thf(f524,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p8 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p7 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f525,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p8 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p7 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f524]) ).
thf(f526,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p8 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f525]) ).
thf(f527,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f526]) ).
thf(f528,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f527]) ).
thf(f529,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f528]) ).
thf(f530,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p8 @ Y0 ) )
@ ( sK37 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f529]) ).
thf(f531,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK37 @ X1 ) )
=> ( p8 @ ( sK37 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f530]) ).
thf(f532,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK37 @ X1 ) )
=> ( p8 @ ( sK37 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f531]) ).
thf(f533,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p8 @ ( sK37 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f532]) ).
thf(f543,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p8 @ ( sK37 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f533]) ).
thf(f544,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p8 @ ( sK37 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f543]) ).
thf(f545,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p8 @ ( sK37 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f544]) ).
thf(f546,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p8 @ ( sK37 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) )
@ ( sK39 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f545]) ).
thf(f547,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p8 @ ( sK37 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p7 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK39 @ X2 ) )
=> ( p8 @ ( sK39 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f546]) ).
thf(f548,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p8 @ ( sK37 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK39 @ X2 ) )
=> ( p8 @ ( sK39 @ X2 ) ) ) )
| ( $true
= ( p7 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f547]) ).
thf(f549,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p8 @ ( sK37 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p8 @ ( sK39 @ X2 ) ) )
| ( $true
= ( p7 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f548]) ).
thf(f551,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p7 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p6 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f552,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p7 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p6 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f551]) ).
thf(f553,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p7 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f552]) ).
thf(f554,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f553]) ).
thf(f555,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f554]) ).
thf(f556,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f555]) ).
thf(f557,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p7 @ Y0 ) )
@ ( sK40 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f556]) ).
thf(f558,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK40 @ X1 ) )
=> ( p7 @ ( sK40 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f557]) ).
thf(f559,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK40 @ X1 ) )
=> ( p7 @ ( sK40 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f558]) ).
thf(f560,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p7 @ ( sK40 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f559]) ).
thf(f570,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p7 @ ( sK40 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f560]) ).
thf(f571,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p7 @ ( sK40 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f570]) ).
thf(f572,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p7 @ ( sK40 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f571]) ).
thf(f573,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p7 @ ( sK40 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) )
@ ( sK42 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f572]) ).
thf(f574,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p7 @ ( sK40 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p6 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK42 @ X2 ) )
=> ( p7 @ ( sK42 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f573]) ).
thf(f575,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p7 @ ( sK40 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK42 @ X2 ) )
=> ( p7 @ ( sK42 @ X2 ) ) ) )
| ( $true
= ( p6 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f574]) ).
thf(f576,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p7 @ ( sK40 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p7 @ ( sK42 @ X2 ) ) )
| ( $true
= ( p6 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f575]) ).
thf(f578,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p6 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p5 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f579,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p6 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p5 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f578]) ).
thf(f580,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p6 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f579]) ).
thf(f581,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f580]) ).
thf(f582,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f581]) ).
thf(f583,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f582]) ).
thf(f584,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p6 @ Y0 ) )
@ ( sK43 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f583]) ).
thf(f585,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK43 @ X1 ) )
=> ( p6 @ ( sK43 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f584]) ).
thf(f586,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK43 @ X1 ) )
=> ( p6 @ ( sK43 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f585]) ).
thf(f587,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p6 @ ( sK43 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f586]) ).
thf(f597,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p6 @ ( sK43 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f587]) ).
thf(f598,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p6 @ ( sK43 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f597]) ).
thf(f599,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p6 @ ( sK43 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f598]) ).
thf(f600,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p6 @ ( sK43 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) )
@ ( sK45 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f599]) ).
thf(f601,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p6 @ ( sK43 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p5 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK45 @ X2 ) )
=> ( p6 @ ( sK45 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f600]) ).
thf(f602,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p6 @ ( sK43 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK45 @ X2 ) )
=> ( p6 @ ( sK45 @ X2 ) ) ) )
| ( $true
= ( p5 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f601]) ).
thf(f603,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p6 @ ( sK43 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p6 @ ( sK45 @ X2 ) ) )
| ( $true
= ( p5 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f602]) ).
thf(f605,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p5 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p4 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f606,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p5 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p4 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f605]) ).
thf(f607,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f606]) ).
thf(f608,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f607]) ).
thf(f609,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f608]) ).
thf(f610,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f609]) ).
thf(f611,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) )
@ ( sK46 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f610]) ).
thf(f612,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK46 @ X1 ) )
=> ( p5 @ ( sK46 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f611]) ).
thf(f613,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK46 @ X1 ) )
=> ( p5 @ ( sK46 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f612]) ).
thf(f614,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p5 @ ( sK46 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f613]) ).
thf(f624,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p5 @ ( sK46 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f614]) ).
thf(f625,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p5 @ ( sK46 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f624]) ).
thf(f626,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p5 @ ( sK46 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f625]) ).
thf(f627,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p5 @ ( sK46 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) )
@ ( sK48 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f626]) ).
thf(f628,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p5 @ ( sK46 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p4 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK48 @ X2 ) )
=> ( p5 @ ( sK48 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f627]) ).
thf(f629,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p5 @ ( sK46 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK48 @ X2 ) )
=> ( p5 @ ( sK48 @ X2 ) ) ) )
| ( $true
= ( p4 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f628]) ).
thf(f630,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p5 @ ( sK46 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p5 @ ( sK48 @ X2 ) ) )
| ( $true
= ( p4 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f629]) ).
thf(f632,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p3 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f633,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p3 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f632]) ).
thf(f634,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f633]) ).
thf(f635,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f634]) ).
thf(f636,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f635]) ).
thf(f637,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f636]) ).
thf(f638,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) )
@ ( sK49 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f637]) ).
thf(f639,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK49 @ X1 ) )
=> ( p4 @ ( sK49 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f638]) ).
thf(f640,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK49 @ X1 ) )
=> ( p4 @ ( sK49 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f639]) ).
thf(f641,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p4 @ ( sK49 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f640]) ).
thf(f651,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p4 @ ( sK49 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f641]) ).
thf(f652,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p4 @ ( sK49 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f651]) ).
thf(f653,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p4 @ ( sK49 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f652]) ).
thf(f654,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p4 @ ( sK49 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) )
@ ( sK51 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f653]) ).
thf(f655,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p4 @ ( sK49 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p3 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK51 @ X2 ) )
=> ( p4 @ ( sK51 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f654]) ).
thf(f656,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p4 @ ( sK49 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK51 @ X2 ) )
=> ( p4 @ ( sK51 @ X2 ) ) ) )
| ( $true
= ( p3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f655]) ).
thf(f657,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p4 @ ( sK49 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p4 @ ( sK51 @ X2 ) ) )
| ( $true
= ( p3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f656]) ).
thf(f659,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f660,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f659]) ).
thf(f661,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f660]) ).
thf(f662,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f661]) ).
thf(f663,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f662]) ).
thf(f664,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f663]) ).
thf(f665,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) )
@ ( sK52 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f664]) ).
thf(f666,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK52 @ X1 ) )
=> ( p3 @ ( sK52 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f665]) ).
thf(f667,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK52 @ X1 ) )
=> ( p3 @ ( sK52 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f666]) ).
thf(f668,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p3 @ ( sK52 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f667]) ).
thf(f678,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p3 @ ( sK52 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f668]) ).
thf(f679,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p3 @ ( sK52 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f678]) ).
thf(f680,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p3 @ ( sK52 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f679]) ).
thf(f681,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p3 @ ( sK52 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) )
@ ( sK54 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f680]) ).
thf(f682,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p3 @ ( sK52 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p2 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK54 @ X2 ) )
=> ( p3 @ ( sK54 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f681]) ).
thf(f683,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p3 @ ( sK52 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK54 @ X2 ) )
=> ( p3 @ ( sK54 @ X2 ) ) ) )
| ( $true
= ( p2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f682]) ).
thf(f684,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p3 @ ( sK52 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p3 @ ( sK54 @ X2 ) ) )
| ( $true
= ( p2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f683]) ).
thf(f686,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f178]) ).
thf(f687,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f686]) ).
thf(f688,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f687]) ).
thf(f689,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f688]) ).
thf(f690,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f689]) ).
thf(f691,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f690]) ).
thf(f692,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) )
@ ( sK55 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f691]) ).
thf(f693,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK55 @ X1 ) )
=> ( p2 @ ( sK55 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f692]) ).
thf(f694,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK55 @ X1 ) )
=> ( p2 @ ( sK55 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f693]) ).
thf(f695,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p2 @ ( sK55 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f694]) ).
thf(f705,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p2 @ ( sK55 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f695]) ).
thf(f706,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p2 @ ( sK55 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f705]) ).
thf(f707,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p2 @ ( sK55 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f706]) ).
thf(f708,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p2 @ ( sK55 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) )
@ ( sK57 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f707]) ).
thf(f709,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p2 @ ( sK55 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK57 @ X2 ) )
=> ( p2 @ ( sK57 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f708]) ).
thf(f710,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p2 @ ( sK55 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK57 @ X2 ) )
=> ( p2 @ ( sK57 @ X2 ) ) ) )
| ( $true
= ( p1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f709]) ).
thf(f711,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p2 @ ( sK55 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p2 @ ( sK57 @ X2 ) ) )
| ( $true
= ( p1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f710]) ).
thf(f713,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f714,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p0 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f713]) ).
thf(f715,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f714]) ).
thf(f716,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f715]) ).
thf(f717,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f716]) ).
thf(f718,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f717]) ).
thf(f719,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) )
@ ( sK58 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f718]) ).
thf(f720,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK58 @ X1 ) )
=> ( p1 @ ( sK58 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f719]) ).
thf(f721,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK58 @ X1 ) )
=> ( p1 @ ( sK58 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f720]) ).
thf(f722,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK58 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f721]) ).
thf(f732,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK58 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f722]) ).
thf(f733,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK58 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f732]) ).
thf(f734,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK58 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f733]) ).
thf(f735,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK58 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) )
@ ( sK60 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f734]) ).
thf(f736,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK58 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p0 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK60 @ X2 ) )
=> ( p1 @ ( sK60 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f735]) ).
thf(f737,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK58 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK60 @ X2 ) )
=> ( p1 @ ( sK60 @ X2 ) ) ) )
| ( $true
= ( p0 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f736]) ).
thf(f738,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK58 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p1 @ ( sK60 @ X2 ) ) )
| ( $true
= ( p0 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f737]) ).
thf(f740,plain,
( $true
= ( !! @ $i @ p20 ) ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f741,plain,
! [X1: $i] :
( $true
= ( p20 @ X1 ) ),
inference(pi_proxy_clausification,[],[f740]) ).
thf(f962,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p20 @ ( sK3 @ X2 ) ) )
| ( $true
= ( p19 @ X3 ) ) ),
inference(forward_demodulation,[],[f225,f741]) ).
thf(f963,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p20 @ ( sK3 @ X2 ) ) )
| ( $true
= ( p19 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f962]) ).
thf(f964,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( p19 @ X3 ) ) ),
inference(forward_demodulation,[],[f963,f741]) ).
thf(f965,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p19 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f964]) ).
thf(f970,definition,
( spl61_6
<=> ! [X3: $i] :
( $true
= ( p19 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl61_6])],[avatar_definition]) ).
thf(f971,plain,
( ! [X3: $i] :
( $true
= ( p19 @ X3 ) )
| ~ spl61_6 ),
inference(avatar_component_clause,[],[f970]) ).
thf(f980,plain,
! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p19 @ X0 ) ) ),
inference(equality_factoring,[],[f965]) ).
thf(f983,plain,
! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p19 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f980]) ).
thf(f992,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p19 @ X0 ) ) ),
inference(forward_demodulation,[],[f983,f122]) ).
thf(f993,plain,
! [X0: $i] :
( $true
= ( p19 @ X0 ) ),
inference(trivial_inequality_removal,[],[f992]) ).
thf(f1141,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p19 @ ( sK6 @ X2 ) ) )
| ( $true
= ( p18 @ X3 ) ) )
| ~ spl61_6 ),
inference(forward_demodulation,[],[f252,f971]) ).
thf(f1142,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p19 @ ( sK6 @ X2 ) ) )
| ( $true
= ( p18 @ X3 ) ) )
| ~ spl61_6 ),
inference(trivial_inequality_removal,[],[f1141]) ).
thf(f1143,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( p18 @ X3 ) ) )
| ~ spl61_6 ),
inference(forward_demodulation,[],[f1142,f971]) ).
thf(f1144,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p18 @ X3 ) ) )
| ~ spl61_6 ),
inference(trivial_inequality_removal,[],[f1143]) ).
thf(f1146,definition,
( spl61_7
<=> ! [X3: $i] :
( $true
= ( p18 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl61_7])],[avatar_definition]) ).
thf(f1147,plain,
( ! [X3: $i] :
( $true
= ( p18 @ X3 ) )
| ~ spl61_7 ),
inference(avatar_component_clause,[],[f1146]) ).
thf(f1168,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p18 @ X0 ) ) )
| ~ spl61_6 ),
inference(equality_factoring,[],[f1144]) ).
thf(f1171,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p18 @ X0 ) ) )
| ~ spl61_6 ),
inference(trivial_inequality_removal,[],[f1168]) ).
thf(f1188,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p18 @ X0 ) ) )
| ~ spl61_6 ),
inference(forward_demodulation,[],[f1171,f122]) ).
thf(f1189,plain,
( ! [X0: $i] :
( $true
= ( p18 @ X0 ) )
| ~ spl61_6 ),
inference(trivial_inequality_removal,[],[f1188]) ).
thf(f1190,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p18 @ ( sK9 @ X2 ) ) )
| ( $true
= ( p17 @ X3 ) ) )
| ~ spl61_7 ),
inference(forward_demodulation,[],[f279,f1147]) ).
thf(f1191,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p18 @ ( sK9 @ X2 ) ) )
| ( $true
= ( p17 @ X3 ) ) )
| ~ spl61_7 ),
inference(trivial_inequality_removal,[],[f1190]) ).
thf(f1192,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( p17 @ X3 ) ) )
| ~ spl61_7 ),
inference(forward_demodulation,[],[f1191,f1147]) ).
thf(f1193,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p17 @ X3 ) ) )
| ~ spl61_7 ),
inference(trivial_inequality_removal,[],[f1192]) ).
thf(f1195,definition,
( spl61_8
<=> ! [X3: $i] :
( $true
= ( p17 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl61_8])],[avatar_definition]) ).
thf(f1196,plain,
( ! [X3: $i] :
( $true
= ( p17 @ X3 ) )
| ~ spl61_8 ),
inference(avatar_component_clause,[],[f1195]) ).
thf(f1217,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p17 @ X0 ) ) )
| ~ spl61_7 ),
inference(equality_factoring,[],[f1193]) ).
thf(f1220,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p17 @ X0 ) ) )
| ~ spl61_7 ),
inference(trivial_inequality_removal,[],[f1217]) ).
thf(f1237,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p17 @ X0 ) ) )
| ~ spl61_7 ),
inference(forward_demodulation,[],[f1220,f122]) ).
thf(f1238,plain,
( ! [X0: $i] :
( $true
= ( p17 @ X0 ) )
| ~ spl61_7 ),
inference(trivial_inequality_removal,[],[f1237]) ).
thf(f1239,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p17 @ ( sK12 @ X2 ) ) )
| ( $true
= ( p16 @ X3 ) ) )
| ~ spl61_8 ),
inference(forward_demodulation,[],[f306,f1196]) ).
thf(f1240,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p17 @ ( sK12 @ X2 ) ) )
| ( $true
= ( p16 @ X3 ) ) )
| ~ spl61_8 ),
inference(trivial_inequality_removal,[],[f1239]) ).
thf(f1241,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( p16 @ X3 ) ) )
| ~ spl61_8 ),
inference(forward_demodulation,[],[f1240,f1196]) ).
thf(f1242,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p16 @ X3 ) ) )
| ~ spl61_8 ),
inference(trivial_inequality_removal,[],[f1241]) ).
thf(f1244,definition,
( spl61_9
<=> ! [X3: $i] :
( $true
= ( p16 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl61_9])],[avatar_definition]) ).
thf(f1245,plain,
( ! [X3: $i] :
( $true
= ( p16 @ X3 ) )
| ~ spl61_9 ),
inference(avatar_component_clause,[],[f1244]) ).
thf(f1267,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p16 @ X0 ) ) )
| ~ spl61_8 ),
inference(equality_factoring,[],[f1242]) ).
thf(f1268,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p16 @ X0 ) ) )
| ~ spl61_8 ),
inference(trivial_inequality_removal,[],[f1267]) ).
thf(f1284,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p16 @ X0 ) ) )
| ~ spl61_8 ),
inference(forward_demodulation,[],[f1268,f122]) ).
thf(f1285,plain,
( ! [X0: $i] :
( $true
= ( p16 @ X0 ) )
| ~ spl61_8 ),
inference(trivial_inequality_removal,[],[f1284]) ).
thf(f1288,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p16 @ ( sK15 @ X2 ) ) )
| ( $true
= ( p15 @ X3 ) ) )
| ~ spl61_9 ),
inference(forward_demodulation,[],[f333,f1245]) ).
thf(f1289,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p16 @ ( sK15 @ X2 ) ) )
| ( $true
= ( p15 @ X3 ) ) )
| ~ spl61_9 ),
inference(trivial_inequality_removal,[],[f1288]) ).
thf(f1290,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( p15 @ X3 ) ) )
| ~ spl61_9 ),
inference(forward_demodulation,[],[f1289,f1245]) ).
thf(f1291,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p15 @ X3 ) ) )
| ~ spl61_9 ),
inference(trivial_inequality_removal,[],[f1290]) ).
thf(f1293,definition,
( spl61_10
<=> ! [X3: $i] :
( $true
= ( p15 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl61_10])],[avatar_definition]) ).
thf(f1294,plain,
( ! [X3: $i] :
( $true
= ( p15 @ X3 ) )
| ~ spl61_10 ),
inference(avatar_component_clause,[],[f1293]) ).
thf(f1315,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p15 @ X0 ) ) )
| ~ spl61_9 ),
inference(equality_factoring,[],[f1291]) ).
thf(f1318,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p15 @ X0 ) ) )
| ~ spl61_9 ),
inference(trivial_inequality_removal,[],[f1315]) ).
thf(f1335,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p15 @ X0 ) ) )
| ~ spl61_9 ),
inference(forward_demodulation,[],[f1318,f122]) ).
thf(f1336,plain,
( ! [X0: $i] :
( $true
= ( p15 @ X0 ) )
| ~ spl61_9 ),
inference(trivial_inequality_removal,[],[f1335]) ).
thf(f1337,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p15 @ ( sK18 @ X2 ) ) )
| ( $true
= ( p14 @ X3 ) ) )
| ~ spl61_10 ),
inference(forward_demodulation,[],[f360,f1294]) ).
thf(f1338,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p15 @ ( sK18 @ X2 ) ) )
| ( $true
= ( p14 @ X3 ) ) )
| ~ spl61_10 ),
inference(trivial_inequality_removal,[],[f1337]) ).
thf(f1339,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( p14 @ X3 ) ) )
| ~ spl61_10 ),
inference(forward_demodulation,[],[f1338,f1294]) ).
thf(f1340,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p14 @ X3 ) ) )
| ~ spl61_10 ),
inference(trivial_inequality_removal,[],[f1339]) ).
thf(f1342,definition,
( spl61_11
<=> ! [X3: $i] :
( $true
= ( p14 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl61_11])],[avatar_definition]) ).
thf(f1343,plain,
( ! [X3: $i] :
( $true
= ( p14 @ X3 ) )
| ~ spl61_11 ),
inference(avatar_component_clause,[],[f1342]) ).
thf(f1364,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p14 @ X0 ) ) )
| ~ spl61_10 ),
inference(equality_factoring,[],[f1340]) ).
thf(f1367,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p14 @ X0 ) ) )
| ~ spl61_10 ),
inference(trivial_inequality_removal,[],[f1364]) ).
thf(f1384,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p14 @ X0 ) ) )
| ~ spl61_10 ),
inference(forward_demodulation,[],[f1367,f122]) ).
thf(f1385,plain,
( ! [X0: $i] :
( $true
= ( p14 @ X0 ) )
| ~ spl61_10 ),
inference(trivial_inequality_removal,[],[f1384]) ).
thf(f1386,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p14 @ ( sK21 @ X2 ) ) )
| ( $true
= ( p13 @ X3 ) ) )
| ~ spl61_11 ),
inference(forward_demodulation,[],[f387,f1343]) ).
thf(f1387,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p14 @ ( sK21 @ X2 ) ) )
| ( $true
= ( p13 @ X3 ) ) )
| ~ spl61_11 ),
inference(trivial_inequality_removal,[],[f1386]) ).
thf(f1388,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( p13 @ X3 ) ) )
| ~ spl61_11 ),
inference(forward_demodulation,[],[f1387,f1343]) ).
thf(f1389,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p13 @ X3 ) ) )
| ~ spl61_11 ),
inference(trivial_inequality_removal,[],[f1388]) ).
thf(f1391,definition,
( spl61_12
<=> ! [X3: $i] :
( $true
= ( p13 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl61_12])],[avatar_definition]) ).
thf(f1392,plain,
( ! [X3: $i] :
( $true
= ( p13 @ X3 ) )
| ~ spl61_12 ),
inference(avatar_component_clause,[],[f1391]) ).
thf(f1414,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p13 @ X0 ) ) )
| ~ spl61_11 ),
inference(equality_factoring,[],[f1389]) ).
thf(f1415,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p13 @ X0 ) ) )
| ~ spl61_11 ),
inference(trivial_inequality_removal,[],[f1414]) ).
thf(f1431,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p13 @ X0 ) ) )
| ~ spl61_11 ),
inference(forward_demodulation,[],[f1415,f122]) ).
thf(f1432,plain,
( ! [X0: $i] :
( $true
= ( p13 @ X0 ) )
| ~ spl61_11 ),
inference(trivial_inequality_removal,[],[f1431]) ).
thf(f1435,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p13 @ ( sK24 @ X2 ) ) )
| ( $true
= ( p12 @ X3 ) ) )
| ~ spl61_12 ),
inference(forward_demodulation,[],[f414,f1392]) ).
thf(f1436,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p13 @ ( sK24 @ X2 ) ) )
| ( $true
= ( p12 @ X3 ) ) )
| ~ spl61_12 ),
inference(trivial_inequality_removal,[],[f1435]) ).
thf(f1437,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( p12 @ X3 ) ) )
| ~ spl61_12 ),
inference(forward_demodulation,[],[f1436,f1392]) ).
thf(f1438,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p12 @ X3 ) ) )
| ~ spl61_12 ),
inference(trivial_inequality_removal,[],[f1437]) ).
thf(f1440,definition,
( spl61_13
<=> ! [X3: $i] :
( $true
= ( p12 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl61_13])],[avatar_definition]) ).
thf(f1441,plain,
( ! [X3: $i] :
( $true
= ( p12 @ X3 ) )
| ~ spl61_13 ),
inference(avatar_component_clause,[],[f1440]) ).
thf(f1463,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p12 @ X0 ) ) )
| ~ spl61_12 ),
inference(equality_factoring,[],[f1438]) ).
thf(f1464,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p12 @ X0 ) ) )
| ~ spl61_12 ),
inference(trivial_inequality_removal,[],[f1463]) ).
thf(f1480,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p12 @ X0 ) ) )
| ~ spl61_12 ),
inference(forward_demodulation,[],[f1464,f122]) ).
thf(f1481,plain,
( ! [X0: $i] :
( $true
= ( p12 @ X0 ) )
| ~ spl61_12 ),
inference(trivial_inequality_removal,[],[f1480]) ).
thf(f1484,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p12 @ ( sK27 @ X2 ) ) )
| ( $true
= ( p11 @ X3 ) ) )
| ~ spl61_13 ),
inference(forward_demodulation,[],[f441,f1441]) ).
thf(f1485,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p12 @ ( sK27 @ X2 ) ) )
| ( $true
= ( p11 @ X3 ) ) )
| ~ spl61_13 ),
inference(trivial_inequality_removal,[],[f1484]) ).
thf(f1486,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( p11 @ X3 ) ) )
| ~ spl61_13 ),
inference(forward_demodulation,[],[f1485,f1441]) ).
thf(f1487,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p11 @ X3 ) ) )
| ~ spl61_13 ),
inference(trivial_inequality_removal,[],[f1486]) ).
thf(f1489,definition,
( spl61_14
<=> ! [X3: $i] :
( $true
= ( p11 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl61_14])],[avatar_definition]) ).
thf(f1490,plain,
( ! [X3: $i] :
( $true
= ( p11 @ X3 ) )
| ~ spl61_14 ),
inference(avatar_component_clause,[],[f1489]) ).
thf(f1512,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p11 @ X0 ) ) )
| ~ spl61_13 ),
inference(equality_factoring,[],[f1487]) ).
thf(f1513,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p11 @ X0 ) ) )
| ~ spl61_13 ),
inference(trivial_inequality_removal,[],[f1512]) ).
thf(f1529,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p11 @ X0 ) ) )
| ~ spl61_13 ),
inference(forward_demodulation,[],[f1513,f122]) ).
thf(f1530,plain,
( ! [X0: $i] :
( $true
= ( p11 @ X0 ) )
| ~ spl61_13 ),
inference(trivial_inequality_removal,[],[f1529]) ).
thf(f1533,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p11 @ ( sK30 @ X2 ) ) )
| ( $true
= ( p10 @ X3 ) ) )
| ~ spl61_14 ),
inference(forward_demodulation,[],[f468,f1490]) ).
thf(f1534,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p11 @ ( sK30 @ X2 ) ) )
| ( $true
= ( p10 @ X3 ) ) )
| ~ spl61_14 ),
inference(trivial_inequality_removal,[],[f1533]) ).
thf(f1535,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( p10 @ X3 ) ) )
| ~ spl61_14 ),
inference(forward_demodulation,[],[f1534,f1490]) ).
thf(f1536,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p10 @ X3 ) ) )
| ~ spl61_14 ),
inference(trivial_inequality_removal,[],[f1535]) ).
thf(f1538,definition,
( spl61_15
<=> ! [X3: $i] :
( $true
= ( p10 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl61_15])],[avatar_definition]) ).
thf(f1539,plain,
( ! [X3: $i] :
( $true
= ( p10 @ X3 ) )
| ~ spl61_15 ),
inference(avatar_component_clause,[],[f1538]) ).
thf(f1561,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p10 @ X0 ) ) )
| ~ spl61_14 ),
inference(equality_factoring,[],[f1536]) ).
thf(f1562,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p10 @ X0 ) ) )
| ~ spl61_14 ),
inference(trivial_inequality_removal,[],[f1561]) ).
thf(f1578,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p10 @ X0 ) ) )
| ~ spl61_14 ),
inference(forward_demodulation,[],[f1562,f122]) ).
thf(f1579,plain,
( ! [X0: $i] :
( $true
= ( p10 @ X0 ) )
| ~ spl61_14 ),
inference(trivial_inequality_removal,[],[f1578]) ).
thf(f1582,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p10 @ ( sK33 @ X2 ) ) )
| ( $true
= ( p9 @ X3 ) ) )
| ~ spl61_15 ),
inference(forward_demodulation,[],[f495,f1539]) ).
thf(f1583,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p10 @ ( sK33 @ X2 ) ) )
| ( $true
= ( p9 @ X3 ) ) )
| ~ spl61_15 ),
inference(trivial_inequality_removal,[],[f1582]) ).
thf(f1584,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( p9 @ X3 ) ) )
| ~ spl61_15 ),
inference(forward_demodulation,[],[f1583,f1539]) ).
thf(f1585,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p9 @ X3 ) ) )
| ~ spl61_15 ),
inference(trivial_inequality_removal,[],[f1584]) ).
thf(f1587,definition,
( spl61_16
<=> ! [X3: $i] :
( $true
= ( p9 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl61_16])],[avatar_definition]) ).
thf(f1588,plain,
( ! [X3: $i] :
( $true
= ( p9 @ X3 ) )
| ~ spl61_16 ),
inference(avatar_component_clause,[],[f1587]) ).
thf(f1610,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p9 @ X0 ) ) )
| ~ spl61_15 ),
inference(equality_factoring,[],[f1585]) ).
thf(f1611,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p9 @ X0 ) ) )
| ~ spl61_15 ),
inference(trivial_inequality_removal,[],[f1610]) ).
thf(f1627,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p9 @ X0 ) ) )
| ~ spl61_15 ),
inference(forward_demodulation,[],[f1611,f122]) ).
thf(f1628,plain,
( ! [X0: $i] :
( $true
= ( p9 @ X0 ) )
| ~ spl61_15 ),
inference(trivial_inequality_removal,[],[f1627]) ).
thf(f1631,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p9 @ ( sK36 @ X2 ) ) )
| ( $true
= ( p8 @ X3 ) ) )
| ~ spl61_16 ),
inference(forward_demodulation,[],[f522,f1588]) ).
thf(f1632,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p9 @ ( sK36 @ X2 ) ) )
| ( $true
= ( p8 @ X3 ) ) )
| ~ spl61_16 ),
inference(trivial_inequality_removal,[],[f1631]) ).
thf(f1633,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( p8 @ X3 ) ) )
| ~ spl61_16 ),
inference(forward_demodulation,[],[f1632,f1588]) ).
thf(f1634,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p8 @ X3 ) ) )
| ~ spl61_16 ),
inference(trivial_inequality_removal,[],[f1633]) ).
thf(f1636,definition,
( spl61_17
<=> ! [X3: $i] :
( $true
= ( p8 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl61_17])],[avatar_definition]) ).
thf(f1637,plain,
( ! [X3: $i] :
( $true
= ( p8 @ X3 ) )
| ~ spl61_17 ),
inference(avatar_component_clause,[],[f1636]) ).
thf(f1658,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p8 @ X0 ) ) )
| ~ spl61_16 ),
inference(equality_factoring,[],[f1634]) ).
thf(f1661,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p8 @ X0 ) ) )
| ~ spl61_16 ),
inference(trivial_inequality_removal,[],[f1658]) ).
thf(f1678,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p8 @ X0 ) ) )
| ~ spl61_16 ),
inference(forward_demodulation,[],[f1661,f122]) ).
thf(f1679,plain,
( ! [X0: $i] :
( $true
= ( p8 @ X0 ) )
| ~ spl61_16 ),
inference(trivial_inequality_removal,[],[f1678]) ).
thf(f1680,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p8 @ ( sK39 @ X2 ) ) )
| ( $true
= ( p7 @ X3 ) ) )
| ~ spl61_17 ),
inference(forward_demodulation,[],[f549,f1637]) ).
thf(f1681,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p8 @ ( sK39 @ X2 ) ) )
| ( $true
= ( p7 @ X3 ) ) )
| ~ spl61_17 ),
inference(trivial_inequality_removal,[],[f1680]) ).
thf(f1682,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( p7 @ X3 ) ) )
| ~ spl61_17 ),
inference(forward_demodulation,[],[f1681,f1637]) ).
thf(f1683,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p7 @ X3 ) ) )
| ~ spl61_17 ),
inference(trivial_inequality_removal,[],[f1682]) ).
thf(f1685,definition,
( spl61_18
<=> ! [X3: $i] :
( $true
= ( p7 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl61_18])],[avatar_definition]) ).
thf(f1686,plain,
( ! [X3: $i] :
( $true
= ( p7 @ X3 ) )
| ~ spl61_18 ),
inference(avatar_component_clause,[],[f1685]) ).
thf(f1707,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p7 @ X0 ) ) )
| ~ spl61_17 ),
inference(equality_factoring,[],[f1683]) ).
thf(f1710,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p7 @ X0 ) ) )
| ~ spl61_17 ),
inference(trivial_inequality_removal,[],[f1707]) ).
thf(f1727,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p7 @ X0 ) ) )
| ~ spl61_17 ),
inference(forward_demodulation,[],[f1710,f122]) ).
thf(f1728,plain,
( ! [X0: $i] :
( $true
= ( p7 @ X0 ) )
| ~ spl61_17 ),
inference(trivial_inequality_removal,[],[f1727]) ).
thf(f1729,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p7 @ ( sK42 @ X2 ) ) )
| ( $true
= ( p6 @ X3 ) ) )
| ~ spl61_18 ),
inference(forward_demodulation,[],[f576,f1686]) ).
thf(f1730,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p7 @ ( sK42 @ X2 ) ) )
| ( $true
= ( p6 @ X3 ) ) )
| ~ spl61_18 ),
inference(trivial_inequality_removal,[],[f1729]) ).
thf(f1731,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( p6 @ X3 ) ) )
| ~ spl61_18 ),
inference(forward_demodulation,[],[f1730,f1686]) ).
thf(f1732,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p6 @ X3 ) ) )
| ~ spl61_18 ),
inference(trivial_inequality_removal,[],[f1731]) ).
thf(f1734,definition,
( spl61_19
<=> ! [X3: $i] :
( $true
= ( p6 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl61_19])],[avatar_definition]) ).
thf(f1735,plain,
( ! [X3: $i] :
( $true
= ( p6 @ X3 ) )
| ~ spl61_19 ),
inference(avatar_component_clause,[],[f1734]) ).
thf(f1757,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p6 @ X0 ) ) )
| ~ spl61_18 ),
inference(equality_factoring,[],[f1732]) ).
thf(f1758,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p6 @ X0 ) ) )
| ~ spl61_18 ),
inference(trivial_inequality_removal,[],[f1757]) ).
thf(f1774,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p6 @ X0 ) ) )
| ~ spl61_18 ),
inference(forward_demodulation,[],[f1758,f122]) ).
thf(f1775,plain,
( ! [X0: $i] :
( $true
= ( p6 @ X0 ) )
| ~ spl61_18 ),
inference(trivial_inequality_removal,[],[f1774]) ).
thf(f1778,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p6 @ ( sK45 @ X2 ) ) )
| ( $true
= ( p5 @ X3 ) ) )
| ~ spl61_19 ),
inference(forward_demodulation,[],[f603,f1735]) ).
thf(f1779,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p6 @ ( sK45 @ X2 ) ) )
| ( $true
= ( p5 @ X3 ) ) )
| ~ spl61_19 ),
inference(trivial_inequality_removal,[],[f1778]) ).
thf(f1780,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( p5 @ X3 ) ) )
| ~ spl61_19 ),
inference(forward_demodulation,[],[f1779,f1735]) ).
thf(f1781,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p5 @ X3 ) ) )
| ~ spl61_19 ),
inference(trivial_inequality_removal,[],[f1780]) ).
thf(f1783,definition,
( spl61_20
<=> ! [X3: $i] :
( $true
= ( p5 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl61_20])],[avatar_definition]) ).
thf(f1784,plain,
( ! [X3: $i] :
( $true
= ( p5 @ X3 ) )
| ~ spl61_20 ),
inference(avatar_component_clause,[],[f1783]) ).
thf(f1805,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p5 @ X0 ) ) )
| ~ spl61_19 ),
inference(equality_factoring,[],[f1781]) ).
thf(f1808,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p5 @ X0 ) ) )
| ~ spl61_19 ),
inference(trivial_inequality_removal,[],[f1805]) ).
thf(f1825,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p5 @ X0 ) ) )
| ~ spl61_19 ),
inference(forward_demodulation,[],[f1808,f122]) ).
thf(f1826,plain,
( ! [X0: $i] :
( $true
= ( p5 @ X0 ) )
| ~ spl61_19 ),
inference(trivial_inequality_removal,[],[f1825]) ).
thf(f1827,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p5 @ ( sK48 @ X2 ) ) )
| ( $true
= ( p4 @ X3 ) ) )
| ~ spl61_20 ),
inference(forward_demodulation,[],[f630,f1784]) ).
thf(f1828,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p5 @ ( sK48 @ X2 ) ) )
| ( $true
= ( p4 @ X3 ) ) )
| ~ spl61_20 ),
inference(trivial_inequality_removal,[],[f1827]) ).
thf(f1829,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( p4 @ X3 ) ) )
| ~ spl61_20 ),
inference(forward_demodulation,[],[f1828,f1784]) ).
thf(f1830,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p4 @ X3 ) ) )
| ~ spl61_20 ),
inference(trivial_inequality_removal,[],[f1829]) ).
thf(f1832,definition,
( spl61_21
<=> ! [X3: $i] :
( $true
= ( p4 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl61_21])],[avatar_definition]) ).
thf(f1833,plain,
( ! [X3: $i] :
( $true
= ( p4 @ X3 ) )
| ~ spl61_21 ),
inference(avatar_component_clause,[],[f1832]) ).
thf(f1855,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p4 @ X0 ) ) )
| ~ spl61_20 ),
inference(equality_factoring,[],[f1830]) ).
thf(f1856,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p4 @ X0 ) ) )
| ~ spl61_20 ),
inference(trivial_inequality_removal,[],[f1855]) ).
thf(f1872,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p4 @ X0 ) ) )
| ~ spl61_20 ),
inference(forward_demodulation,[],[f1856,f122]) ).
thf(f1873,plain,
( ! [X0: $i] :
( $true
= ( p4 @ X0 ) )
| ~ spl61_20 ),
inference(trivial_inequality_removal,[],[f1872]) ).
thf(f1876,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p4 @ ( sK51 @ X2 ) ) )
| ( $true
= ( p3 @ X3 ) ) )
| ~ spl61_21 ),
inference(forward_demodulation,[],[f657,f1833]) ).
thf(f1877,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p4 @ ( sK51 @ X2 ) ) )
| ( $true
= ( p3 @ X3 ) ) )
| ~ spl61_21 ),
inference(trivial_inequality_removal,[],[f1876]) ).
thf(f1878,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( p3 @ X3 ) ) )
| ~ spl61_21 ),
inference(forward_demodulation,[],[f1877,f1833]) ).
thf(f1879,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p3 @ X3 ) ) )
| ~ spl61_21 ),
inference(trivial_inequality_removal,[],[f1878]) ).
thf(f1881,definition,
( spl61_22
<=> ! [X3: $i] :
( $true
= ( p3 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl61_22])],[avatar_definition]) ).
thf(f1882,plain,
( ! [X3: $i] :
( $true
= ( p3 @ X3 ) )
| ~ spl61_22 ),
inference(avatar_component_clause,[],[f1881]) ).
thf(f1903,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p3 @ X0 ) ) )
| ~ spl61_21 ),
inference(equality_factoring,[],[f1879]) ).
thf(f1906,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p3 @ X0 ) ) )
| ~ spl61_21 ),
inference(trivial_inequality_removal,[],[f1903]) ).
thf(f1923,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p3 @ X0 ) ) )
| ~ spl61_21 ),
inference(forward_demodulation,[],[f1906,f122]) ).
thf(f1924,plain,
( ! [X0: $i] :
( $true
= ( p3 @ X0 ) )
| ~ spl61_21 ),
inference(trivial_inequality_removal,[],[f1923]) ).
thf(f1925,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p3 @ ( sK54 @ X2 ) ) )
| ( $true
= ( p2 @ X3 ) ) )
| ~ spl61_22 ),
inference(forward_demodulation,[],[f684,f1882]) ).
thf(f1926,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p3 @ ( sK54 @ X2 ) ) )
| ( $true
= ( p2 @ X3 ) ) )
| ~ spl61_22 ),
inference(trivial_inequality_removal,[],[f1925]) ).
thf(f1927,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( p2 @ X3 ) ) )
| ~ spl61_22 ),
inference(forward_demodulation,[],[f1926,f1882]) ).
thf(f1928,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p2 @ X3 ) ) )
| ~ spl61_22 ),
inference(trivial_inequality_removal,[],[f1927]) ).
thf(f1930,definition,
( spl61_23
<=> ! [X3: $i] :
( $true
= ( p2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl61_23])],[avatar_definition]) ).
thf(f1931,plain,
( ! [X3: $i] :
( $true
= ( p2 @ X3 ) )
| ~ spl61_23 ),
inference(avatar_component_clause,[],[f1930]) ).
thf(f1952,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p2 @ X0 ) ) )
| ~ spl61_22 ),
inference(equality_factoring,[],[f1928]) ).
thf(f1955,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p2 @ X0 ) ) )
| ~ spl61_22 ),
inference(trivial_inequality_removal,[],[f1952]) ).
thf(f1972,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p2 @ X0 ) ) )
| ~ spl61_22 ),
inference(forward_demodulation,[],[f1955,f122]) ).
thf(f1973,plain,
( ! [X0: $i] :
( $true
= ( p2 @ X0 ) )
| ~ spl61_22 ),
inference(trivial_inequality_removal,[],[f1972]) ).
thf(f1974,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p2 @ ( sK57 @ X2 ) ) )
| ( $true
= ( p1 @ X3 ) ) )
| ~ spl61_23 ),
inference(forward_demodulation,[],[f711,f1931]) ).
thf(f1975,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p2 @ ( sK57 @ X2 ) ) )
| ( $true
= ( p1 @ X3 ) ) )
| ~ spl61_23 ),
inference(trivial_inequality_removal,[],[f1974]) ).
thf(f1976,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( p1 @ X3 ) ) )
| ~ spl61_23 ),
inference(forward_demodulation,[],[f1975,f1931]) ).
thf(f1977,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p1 @ X3 ) ) )
| ~ spl61_23 ),
inference(trivial_inequality_removal,[],[f1976]) ).
thf(f1979,definition,
( spl61_24
<=> ! [X3: $i] :
( $true
= ( p1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl61_24])],[avatar_definition]) ).
thf(f1980,plain,
( ! [X3: $i] :
( $true
= ( p1 @ X3 ) )
| ~ spl61_24 ),
inference(avatar_component_clause,[],[f1979]) ).
thf(f2001,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p1 @ X0 ) ) )
| ~ spl61_23 ),
inference(equality_factoring,[],[f1977]) ).
thf(f2004,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p1 @ X0 ) ) )
| ~ spl61_23 ),
inference(trivial_inequality_removal,[],[f2001]) ).
thf(f2021,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p1 @ X0 ) ) )
| ~ spl61_23 ),
inference(forward_demodulation,[],[f2004,f122]) ).
thf(f2022,plain,
( ! [X0: $i] :
( $true
= ( p1 @ X0 ) )
| ~ spl61_23 ),
inference(trivial_inequality_removal,[],[f2021]) ).
thf(f2023,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p1 @ ( sK60 @ X2 ) ) )
| ( $true
= ( p0 @ X3 ) ) )
| ~ spl61_24 ),
inference(forward_demodulation,[],[f738,f1980]) ).
thf(f2024,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p1 @ ( sK60 @ X2 ) ) )
| ( $true
= ( p0 @ X3 ) ) )
| ~ spl61_24 ),
inference(trivial_inequality_removal,[],[f2023]) ).
thf(f2025,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( p0 @ X3 ) ) )
| ~ spl61_24 ),
inference(forward_demodulation,[],[f2024,f1980]) ).
thf(f2026,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p0 @ X3 ) ) )
| ~ spl61_24 ),
inference(trivial_inequality_removal,[],[f2025]) ).
thf(f2028,definition,
( spl61_25
<=> ! [X3: $i] :
( $true
= ( p0 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl61_25])],[avatar_definition]) ).
thf(f2029,plain,
( ! [X3: $i] :
( $true
= ( p0 @ X3 ) )
| ~ spl61_25 ),
inference(avatar_component_clause,[],[f2028]) ).
thf(f2051,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p0 @ X0 ) ) )
| ~ spl61_24 ),
inference(equality_factoring,[],[f2026]) ).
thf(f2052,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p0 @ X0 ) ) )
| ~ spl61_24 ),
inference(trivial_inequality_removal,[],[f2051]) ).
thf(f2068,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p0 @ X0 ) ) )
| ~ spl61_24 ),
inference(forward_demodulation,[],[f2052,f122]) ).
thf(f2069,plain,
( ! [X0: $i] :
( $true
= ( p0 @ X0 ) )
| ~ spl61_24 ),
inference(trivial_inequality_removal,[],[f2068]) ).
thf(f2072,plain,
( ( $true = $false )
| ~ spl61_25 ),
inference(constrained_superposition,[],[f2029,f199]) ).
thf(f2076,plain,
( $false
| ~ spl61_25 ),
inference(trivial_inequality_removal,[],[f2072]) ).
thf(f2077,plain,
~ spl61_25,
inference(avatar_contradiction_clause,[],[f2076]) ).
thf(f2078,plain,
( spl61_25
| ~ spl61_24 ),
inference(avatar_split_clause,[],[f2069,f1979,f2028]) ).
thf(f2079,plain,
( ! [X1: $i] :
( $true
= ( p1 @ X1 ) )
| ~ spl61_23 ),
inference(global_subsumption,[],[f2022]) ).
thf(f2083,plain,
( spl61_24
| ~ spl61_23 ),
inference(avatar_split_clause,[],[f2079,f1930,f1979]) ).
thf(f2084,plain,
( ! [X1: $i] :
( $true
= ( p2 @ X1 ) )
| ~ spl61_22 ),
inference(global_subsumption,[],[f1973]) ).
thf(f2088,plain,
( spl61_23
| ~ spl61_22 ),
inference(avatar_split_clause,[],[f2084,f1881,f1930]) ).
thf(f2089,plain,
( ! [X1: $i] :
( $true
= ( p3 @ X1 ) )
| ~ spl61_21 ),
inference(global_subsumption,[],[f1924]) ).
thf(f2093,plain,
( spl61_22
| ~ spl61_21 ),
inference(avatar_split_clause,[],[f2089,f1832,f1881]) ).
thf(f2098,plain,
( spl61_21
| ~ spl61_20 ),
inference(avatar_split_clause,[],[f1873,f1783,f1832]) ).
thf(f2099,plain,
( ! [X1: $i] :
( $true
= ( p5 @ X1 ) )
| ~ spl61_19 ),
inference(global_subsumption,[],[f1826]) ).
thf(f2103,plain,
( spl61_20
| ~ spl61_19 ),
inference(avatar_split_clause,[],[f2099,f1734,f1783]) ).
thf(f2108,plain,
( spl61_19
| ~ spl61_18 ),
inference(avatar_split_clause,[],[f1775,f1685,f1734]) ).
thf(f2109,plain,
( ! [X1: $i] :
( $true
= ( p7 @ X1 ) )
| ~ spl61_17 ),
inference(global_subsumption,[],[f1728]) ).
thf(f2113,plain,
( spl61_18
| ~ spl61_17 ),
inference(avatar_split_clause,[],[f2109,f1636,f1685]) ).
thf(f2114,plain,
( ! [X1: $i] :
( $true
= ( p8 @ X1 ) )
| ~ spl61_16 ),
inference(global_subsumption,[],[f1679]) ).
thf(f2118,plain,
( spl61_17
| ~ spl61_16 ),
inference(avatar_split_clause,[],[f2114,f1587,f1636]) ).
thf(f2123,plain,
( spl61_16
| ~ spl61_15 ),
inference(avatar_split_clause,[],[f1628,f1538,f1587]) ).
thf(f2128,plain,
( spl61_15
| ~ spl61_14 ),
inference(avatar_split_clause,[],[f1579,f1489,f1538]) ).
thf(f2133,plain,
( spl61_14
| ~ spl61_13 ),
inference(avatar_split_clause,[],[f1530,f1440,f1489]) ).
thf(f2138,plain,
( spl61_13
| ~ spl61_12 ),
inference(avatar_split_clause,[],[f1481,f1391,f1440]) ).
thf(f2143,plain,
( spl61_12
| ~ spl61_11 ),
inference(avatar_split_clause,[],[f1432,f1342,f1391]) ).
thf(f2144,plain,
( ! [X1: $i] :
( $true
= ( p14 @ X1 ) )
| ~ spl61_10 ),
inference(global_subsumption,[],[f1385]) ).
thf(f2148,plain,
( spl61_11
| ~ spl61_10 ),
inference(avatar_split_clause,[],[f2144,f1293,f1342]) ).
thf(f2149,plain,
( ! [X1: $i] :
( $true
= ( p15 @ X1 ) )
| ~ spl61_9 ),
inference(global_subsumption,[],[f1336]) ).
thf(f2153,plain,
( spl61_10
| ~ spl61_9 ),
inference(avatar_split_clause,[],[f2149,f1244,f1293]) ).
thf(f2158,plain,
( spl61_9
| ~ spl61_8 ),
inference(avatar_split_clause,[],[f1285,f1195,f1244]) ).
thf(f2159,plain,
( ! [X1: $i] :
( $true
= ( p17 @ X1 ) )
| ~ spl61_7 ),
inference(global_subsumption,[],[f1238]) ).
thf(f2163,plain,
( spl61_8
| ~ spl61_7 ),
inference(avatar_split_clause,[],[f2159,f1146,f1195]) ).
thf(f2164,plain,
( ! [X1: $i] :
( $true
= ( p18 @ X1 ) )
| ~ spl61_6 ),
inference(global_subsumption,[],[f1189]) ).
thf(f2168,plain,
( spl61_7
| ~ spl61_6 ),
inference(avatar_split_clause,[],[f2164,f970,f1146]) ).
thf(f2169,plain,
! [X1: $i] :
( $true
= ( p19 @ X1 ) ),
inference(global_subsumption,[],[f993]) ).
thf(f2173,plain,
spl61_6,
inference(avatar_split_clause,[],[f2169,f970]) ).
cnf(s405,plain,
~ spl61_25,
inference(sat_conversion,[],[f2077]) ).
cnf(s407,plain,
( ~ spl61_24
| spl61_25 ),
inference(sat_conversion,[],[f2078]) ).
cnf(s420,plain,
( ~ spl61_23
| spl61_24 ),
inference(sat_conversion,[],[f2083]) ).
cnf(s433,plain,
( ~ spl61_22
| spl61_23 ),
inference(sat_conversion,[],[f2088]) ).
cnf(s446,plain,
( ~ spl61_21
| spl61_22 ),
inference(sat_conversion,[],[f2093]) ).
cnf(s459,plain,
( ~ spl61_20
| spl61_21 ),
inference(sat_conversion,[],[f2098]) ).
cnf(s472,plain,
( ~ spl61_19
| spl61_20 ),
inference(sat_conversion,[],[f2103]) ).
cnf(s485,plain,
( ~ spl61_18
| spl61_19 ),
inference(sat_conversion,[],[f2108]) ).
cnf(s498,plain,
( ~ spl61_17
| spl61_18 ),
inference(sat_conversion,[],[f2113]) ).
cnf(s511,plain,
( ~ spl61_16
| spl61_17 ),
inference(sat_conversion,[],[f2118]) ).
cnf(s524,plain,
( ~ spl61_15
| spl61_16 ),
inference(sat_conversion,[],[f2123]) ).
cnf(s537,plain,
( ~ spl61_14
| spl61_15 ),
inference(sat_conversion,[],[f2128]) ).
cnf(s550,plain,
( ~ spl61_13
| spl61_14 ),
inference(sat_conversion,[],[f2133]) ).
cnf(s563,plain,
( ~ spl61_12
| spl61_13 ),
inference(sat_conversion,[],[f2138]) ).
cnf(s576,plain,
( ~ spl61_11
| spl61_12 ),
inference(sat_conversion,[],[f2143]) ).
cnf(s589,plain,
( ~ spl61_10
| spl61_11 ),
inference(sat_conversion,[],[f2148]) ).
cnf(s602,plain,
( ~ spl61_9
| spl61_10 ),
inference(sat_conversion,[],[f2153]) ).
cnf(s615,plain,
( ~ spl61_8
| spl61_9 ),
inference(sat_conversion,[],[f2158]) ).
cnf(s628,plain,
( ~ spl61_7
| spl61_8 ),
inference(sat_conversion,[],[f2163]) ).
cnf(s641,plain,
( ~ spl61_6
| spl61_7 ),
inference(sat_conversion,[],[f2168]) ).
cnf(s654,plain,
spl61_6,
inference(sat_conversion,[],[f2173]) ).
cnf(s655,plain,
spl61_7,
inference(rat,[],[s641,s654]) ).
cnf(s656,plain,
spl61_8,
inference(rat,[],[s628,s655]) ).
cnf(s657,plain,
spl61_9,
inference(rat,[],[s615,s656]) ).
cnf(s658,plain,
spl61_10,
inference(rat,[],[s602,s657]) ).
cnf(s659,plain,
spl61_11,
inference(rat,[],[s589,s658]) ).
cnf(s660,plain,
spl61_12,
inference(rat,[],[s576,s659]) ).
cnf(s661,plain,
spl61_13,
inference(rat,[],[s563,s660]) ).
cnf(s662,plain,
spl61_14,
inference(rat,[],[s550,s661]) ).
cnf(s663,plain,
spl61_15,
inference(rat,[],[s537,s662]) ).
cnf(s664,plain,
spl61_16,
inference(rat,[],[s524,s663]) ).
cnf(s665,plain,
spl61_17,
inference(rat,[],[s511,s664]) ).
cnf(s666,plain,
spl61_18,
inference(rat,[],[s498,s665]) ).
cnf(s667,plain,
spl61_19,
inference(rat,[],[s485,s666]) ).
cnf(s668,plain,
spl61_20,
inference(rat,[],[s472,s667]) ).
cnf(s669,plain,
spl61_21,
inference(rat,[],[s459,s668]) ).
cnf(s670,plain,
spl61_22,
inference(rat,[],[s446,s669]) ).
cnf(s671,plain,
spl61_23,
inference(rat,[],[s433,s670]) ).
cnf(s672,plain,
spl61_24,
inference(rat,[],[s420,s671]) ).
cnf(s673,plain,
spl61_25,
inference(rat,[],[s407,s672]) ).
cnf(s674,plain,
$false,
inference(rat,[],[s405,s673]) ).
thf(f2174,plain,
$false,
inference(avatar_sat_refutation,[],[s674]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO068^4.020 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n008.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:30:09 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 0.20/0.34 % (3375550)Will run a generic schedule for satisfiability detection.
% 0.20/0.34 % (3375557)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=405960593:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.34 % (3375556)% WARNING: option uhcvi not known.
% 0.20/0.34 % (3375555)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4173775293_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.34 % (3375556)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3432998975:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.34 % (3375556)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.34 % Exception at run slice level
% 0.20/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.34 % (3375556)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.34 % (3375559)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2345041208:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.34 % (3375559)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.34 % (3375565)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1976710729:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.34 % (3375558)dis+10_1_sil=32000:sp=arity:random_seed=53122186:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.34 % (3375560)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1463731666:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.34 % (3375561)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4161625733:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.34 % Exception at run slice level
% 0.20/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.34 % (3375557) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3375550-3375557"...
% 0.20/0.34 % (3375571)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2787873146:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.34 % (3375557)...printing done.
% 0.20/0.34 % (3375557)Refutation found. Thanks to Tanya!
% 0.20/0.34 % SZS status Theorem for theBenchmark
% 0.20/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.35 % (3375557)------------------------------
% 0.20/0.35 % (3375557)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3375557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3375557)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3375557)Termination reason: Refutation
% 0.20/0.35 % (3375557)Time elapsed: 0.065 s
% 0.20/0.35 % (3375557)Peak memory usage: 14 MB
% 0.20/0.35 % (3375557)Instructions burned: 265 (million)
% 0.20/0.35 % (3375550)Success in time 0.099 s
% 0.20/0.35 % Vampire exiting
%------------------------------------------------------------------------------