%------------------------------------------------------------------------------
% File : Vampire---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/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:46:29 AM UTC 2026
% Result : Theorem 0.21s 0.36s
% Output : Refutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 116
% Number of leaves : 34
% Syntax : Number of formulae : 669 ( 190 unt; 0 typ; 4 def)
% Number of atoms : 7569 (1554 equ; 0 cnn)
% Maximal formula atoms : 9 ( 11 avg)
% Number of connectives : 11324 ( 401 ~;1256 |; 0 &;7776 @)
% ( 3 <=>;1053 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 499 ( 499 >; 0 *; 0 +; 0 <<)
% Number of symbols : 121 ( 117 usr; 8 con; 0-4 aty)
% ( 835 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 2517 ( 0 sgn 849 !; 0 ?;2517 :)
% 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_42,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_44,type,
vNOT: $o > $o ).
thf(func_def_45,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
vOR: $o > $o > $o ).
thf(func_def_51,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
vAND: $o > $o > $o ).
thf(func_def_53,type,
vIMP: $o > $o > $o ).
thf(func_def_54,type,
sF0: $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_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(func_def_115,type,
sK61: $i > $i ).
thf(f1,axiom,
! [X0: $i] : ( irel @ X0 @ X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',refl_axiom) ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).
thf(f8,axiom,
( ( ^ [X0: $i > $o] : X0 )
= iatom ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL010^0.ax',iimplies) ).
thf(f18,axiom,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,axiom,
ivalid @ ( iatom @ p20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).
thf(f23,axiom,
ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2) ).
thf(f24,axiom,
ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom3) ).
thf(f25,axiom,
ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom4) ).
thf(f26,axiom,
ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom5) ).
thf(f27,axiom,
ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom6) ).
thf(f28,axiom,
ivalid @ ( iimplies @ ( iatom @ p6 ) @ ( iimplies @ ( iatom @ p6 ) @ ( iatom @ p5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom7) ).
thf(f29,axiom,
ivalid @ ( iimplies @ ( iatom @ p7 ) @ ( iimplies @ ( iatom @ p7 ) @ ( iatom @ p6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom8) ).
thf(f30,axiom,
ivalid @ ( iimplies @ ( iatom @ p8 ) @ ( iimplies @ ( iatom @ p8 ) @ ( iatom @ p7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom9) ).
thf(f31,axiom,
ivalid @ ( iimplies @ ( iatom @ p9 ) @ ( iimplies @ ( iatom @ p9 ) @ ( iatom @ p8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom10) ).
thf(f32,axiom,
ivalid @ ( iimplies @ ( iatom @ p10 ) @ ( iimplies @ ( iatom @ p10 ) @ ( iatom @ p9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom11) ).
thf(f33,axiom,
ivalid @ ( iimplies @ ( iatom @ p11 ) @ ( iimplies @ ( iatom @ p11 ) @ ( iatom @ p10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom12) ).
thf(f34,axiom,
ivalid @ ( iimplies @ ( iatom @ p12 ) @ ( iimplies @ ( iatom @ p12 ) @ ( iatom @ p11 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom13) ).
thf(f35,axiom,
ivalid @ ( iimplies @ ( iatom @ p13 ) @ ( iimplies @ ( iatom @ p13 ) @ ( iatom @ p12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom14) ).
thf(f36,axiom,
ivalid @ ( iimplies @ ( iatom @ p14 ) @ ( iimplies @ ( iatom @ p14 ) @ ( iatom @ p13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom15) ).
thf(f37,axiom,
ivalid @ ( iimplies @ ( iatom @ p15 ) @ ( iimplies @ ( iatom @ p15 ) @ ( iatom @ p14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom16) ).
thf(f38,axiom,
ivalid @ ( iimplies @ ( iatom @ p16 ) @ ( iimplies @ ( iatom @ p16 ) @ ( iatom @ p15 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom17) ).
thf(f39,axiom,
ivalid @ ( iimplies @ ( iatom @ p17 ) @ ( iimplies @ ( iatom @ p17 ) @ ( iatom @ p16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom18) ).
thf(f40,axiom,
ivalid @ ( iimplies @ ( iatom @ p18 ) @ ( iimplies @ ( iatom @ p18 ) @ ( iatom @ p17 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom19) ).
thf(f41,axiom,
ivalid @ ( iimplies @ ( iatom @ p19 ) @ ( iimplies @ ( iatom @ p19 ) @ ( iatom @ p18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom20) ).
thf(f42,axiom,
ivalid @ ( iimplies @ ( iatom @ p20 ) @ ( iimplies @ ( iatom @ p20 ) @ ( iatom @ p19 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom21) ).
thf(f43,conjecture,
ivalid @ ( iatom @ p0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f44,negated_conjecture,
~ ( ivalid @ ( iatom @ p0 ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
thf(f45,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f46,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f47,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f51,plain,
ivalid @ ( iimplies @ ( iatom @ p7 ) @ ( iimplies @ ( iatom @ p7 ) @ ( iatom @ p6 ) ) ),
inference(rectify,[],[f29]) ).
thf(f52,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p7 ) @ ( iimplies @ ( iatom @ p7 ) @ ( iatom @ p6 ) ) ) )
= $true ),
inference(fool_elimination,[],[f51]) ).
thf(f53,plain,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f54,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f59,plain,
ivalid @ ( iimplies @ ( iatom @ p13 ) @ ( iimplies @ ( iatom @ p13 ) @ ( iatom @ p12 ) ) ),
inference(rectify,[],[f35]) ).
thf(f60,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p13 ) @ ( iimplies @ ( iatom @ p13 ) @ ( iatom @ p12 ) ) ) )
= $true ),
inference(fool_elimination,[],[f59]) ).
thf(f62,plain,
ivalid @ ( iimplies @ ( iatom @ p14 ) @ ( iimplies @ ( iatom @ p14 ) @ ( iatom @ p13 ) ) ),
inference(rectify,[],[f36]) ).
thf(f63,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p14 ) @ ( iimplies @ ( iatom @ p14 ) @ ( iatom @ p13 ) ) ) )
= $true ),
inference(fool_elimination,[],[f62]) ).
thf(f64,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f65,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f64]) ).
thf(f66,plain,
ivalid @ ( iimplies @ ( iatom @ p11 ) @ ( iimplies @ ( iatom @ p11 ) @ ( iatom @ p10 ) ) ),
inference(rectify,[],[f33]) ).
thf(f67,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p11 ) @ ( iimplies @ ( iatom @ p11 ) @ ( iatom @ p10 ) ) ) )
= $true ),
inference(fool_elimination,[],[f66]) ).
thf(f70,plain,
ivalid @ ( iimplies @ ( iatom @ p17 ) @ ( iimplies @ ( iatom @ p17 ) @ ( iatom @ p16 ) ) ),
inference(rectify,[],[f39]) ).
thf(f71,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p17 ) @ ( iimplies @ ( iatom @ p17 ) @ ( iatom @ p16 ) ) ) )
= $true ),
inference(fool_elimination,[],[f70]) ).
thf(f73,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f74,plain,
ivalid @ ( iimplies @ ( iatom @ p12 ) @ ( iimplies @ ( iatom @ p12 ) @ ( iatom @ p11 ) ) ),
inference(rectify,[],[f34]) ).
thf(f75,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p12 ) @ ( iimplies @ ( iatom @ p12 ) @ ( iatom @ p11 ) ) ) )
= $true ),
inference(fool_elimination,[],[f74]) ).
thf(f78,plain,
ivalid @ ( iimplies @ ( iatom @ p15 ) @ ( iimplies @ ( iatom @ p15 ) @ ( iatom @ p14 ) ) ),
inference(rectify,[],[f37]) ).
thf(f79,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p15 ) @ ( iimplies @ ( iatom @ p15 ) @ ( iatom @ p14 ) ) ) )
= $true ),
inference(fool_elimination,[],[f78]) ).
thf(f80,plain,
ivalid @ ( iimplies @ ( iatom @ p20 ) @ ( iimplies @ ( iatom @ p20 ) @ ( iatom @ p19 ) ) ),
inference(rectify,[],[f42]) ).
thf(f81,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p20 ) @ ( iimplies @ ( iatom @ p20 ) @ ( iatom @ p19 ) ) ) )
= $true ),
inference(fool_elimination,[],[f80]) ).
thf(f82,plain,
ivalid @ ( iimplies @ ( iatom @ p19 ) @ ( iimplies @ ( iatom @ p19 ) @ ( iatom @ p18 ) ) ),
inference(rectify,[],[f41]) ).
thf(f83,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p19 ) @ ( iimplies @ ( iatom @ p19 ) @ ( iatom @ p18 ) ) ) )
= $true ),
inference(fool_elimination,[],[f82]) ).
thf(f84,plain,
ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ),
inference(rectify,[],[f26]) ).
thf(f85,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ) )
= $true ),
inference(fool_elimination,[],[f84]) ).
thf(f86,plain,
ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ),
inference(rectify,[],[f27]) ).
thf(f87,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ) )
= $true ),
inference(fool_elimination,[],[f86]) ).
thf(f88,plain,
ivalid @ ( iimplies @ ( iatom @ p16 ) @ ( iimplies @ ( iatom @ p16 ) @ ( iatom @ p15 ) ) ),
inference(rectify,[],[f38]) ).
thf(f89,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p16 ) @ ( iimplies @ ( iatom @ p16 ) @ ( iatom @ p15 ) ) ) )
= $true ),
inference(fool_elimination,[],[f88]) ).
thf(f90,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f91,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f92,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f93,plain,
ivalid @ ( iimplies @ ( iatom @ p18 ) @ ( iimplies @ ( iatom @ p18 ) @ ( iatom @ p17 ) ) ),
inference(rectify,[],[f40]) ).
thf(f94,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p18 ) @ ( iimplies @ ( iatom @ p18 ) @ ( iatom @ p17 ) ) ) )
= $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 @ ( iatom @ p0 ) ),
inference(rectify,[],[f44]) ).
thf(f98,plain,
( ( ivalid @ ( iatom @ p0 ) )
!= $true ),
inference(fool_elimination,[],[f97]) ).
thf(f99,plain,
ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ),
inference(rectify,[],[f25]) ).
thf(f100,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ) )
= $true ),
inference(fool_elimination,[],[f99]) ).
thf(f101,plain,
ivalid @ ( iimplies @ ( iatom @ p8 ) @ ( iimplies @ ( iatom @ p8 ) @ ( iatom @ p7 ) ) ),
inference(rectify,[],[f30]) ).
thf(f102,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p8 ) @ ( iimplies @ ( iatom @ p8 ) @ ( iatom @ p7 ) ) ) )
= $true ),
inference(fool_elimination,[],[f101]) ).
thf(f103,plain,
! [X0: $i] : ( irel @ X0 @ X0 ),
inference(rectify,[],[f1]) ).
thf(f104,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f103]) ).
thf(f105,plain,
ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ),
inference(rectify,[],[f23]) ).
thf(f106,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ) )
= $true ),
inference(fool_elimination,[],[f105]) ).
thf(f107,plain,
ivalid @ ( iimplies @ ( iatom @ p6 ) @ ( iimplies @ ( iatom @ p6 ) @ ( iatom @ p5 ) ) ),
inference(rectify,[],[f28]) ).
thf(f108,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p6 ) @ ( iimplies @ ( iatom @ p6 ) @ ( iatom @ p5 ) ) ) )
= $true ),
inference(fool_elimination,[],[f107]) ).
thf(f109,plain,
ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ),
inference(rectify,[],[f24]) ).
thf(f110,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ) )
= $true ),
inference(fool_elimination,[],[f109]) ).
thf(f113,plain,
ivalid @ ( iimplies @ ( iatom @ p9 ) @ ( iimplies @ ( iatom @ p9 ) @ ( iatom @ p8 ) ) ),
inference(rectify,[],[f31]) ).
thf(f114,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p9 ) @ ( iimplies @ ( iatom @ p9 ) @ ( iatom @ p8 ) ) ) )
= $true ),
inference(fool_elimination,[],[f113]) ).
thf(f117,plain,
ivalid @ ( iatom @ p20 ),
inference(rectify,[],[f22]) ).
thf(f118,plain,
( ( ivalid @ ( iatom @ p20 ) )
= $true ),
inference(fool_elimination,[],[f117]) ).
thf(f119,plain,
( ( ivalid @ ( iatom @ p0 ) )
!= $true ),
inference(flattening,[],[f98]) ).
thf(f124,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p10 ) @ ( iimplies @ ( iatom @ p10 ) @ ( iatom @ p9 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f96]) ).
thf(f125,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f126,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p19 ) @ ( iimplies @ ( iatom @ p19 ) @ ( iatom @ p18 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f83]) ).
thf(f127,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f73]) ).
thf(f128,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p17 ) @ ( iimplies @ ( iatom @ p17 ) @ ( iatom @ p16 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f71]) ).
thf(f129,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f130,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f87]) ).
thf(f131,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f132,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p16 ) @ ( iimplies @ ( iatom @ p16 ) @ ( iatom @ p15 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f89]) ).
thf(f135,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f136,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f104]) ).
thf(f137,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f140,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p20 ) @ ( iimplies @ ( iatom @ p20 ) @ ( iatom @ p19 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f81]) ).
thf(f142,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p12 ) @ ( iimplies @ ( iatom @ p12 ) @ ( iatom @ p11 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f75]) ).
thf(f144,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f100]) ).
thf(f145,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p18 ) @ ( iimplies @ ( iatom @ p18 ) @ ( iatom @ p17 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f94]) ).
thf(f146,plain,
( ( ivalid @ ( iatom @ p0 ) )
!= $true ),
inference(cnf_transformation,[],[f119]) ).
thf(f147,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p15 ) @ ( iimplies @ ( iatom @ p15 ) @ ( iatom @ p14 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f79]) ).
thf(f148,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f106]) ).
thf(f150,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p7 ) @ ( iimplies @ ( iatom @ p7 ) @ ( iatom @ p6 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f52]) ).
thf(f151,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p11 ) @ ( iimplies @ ( iatom @ p11 ) @ ( iatom @ p10 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f67]) ).
thf(f152,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f153,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p13 ) @ ( iimplies @ ( iatom @ p13 ) @ ( iatom @ p12 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f60]) ).
thf(f155,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p9 ) @ ( iimplies @ ( iatom @ p9 ) @ ( iatom @ p8 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f114]) ).
thf(f156,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f85]) ).
thf(f158,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f110]) ).
thf(f160,plain,
( ( ivalid @ ( iatom @ p20 ) )
= $true ),
inference(cnf_transformation,[],[f118]) ).
thf(f161,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p8 ) @ ( iimplies @ ( iatom @ p8 ) @ ( iatom @ p7 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f102]) ).
thf(f163,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p14 ) @ ( iimplies @ ( iatom @ p14 ) @ ( iatom @ p13 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f63]) ).
thf(f165,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p6 ) @ ( iimplies @ ( iatom @ p6 ) @ ( iatom @ p5 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f108]) ).
thf(f168,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f127,f131,f135]) ).
thf(f173,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ 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,[],[f129,f168,f152,f152]) ).
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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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,[],[f124,f137,f173,f125,f173,f125,f125]) ).
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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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,[],[f126,f137,f173,f125,f173,f125,f125]) ).
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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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,[],[f128,f137,f173,f125,f173,f125,f125]) ).
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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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,[],[f130,f137,f173,f125,f173,f125,f125]) ).
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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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,[],[f132,f137,f173,f125,f173,f125,f125]) ).
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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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,[],[f140,f137,f173,f125,f173,f125,f125]) ).
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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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,[],[f142,f137,f173,f125,f173,f125,f125]) ).
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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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,[],[f144,f137,f173,f125,f173,f125,f125]) ).
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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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,[],[f145,f137,f173,f125,f173,f125,f125]) ).
thf(f186,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p0 ) ) ),
inference(definition_unfolding,[],[f146,f137,f125]) ).
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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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,[],[f147,f137,f173,f125,f173,f125,f125]) ).
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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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,[],[f148,f137,f173,f125,f173,f125,f125]) ).
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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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,f137,f173,f125,f173,f125,f125]) ).
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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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,[],[f151,f137,f173,f125,f173,f125,f125]) ).
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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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,[],[f153,f137,f173,f125,f173,f125,f125]) ).
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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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,[],[f155,f137,f173,f125,f173,f125,f125]) ).
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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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,[],[f156,f137,f173,f125,f173,f125,f125]) ).
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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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,[],[f158,f137,f173,f125,f173,f125,f125]) ).
thf(f195,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p20 ) ) ),
inference(definition_unfolding,[],[f160,f137,f125]) ).
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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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,[],[f161,f137,f173,f125,f173,f125,f125]) ).
thf(f197,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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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,[],[f163,f137,f173,f125,f173,f125,f125]) ).
thf(f198,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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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,[],[f165,f137,f173,f125,f173,f125,f125]) ).
thf(f199,definition,
( sF0
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p0 ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f200,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p0 ) )
= sF0 ),
inference(reorient_equations,[],[f199]) ).
thf(f201,plain,
$true != sF0,
inference(definition_folding,[],[f186,f200]) ).
thf(f202,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p16 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p17 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f203,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p16 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p17 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p17 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f203]) ).
thf(f205,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p17 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p17 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f205]) ).
thf(f207,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 )
=> ( p17 @ Y1 ) ) ) ) )
@ X2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p17 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p17 @ Y0 ) )
@ ( sK1 @ X1 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( irel @ X1 @ ( sK1 @ X1 ) )
=> ( p17 @ ( sK1 @ X1 ) ) ) )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f208]) ).
thf(f210,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) ) ) ) ) )
| ( ( p17 @ ( sK1 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f209]) ).
thf(f222,plain,
! [X2: $i,X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p17 @ ( sK1 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f210]) ).
thf(f223,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) ) ) )
| ( ( p17 @ ( sK1 @ X1 ) )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f222]) ).
thf(f224,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( p17 @ ( sK1 @ X1 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) )
@ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p17 @ ( sK1 @ X1 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f224]) ).
thf(f226,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p17 @ ( sK1 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) )
@ ( sK3 @ X2 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) )
@ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X2 @ X3 )
=> ( p16 @ X3 ) ) )
| ( ( ( irel @ X2 @ ( sK3 @ X2 ) )
=> ( p17 @ ( sK3 @ X2 ) ) )
= $false )
| ( ( p17 @ ( sK1 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f226]) ).
thf(f228,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p17 @ ( sK1 @ X1 ) )
= $false )
| ( ( ( irel @ X2 @ ( sK3 @ X2 ) )
=> ( p17 @ ( sK3 @ X2 ) ) )
= $false )
| ( $true
= ( p16 @ X3 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( p17 @ ( sK1 @ X1 ) )
= $false )
| ( $true
= ( p16 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p17 @ ( sK3 @ X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f228]) ).
thf(f231,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p11 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p12 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f232,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p11 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p12 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p11 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p12 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f232]) ).
thf(f234,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p12 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p11 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f233]) ).
thf(f235,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p12 @ Y0 ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p11 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f234]) ).
thf(f236,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p11 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p12 @ Y0 ) )
@ ( sK4 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p12 @ Y0 ) )
@ ( sK4 @ X1 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p11 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) ) ) ) )
= $true )
| ( ( ( irel @ X1 @ ( sK4 @ X1 ) )
=> ( p12 @ ( sK4 @ X1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f237]) ).
thf(f239,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) ) ) ) )
| ( ( ( irel @ X1 @ ( sK4 @ X1 ) )
=> ( p12 @ ( sK4 @ X1 ) ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f238]) ).
thf(f240,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ ( sK4 @ X1 ) )
=> ( p12 @ ( sK4 @ X1 ) ) )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) ) ) ) )
| ( $false
= ( p12 @ ( sK4 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f240]) ).
thf(f251,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p12 @ ( sK4 @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f241]) ).
thf(f252,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) )
@ ( sK6 @ X2 ) ) )
| ( $false
= ( p12 @ ( sK4 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f251]) ).
thf(f253,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p12 @ ( sK4 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) )
@ ( sK6 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f252]) ).
thf(f254,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( irel @ X2 @ ( sK6 @ X2 ) )
=> ( p12 @ ( sK6 @ X2 ) ) ) )
| ( $false
= ( p12 @ ( sK4 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p11 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f253]) ).
thf(f255,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X2 @ X3 )
=> ( p11 @ X3 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p12 @ ( sK6 @ X2 ) )
= $false )
| ( $false
= ( p12 @ ( sK4 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f254]) ).
thf(f258,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p11 @ X3 ) )
| ( ( p12 @ ( sK6 @ X2 ) )
= $false )
| ( $false
= ( p12 @ ( sK4 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f255]) ).
thf(f259,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p9 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p10 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f260,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p9 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p10 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f259]) ).
thf(f261,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f260]) ).
thf(f262,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f261]) ).
thf(f263,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 )
=> ( p10 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f262]) ).
thf(f264,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p10 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(not_proxy_clausification,[],[f263]) ).
thf(f265,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 )
=> ( p10 @ Y1 ) ) ) ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p10 @ Y0 ) )
@ ( sK7 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f264]) ).
thf(f266,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ ( sK7 @ X1 ) )
=> ( p10 @ ( sK7 @ X1 ) ) )
= $false )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f265]) ).
thf(f267,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ) )
| ( $false
= ( p10 @ ( sK7 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f266]) ).
thf(f278,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) )
| ( $false
= ( p10 @ ( sK7 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f267]) ).
thf(f279,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) )
| ( $false
= ( p10 @ ( sK7 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f278]) ).
thf(f280,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p10 @ ( sK7 @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f279]) ).
thf(f281,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) )
@ ( sK9 @ X2 ) ) )
| ( $false
= ( p10 @ ( sK7 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f280]) ).
thf(f282,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) )
@ X3 ) )
| ( $false
= ( p10 @ ( sK7 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) )
@ ( sK9 @ X2 ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f281]) ).
thf(f283,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p10 @ ( sK7 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ( irel @ X2 @ ( sK9 @ X2 ) )
=> ( p10 @ ( sK9 @ X2 ) ) )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p9 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f282]) ).
thf(f284,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p10 @ ( sK7 @ X1 ) ) )
| ( ( p10 @ ( sK9 @ X2 ) )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p9 @ X3 ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f283]) ).
thf(f287,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( p9 @ X3 ) )
| ( $false
= ( p10 @ ( sK7 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p10 @ ( sK9 @ X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f284]) ).
thf(f288,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p18 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p19 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f178]) ).
thf(f289,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p18 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p19 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f288]) ).
thf(f290,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p19 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f289]) ).
thf(f291,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p19 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f290]) ).
thf(f292,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p19 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f291]) ).
thf(f293,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p19 @ Y0 ) ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f292]) ).
thf(f294,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 )
=> ( p19 @ Y1 ) ) ) ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p19 @ Y0 ) )
@ ( sK10 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f293]) ).
thf(f295,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) ) ) ) ) )
| ( ( ( irel @ X1 @ ( sK10 @ X1 ) )
=> ( p19 @ ( sK10 @ X1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f294]) ).
thf(f296,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) ) ) ) )
| ( ( ( irel @ X1 @ ( sK10 @ X1 ) )
=> ( p19 @ ( sK10 @ X1 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f295]) ).
thf(f297,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ ( sK10 @ X1 ) )
=> ( p19 @ ( sK10 @ X1 ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f296]) ).
thf(f298,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) ) ) )
| ( ( p19 @ ( sK10 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f297]) ).
thf(f307,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p19 @ ( sK10 @ X1 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f298]) ).
thf(f308,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) )
@ ( sK12 @ X2 ) )
= $false )
| ( ( p19 @ ( sK10 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f307]) ).
thf(f309,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) )
@ X3 ) )
| ( ( p19 @ ( sK10 @ X1 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) )
@ ( sK12 @ X2 ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f308]) ).
thf(f310,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( p19 @ ( sK10 @ X1 ) )
= $false )
| ( $false
= ( ( irel @ X2 @ ( sK12 @ X2 ) )
=> ( p19 @ ( sK12 @ X2 ) ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p18 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f309]) ).
thf(f311,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p18 @ X3 ) ) )
| ( ( p19 @ ( sK10 @ X1 ) )
= $false )
| ( ( p19 @ ( sK12 @ X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f310]) ).
thf(f314,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( p19 @ ( sK10 @ X1 ) )
= $false )
| ( $true
= ( p18 @ X3 ) )
| ( ( p19 @ ( sK12 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f311]) ).
thf(f316,plain,
( ( $true = sF0 )
| ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p0 ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f200]) ).
thf(f317,plain,
( ( $true = sF0 )
| ( ( !! @ $i @ p0 )
= $false ) ),
inference(beta-eta_normalization,[],[f316]) ).
thf(f318,plain,
( ( $true = sF0 )
| ( ( p0 @ sK13 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f317]) ).
thf(f321,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p17 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p18 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f322,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p17 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p18 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f321]) ).
thf(f323,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p18 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f322]) ).
thf(f324,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p18 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f323]) ).
thf(f325,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p18 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f324]) ).
thf(f326,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p18 @ Y0 ) ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f325]) ).
thf(f327,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p18 @ Y0 ) )
@ ( sK14 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p17 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p18 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f326]) ).
thf(f328,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( irel @ X1 @ ( sK14 @ X1 ) )
=> ( p18 @ ( sK14 @ X1 ) ) ) )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f327]) ).
thf(f329,plain,
! [X2: $i,X1: $i] :
( ( ( p18 @ ( sK14 @ X1 ) )
= $false )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f328]) ).
thf(f340,plain,
! [X2: $i,X1: $i] :
( ( ( p18 @ ( sK14 @ X1 ) )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f329]) ).
thf(f341,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) ) ) ) )
| ( ( p18 @ ( sK14 @ X1 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f340]) ).
thf(f342,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p18 @ ( sK14 @ X1 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f341]) ).
thf(f343,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p18 @ ( sK14 @ X1 ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) )
@ ( sK16 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f342]) ).
thf(f344,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( p18 @ ( sK14 @ X1 ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p18 @ Y0 ) )
@ ( sK16 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p17 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f343]) ).
thf(f345,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p18 @ ( sK14 @ X1 ) )
= $false )
| ( $false
= ( ( irel @ X2 @ ( sK16 @ X2 ) )
=> ( p18 @ ( sK16 @ X2 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p17 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f344]) ).
thf(f346,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p17 @ X3 ) ) )
| ( ( p18 @ ( sK14 @ X1 ) )
= $false )
| ( ( p18 @ ( sK16 @ X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f345]) ).
thf(f349,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( p17 @ X3 ) )
| ( ( p18 @ ( sK16 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p18 @ ( sK14 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f346]) ).
thf(f350,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p4 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p5 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f351,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p4 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p5 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f350]) ).
thf(f352,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f351]) ).
thf(f353,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f352]) ).
thf(f354,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f353]) ).
thf(f355,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f354]) ).
thf(f356,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) )
@ ( sK17 @ X1 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f355]) ).
thf(f357,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ ( sK17 @ X1 ) )
=> ( p5 @ ( sK17 @ X1 ) ) )
= $false )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f356]) ).
thf(f358,plain,
! [X2: $i,X1: $i] :
( ( ( p5 @ ( sK17 @ X1 ) )
= $false )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f357]) ).
thf(f370,plain,
! [X2: $i,X1: $i] :
( ( ( p5 @ ( sK17 @ X1 ) )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f358]) ).
thf(f371,plain,
! [X2: $i,X1: $i] :
( ( ( p5 @ ( sK17 @ X1 ) )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f370]) ).
thf(f372,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) )
| ( ( p5 @ ( sK17 @ X1 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f371]) ).
thf(f373,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) )
@ ( sK19 @ X2 ) )
= $false )
| ( ( p5 @ ( sK17 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f372]) ).
thf(f374,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) )
@ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) )
@ ( sK19 @ X2 ) )
= $false )
| ( ( p5 @ ( sK17 @ X1 ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f373]) ).
thf(f375,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p5 @ ( sK17 @ X1 ) )
= $false )
| ( $false
= ( ( irel @ X2 @ ( sK19 @ X2 ) )
=> ( p5 @ ( sK19 @ X2 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p4 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f374]) ).
thf(f376,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p4 @ X3 ) ) )
| ( ( p5 @ ( sK19 @ X2 ) )
= $false )
| ( ( p5 @ ( sK17 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f375]) ).
thf(f379,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( p5 @ ( sK17 @ X1 ) )
= $false )
| ( ( p5 @ ( sK19 @ X2 ) )
= $false )
| ( $true
= ( p4 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f376]) ).
thf(f380,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p6 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p7 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f189]) ).
thf(f381,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p6 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p7 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f380]) ).
thf(f382,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f381]) ).
thf(f383,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f382]) ).
thf(f384,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f383]) ).
thf(f385,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p7 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(not_proxy_clausification,[],[f384]) ).
thf(f386,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p7 @ Y0 ) )
@ ( sK20 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f385]) ).
thf(f387,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( irel @ X1 @ ( sK20 @ X1 ) )
=> ( p7 @ ( sK20 @ X1 ) ) ) )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f386]) ).
thf(f388,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ) )
| ( $false
= ( p7 @ ( sK20 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f387]) ).
thf(f400,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) )
| ( $false
= ( p7 @ ( sK20 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f388]) ).
thf(f401,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p7 @ ( sK20 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f400]) ).
thf(f402,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p7 @ ( sK20 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f401]) ).
thf(f403,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p7 @ ( sK20 @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f402]) ).
thf(f404,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p7 @ ( sK20 @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) )
@ ( sK22 @ X2 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) )
@ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f403]) ).
thf(f405,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p6 @ X3 ) ) )
| ( $false
= ( p7 @ ( sK20 @ X1 ) ) )
| ( ( ( irel @ X2 @ ( sK22 @ X2 ) )
=> ( p7 @ ( sK22 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f404]) ).
thf(f406,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p6 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ( irel @ X2 @ ( sK22 @ X2 ) )
=> ( p7 @ ( sK22 @ X2 ) ) )
= $false )
| ( $false
= ( p7 @ ( sK20 @ X1 ) ) )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f405]) ).
thf(f407,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( $false
= ( p7 @ ( sK22 @ X2 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p7 @ ( sK20 @ X1 ) ) )
| ( $true
= ( p6 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f406]) ).
thf(f409,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p8 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p9 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f410,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p8 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p9 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f409]) ).
thf(f411,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f410]) ).
thf(f412,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f411]) ).
thf(f413,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p9 @ Y0 ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f412]) ).
thf(f414,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p9 @ Y0 ) )
@ ( sK23 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f413]) ).
thf(f415,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p9 @ Y0 ) )
@ ( sK23 @ X1 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f414]) ).
thf(f416,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ ( sK23 @ X1 ) )
=> ( p9 @ ( sK23 @ X1 ) ) )
= $false )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f415]) ).
thf(f417,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p9 @ ( sK23 @ X1 ) ) )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f416]) ).
thf(f428,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) )
| ( $false
= ( p9 @ ( sK23 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f417]) ).
thf(f429,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) )
| ( $false
= ( p9 @ ( sK23 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f428]) ).
thf(f430,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p9 @ ( sK23 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f429]) ).
thf(f431,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p9 @ ( sK23 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) )
@ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f430]) ).
thf(f432,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p9 @ ( sK23 @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) )
@ ( sK25 @ X2 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) )
@ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f431]) ).
thf(f433,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( irel @ X2 @ ( sK25 @ X2 ) )
=> ( p9 @ ( sK25 @ X2 ) ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p8 @ X3 ) ) )
| ( $false
= ( p9 @ ( sK23 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f432]) ).
thf(f434,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p9 @ ( sK23 @ X1 ) ) )
| ( ( p9 @ ( sK25 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p8 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f433]) ).
thf(f437,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( $false
= ( p9 @ ( sK23 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p9 @ ( sK25 @ X2 ) )
= $false )
| ( $true
= ( p8 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f434]) ).
thf(f438,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p5 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p6 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f198]) ).
thf(f439,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p5 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p6 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f438]) ).
thf(f440,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f439]) ).
thf(f441,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f440]) ).
thf(f442,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 )
=> ( p6 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f441]) ).
thf(f443,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p6 @ Y0 ) ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(not_proxy_clausification,[],[f442]) ).
thf(f444,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 )
=> ( p6 @ Y1 ) ) ) ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p6 @ Y0 ) )
@ ( sK26 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f443]) ).
thf(f445,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ ( sK26 @ X1 ) )
=> ( p6 @ ( sK26 @ X1 ) ) )
= $false )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f444]) ).
thf(f446,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ) )
| ( $false
= ( p6 @ ( sK26 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f445]) ).
thf(f458,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p6 @ ( sK26 @ X1 ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f446]) ).
thf(f459,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p6 @ ( sK26 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f458]) ).
thf(f460,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) )
| ( $false
= ( p6 @ ( sK26 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f459]) ).
thf(f461,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) )
@ ( sK28 @ X2 ) )
= $false )
| ( $false
= ( p6 @ ( sK26 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f460]) ).
thf(f462,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) )
@ ( sK28 @ X2 ) )
= $false )
| ( $false
= ( p6 @ ( sK26 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f461]) ).
thf(f463,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( irel @ X2 @ ( sK28 @ X2 ) )
=> ( p6 @ ( sK28 @ X2 ) ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ( irel @ X2 @ X3 )
=> ( p5 @ X3 ) )
= $true )
| ( $false
= ( p6 @ ( sK26 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f462]) ).
thf(f464,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p6 @ ( sK26 @ X1 ) ) )
| ( ( ( irel @ X2 @ X3 )
=> ( p5 @ X3 ) )
= $true )
| ( ( p6 @ ( sK28 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f463]) ).
thf(f467,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( p5 @ X3 ) )
| ( ( p6 @ ( sK28 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p6 @ ( sK26 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f464]) ).
thf(f468,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p7 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p8 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f196]) ).
thf(f469,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p7 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p8 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f468]) ).
thf(f470,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f469]) ).
thf(f471,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f470]) ).
thf(f472,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p8 @ Y0 ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f471]) ).
thf(f473,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p8 @ Y0 ) )
@ ( sK29 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f472]) ).
thf(f474,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 )
=> ( p8 @ Y1 ) ) ) ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p8 @ Y0 ) )
@ ( sK29 @ X1 ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f473]) ).
thf(f475,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK29 @ X1 ) )
=> ( p8 @ ( sK29 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f474]) ).
thf(f476,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK29 @ X1 ) )
=> ( p8 @ ( sK29 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f475]) ).
thf(f477,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK29 @ X1 ) )
=> ( p8 @ ( sK29 @ X1 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f476]) ).
thf(f478,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) )
@ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK29 @ X1 ) )
=> ( p8 @ ( sK29 @ X1 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f477]) ).
thf(f479,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( irel @ X1 @ ( sK29 @ X1 ) )
=> ( p8 @ ( sK29 @ X1 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) )
@ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f478]) ).
thf(f480,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) )
@ X3 ) )
| ( ( p8 @ ( sK29 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f479]) ).
thf(f488,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) )
@ ( sK31 @ X2 ) )
= $false )
| ( ( p8 @ ( sK29 @ X1 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) )
@ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f480]) ).
thf(f489,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( irel @ X2 @ ( sK31 @ X2 ) )
=> ( p8 @ ( sK31 @ X2 ) ) )
= $false )
| ( ( p8 @ ( sK29 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p7 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f488]) ).
thf(f490,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p8 @ ( sK31 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p7 @ X3 ) ) )
| ( ( p8 @ ( sK29 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f489]) ).
thf(f493,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( p8 @ ( sK29 @ X1 ) )
= $false )
| ( $true
= ( p7 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p8 @ ( sK31 @ X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f490]) ).
thf(f494,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p14 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p15 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p15 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f495,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p14 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p15 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p15 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f494]) ).
thf(f496,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p14 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p15 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p15 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f495]) ).
thf(f497,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p14 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p15 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p15 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f496]) ).
thf(f498,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 )
=> ( p15 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p15 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f497]) ).
thf(f499,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 )
=> ( p15 @ Y1 ) ) ) ) )
@ X2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p15 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f498]) ).
thf(f500,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 )
=> ( p15 @ Y1 ) ) ) ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p15 @ Y0 ) )
@ ( sK32 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f499]) ).
thf(f501,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) ) ) ) ) )
| ( ( ( irel @ X1 @ ( sK32 @ X1 ) )
=> ( p15 @ ( sK32 @ X1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f500]) ).
thf(f502,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ ( sK32 @ X1 ) )
=> ( p15 @ ( sK32 @ X1 ) ) )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f501]) ).
thf(f503,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) ) ) ) )
| ( ( p15 @ ( sK32 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f502]) ).
thf(f513,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) ) ) ) )
| ( ( p15 @ ( sK32 @ X1 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f503]) ).
thf(f514,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) ) ) )
| ( ( p15 @ ( sK32 @ X1 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f513]) ).
thf(f515,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) )
@ ( sK34 @ X2 ) ) )
| ( ( p15 @ ( sK32 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f514]) ).
thf(f516,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) )
@ ( sK34 @ X2 ) ) )
| ( ( p15 @ ( sK32 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f515]) ).
thf(f517,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X2 @ X3 )
=> ( p14 @ X3 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ( irel @ X2 @ ( sK34 @ X2 ) )
=> ( p15 @ ( sK34 @ X2 ) ) )
= $false )
| ( ( p15 @ ( sK32 @ X1 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f516]) ).
thf(f518,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( irel @ X2 @ ( sK34 @ X2 ) )
=> ( p15 @ ( sK34 @ X2 ) ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p15 @ ( sK32 @ X1 ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( p14 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f517]) ).
thf(f519,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( p15 @ ( sK34 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p15 @ ( sK32 @ X1 ) )
= $false )
| ( $true
= ( p14 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f518]) ).
thf(f521,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p10 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p11 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p11 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f190]) ).
thf(f522,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p10 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p11 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p11 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f521]) ).
thf(f523,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p11 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p11 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f522]) ).
thf(f524,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p11 @ Y1 ) ) ) ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p11 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f523]) ).
thf(f525,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 )
=> ( p11 @ Y1 ) ) ) ) )
@ X2 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p11 @ Y0 ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f524]) ).
thf(f526,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 )
=> ( p11 @ Y1 ) ) ) ) )
@ X2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p11 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f525]) ).
thf(f527,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p11 @ Y0 ) )
@ ( sK35 @ X1 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p11 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f526]) ).
thf(f528,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) ) ) ) ) )
| ( ( ( irel @ X1 @ ( sK35 @ X1 ) )
=> ( p11 @ ( sK35 @ X1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f527]) ).
thf(f529,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( ( irel @ X1 @ ( sK35 @ X1 ) )
=> ( p11 @ ( sK35 @ X1 ) ) )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f528]) ).
thf(f530,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( p11 @ ( sK35 @ X1 ) )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f529]) ).
thf(f540,plain,
! [X2: $i,X1: $i] :
( ( ( p11 @ ( sK35 @ X1 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f530]) ).
thf(f541,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) )
@ X3 ) )
| ( ( p11 @ ( sK35 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f540]) ).
thf(f542,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) )
@ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p11 @ ( sK35 @ X1 ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f541]) ).
thf(f543,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p11 @ Y0 ) )
@ ( sK37 @ X2 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p11 @ ( sK35 @ X1 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) )
@ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f542]) ).
thf(f544,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( irel @ X2 @ ( sK37 @ X2 ) )
=> ( p11 @ ( sK37 @ X2 ) ) ) )
| ( ( p11 @ ( sK35 @ X1 ) )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p10 @ X3 ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f543]) ).
thf(f545,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p11 @ ( sK35 @ X1 ) )
= $false )
| ( ( p11 @ ( sK37 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p10 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f544]) ).
thf(f548,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( p10 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p11 @ ( sK35 @ X1 ) )
= $false )
| ( ( p11 @ ( sK37 @ X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f545]) ).
thf(f549,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p13 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p14 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p14 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f197]) ).
thf(f550,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p13 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p14 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p14 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f549]) ).
thf(f551,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p13 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p14 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p14 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f550]) ).
thf(f552,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p13 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p14 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p14 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f551]) ).
thf(f553,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 )
=> ( p14 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p14 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f552]) ).
thf(f554,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p14 @ Y0 ) ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p13 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p14 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(not_proxy_clausification,[],[f553]) ).
thf(f555,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 )
=> ( p14 @ Y1 ) ) ) ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p14 @ Y0 ) )
@ ( sK38 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f554]) ).
thf(f556,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ ( sK38 @ X1 ) )
=> ( p14 @ ( sK38 @ X1 ) ) )
= $false )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f555]) ).
thf(f557,plain,
! [X2: $i,X1: $i] :
( ( ( p14 @ ( sK38 @ X1 ) )
= $false )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f556]) ).
thf(f569,plain,
! [X2: $i,X1: $i] :
( ( ( p14 @ ( sK38 @ X1 ) )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f557]) ).
thf(f570,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) ) ) )
| ( ( p14 @ ( sK38 @ X1 ) )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f569]) ).
thf(f571,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p14 @ ( sK38 @ X1 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f570]) ).
thf(f572,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p14 @ ( sK38 @ X1 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) )
@ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f571]) ).
thf(f573,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( p14 @ ( sK38 @ X1 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p14 @ Y0 ) )
@ ( sK40 @ X2 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) )
@ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f572]) ).
thf(f574,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X2 @ X3 )
=> ( p13 @ X3 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p14 @ ( sK38 @ X1 ) )
= $false )
| ( ( ( irel @ X2 @ ( sK40 @ X2 ) )
=> ( p14 @ ( sK40 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f573]) ).
thf(f575,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p13 @ X3 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( ( irel @ X2 @ ( sK40 @ X2 ) )
=> ( p14 @ ( sK40 @ X2 ) ) )
= $false )
| ( ( p14 @ ( sK38 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f574]) ).
thf(f576,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( p14 @ ( sK38 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p13 @ X3 ) )
| ( ( p14 @ ( sK40 @ X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f575]) ).
thf(f578,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p15 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p16 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f579,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p15 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p16 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f578]) ).
thf(f580,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p15 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p16 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f579]) ).
thf(f581,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p16 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p15 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f580]) ).
thf(f582,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p16 @ Y0 ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p15 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f581]) ).
thf(f583,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p16 @ Y0 ) )
@ ( sK41 @ X1 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p15 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f582]) ).
thf(f584,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p16 @ Y0 ) )
@ ( sK41 @ X1 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p15 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p16 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f583]) ).
thf(f585,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) ) ) ) ) )
| ( ( ( irel @ X1 @ ( sK41 @ X1 ) )
=> ( p16 @ ( sK41 @ X1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f584]) ).
thf(f586,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ ( sK41 @ X1 ) )
=> ( p16 @ ( sK41 @ X1 ) ) )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f585]) ).
thf(f587,plain,
! [X2: $i,X1: $i] :
( ( ( p16 @ ( sK41 @ X1 ) )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f586]) ).
thf(f597,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) ) ) ) )
| ( ( p16 @ ( sK41 @ X1 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f587]) ).
thf(f598,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p16 @ ( sK41 @ X1 ) )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) )
@ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f597]) ).
thf(f599,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) )
@ X3 ) )
| ( ( p16 @ ( sK41 @ X1 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f598]) ).
thf(f600,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p15 @ Y0 ) )
@ X3 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p16 @ Y0 ) )
@ ( sK43 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p16 @ ( sK41 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f599]) ).
thf(f601,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p16 @ ( sK41 @ X1 ) )
= $false )
| ( ( ( irel @ X2 @ X3 )
=> ( p15 @ X3 ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ( irel @ X2 @ ( sK43 @ X2 ) )
=> ( p16 @ ( sK43 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f600]) ).
thf(f602,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p16 @ ( sK41 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ( irel @ X2 @ ( sK43 @ X2 ) )
=> ( p16 @ ( sK43 @ X2 ) ) )
= $false )
| ( $true
= ( p15 @ X3 ) )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f601]) ).
thf(f603,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( p15 @ X3 ) )
| ( $false
= ( p16 @ ( sK43 @ X2 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p16 @ ( sK41 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f602]) ).
thf(f605,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p19 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p20 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p20 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f606,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p19 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p20 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p20 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f605]) ).
thf(f607,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p20 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p20 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f606]) ).
thf(f608,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p20 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p20 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f607]) ).
thf(f609,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p20 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p20 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f608]) ).
thf(f610,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p20 @ Y0 ) ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p20 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(not_proxy_clausification,[],[f609]) ).
thf(f611,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p20 @ Y0 ) )
@ ( sK44 @ X1 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p19 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p20 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f610]) ).
thf(f612,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p20 @ Y0 ) ) ) ) ) )
| ( ( ( irel @ X1 @ ( sK44 @ X1 ) )
=> ( p20 @ ( sK44 @ X1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f611]) ).
thf(f613,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p20 @ Y0 ) ) ) ) )
| ( ( ( irel @ X1 @ ( sK44 @ X1 ) )
=> ( p20 @ ( sK44 @ X1 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f612]) ).
thf(f614,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p20 @ Y0 ) ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) ) ) )
| ( ( ( irel @ X1 @ ( sK44 @ X1 ) )
=> ( p20 @ ( sK44 @ X1 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f613]) ).
thf(f615,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ ( sK44 @ X1 ) )
=> ( p20 @ ( sK44 @ X1 ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p20 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f614]) ).
thf(f616,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p20 @ Y0 ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) ) ) )
| ( ( p20 @ ( sK44 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f615]) ).
thf(f625,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p20 @ ( sK44 @ X1 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p20 @ Y0 ) )
@ ( sK46 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f616]) ).
thf(f626,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p20 @ ( sK44 @ X1 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p20 @ Y0 ) )
@ ( sK46 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p19 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f625]) ).
thf(f627,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p20 @ ( sK44 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ( irel @ X2 @ ( sK46 @ X2 ) )
=> ( p20 @ ( sK46 @ X2 ) ) )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p19 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f626]) ).
thf(f628,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X2 @ X3 )
=> ( p19 @ X3 ) ) )
| ( ( p20 @ ( sK44 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p20 @ ( sK46 @ X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f627]) ).
thf(f631,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p19 @ X3 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( p20 @ ( sK44 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p20 @ ( sK46 @ X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f628]) ).
thf(f632,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p3 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f633,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p3 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f632]) ).
thf(f634,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f633]) ).
thf(f635,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ 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 )
=> ( p2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f635]) ).
thf(f637,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(not_proxy_clausification,[],[f636]) ).
thf(f638,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) )
@ ( sK47 @ X1 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f637]) ).
thf(f639,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( irel @ X1 @ ( sK47 @ X1 ) )
=> ( p3 @ ( sK47 @ X1 ) ) ) )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f638]) ).
thf(f640,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) )
| ( $false
= ( p3 @ ( sK47 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f639]) ).
thf(f651,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) )
| ( $false
= ( p3 @ ( sK47 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f640]) ).
thf(f652,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
| ( $false
= ( p3 @ ( sK47 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f651]) ).
thf(f653,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) )
| ( $false
= ( p3 @ ( sK47 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f652]) ).
thf(f654,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p3 @ ( sK47 @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) )
@ ( sK49 @ X2 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f653]) ).
thf(f655,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p3 @ ( sK47 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) )
@ X3 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) )
@ ( sK49 @ X2 ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f654]) ).
thf(f656,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X2 @ X3 )
=> ( p2 @ X3 ) ) )
| ( $false
= ( p3 @ ( sK47 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X2 @ ( sK49 @ X2 ) )
=> ( p3 @ ( sK49 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f655]) ).
thf(f657,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p3 @ ( sK47 @ X1 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK49 @ X2 ) )
=> ( p3 @ ( sK49 @ X2 ) ) ) )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f656]) ).
thf(f658,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( p2 @ X3 ) )
| ( $false
= ( p3 @ ( sK47 @ X1 ) ) )
| ( ( p3 @ ( sK49 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f657]) ).
thf(f660,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p3 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p4 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f193]) ).
thf(f661,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p3 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p4 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[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 )
=> ( p4 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f661]) ).
thf(f663,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f662]) ).
thf(f664,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(pi_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 )
=> ( p4 @ Y1 ) ) ) ) )
@ X2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f664]) ).
thf(f666,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 )
=> ( p4 @ Y1 ) ) ) ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) )
@ ( sK50 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f665]) ).
thf(f667,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ ( sK50 @ X1 ) )
=> ( p4 @ ( sK50 @ X1 ) ) )
= $false )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f666]) ).
thf(f668,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ) )
| ( ( p4 @ ( sK50 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f667]) ).
thf(f679,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) )
| ( ( p4 @ ( sK50 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f668]) ).
thf(f680,plain,
! [X2: $i,X1: $i] :
( ( ( p4 @ ( sK50 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f679]) ).
thf(f681,plain,
! [X2: $i,X1: $i] :
( ( ( p4 @ ( sK50 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f680]) ).
thf(f682,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) )
@ X3 ) )
| ( ( p4 @ ( sK50 @ X1 ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f681]) ).
thf(f683,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p4 @ ( sK50 @ X1 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) )
@ ( sK52 @ X2 ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f682]) ).
thf(f684,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X2 @ X3 )
=> ( p3 @ X3 ) ) )
| ( ( p4 @ ( sK50 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X2 @ ( sK52 @ X2 ) )
=> ( p4 @ ( sK52 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f683]) ).
thf(f685,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p3 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK52 @ X2 ) )
=> ( p4 @ ( sK52 @ X2 ) ) ) )
| ( ( p4 @ ( sK50 @ X1 ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f684]) ).
thf(f686,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( p4 @ ( sK52 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p3 @ X3 ) )
| ( ( p4 @ ( sK50 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f685]) ).
thf(f688,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f194]) ).
thf(f689,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f688]) ).
thf(f690,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f689]) ).
thf(f691,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f690]) ).
thf(f692,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 )
=> ( p2 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f691]) ).
thf(f693,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(not_proxy_clausification,[],[f692]) ).
thf(f694,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) )
@ ( sK53 @ X1 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f693]) ).
thf(f695,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ ( sK53 @ X1 ) )
=> ( p2 @ ( sK53 @ X1 ) ) )
= $false )
| ( ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f694]) ).
thf(f696,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( p2 @ ( sK53 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f695]) ).
thf(f708,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p2 @ ( sK53 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f696]) ).
thf(f709,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p2 @ ( sK53 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f708]) ).
thf(f710,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) )
| ( $false
= ( p2 @ ( sK53 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f709]) ).
thf(f711,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) )
@ ( sK55 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) )
| ( $false
= ( p2 @ ( sK53 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f710]) ).
thf(f712,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) )
@ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) )
@ ( sK55 @ X2 ) )
= $false )
| ( $false
= ( p2 @ ( sK53 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f711]) ).
thf(f713,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p2 @ ( sK53 @ X1 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK55 @ X2 ) )
=> ( p2 @ ( sK55 @ X2 ) ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f712]) ).
thf(f714,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) ) )
| ( ( p2 @ ( sK55 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p2 @ ( sK53 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f713]) ).
thf(f717,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( p2 @ ( sK55 @ X2 ) )
= $false )
| ( $true
= ( p1 @ X3 ) )
| ( $false
= ( p2 @ ( sK53 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f714]) ).
thf(f718,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p12 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p13 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p13 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f719,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p12 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p13 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p13 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f718]) ).
thf(f720,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p13 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p13 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f719]) ).
thf(f721,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p13 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p13 @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f720]) ).
thf(f722,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p13 @ Y1 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p13 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f721]) ).
thf(f723,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 )
=> ( p13 @ Y1 ) ) ) ) )
@ X2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p13 @ Y0 ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f722]) ).
thf(f724,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p13 @ Y0 ) )
@ ( sK56 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p12 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p13 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f723]) ).
thf(f725,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( irel @ X1 @ ( sK56 @ X1 ) )
=> ( p13 @ ( sK56 @ X1 ) ) ) )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f724]) ).
thf(f726,plain,
! [X2: $i,X1: $i] :
( ( ( p13 @ ( sK56 @ X1 ) )
= $false )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f725]) ).
thf(f737,plain,
! [X2: $i,X1: $i] :
( ( ( p13 @ ( sK56 @ X1 ) )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f726]) ).
thf(f738,plain,
! [X2: $i,X1: $i] :
( ( ( p13 @ ( sK56 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f737]) ).
thf(f739,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) ) ) )
| ( ( p13 @ ( sK56 @ X1 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f738]) ).
thf(f740,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) )
@ ( sK58 @ X2 ) )
= $false )
| ( ( p13 @ ( sK56 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f739]) ).
thf(f741,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p13 @ ( sK56 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p13 @ Y0 ) )
@ ( sK58 @ X2 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p12 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f740]) ).
thf(f742,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p13 @ ( sK56 @ X1 ) )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p12 @ X3 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( ( irel @ X2 @ ( sK58 @ X2 ) )
=> ( p13 @ ( sK58 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f741]) ).
thf(f743,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( ( irel @ X2 @ ( sK58 @ X2 ) )
=> ( p13 @ ( sK58 @ X2 ) ) )
= $false )
| ( $true
= ( p12 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p13 @ ( sK56 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f742]) ).
thf(f744,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p12 @ X3 ) )
| ( ( p13 @ ( sK58 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p13 @ ( sK56 @ X1 ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f743]) ).
thf(f746,plain,
( $true
= ( !! @ $i @ p20 ) ),
inference(beta-eta_normalization,[],[f195]) ).
thf(f747,plain,
! [X1: $i] :
( $true
= ( p20 @ X1 ) ),
inference(pi_proxy_clausification,[],[f746]) ).
thf(f748,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f188]) ).
thf(f749,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f748]) ).
thf(f750,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f749]) ).
thf(f751,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f750]) ).
thf(f752,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f751]) ).
thf(f753,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) )
@ ( sK59 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f752]) ).
thf(f754,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) )
@ ( sK59 @ X1 ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f753]) ).
thf(f755,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK59 @ X1 ) )
=> ( p1 @ ( sK59 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f754]) ).
thf(f756,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK59 @ X1 ) )
=> ( p1 @ ( sK59 @ X1 ) ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f755]) ).
thf(f757,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) )
| ( $false
= ( p1 @ ( sK59 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f756]) ).
thf(f767,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p1 @ ( sK59 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f757]) ).
thf(f768,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) )
| ( $false
= ( p1 @ ( sK59 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f767]) ).
thf(f769,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) )
| ( $false
= ( p1 @ ( sK59 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) )
@ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f768]) ).
thf(f770,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) )
@ ( sK61 @ X2 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) )
@ X3 ) )
| ( $false
= ( p1 @ ( sK59 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f769]) ).
thf(f771,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X2 @ X3 )
=> ( p0 @ X3 ) ) )
| ( $false
= ( p1 @ ( sK59 @ X1 ) ) )
| ( ( ( irel @ X2 @ ( sK61 @ X2 ) )
=> ( p1 @ ( sK61 @ X2 ) ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f770]) ).
thf(f772,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p0 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK59 @ X1 ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( ( irel @ X2 @ ( sK61 @ X2 ) )
=> ( p1 @ ( sK61 @ X2 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f771]) ).
thf(f773,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( p0 @ X3 ) )
| ( $false
= ( p1 @ ( sK59 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p1 @ ( sK61 @ X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f772]) ).
thf(f776,definition,
( spl62_1
<=> ( ( p0 @ sK13 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl62_1])],[avatar_definition]) ).
thf(f778,plain,
( ( ( p0 @ sK13 )
= $false )
| ~ spl62_1 ),
inference(avatar_component_clause,[],[f776]) ).
thf(f780,definition,
( spl62_2
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl62_2])],[avatar_definition]) ).
thf(f783,plain,
( spl62_1
| spl62_2 ),
inference(avatar_split_clause,[],[f318,f780,f776]) ).
thf(f785,definition,
( spl62_3
<=> ! [X1: $i] :
( $true
= ( p0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl62_3])],[avatar_definition]) ).
thf(f786,plain,
( ! [X1: $i] :
( $true
= ( p0 @ X1 ) )
| ~ spl62_3 ),
inference(avatar_component_clause,[],[f785]) ).
thf(f792,plain,
~ spl62_2,
inference(avatar_split_clause,[],[f201,f780]) ).
thf(f809,plain,
( ( $true = $false )
| ~ spl62_1
| ~ spl62_3 ),
inference(constrained_superposition,[],[f778,f786]) ).
thf(f812,plain,
( $false
| ~ spl62_1
| ~ spl62_3 ),
inference(trivial_inequality_removal,[],[f809]) ).
thf(f813,plain,
( ~ spl62_1
| ~ spl62_3 ),
inference(avatar_contradiction_clause,[],[f812]) ).
thf(f819,plain,
! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p16 @ X0 ) )
| ( ( p17 @ ( sK1 @ X0 ) )
= $false )
| ( ( p17 @ ( sK3 @ X0 ) )
= $false ) ),
inference(equality_factoring,[],[f229]) ).
thf(f821,plain,
! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( ( p17 @ ( sK1 @ X0 ) )
= $false )
| ( $true
= ( p16 @ X0 ) )
| ( ( p17 @ ( sK3 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f819]) ).
thf(f826,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( p17 @ ( sK1 @ X0 ) )
= $false )
| ( ( p17 @ ( sK3 @ X0 ) )
= $false )
| ( $true
= ( p16 @ X0 ) ) ),
inference(forward_demodulation,[],[f821,f136]) ).
thf(f827,plain,
! [X0: $i] :
( ( ( p17 @ ( sK3 @ X0 ) )
= $false )
| ( ( p17 @ ( sK1 @ X0 ) )
= $false )
| ( $true
= ( p16 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f826]) ).
thf(f845,plain,
! [X0: $i] :
( ( ( p12 @ ( sK4 @ X0 ) )
= $false )
| ( $false != $false )
| ( $true
= ( p11 @ X0 ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( ( p12 @ ( sK6 @ X0 ) )
= $false ) ),
inference(equality_factoring,[],[f258]) ).
thf(f850,plain,
! [X0: $i] :
( ( $true
= ( p11 @ X0 ) )
| ( ( p12 @ ( sK6 @ X0 ) )
= $false )
| ( ( p12 @ ( sK4 @ X0 ) )
= $false )
| ( ( irel @ X0 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f845]) ).
thf(f852,plain,
! [X0: $i] :
( ( ( p12 @ ( sK6 @ X0 ) )
= $false )
| ( ( p12 @ ( sK4 @ X0 ) )
= $false )
| ( $true = $false )
| ( $true
= ( p11 @ X0 ) ) ),
inference(forward_demodulation,[],[f850,f136]) ).
thf(f853,plain,
! [X0: $i] :
( ( ( p12 @ ( sK6 @ X0 ) )
= $false )
| ( $true
= ( p11 @ X0 ) )
| ( ( p12 @ ( sK4 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f852]) ).
thf(f871,plain,
! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $false != $false )
| ( ( p10 @ ( sK9 @ X0 ) )
= $false )
| ( $true
= ( p9 @ X0 ) )
| ( ( p10 @ ( sK7 @ X0 ) )
= $false ) ),
inference(equality_factoring,[],[f287]) ).
thf(f873,plain,
! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p9 @ X0 ) )
| ( ( p10 @ ( sK7 @ X0 ) )
= $false )
| ( ( p10 @ ( sK9 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f871]) ).
thf(f878,plain,
! [X0: $i] :
( ( ( p10 @ ( sK9 @ X0 ) )
= $false )
| ( $true = $false )
| ( $true
= ( p9 @ X0 ) )
| ( ( p10 @ ( sK7 @ X0 ) )
= $false ) ),
inference(forward_demodulation,[],[f873,f136]) ).
thf(f879,plain,
! [X0: $i] :
( ( ( p10 @ ( sK9 @ X0 ) )
= $false )
| ( $true
= ( p9 @ X0 ) )
| ( ( p10 @ ( sK7 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f878]) ).
thf(f885,plain,
! [X0: $i] :
( ( ( p19 @ ( sK12 @ X0 ) )
= $false )
| ( $false != $false )
| ( $false
= ( p19 @ ( sK10 @ X0 ) ) )
| ( ( p18 @ X0 )
= $true )
| ( ( irel @ X0 @ X0 )
= $false ) ),
inference(equality_factoring,[],[f314]) ).
thf(f889,plain,
! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( ( p18 @ X0 )
= $true )
| ( $false
= ( p19 @ ( sK10 @ X0 ) ) )
| ( ( p19 @ ( sK12 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f885]) ).
thf(f892,plain,
! [X0: $i] :
( ( ( p19 @ ( sK12 @ X0 ) )
= $false )
| ( ( p18 @ X0 )
= $true )
| ( $true = $false )
| ( $false
= ( p19 @ ( sK10 @ X0 ) ) ) ),
inference(forward_demodulation,[],[f889,f136]) ).
thf(f893,plain,
! [X0: $i] :
( ( $false
= ( p19 @ ( sK10 @ X0 ) ) )
| ( ( p19 @ ( sK12 @ X0 ) )
= $false )
| ( ( p18 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f892]) ).
thf(f923,plain,
! [X0: $i] :
( ( ( p18 @ ( sK14 @ X0 ) )
= $false )
| ( ( p17 @ X0 )
= $true )
| ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( ( p18 @ ( sK16 @ X0 ) )
= $false ) ),
inference(equality_factoring,[],[f349]) ).
thf(f929,plain,
! [X0: $i] :
( ( ( p17 @ X0 )
= $true )
| ( ( p18 @ ( sK14 @ X0 ) )
= $false )
| ( ( p18 @ ( sK16 @ X0 ) )
= $false )
| ( ( irel @ X0 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f923]) ).
thf(f930,plain,
! [X0: $i] :
( ( ( p18 @ ( sK16 @ X0 ) )
= $false )
| ( $true = $false )
| ( ( p18 @ ( sK14 @ X0 ) )
= $false )
| ( ( p17 @ X0 )
= $true ) ),
inference(forward_demodulation,[],[f929,f136]) ).
thf(f931,plain,
! [X0: $i] :
( ( ( p18 @ ( sK16 @ X0 ) )
= $false )
| ( ( p18 @ ( sK14 @ X0 ) )
= $false )
| ( ( p17 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f930]) ).
thf(f939,plain,
! [X0: $i] :
( ( ( p5 @ ( sK19 @ X0 ) )
= $false )
| ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( ( p5 @ ( sK17 @ X0 ) )
= $false )
| ( $true
= ( p4 @ X0 ) ) ),
inference(equality_factoring,[],[f379]) ).
thf(f944,plain,
! [X0: $i] :
( ( ( p5 @ ( sK19 @ X0 ) )
= $false )
| ( ( p5 @ ( sK17 @ X0 ) )
= $false )
| ( $true
= ( p4 @ X0 ) )
| ( ( irel @ X0 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f939]) ).
thf(f946,plain,
! [X0: $i] :
( ( $true
= ( p4 @ X0 ) )
| ( ( p5 @ ( sK19 @ X0 ) )
= $false )
| ( $true = $false )
| ( ( p5 @ ( sK17 @ X0 ) )
= $false ) ),
inference(forward_demodulation,[],[f944,f136]) ).
thf(f947,plain,
! [X0: $i] :
( ( ( p5 @ ( sK19 @ X0 ) )
= $false )
| ( $true
= ( p4 @ X0 ) )
| ( ( p5 @ ( sK17 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f946]) ).
thf(f975,plain,
! [X0: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p6 @ X0 ) )
| ( ( p7 @ ( sK20 @ X0 ) )
= $false )
| ( ( p7 @ ( sK22 @ X0 ) )
= $false ) ),
inference(equality_factoring,[],[f407]) ).
thf(f978,plain,
! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( ( p7 @ ( sK20 @ X0 ) )
= $false )
| ( $true
= ( p6 @ X0 ) )
| ( ( p7 @ ( sK22 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f975]) ).
thf(f982,plain,
! [X0: $i] :
( ( ( p7 @ ( sK22 @ X0 ) )
= $false )
| ( ( p7 @ ( sK20 @ X0 ) )
= $false )
| ( $true = $false )
| ( $true
= ( p6 @ X0 ) ) ),
inference(forward_demodulation,[],[f978,f136]) ).
thf(f983,plain,
! [X0: $i] :
( ( ( p7 @ ( sK22 @ X0 ) )
= $false )
| ( $true
= ( p6 @ X0 ) )
| ( ( p7 @ ( sK20 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f982]) ).
thf(f1001,plain,
! [X0: $i] :
( ( ( p9 @ ( sK23 @ X0 ) )
= $false )
| ( $false != $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( ( p9 @ ( sK25 @ X0 ) )
= $false )
| ( $true
= ( p8 @ X0 ) ) ),
inference(equality_factoring,[],[f437]) ).
thf(f1003,plain,
! [X0: $i] :
( ( $true
= ( p8 @ X0 ) )
| ( ( p9 @ ( sK23 @ X0 ) )
= $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( ( p9 @ ( sK25 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1001]) ).
thf(f1008,plain,
! [X0: $i] :
( ( ( p9 @ ( sK25 @ X0 ) )
= $false )
| ( $true
= ( p8 @ X0 ) )
| ( ( p9 @ ( sK23 @ X0 ) )
= $false )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f1003,f136]) ).
thf(f1009,plain,
! [X0: $i] :
( ( ( p9 @ ( sK25 @ X0 ) )
= $false )
| ( $true
= ( p8 @ X0 ) )
| ( ( p9 @ ( sK23 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1008]) ).
thf(f1027,plain,
! [X0: $i] :
( ( ( p6 @ ( sK26 @ X0 ) )
= $false )
| ( ( p6 @ ( sK28 @ X0 ) )
= $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $false != $false )
| ( $true
= ( p5 @ X0 ) ) ),
inference(equality_factoring,[],[f467]) ).
thf(f1033,plain,
! [X0: $i] :
( ( $true
= ( p5 @ X0 ) )
| ( ( p6 @ ( sK26 @ X0 ) )
= $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( ( p6 @ ( sK28 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1027]) ).
thf(f1034,plain,
! [X0: $i] :
( ( ( p6 @ ( sK28 @ X0 ) )
= $false )
| ( $true = $false )
| ( ( p6 @ ( sK26 @ X0 ) )
= $false )
| ( $true
= ( p5 @ X0 ) ) ),
inference(forward_demodulation,[],[f1033,f136]) ).
thf(f1035,plain,
! [X0: $i] :
( ( ( p6 @ ( sK28 @ X0 ) )
= $false )
| ( $true
= ( p5 @ X0 ) )
| ( ( p6 @ ( sK26 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1034]) ).
thf(f1053,plain,
! [X0: $i] :
( ( ( p8 @ ( sK31 @ X0 ) )
= $false )
| ( $false
= ( p8 @ ( sK29 @ X0 ) ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $false != $false )
| ( $true
= ( p7 @ X0 ) ) ),
inference(equality_factoring,[],[f493]) ).
thf(f1058,plain,
! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $false
= ( p8 @ ( sK29 @ X0 ) ) )
| ( ( p8 @ ( sK31 @ X0 ) )
= $false )
| ( $true
= ( p7 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1053]) ).
thf(f1060,plain,
! [X0: $i] :
( ( ( p8 @ ( sK31 @ X0 ) )
= $false )
| ( $true
= ( p7 @ X0 ) )
| ( $false
= ( p8 @ ( sK29 @ X0 ) ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f1058,f136]) ).
thf(f1061,plain,
! [X0: $i] :
( ( $false
= ( p8 @ ( sK29 @ X0 ) ) )
| ( ( p8 @ ( sK31 @ X0 ) )
= $false )
| ( $true
= ( p7 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1060]) ).
thf(f1079,plain,
! [X0: $i] :
( ( $false != $false )
| ( ( p15 @ ( sK32 @ X0 ) )
= $false )
| ( ( p14 @ X0 )
= $true )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $false
= ( p15 @ ( sK34 @ X0 ) ) ) ),
inference(equality_factoring,[],[f519]) ).
thf(f1080,plain,
! [X0: $i] :
( ( $false
= ( p15 @ ( sK34 @ X0 ) ) )
| ( ( p14 @ X0 )
= $true )
| ( ( p15 @ ( sK32 @ X0 ) )
= $false )
| ( ( irel @ X0 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f1079]) ).
thf(f1086,plain,
! [X0: $i] :
( ( ( p15 @ ( sK32 @ X0 ) )
= $false )
| ( $true = $false )
| ( $false
= ( p15 @ ( sK34 @ X0 ) ) )
| ( ( p14 @ X0 )
= $true ) ),
inference(forward_demodulation,[],[f1080,f136]) ).
thf(f1087,plain,
! [X0: $i] :
( ( $false
= ( p15 @ ( sK34 @ X0 ) ) )
| ( ( p14 @ X0 )
= $true )
| ( ( p15 @ ( sK32 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1086]) ).
thf(f1105,plain,
! [X0: $i] :
( ( $false
= ( p11 @ ( sK37 @ X0 ) ) )
| ( ( p11 @ ( sK35 @ X0 ) )
= $false )
| ( $true
= ( p10 @ X0 ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $false != $false ) ),
inference(equality_factoring,[],[f548]) ).
thf(f1106,plain,
! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $false
= ( p11 @ ( sK37 @ X0 ) ) )
| ( $true
= ( p10 @ X0 ) )
| ( ( p11 @ ( sK35 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1105]) ).
thf(f1112,plain,
! [X0: $i] :
( ( $false
= ( p11 @ ( sK37 @ X0 ) ) )
| ( $true
= ( p10 @ X0 ) )
| ( ( p11 @ ( sK35 @ X0 ) )
= $false )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f1106,f136]) ).
thf(f1113,plain,
! [X0: $i] :
( ( $false
= ( p11 @ ( sK37 @ X0 ) ) )
| ( $true
= ( p10 @ X0 ) )
| ( ( p11 @ ( sK35 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1112]) ).
thf(f1119,plain,
! [X0: $i] :
( ( $false != $false )
| ( $true
= ( p13 @ X0 ) )
| ( ( p14 @ ( sK40 @ X0 ) )
= $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $false
= ( p14 @ ( sK38 @ X0 ) ) ) ),
inference(equality_factoring,[],[f576]) ).
thf(f1125,plain,
! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p13 @ X0 ) )
| ( ( p14 @ ( sK40 @ X0 ) )
= $false )
| ( $false
= ( p14 @ ( sK38 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f1119]) ).
thf(f1126,plain,
! [X0: $i] :
( ( $false
= ( p14 @ ( sK38 @ X0 ) ) )
| ( $true = $false )
| ( ( p14 @ ( sK40 @ X0 ) )
= $false )
| ( $true
= ( p13 @ X0 ) ) ),
inference(forward_demodulation,[],[f1125,f136]) ).
thf(f1127,plain,
! [X0: $i] :
( ( $false
= ( p14 @ ( sK38 @ X0 ) ) )
| ( ( p14 @ ( sK40 @ X0 ) )
= $false )
| ( $true
= ( p13 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1126]) ).
thf(f1157,plain,
! [X0: $i] :
( ( ( p16 @ ( sK41 @ X0 ) )
= $false )
| ( $false != $false )
| ( ( p16 @ ( sK43 @ X0 ) )
= $false )
| ( $true
= ( p15 @ X0 ) )
| ( ( irel @ X0 @ X0 )
= $false ) ),
inference(equality_factoring,[],[f603]) ).
thf(f1161,plain,
! [X0: $i] :
( ( $true
= ( p15 @ X0 ) )
| ( ( p16 @ ( sK43 @ X0 ) )
= $false )
| ( ( p16 @ ( sK41 @ X0 ) )
= $false )
| ( ( irel @ X0 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f1157]) ).
thf(f1164,plain,
! [X0: $i] :
( ( ( p16 @ ( sK41 @ X0 ) )
= $false )
| ( $true
= ( p15 @ X0 ) )
| ( $true = $false )
| ( ( p16 @ ( sK43 @ X0 ) )
= $false ) ),
inference(forward_demodulation,[],[f1161,f136]) ).
thf(f1165,plain,
! [X0: $i] :
( ( ( p16 @ ( sK43 @ X0 ) )
= $false )
| ( $true
= ( p15 @ X0 ) )
| ( ( p16 @ ( sK41 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1164]) ).
thf(f1168,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( p19 @ X3 ) )
| ( ( p20 @ ( sK46 @ X2 ) )
= $false ) ),
inference(forward_demodulation,[],[f631,f747]) ).
thf(f1169,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( p20 @ ( sK46 @ X2 ) )
= $false )
| ( $true
= ( p19 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f1168]) ).
thf(f1170,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p19 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f1169,f747]) ).
thf(f1171,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p19 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f1170]) ).
thf(f1177,plain,
! [X0: $i] :
( ( $true
= ( p19 @ X0 ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $false != $false ) ),
inference(equality_factoring,[],[f1171]) ).
thf(f1183,plain,
! [X0: $i] :
( ( $true
= ( p19 @ X0 ) )
| ( ( irel @ X0 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f1177]) ).
thf(f1184,plain,
! [X0: $i] :
( ( $true
= ( p19 @ X0 ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f1183,f136]) ).
thf(f1185,plain,
! [X0: $i] :
( $true
= ( p19 @ X0 ) ),
inference(trivial_inequality_removal,[],[f1184]) ).
thf(f1186,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( p18 @ X0 )
= $true )
| ( ( p19 @ ( sK12 @ X0 ) )
= $false ) ),
inference(constrained_superposition,[],[f1185,f893]) ).
thf(f1188,plain,
! [X0: $i] :
( ( ( p19 @ ( sK12 @ X0 ) )
= $false )
| ( ( p18 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f1186]) ).
thf(f1190,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( p18 @ X0 )
= $true ) ),
inference(forward_demodulation,[],[f1188,f1185]) ).
thf(f1191,plain,
! [X0: $i] :
( ( p18 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f1190]) ).
thf(f1195,plain,
! [X0: $i] :
( ( ( p18 @ ( sK14 @ X0 ) )
= $false )
| ( $true = $false )
| ( ( p17 @ X0 )
= $true ) ),
inference(constrained_superposition,[],[f931,f1191]) ).
thf(f1196,plain,
! [X0: $i] :
( ( ( p17 @ X0 )
= $true )
| ( ( p18 @ ( sK14 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1195]) ).
thf(f1198,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( p17 @ X0 )
= $true ) ),
inference(forward_demodulation,[],[f1196,f1191]) ).
thf(f1199,plain,
! [X0: $i] :
( ( p17 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f1198]) ).
thf(f1202,plain,
! [X0: $i] :
( ( ( p17 @ ( sK1 @ X0 ) )
= $false )
| ( $true
= ( p16 @ X0 ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f1199,f827]) ).
thf(f1204,plain,
! [X0: $i] :
( ( $true
= ( p16 @ X0 ) )
| ( ( p17 @ ( sK1 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1202]) ).
thf(f1206,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p16 @ X0 ) ) ),
inference(forward_demodulation,[],[f1204,f1199]) ).
thf(f1207,plain,
! [X0: $i] :
( $true
= ( p16 @ X0 ) ),
inference(trivial_inequality_removal,[],[f1206]) ).
thf(f1210,plain,
! [X0: $i] :
( ( ( p16 @ ( sK41 @ X0 ) )
= $false )
| ( $true
= ( p15 @ X0 ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f1207,f1165]) ).
thf(f1212,plain,
! [X0: $i] :
( ( $true
= ( p15 @ X0 ) )
| ( ( p16 @ ( sK41 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1210]) ).
thf(f1214,plain,
! [X0: $i] :
( ( $true
= ( p15 @ X0 ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f1212,f1207]) ).
thf(f1215,plain,
! [X0: $i] :
( $true
= ( p15 @ X0 ) ),
inference(trivial_inequality_removal,[],[f1214]) ).
thf(f1223,plain,
! [X0: $i] :
( ( $false != $false )
| ( ( p3 @ ( sK47 @ X0 ) )
= $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p2 @ X0 ) )
| ( ( p3 @ ( sK49 @ X0 ) )
= $false ) ),
inference(equality_factoring,[],[f658]) ).
thf(f1224,plain,
! [X0: $i] :
( ( $true
= ( p2 @ X0 ) )
| ( ( p3 @ ( sK47 @ X0 ) )
= $false )
| ( ( p3 @ ( sK49 @ X0 ) )
= $false )
| ( ( irel @ X0 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f1223]) ).
thf(f1230,plain,
! [X0: $i] :
( ( ( p3 @ ( sK49 @ X0 ) )
= $false )
| ( ( p3 @ ( sK47 @ X0 ) )
= $false )
| ( $true
= ( p2 @ X0 ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f1224,f136]) ).
thf(f1231,plain,
! [X0: $i] :
( ( ( p3 @ ( sK49 @ X0 ) )
= $false )
| ( ( p3 @ ( sK47 @ X0 ) )
= $false )
| ( $true
= ( p2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1230]) ).
thf(f1232,plain,
! [X0: $i] :
( ( ( p15 @ ( sK32 @ X0 ) )
= $false )
| ( $true = $false )
| ( ( p14 @ X0 )
= $true ) ),
inference(constrained_superposition,[],[f1215,f1087]) ).
thf(f1234,plain,
! [X0: $i] :
( ( ( p15 @ ( sK32 @ X0 ) )
= $false )
| ( ( p14 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f1232]) ).
thf(f1236,plain,
! [X0: $i] :
( ( ( p14 @ X0 )
= $true )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f1234,f1215]) ).
thf(f1237,plain,
! [X0: $i] :
( ( p14 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f1236]) ).
thf(f1240,plain,
! [X0: $i] :
( ( ( p14 @ ( sK40 @ X0 ) )
= $false )
| ( $true = $false )
| ( $true
= ( p13 @ X0 ) ) ),
inference(constrained_superposition,[],[f1237,f1127]) ).
thf(f1242,plain,
! [X0: $i] :
( ( $true
= ( p13 @ X0 ) )
| ( ( p14 @ ( sK40 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1240]) ).
thf(f1244,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p13 @ X0 ) ) ),
inference(forward_demodulation,[],[f1242,f1237]) ).
thf(f1245,plain,
! [X0: $i] :
( $true
= ( p13 @ X0 ) ),
inference(trivial_inequality_removal,[],[f1244]) ).
thf(f1253,plain,
! [X0: $i] :
( ( $true
= ( p3 @ X0 ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( ( p4 @ ( sK50 @ X0 ) )
= $false )
| ( $false != $false )
| ( ( p4 @ ( sK52 @ X0 ) )
= $false ) ),
inference(equality_factoring,[],[f686]) ).
thf(f1254,plain,
! [X0: $i] :
( ( ( p4 @ ( sK50 @ X0 ) )
= $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( ( p4 @ ( sK52 @ X0 ) )
= $false )
| ( $true
= ( p3 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1253]) ).
thf(f1260,plain,
! [X0: $i] :
( ( ( p4 @ ( sK50 @ X0 ) )
= $false )
| ( ( p4 @ ( sK52 @ X0 ) )
= $false )
| ( $true = $false )
| ( $true
= ( p3 @ X0 ) ) ),
inference(forward_demodulation,[],[f1254,f136]) ).
thf(f1261,plain,
! [X0: $i] :
( ( ( p4 @ ( sK52 @ X0 ) )
= $false )
| ( ( p4 @ ( sK50 @ X0 ) )
= $false )
| ( $true
= ( p3 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1260]) ).
thf(f1291,plain,
! [X0: $i] :
( ( $true
= ( p1 @ X0 ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $false != $false )
| ( ( p2 @ ( sK55 @ X0 ) )
= $false )
| ( ( p2 @ ( sK53 @ X0 ) )
= $false ) ),
inference(equality_factoring,[],[f717]) ).
thf(f1297,plain,
! [X0: $i] :
( ( ( p2 @ ( sK53 @ X0 ) )
= $false )
| ( $true
= ( p1 @ X0 ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( ( p2 @ ( sK55 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1291]) ).
thf(f1298,plain,
! [X0: $i] :
( ( ( p2 @ ( sK55 @ X0 ) )
= $false )
| ( $true
= ( p1 @ X0 ) )
| ( ( p2 @ ( sK53 @ X0 ) )
= $false )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f1297,f136]) ).
thf(f1299,plain,
! [X0: $i] :
( ( ( p2 @ ( sK55 @ X0 ) )
= $false )
| ( ( p2 @ ( sK53 @ X0 ) )
= $false )
| ( $true
= ( p1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1298]) ).
thf(f1312,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( p13 @ ( sK56 @ X1 ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true = $false )
| ( $true
= ( p12 @ X3 ) ) ),
inference(forward_demodulation,[],[f744,f1245]) ).
thf(f1313,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p12 @ X3 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( p13 @ ( sK56 @ X1 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1312]) ).
thf(f1314,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( $true = $false )
| ( $true
= ( p12 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f1313,f1245]) ).
thf(f1315,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p12 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f1314]) ).
thf(f1321,plain,
! [X0: $i] :
( ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p12 @ X0 ) )
| ( $false != $false ) ),
inference(equality_factoring,[],[f1315]) ).
thf(f1324,plain,
! [X0: $i] :
( ( $true
= ( p12 @ X0 ) )
| ( ( irel @ X0 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f1321]) ).
thf(f1328,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p12 @ X0 ) ) ),
inference(forward_demodulation,[],[f1324,f136]) ).
thf(f1329,plain,
! [X0: $i] :
( $true
= ( p12 @ X0 ) ),
inference(trivial_inequality_removal,[],[f1328]) ).
thf(f1331,plain,
! [X0: $i] :
( ( $true
= ( p11 @ X0 ) )
| ( $true = $false )
| ( ( p12 @ ( sK4 @ X0 ) )
= $false ) ),
inference(constrained_superposition,[],[f853,f1329]) ).
thf(f1332,plain,
! [X0: $i] :
( ( ( p12 @ ( sK4 @ X0 ) )
= $false )
| ( $true
= ( p11 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1331]) ).
thf(f1334,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p11 @ X0 ) ) ),
inference(forward_demodulation,[],[f1332,f1329]) ).
thf(f1335,plain,
! [X0: $i] :
( $true
= ( p11 @ X0 ) ),
inference(trivial_inequality_removal,[],[f1334]) ).
thf(f1343,plain,
! [X0: $i] :
( ( $true
= ( p0 @ X0 ) )
| ( ( p1 @ ( sK59 @ X0 ) )
= $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( ( p1 @ ( sK61 @ X0 ) )
= $false )
| ( $false != $false ) ),
inference(equality_factoring,[],[f773]) ).
thf(f1344,plain,
! [X0: $i] :
( ( ( p1 @ ( sK59 @ X0 ) )
= $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p0 @ X0 ) )
| ( ( p1 @ ( sK61 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1343]) ).
thf(f1350,plain,
! [X0: $i] :
( ( ( p1 @ ( sK61 @ X0 ) )
= $false )
| ( $true = $false )
| ( $true
= ( p0 @ X0 ) )
| ( ( p1 @ ( sK59 @ X0 ) )
= $false ) ),
inference(forward_demodulation,[],[f1344,f136]) ).
thf(f1351,plain,
! [X0: $i] :
( ( ( p1 @ ( sK59 @ X0 ) )
= $false )
| ( $true
= ( p0 @ X0 ) )
| ( ( p1 @ ( sK61 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1350]) ).
thf(f1353,plain,
! [X0: $i] :
( ( ( p11 @ ( sK35 @ X0 ) )
= $false )
| ( $true
= ( p10 @ X0 ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f1113,f1335]) ).
thf(f1354,plain,
! [X0: $i] :
( ( ( p11 @ ( sK35 @ X0 ) )
= $false )
| ( $true
= ( p10 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1353]) ).
thf(f1356,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p10 @ X0 ) ) ),
inference(forward_demodulation,[],[f1354,f1335]) ).
thf(f1357,plain,
! [X0: $i] :
( $true
= ( p10 @ X0 ) ),
inference(trivial_inequality_removal,[],[f1356]) ).
thf(f1361,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( p10 @ ( sK7 @ X0 ) )
= $false )
| ( $true
= ( p9 @ X0 ) ) ),
inference(constrained_superposition,[],[f879,f1357]) ).
thf(f1362,plain,
! [X0: $i] :
( ( ( p10 @ ( sK7 @ X0 ) )
= $false )
| ( $true
= ( p9 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1361]) ).
thf(f1364,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p9 @ X0 ) ) ),
inference(forward_demodulation,[],[f1362,f1357]) ).
thf(f1365,plain,
! [X0: $i] :
( $true
= ( p9 @ X0 ) ),
inference(trivial_inequality_removal,[],[f1364]) ).
thf(f1369,plain,
! [X0: $i] :
( ( ( p9 @ ( sK23 @ X0 ) )
= $false )
| ( $true = $false )
| ( $true
= ( p8 @ X0 ) ) ),
inference(constrained_superposition,[],[f1009,f1365]) ).
thf(f1370,plain,
! [X0: $i] :
( ( ( p9 @ ( sK23 @ X0 ) )
= $false )
| ( $true
= ( p8 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1369]) ).
thf(f1372,plain,
! [X0: $i] :
( ( $true
= ( p8 @ X0 ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f1370,f1365]) ).
thf(f1373,plain,
! [X0: $i] :
( $true
= ( p8 @ X0 ) ),
inference(trivial_inequality_removal,[],[f1372]) ).
thf(f1376,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( p8 @ ( sK31 @ X0 ) )
= $false )
| ( $true
= ( p7 @ X0 ) ) ),
inference(constrained_superposition,[],[f1373,f1061]) ).
thf(f1378,plain,
! [X0: $i] :
( ( ( p8 @ ( sK31 @ X0 ) )
= $false )
| ( $true
= ( p7 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1376]) ).
thf(f1380,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p7 @ X0 ) ) ),
inference(forward_demodulation,[],[f1378,f1373]) ).
thf(f1381,plain,
! [X0: $i] :
( $true
= ( p7 @ X0 ) ),
inference(trivial_inequality_removal,[],[f1380]) ).
thf(f1384,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p6 @ X0 ) )
| ( ( p7 @ ( sK20 @ X0 ) )
= $false ) ),
inference(constrained_superposition,[],[f1381,f983]) ).
thf(f1386,plain,
! [X0: $i] :
( ( ( p7 @ ( sK20 @ X0 ) )
= $false )
| ( $true
= ( p6 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1384]) ).
thf(f1388,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p6 @ X0 ) ) ),
inference(forward_demodulation,[],[f1386,f1381]) ).
thf(f1389,plain,
! [X0: $i] :
( $true
= ( p6 @ X0 ) ),
inference(trivial_inequality_removal,[],[f1388]) ).
thf(f1392,plain,
! [X0: $i] :
( ( $true
= ( p5 @ X0 ) )
| ( $true = $false )
| ( ( p6 @ ( sK26 @ X0 ) )
= $false ) ),
inference(constrained_superposition,[],[f1389,f1035]) ).
thf(f1394,plain,
! [X0: $i] :
( ( ( p6 @ ( sK26 @ X0 ) )
= $false )
| ( $true
= ( p5 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1392]) ).
thf(f1396,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p5 @ X0 ) ) ),
inference(forward_demodulation,[],[f1394,f1389]) ).
thf(f1397,plain,
! [X0: $i] :
( $true
= ( p5 @ X0 ) ),
inference(trivial_inequality_removal,[],[f1396]) ).
thf(f1400,plain,
! [X0: $i] :
( ( $true
= ( p4 @ X0 ) )
| ( $true = $false )
| ( ( p5 @ ( sK17 @ X0 ) )
= $false ) ),
inference(constrained_superposition,[],[f1397,f947]) ).
thf(f1402,plain,
! [X0: $i] :
( ( ( p5 @ ( sK17 @ X0 ) )
= $false )
| ( $true
= ( p4 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1400]) ).
thf(f1404,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p4 @ X0 ) ) ),
inference(forward_demodulation,[],[f1402,f1397]) ).
thf(f1405,plain,
! [X0: $i] :
( $true
= ( p4 @ X0 ) ),
inference(trivial_inequality_removal,[],[f1404]) ).
thf(f1409,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p3 @ X0 ) )
| ( ( p4 @ ( sK50 @ X0 ) )
= $false ) ),
inference(constrained_superposition,[],[f1261,f1405]) ).
thf(f1410,plain,
! [X0: $i] :
( ( ( p4 @ ( sK50 @ X0 ) )
= $false )
| ( $true
= ( p3 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1409]) ).
thf(f1412,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p3 @ X0 ) ) ),
inference(forward_demodulation,[],[f1410,f1405]) ).
thf(f1413,plain,
! [X0: $i] :
( $true
= ( p3 @ X0 ) ),
inference(trivial_inequality_removal,[],[f1412]) ).
thf(f1417,plain,
! [X0: $i] :
( ( $true
= ( p2 @ X0 ) )
| ( $true = $false )
| ( ( p3 @ ( sK47 @ X0 ) )
= $false ) ),
inference(constrained_superposition,[],[f1231,f1413]) ).
thf(f1418,plain,
! [X0: $i] :
( ( ( p3 @ ( sK47 @ X0 ) )
= $false )
| ( $true
= ( p2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1417]) ).
thf(f1420,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p2 @ X0 ) ) ),
inference(forward_demodulation,[],[f1418,f1413]) ).
thf(f1421,plain,
! [X0: $i] :
( $true
= ( p2 @ X0 ) ),
inference(trivial_inequality_removal,[],[f1420]) ).
thf(f1425,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p1 @ X0 ) )
| ( ( p2 @ ( sK53 @ X0 ) )
= $false ) ),
inference(constrained_superposition,[],[f1299,f1421]) ).
thf(f1426,plain,
! [X0: $i] :
( ( $true
= ( p1 @ X0 ) )
| ( ( p2 @ ( sK53 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1425]) ).
thf(f1428,plain,
! [X0: $i] :
( ( $true
= ( p1 @ X0 ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f1426,f1421]) ).
thf(f1429,plain,
! [X0: $i] :
( $true
= ( p1 @ X0 ) ),
inference(trivial_inequality_removal,[],[f1428]) ).
thf(f1432,plain,
! [X0: $i] :
( ( ( p1 @ ( sK61 @ X0 ) )
= $false )
| ( $true
= ( p0 @ X0 ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f1351,f1429]) ).
thf(f1433,plain,
! [X0: $i] :
( ( $true
= ( p0 @ X0 ) )
| ( ( p1 @ ( sK61 @ X0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1432]) ).
thf(f1434,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p0 @ X0 ) ) ),
inference(forward_demodulation,[],[f1433,f1429]) ).
thf(f1435,plain,
! [X0: $i] :
( $true
= ( p0 @ X0 ) ),
inference(trivial_inequality_removal,[],[f1434]) ).
thf(f1436,plain,
spl62_3,
inference(avatar_split_clause,[],[f1435,f785]) ).
cnf(s1,plain,
( spl62_1
| spl62_2 ),
inference(sat_conversion,[],[f783]) ).
cnf(s3,plain,
~ spl62_2,
inference(sat_conversion,[],[f792]) ).
cnf(s6,plain,
( ~ spl62_1
| ~ spl62_3 ),
inference(sat_conversion,[],[f813]) ).
cnf(s7,plain,
spl62_3,
inference(sat_conversion,[],[f1436]) ).
cnf(s8,plain,
~ spl62_1,
inference(rat,[],[s6,s7]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s3,s8]) ).
thf(f1437,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO068^4.020 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n016.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 16:34:20 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.36 % (567667)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.36 % (567675)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2810422703:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.36 % (567678)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.36 % (567678)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.36 % (567673)lrs+10_16_si=on:nwc=1.5:random_seed=3358280562:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.36 % (567672)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3486781077:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.36 % (567674)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2821536054:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.36 % (567676)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1240398888:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.36 % (567677)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=255117153:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.36 % (567678)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1163161194:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.36 % (567674)Instruction limit reached!
% 0.21/0.36 % (567674)------------------------------
% 0.21/0.36 % (567674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (567674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (567674)CaDiCaL version: 2.1.3
% 0.21/0.36 % (567674)Termination reason: Instruction limit
% 0.21/0.36 % (567674)Termination phase: Property scanning
% 0.21/0.36 % (567674)Time elapsed: 0.002 s
% 0.21/0.36 % (567674)Peak memory usage: 10 MB
% 0.21/0.36 % (567674)Instructions burned: 4 (million)
% 0.21/0.36 % (567673)Instruction limit reached!
% 0.21/0.36 % (567673)------------------------------
% 0.21/0.36 % (567673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (567673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (567673)CaDiCaL version: 2.1.3
% 0.21/0.36 % (567673)Termination reason: Instruction limit
% 0.21/0.36 % (567673)Termination phase: Property scanning
% 0.21/0.36 % (567673)Time elapsed: 0.007 s
% 0.21/0.36 % (567673)Peak memory usage: 10 MB
% 0.21/0.36 % (567673)Instructions burned: 18 (million)
% 0.21/0.36 % (567676)Instruction limit reached!
% 0.21/0.36 % (567676)------------------------------
% 0.21/0.36 % (567676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (567676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (567676)CaDiCaL version: 2.1.3
% 0.21/0.36 % (567676)Termination reason: Instruction limit
% 0.21/0.36 % (567676)Termination phase: Saturation
% 0.21/0.36 % (567676)Time elapsed: 0.014 s
% 0.21/0.36 % (567676)Peak memory usage: 11 MB
% 0.21/0.36 % (567676)Instructions burned: 25 (million)
% 0.21/0.36 % (567686)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3850602665:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.36 % (567686)Instruction limit reached!
% 0.21/0.36 % (567686)------------------------------
% 0.21/0.36 % (567686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (567686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (567686)CaDiCaL version: 2.1.3
% 0.21/0.36 % (567686)Termination reason: Instruction limit
% 0.21/0.36 % (567686)Termination phase: shuffling
% 0.21/0.36 % (567686)Time elapsed: 0.001 s
% 0.21/0.36 % (567686)Peak memory usage: 9 MB
% 0.21/0.36 % (567686)Instructions burned: 2 (million)
% 0.21/0.36 % (567687)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2905247190:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.36 % (567687)Instruction limit reached!
% 0.21/0.36 % (567687)------------------------------
% 0.21/0.36 % (567687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (567687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (567687)CaDiCaL version: 2.1.3
% 0.21/0.36 % (567687)Termination reason: Instruction limit
% 0.21/0.36 % (567687)Termination phase: Function definition elimination
% 0.21/0.36 % (567687)Time elapsed: 0.003 s
% 0.21/0.36 % (567687)Peak memory usage: 10 MB
% 0.21/0.36 % (567687)Instructions burned: 7 (million)
% 0.21/0.36 % (567688)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.36 % (567688)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1038476171:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.36 % (567677)Instruction limit reached!
% 0.21/0.36 % (567677)------------------------------
% 0.21/0.36 % (567677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (567677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (567677)CaDiCaL version: 2.1.3
% 0.21/0.36 % (567677)Termination reason: Instruction limit
% 0.21/0.36 % (567677)Termination phase: Saturation
% 0.21/0.36 % (567677)Time elapsed: 0.034 s
% 0.21/0.36 % (567677)Peak memory usage: 12 MB
% 0.21/0.36 % (567677)Instructions burned: 76 (million)
% 0.21/0.36 % (567688)Instruction limit reached!
% 0.21/0.36 % (567688)------------------------------
% 0.21/0.36 % (567688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (567688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (567688)CaDiCaL version: 2.1.3
% 0.21/0.36 % (567688)Termination reason: Instruction limit
% 0.21/0.36 % (567688)Termination phase: Function definition elimination
% 0.21/0.36 % (567688)Time elapsed: 0.003 s
% 0.21/0.36 % (567688)Peak memory usage: 10 MB
% 0.21/0.36 % (567688)Instructions burned: 7 (million)
% 0.21/0.36 % (567672)Instruction limit reached!
% 0.21/0.36 % (567672)------------------------------
% 0.21/0.36 % (567672)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (567672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (567672)CaDiCaL version: 2.1.3
% 0.21/0.36 % (567672)Termination reason: Instruction limit
% 0.21/0.36 % (567672)Termination phase: Saturation
% 0.21/0.36 % (567672)Time elapsed: 0.039 s
% 0.21/0.36 % (567672)Peak memory usage: 12 MB
% 0.21/0.36 % (567672)Instructions burned: 88 (million)
% 0.21/0.36 % (567690)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3977507237:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.36 % (567692)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.36 % (567692)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.36 % (567690)Instruction limit reached!
% 0.21/0.36 % (567690)------------------------------
% 0.21/0.36 % (567690)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (567690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (567690)CaDiCaL version: 2.1.3
% 0.21/0.36 % (567690)Termination reason: Instruction limit
% 0.21/0.36 % (567690)Termination phase: Property scanning
% 0.21/0.36 % (567690)Time elapsed: 0.005 s
% 0.21/0.36 % (567690)Peak memory usage: 10 MB
% 0.21/0.36 % (567690)Instructions burned: 12 (million)
% 0.21/0.36 % (567692)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2061451572:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.21/0.36 % (567678) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-567667-567678"...
% 0.21/0.36 % (567694)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3320030624:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.21/0.36 % (567696)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.21/0.36 % (567695)lrs+10_1_si=on:cs=on:random_seed=837038080:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.21/0.36 % (567696)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=3376746960:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.36 % (567695)Instruction limit reached!
% 0.21/0.36 % (567695)------------------------------
% 0.21/0.36 % (567695)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (567695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (567695)CaDiCaL version: 2.1.3
% 0.21/0.36 % (567695)Termination reason: Instruction limit
% 0.21/0.36 % (567695)Termination phase: Property scanning
% 0.21/0.36 % (567695)Time elapsed: 0.004 s
% 0.21/0.36 % (567695)Peak memory usage: 10 MB
% 0.21/0.36 % (567695)Instructions burned: 10 (million)
% 0.21/0.36 % (567692)Instruction limit reached!
% 0.21/0.36 % (567692)------------------------------
% 0.21/0.36 % (567692)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (567692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (567692)CaDiCaL version: 2.1.3
% 0.21/0.36 % (567692)Termination reason: Instruction limit
% 0.21/0.36 % (567692)Termination phase: Saturation
% 0.21/0.36 % (567692)Time elapsed: 0.012 s
% 0.21/0.36 % (567692)Peak memory usage: 11 MB
% 0.21/0.36 % (567692)Instructions burned: 28 (million)
% 0.21/0.36 % (567696)Instruction limit reached!
% 0.21/0.36 % (567696)------------------------------
% 0.21/0.36 % (567696)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (567696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (567696)CaDiCaL version: 2.1.3
% 0.21/0.36 % (567696)Termination reason: Instruction limit
% 0.21/0.36 % (567696)Termination phase: Property scanning
% 0.21/0.36 % (567696)Time elapsed: 0.002 s
% 0.21/0.36 % (567696)Peak memory usage: 10 MB
% 0.21/0.36 % (567696)Instructions burned: 3 (million)
% 0.21/0.36 % (567698)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=106472579:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.21/0.36 % (567698)Refutation not found, incomplete strategy
% 0.21/0.36 % (567698)------------------------------
% 0.21/0.36 % (567698)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (567698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (567698)CaDiCaL version: 2.1.3
% 0.21/0.36 % (567698)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.36 % (567698)Time elapsed: 0.006 s
% 0.21/0.36 % (567698)Peak memory usage: 12 MB
% 0.21/0.36 % (567698)Instructions burned: 11 (million)
% 0.21/0.36 % (567698)------------------------------
% 0.21/0.36 % (567698)------------------------------
% 0.21/0.36 % (567703)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3312368676:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.21/0.36 % (567704)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=4121078951:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.21/0.36 % (567705)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3755188308:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.21/0.36 % (567678)...printing done.
% 0.21/0.36 % (567703)Refutation not found, incomplete strategy
% 0.21/0.36 % (567703)------------------------------
% 0.21/0.36 % (567703)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (567703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (567703)CaDiCaL version: 2.1.3
% 0.21/0.36 % (567703)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.36 % (567703)Time elapsed: 0.003 s
% 0.21/0.36 % (567703)Peak memory usage: 12 MB
% 0.21/0.36 % (567703)Instructions burned: 6 (million)
% 0.21/0.36 % (567678)Refutation found. Thanks to Tanya!
% 0.21/0.36 % SZS status Theorem for theBenchmark
% 0.21/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.58/0.37 % (567678)------------------------------
% 0.58/0.37 % (567678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.37 % (567678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.37 % (567678)CaDiCaL version: 2.1.3
% 0.58/0.37 % (567678)Termination reason: Refutation
% 0.58/0.37 % (567678)Time elapsed: 0.079 s
% 0.58/0.37 % (567678)Peak memory usage: 14 MB
% 0.58/0.37 % (567678)Instructions burned: 174 (million)
% 0.58/0.37 % (567667)Success in time 0.113 s
% 0.58/0.37 % Vampire exiting
%------------------------------------------------------------------------------