%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO068^4.010 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:48:53 AM UTC 2026
% Result : Theorem 0.33s 0.46s
% Output : Refutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 69
% Number of leaves : 20
% Syntax : Number of formulae : 349 ( 114 unt; 0 typ; 0 def)
% Number of atoms : 3846 ( 801 equ; 0 cnn)
% Maximal formula atoms : 9 ( 11 avg)
% Number of connectives : 5732 ( 213 ~; 636 |; 0 &;3947 @)
% ( 0 <=>; 526 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 273 ( 273 >; 0 *; 0 +; 0 <<)
% Number of symbols : 77 ( 73 usr; 4 con; 0-4 aty)
% ( 410 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1308 ( 869 ^; 439 !; 0 ?;1308 :)
% 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,
p2: $i > $o ).
thf(func_def_25,type,
p3: $i > $o ).
thf(func_def_26,type,
p4: $i > $o ).
thf(func_def_27,type,
p5: $i > $o ).
thf(func_def_28,type,
p6: $i > $o ).
thf(func_def_29,type,
p7: $i > $o ).
thf(func_def_30,type,
p8: $i > $o ).
thf(func_def_31,type,
p9: $i > $o ).
thf(func_def_34,type,
vNOT: $o > $o ).
thf(func_def_35,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_38,type,
vOR: $o > $o > $o ).
thf(func_def_39,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vAND: $o > $o > $o ).
thf(func_def_41,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
vIMP: $o > $o > $o ).
thf(func_def_43,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_45,type,
sK1: $i > $i ).
thf(func_def_46,type,
sK2: $i > $i ).
thf(func_def_47,type,
sK3: $i > $i ).
thf(func_def_48,type,
sK4: $i > $i ).
thf(func_def_49,type,
sK5: $i > $i ).
thf(func_def_50,type,
sK6: $i > $i ).
thf(func_def_51,type,
sK7: $i > $i ).
thf(func_def_52,type,
sK8: $i > $i ).
thf(func_def_53,type,
sK9: $i > $i ).
thf(func_def_54,type,
sK10: $i > $i ).
thf(func_def_55,type,
sK11: $i > $i ).
thf(func_def_56,type,
sK12: $i > $i ).
thf(func_def_57,type,
sK13: $i > $i ).
thf(func_def_58,type,
sK14: $i > $i ).
thf(func_def_59,type,
sK15: $i > $i ).
thf(func_def_60,type,
sK16: $i > $i ).
thf(func_def_61,type,
sK17: $i > $i ).
thf(func_def_62,type,
sK18: $i > $i ).
thf(func_def_63,type,
sK19: $i > $i ).
thf(func_def_64,type,
sK20: $i > $i ).
thf(func_def_65,type,
sK21: $i > $i ).
thf(func_def_66,type,
sK22: $i > $i ).
thf(func_def_67,type,
sK23: $i > $i ).
thf(func_def_68,type,
sK24: $i > $i ).
thf(func_def_69,type,
sK25: $i > $i ).
thf(func_def_70,type,
sK26: $i > $i ).
thf(func_def_71,type,
sK27: $i > $i ).
thf(func_def_72,type,
sK28: $i > $i ).
thf(func_def_73,type,
sK29: $i > $i ).
thf(func_def_74,type,
sK30: $i > $i ).
thf(f1,axiom,
! [X0: $i] : ( irel @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',refl_axiom) ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mimplies) ).
thf(f7,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).
thf(f8,axiom,
( iatom
= ( ^ [X0: $i > $o] : X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iatom) ).
thf(f14,axiom,
( iimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mimplies @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iimplies) ).
thf(f18,axiom,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,axiom,
ivalid @ ( iatom @ p10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1) ).
thf(f23,axiom,
ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2) ).
thf(f24,axiom,
ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom3) ).
thf(f25,axiom,
ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom4) ).
thf(f26,axiom,
ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom5) ).
thf(f27,axiom,
ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom6) ).
thf(f28,axiom,
ivalid @ ( iimplies @ ( iatom @ p6 ) @ ( iimplies @ ( iatom @ p6 ) @ ( iatom @ p5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom7) ).
thf(f29,axiom,
ivalid @ ( iimplies @ ( iatom @ p7 ) @ ( iimplies @ ( iatom @ p7 ) @ ( iatom @ p6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom8) ).
thf(f30,axiom,
ivalid @ ( iimplies @ ( iatom @ p8 ) @ ( iimplies @ ( iatom @ p8 ) @ ( iatom @ p7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom9) ).
thf(f31,axiom,
ivalid @ ( iimplies @ ( iatom @ p9 ) @ ( iimplies @ ( iatom @ p9 ) @ ( iatom @ p8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom10) ).
thf(f32,axiom,
ivalid @ ( iimplies @ ( iatom @ p10 ) @ ( iimplies @ ( iatom @ p10 ) @ ( iatom @ p9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom11) ).
thf(f33,conjecture,
ivalid @ ( iatom @ p0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f34,negated_conjecture,
~ ( ivalid @ ( iatom @ p0 ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
thf(f35,plain,
! [X0: $i] : ( irel @ X0 @ X0 ),
inference(rectify,[],[f1]) ).
thf(f36,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f35]) ).
thf(f39,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f40,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f42,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f45,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f46,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f47,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f48,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f53,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f57,plain,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f58,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f65,plain,
ivalid @ ( iatom @ p10 ),
inference(rectify,[],[f22]) ).
thf(f66,plain,
( ( ivalid @ ( iatom @ p10 ) )
= $true ),
inference(fool_elimination,[],[f65]) ).
thf(f67,plain,
ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ),
inference(rectify,[],[f23]) ).
thf(f68,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ) )
= $true ),
inference(fool_elimination,[],[f67]) ).
thf(f69,plain,
ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ),
inference(rectify,[],[f24]) ).
thf(f70,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ) )
= $true ),
inference(fool_elimination,[],[f69]) ).
thf(f71,plain,
ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ),
inference(rectify,[],[f25]) ).
thf(f72,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ) )
= $true ),
inference(fool_elimination,[],[f71]) ).
thf(f73,plain,
ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ),
inference(rectify,[],[f26]) ).
thf(f74,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ) )
= $true ),
inference(fool_elimination,[],[f73]) ).
thf(f75,plain,
ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ),
inference(rectify,[],[f27]) ).
thf(f76,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ) )
= $true ),
inference(fool_elimination,[],[f75]) ).
thf(f77,plain,
ivalid @ ( iimplies @ ( iatom @ p6 ) @ ( iimplies @ ( iatom @ p6 ) @ ( iatom @ p5 ) ) ),
inference(rectify,[],[f28]) ).
thf(f78,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p6 ) @ ( iimplies @ ( iatom @ p6 ) @ ( iatom @ p5 ) ) ) )
= $true ),
inference(fool_elimination,[],[f77]) ).
thf(f79,plain,
ivalid @ ( iimplies @ ( iatom @ p7 ) @ ( iimplies @ ( iatom @ p7 ) @ ( iatom @ p6 ) ) ),
inference(rectify,[],[f29]) ).
thf(f80,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p7 ) @ ( iimplies @ ( iatom @ p7 ) @ ( iatom @ p6 ) ) ) )
= $true ),
inference(fool_elimination,[],[f79]) ).
thf(f81,plain,
ivalid @ ( iimplies @ ( iatom @ p8 ) @ ( iimplies @ ( iatom @ p8 ) @ ( iatom @ p7 ) ) ),
inference(rectify,[],[f30]) ).
thf(f82,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p8 ) @ ( iimplies @ ( iatom @ p8 ) @ ( iatom @ p7 ) ) ) )
= $true ),
inference(fool_elimination,[],[f81]) ).
thf(f83,plain,
ivalid @ ( iimplies @ ( iatom @ p9 ) @ ( iimplies @ ( iatom @ p9 ) @ ( iatom @ p8 ) ) ),
inference(rectify,[],[f31]) ).
thf(f84,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p9 ) @ ( iimplies @ ( iatom @ p9 ) @ ( iatom @ p8 ) ) ) )
= $true ),
inference(fool_elimination,[],[f83]) ).
thf(f85,plain,
ivalid @ ( iimplies @ ( iatom @ p10 ) @ ( iimplies @ ( iatom @ p10 ) @ ( iatom @ p9 ) ) ),
inference(rectify,[],[f32]) ).
thf(f86,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p10 ) @ ( iimplies @ ( iatom @ p10 ) @ ( iatom @ p9 ) ) ) )
= $true ),
inference(fool_elimination,[],[f85]) ).
thf(f87,plain,
~ ( ivalid @ ( iatom @ p0 ) ),
inference(rectify,[],[f34]) ).
thf(f88,plain,
( ( ivalid @ ( iatom @ p0 ) )
!= $true ),
inference(fool_elimination,[],[f87]) ).
thf(f89,plain,
( ( ivalid @ ( iatom @ p0 ) )
!= $true ),
inference(flattening,[],[f88]) ).
thf(f92,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f36]) ).
thf(f94,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f95,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f97,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f98,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f99,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f105,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f109,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f113,plain,
( ( ivalid @ ( iatom @ p10 ) )
= $true ),
inference(cnf_transformation,[],[f66]) ).
thf(f114,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f68]) ).
thf(f115,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f70]) ).
thf(f116,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f72]) ).
thf(f117,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f74]) ).
thf(f118,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f76]) ).
thf(f119,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p6 ) @ ( iimplies @ ( iatom @ p6 ) @ ( iatom @ p5 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f78]) ).
thf(f120,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p7 ) @ ( iimplies @ ( iatom @ p7 ) @ ( iatom @ p6 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f80]) ).
thf(f121,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p8 ) @ ( iimplies @ ( iatom @ p8 ) @ ( iatom @ p7 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f82]) ).
thf(f122,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p9 ) @ ( iimplies @ ( iatom @ p9 ) @ ( iatom @ p8 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f84]) ).
thf(f123,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p10 ) @ ( iimplies @ ( iatom @ p10 ) @ ( iatom @ p9 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f86]) ).
thf(f124,plain,
( ( ivalid @ ( iatom @ p0 ) )
!= $true ),
inference(cnf_transformation,[],[f89]) ).
thf(f127,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f97,f95,f94]) ).
thf(f132,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f105,f127,f98,f98]) ).
thf(f136,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p10 ) ) ),
inference(definition_unfolding,[],[f113,f109,f99]) ).
thf(f137,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p1 )
@ ( ^ [Y0: $i > $o] : Y0
@ p0 ) ) ) ) ),
inference(definition_unfolding,[],[f114,f109,f132,f99,f132,f99,f99]) ).
thf(f138,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p2 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p2 )
@ ( ^ [Y0: $i > $o] : Y0
@ p1 ) ) ) ) ),
inference(definition_unfolding,[],[f115,f109,f132,f99,f132,f99,f99]) ).
thf(f139,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p3 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p3 )
@ ( ^ [Y0: $i > $o] : Y0
@ p2 ) ) ) ) ),
inference(definition_unfolding,[],[f116,f109,f132,f99,f132,f99,f99]) ).
thf(f140,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p4 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p4 )
@ ( ^ [Y0: $i > $o] : Y0
@ p3 ) ) ) ) ),
inference(definition_unfolding,[],[f117,f109,f132,f99,f132,f99,f99]) ).
thf(f141,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p5 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p5 )
@ ( ^ [Y0: $i > $o] : Y0
@ p4 ) ) ) ) ),
inference(definition_unfolding,[],[f118,f109,f132,f99,f132,f99,f99]) ).
thf(f142,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p6 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p6 )
@ ( ^ [Y0: $i > $o] : Y0
@ p5 ) ) ) ) ),
inference(definition_unfolding,[],[f119,f109,f132,f99,f132,f99,f99]) ).
thf(f143,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p7 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p7 )
@ ( ^ [Y0: $i > $o] : Y0
@ p6 ) ) ) ) ),
inference(definition_unfolding,[],[f120,f109,f132,f99,f132,f99,f99]) ).
thf(f144,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p8 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p8 )
@ ( ^ [Y0: $i > $o] : Y0
@ p7 ) ) ) ) ),
inference(definition_unfolding,[],[f121,f109,f132,f99,f132,f99,f99]) ).
thf(f145,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p9 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p9 )
@ ( ^ [Y0: $i > $o] : Y0
@ p8 ) ) ) ) ),
inference(definition_unfolding,[],[f122,f109,f132,f99,f132,f99,f99]) ).
thf(f146,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p10 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p10 )
@ ( ^ [Y0: $i > $o] : Y0
@ p9 ) ) ) ) ),
inference(definition_unfolding,[],[f123,f109,f132,f99,f132,f99,f99]) ).
thf(f147,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p0 ) ) ),
inference(definition_unfolding,[],[f124,f109,f99]) ).
thf(f148,plain,
( $true
!= ( !! @ $i @ p0 ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f149,plain,
( $false
= ( p0 @ sK0 ) ),
inference(sigma_proxy_clausification,[],[f148]) ).
thf(f150,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p10 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p9 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f151,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p10 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p9 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p10 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p10 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p10 @ Y0 ) )
@ ( sK1 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK1 @ X1 ) )
=> ( p10 @ ( sK1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK1 @ X1 ) )
=> ( p10 @ ( sK1 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p10 @ ( sK1 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f158]) ).
thf(f169,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p10 @ ( sK1 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f170,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p10 @ ( sK1 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p10 @ ( sK1 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p10 @ ( sK1 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p10 @ Y0 ) )
@ ( sK3 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p10 @ ( sK1 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p9 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK3 @ X2 ) )
=> ( p10 @ ( sK3 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p10 @ ( sK1 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK3 @ X2 ) )
=> ( p10 @ ( sK3 @ X2 ) ) ) )
| ( $true
= ( p9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p10 @ ( sK3 @ X2 ) ) )
| ( $false
= ( p10 @ ( sK1 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p9 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f174]) ).
thf(f177,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p9 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p8 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f178,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p9 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p8 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p9 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p9 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p9 @ Y0 ) )
@ ( sK4 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK4 @ X1 ) )
=> ( p9 @ ( sK4 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK4 @ X1 ) )
=> ( p9 @ ( sK4 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p9 @ ( sK4 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f185]) ).
thf(f196,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p9 @ ( sK4 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f186]) ).
thf(f197,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p9 @ ( sK4 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p9 @ ( sK4 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p9 @ ( sK4 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p9 @ Y0 ) )
@ ( sK6 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p9 @ ( sK4 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p8 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK6 @ X2 ) )
=> ( p9 @ ( sK6 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f199]) ).
thf(f201,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p9 @ ( sK4 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK6 @ X2 ) )
=> ( p9 @ ( sK6 @ X2 ) ) ) )
| ( $true
= ( p8 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p9 @ ( sK6 @ X2 ) ) )
| ( $false
= ( p9 @ ( sK4 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p8 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f201]) ).
thf(f204,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p8 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p7 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f205,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p8 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p7 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p8 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f207,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p8 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p8 @ Y0 ) )
@ ( sK7 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK7 @ X1 ) )
=> ( p8 @ ( sK7 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f210]) ).
thf(f212,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK7 @ X1 ) )
=> ( p8 @ ( sK7 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f211]) ).
thf(f213,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p8 @ ( sK7 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f212]) ).
thf(f223,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p8 @ ( sK7 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f213]) ).
thf(f224,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p8 @ ( sK7 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p8 @ ( sK7 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f224]) ).
thf(f226,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p8 @ ( sK7 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p8 @ Y0 ) )
@ ( sK9 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p8 @ ( sK7 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p7 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK9 @ X2 ) )
=> ( p8 @ ( sK9 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f226]) ).
thf(f228,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p8 @ ( sK7 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK9 @ X2 ) )
=> ( p8 @ ( sK9 @ X2 ) ) ) )
| ( $true
= ( p7 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p8 @ ( sK9 @ X2 ) ) )
| ( $false
= ( p8 @ ( sK7 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p7 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f228]) ).
thf(f231,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p7 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p6 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f232,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p7 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p6 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p7 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f232]) ).
thf(f234,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f233]) ).
thf(f235,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f234]) ).
thf(f236,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p7 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p7 @ Y0 ) )
@ ( sK10 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK10 @ X1 ) )
=> ( p7 @ ( sK10 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f237]) ).
thf(f239,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK10 @ X1 ) )
=> ( p7 @ ( sK10 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f238]) ).
thf(f240,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p7 @ ( sK10 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f239]) ).
thf(f250,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p7 @ ( sK10 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f240]) ).
thf(f251,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p7 @ ( sK10 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f250]) ).
thf(f252,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p7 @ ( sK10 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f251]) ).
thf(f253,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p7 @ ( sK10 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p7 @ Y0 ) )
@ ( sK12 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f252]) ).
thf(f254,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p7 @ ( sK10 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p6 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK12 @ X2 ) )
=> ( p7 @ ( sK12 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f253]) ).
thf(f255,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p7 @ ( sK10 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK12 @ X2 ) )
=> ( p7 @ ( sK12 @ X2 ) ) ) )
| ( $true
= ( p6 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f254]) ).
thf(f256,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p7 @ ( sK12 @ X2 ) ) )
| ( $false
= ( p7 @ ( sK10 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p6 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f255]) ).
thf(f258,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p6 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p5 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f142]) ).
thf(f259,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p6 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p5 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f258]) ).
thf(f260,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p6 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f259]) ).
thf(f261,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f260]) ).
thf(f262,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f261]) ).
thf(f263,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f262]) ).
thf(f264,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p6 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p6 @ Y0 ) )
@ ( sK13 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f263]) ).
thf(f265,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK13 @ X1 ) )
=> ( p6 @ ( sK13 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f264]) ).
thf(f266,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK13 @ X1 ) )
=> ( p6 @ ( sK13 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f265]) ).
thf(f267,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p6 @ ( sK13 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f266]) ).
thf(f277,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p6 @ ( sK13 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f267]) ).
thf(f278,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p6 @ ( sK13 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f277]) ).
thf(f279,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p6 @ ( sK13 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f278]) ).
thf(f280,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p6 @ ( sK13 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p6 @ Y0 ) )
@ ( sK15 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f279]) ).
thf(f281,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p6 @ ( sK13 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p5 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK15 @ X2 ) )
=> ( p6 @ ( sK15 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f280]) ).
thf(f282,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p6 @ ( sK13 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK15 @ X2 ) )
=> ( p6 @ ( sK15 @ X2 ) ) ) )
| ( $true
= ( p5 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f281]) ).
thf(f283,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p6 @ ( sK15 @ X2 ) ) )
| ( $false
= ( p6 @ ( sK13 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p5 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f282]) ).
thf(f285,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p5 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p4 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f286,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p5 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p4 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f285]) ).
thf(f287,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f286]) ).
thf(f288,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f287]) ).
thf(f289,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f288]) ).
thf(f290,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f289]) ).
thf(f291,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p5 @ Y0 ) )
@ ( sK16 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f290]) ).
thf(f292,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK16 @ X1 ) )
=> ( p5 @ ( sK16 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f291]) ).
thf(f293,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK16 @ X1 ) )
=> ( p5 @ ( sK16 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f292]) ).
thf(f294,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p5 @ ( sK16 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f293]) ).
thf(f304,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p5 @ ( sK16 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f294]) ).
thf(f305,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p5 @ ( sK16 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f304]) ).
thf(f306,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p5 @ ( sK16 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f305]) ).
thf(f307,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p5 @ ( sK16 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p5 @ Y0 ) )
@ ( sK18 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f306]) ).
thf(f308,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p5 @ ( sK16 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p4 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK18 @ X2 ) )
=> ( p5 @ ( sK18 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f307]) ).
thf(f309,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p5 @ ( sK16 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK18 @ X2 ) )
=> ( p5 @ ( sK18 @ X2 ) ) ) )
| ( $true
= ( p4 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f308]) ).
thf(f310,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p5 @ ( sK18 @ X2 ) ) )
| ( $false
= ( p5 @ ( sK16 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p4 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f309]) ).
thf(f312,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p3 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f313,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p3 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f312]) ).
thf(f314,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f313]) ).
thf(f315,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f314]) ).
thf(f316,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f315]) ).
thf(f317,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f316]) ).
thf(f318,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p4 @ Y0 ) )
@ ( sK19 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f317]) ).
thf(f319,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK19 @ X1 ) )
=> ( p4 @ ( sK19 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f318]) ).
thf(f320,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK19 @ X1 ) )
=> ( p4 @ ( sK19 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f319]) ).
thf(f321,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p4 @ ( sK19 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f320]) ).
thf(f331,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p4 @ ( sK19 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f321]) ).
thf(f332,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p4 @ ( sK19 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f331]) ).
thf(f333,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p4 @ ( sK19 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f332]) ).
thf(f334,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p4 @ ( sK19 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p4 @ Y0 ) )
@ ( sK21 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f333]) ).
thf(f335,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p4 @ ( sK19 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p3 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK21 @ X2 ) )
=> ( p4 @ ( sK21 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f334]) ).
thf(f336,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p4 @ ( sK19 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK21 @ X2 ) )
=> ( p4 @ ( sK21 @ X2 ) ) ) )
| ( $true
= ( p3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f335]) ).
thf(f337,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p4 @ ( sK21 @ X2 ) ) )
| ( $false
= ( p4 @ ( sK19 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f336]) ).
thf(f339,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f340,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f339]) ).
thf(f341,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f340]) ).
thf(f342,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f341]) ).
thf(f343,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f342]) ).
thf(f344,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f343]) ).
thf(f345,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p3 @ Y0 ) )
@ ( sK22 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f344]) ).
thf(f346,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK22 @ X1 ) )
=> ( p3 @ ( sK22 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f345]) ).
thf(f347,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK22 @ X1 ) )
=> ( p3 @ ( sK22 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f346]) ).
thf(f348,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p3 @ ( sK22 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f347]) ).
thf(f358,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p3 @ ( sK22 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f348]) ).
thf(f359,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p3 @ ( sK22 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f358]) ).
thf(f360,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p3 @ ( sK22 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f359]) ).
thf(f361,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p3 @ ( sK22 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p3 @ Y0 ) )
@ ( sK24 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f360]) ).
thf(f362,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p3 @ ( sK22 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p2 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK24 @ X2 ) )
=> ( p3 @ ( sK24 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f361]) ).
thf(f363,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p3 @ ( sK22 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK24 @ X2 ) )
=> ( p3 @ ( sK24 @ X2 ) ) ) )
| ( $true
= ( p2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f362]) ).
thf(f364,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p3 @ ( sK24 @ X2 ) ) )
| ( $false
= ( p3 @ ( sK22 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f363]) ).
thf(f366,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f367,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f366]) ).
thf(f368,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f367]) ).
thf(f369,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f368]) ).
thf(f370,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f369]) ).
thf(f371,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f370]) ).
thf(f372,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) )
@ ( sK25 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f371]) ).
thf(f373,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK25 @ X1 ) )
=> ( p2 @ ( sK25 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f372]) ).
thf(f374,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK25 @ X1 ) )
=> ( p2 @ ( sK25 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f373]) ).
thf(f375,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p2 @ ( sK25 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f374]) ).
thf(f385,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p2 @ ( sK25 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f375]) ).
thf(f386,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p2 @ ( sK25 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f385]) ).
thf(f387,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p2 @ ( sK25 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f386]) ).
thf(f388,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p2 @ ( sK25 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) )
@ ( sK27 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f387]) ).
thf(f389,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p2 @ ( sK25 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK27 @ X2 ) )
=> ( p2 @ ( sK27 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f388]) ).
thf(f390,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p2 @ ( sK25 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK27 @ X2 ) )
=> ( p2 @ ( sK27 @ X2 ) ) ) )
| ( $true
= ( p1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f389]) ).
thf(f391,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p2 @ ( sK27 @ X2 ) ) )
| ( $false
= ( p2 @ ( sK25 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f390]) ).
thf(f393,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f137]) ).
thf(f394,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p0 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f393]) ).
thf(f395,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f394]) ).
thf(f396,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f395]) ).
thf(f397,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f396]) ).
thf(f398,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f397]) ).
thf(f399,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p0 @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) )
@ ( sK28 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f398]) ).
thf(f400,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK28 @ X1 ) )
=> ( p1 @ ( sK28 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f399]) ).
thf(f401,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK28 @ X1 ) )
=> ( p1 @ ( sK28 @ X1 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f400]) ).
thf(f402,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK28 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f401]) ).
thf(f412,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK28 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f402]) ).
thf(f413,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK28 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f412]) ).
thf(f414,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK28 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f413]) ).
thf(f415,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK28 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p0 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) )
@ ( sK30 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f414]) ).
thf(f416,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK28 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( p0 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK30 @ X2 ) )
=> ( p1 @ ( sK30 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f415]) ).
thf(f417,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p1 @ ( sK28 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK30 @ X2 ) )
=> ( p1 @ ( sK30 @ X2 ) ) ) )
| ( $true
= ( p0 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f416]) ).
thf(f418,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p1 @ ( sK30 @ X2 ) ) )
| ( $false
= ( p1 @ ( sK28 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p0 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f417]) ).
thf(f420,plain,
( $true
= ( !! @ $i @ p10 ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f421,plain,
! [X1: $i] :
( $true
= ( p10 @ X1 ) ),
inference(pi_proxy_clausification,[],[f420]) ).
thf(f579,plain,
! [X0: $i] :
( ( $false != $false )
| ( $false
= ( p10 @ ( sK3 @ X0 ) ) )
| ( $false
= ( p10 @ ( sK1 @ X0 ) ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p9 @ X0 ) ) ),
inference(equality_factoring,[],[f175]) ).
thf(f580,plain,
! [X0: $i] :
( ( $false
= ( p10 @ ( sK3 @ X0 ) ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $false
= ( p10 @ ( sK1 @ X0 ) ) )
| ( $true
= ( p9 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f579]) ).
thf(f609,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( p10 @ ( sK3 @ X0 ) ) )
| ( $false
= ( p10 @ ( sK1 @ X0 ) ) )
| ( $true
= ( p9 @ X0 ) ) ),
inference(constrained_superposition,[],[f92,f580]) ).
thf(f617,plain,
! [X0: $i] :
( ( $true
= ( p9 @ X0 ) )
| ( $false
= ( p10 @ ( sK3 @ X0 ) ) )
| ( $false
= ( p10 @ ( sK1 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f609]) ).
thf(f627,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p9 @ X0 ) )
| ( $false
= ( p10 @ ( sK1 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f421,f617]) ).
thf(f628,plain,
! [X0: $i] :
( ( $true
= ( p9 @ X0 ) )
| ( $false
= ( p10 @ ( sK1 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f627]) ).
thf(f633,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p9 @ X0 ) ) ),
inference(constrained_superposition,[],[f421,f628]) ).
thf(f634,plain,
! [X0: $i] :
( $true
= ( p9 @ X0 ) ),
inference(trivial_inequality_removal,[],[f633]) ).
thf(f664,plain,
! [X0: $i] :
( ( $false != $false )
| ( $false
= ( p9 @ ( sK6 @ X0 ) ) )
| ( $false
= ( p9 @ ( sK4 @ X0 ) ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p8 @ X0 ) ) ),
inference(equality_factoring,[],[f202]) ).
thf(f665,plain,
! [X0: $i] :
( ( $false
= ( p9 @ ( sK6 @ X0 ) ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $false
= ( p9 @ ( sK4 @ X0 ) ) )
| ( $true
= ( p8 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f664]) ).
thf(f694,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( p9 @ ( sK6 @ X0 ) ) )
| ( $false
= ( p9 @ ( sK4 @ X0 ) ) )
| ( $true
= ( p8 @ X0 ) ) ),
inference(constrained_superposition,[],[f92,f665]) ).
thf(f702,plain,
! [X0: $i] :
( ( $false
= ( p9 @ ( sK6 @ X0 ) ) )
| ( $false
= ( p9 @ ( sK4 @ X0 ) ) )
| ( $true
= ( p8 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f694]) ).
thf(f712,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( p9 @ ( sK4 @ X0 ) ) )
| ( $true
= ( p8 @ X0 ) ) ),
inference(constrained_superposition,[],[f634,f702]) ).
thf(f713,plain,
! [X0: $i] :
( ( $false
= ( p9 @ ( sK4 @ X0 ) ) )
| ( $true
= ( p8 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f712]) ).
thf(f739,plain,
! [X0: $i] :
( ( $false != $false )
| ( $false
= ( p8 @ ( sK9 @ X0 ) ) )
| ( $false
= ( p8 @ ( sK7 @ X0 ) ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p7 @ X0 ) ) ),
inference(equality_factoring,[],[f229]) ).
thf(f740,plain,
! [X0: $i] :
( ( $false
= ( p8 @ ( sK9 @ X0 ) ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $false
= ( p8 @ ( sK7 @ X0 ) ) )
| ( $true
= ( p7 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f739]) ).
thf(f760,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p8 @ X0 ) ) ),
inference(constrained_superposition,[],[f634,f713]) ).
thf(f761,plain,
! [X0: $i] :
( $true
= ( p8 @ X0 ) ),
inference(trivial_inequality_removal,[],[f760]) ).
thf(f779,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( p8 @ ( sK9 @ X0 ) ) )
| ( $false
= ( p8 @ ( sK7 @ X0 ) ) )
| ( $true
= ( p7 @ X0 ) ) ),
inference(constrained_superposition,[],[f92,f740]) ).
thf(f787,plain,
! [X0: $i] :
( ( $false
= ( p8 @ ( sK9 @ X0 ) ) )
| ( $false
= ( p8 @ ( sK7 @ X0 ) ) )
| ( $true
= ( p7 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f779]) ).
thf(f797,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( p8 @ ( sK7 @ X0 ) ) )
| ( $true
= ( p7 @ X0 ) ) ),
inference(constrained_superposition,[],[f761,f787]) ).
thf(f798,plain,
! [X0: $i] :
( ( $false
= ( p8 @ ( sK7 @ X0 ) ) )
| ( $true
= ( p7 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f797]) ).
thf(f803,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p7 @ X0 ) ) ),
inference(constrained_superposition,[],[f761,f798]) ).
thf(f804,plain,
! [X0: $i] :
( $true
= ( p7 @ X0 ) ),
inference(trivial_inequality_removal,[],[f803]) ).
thf(f834,plain,
! [X0: $i] :
( ( $false != $false )
| ( $false
= ( p7 @ ( sK12 @ X0 ) ) )
| ( $false
= ( p7 @ ( sK10 @ X0 ) ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p6 @ X0 ) ) ),
inference(equality_factoring,[],[f256]) ).
thf(f835,plain,
! [X0: $i] :
( ( $false
= ( p7 @ ( sK12 @ X0 ) ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $false
= ( p7 @ ( sK10 @ X0 ) ) )
| ( $true
= ( p6 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f834]) ).
thf(f864,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( p7 @ ( sK12 @ X0 ) ) )
| ( $false
= ( p7 @ ( sK10 @ X0 ) ) )
| ( $true
= ( p6 @ X0 ) ) ),
inference(constrained_superposition,[],[f92,f835]) ).
thf(f872,plain,
! [X0: $i] :
( ( $false
= ( p7 @ ( sK12 @ X0 ) ) )
| ( $false
= ( p7 @ ( sK10 @ X0 ) ) )
| ( $true
= ( p6 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f864]) ).
thf(f882,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( p7 @ ( sK10 @ X0 ) ) )
| ( $true
= ( p6 @ X0 ) ) ),
inference(constrained_superposition,[],[f804,f872]) ).
thf(f883,plain,
! [X0: $i] :
( ( $false
= ( p7 @ ( sK10 @ X0 ) ) )
| ( $true
= ( p6 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f882]) ).
thf(f888,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p6 @ X0 ) ) ),
inference(constrained_superposition,[],[f804,f883]) ).
thf(f889,plain,
! [X0: $i] :
( $true
= ( p6 @ X0 ) ),
inference(trivial_inequality_removal,[],[f888]) ).
thf(f919,plain,
! [X0: $i] :
( ( $false != $false )
| ( $false
= ( p6 @ ( sK15 @ X0 ) ) )
| ( $false
= ( p6 @ ( sK13 @ X0 ) ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p5 @ X0 ) ) ),
inference(equality_factoring,[],[f283]) ).
thf(f920,plain,
! [X0: $i] :
( ( $false
= ( p6 @ ( sK15 @ X0 ) ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $false
= ( p6 @ ( sK13 @ X0 ) ) )
| ( $true
= ( p5 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f919]) ).
thf(f949,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( p6 @ ( sK15 @ X0 ) ) )
| ( $false
= ( p6 @ ( sK13 @ X0 ) ) )
| ( $true
= ( p5 @ X0 ) ) ),
inference(constrained_superposition,[],[f92,f920]) ).
thf(f957,plain,
! [X0: $i] :
( ( $false
= ( p6 @ ( sK15 @ X0 ) ) )
| ( $false
= ( p6 @ ( sK13 @ X0 ) ) )
| ( $true
= ( p5 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f949]) ).
thf(f967,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( p6 @ ( sK13 @ X0 ) ) )
| ( $true
= ( p5 @ X0 ) ) ),
inference(constrained_superposition,[],[f889,f957]) ).
thf(f968,plain,
! [X0: $i] :
( ( $false
= ( p6 @ ( sK13 @ X0 ) ) )
| ( $true
= ( p5 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f967]) ).
thf(f973,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p5 @ X0 ) ) ),
inference(constrained_superposition,[],[f889,f968]) ).
thf(f974,plain,
! [X0: $i] :
( $true
= ( p5 @ X0 ) ),
inference(trivial_inequality_removal,[],[f973]) ).
thf(f1004,plain,
! [X0: $i] :
( ( $false != $false )
| ( $false
= ( p5 @ ( sK18 @ X0 ) ) )
| ( $false
= ( p5 @ ( sK16 @ X0 ) ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p4 @ X0 ) ) ),
inference(equality_factoring,[],[f310]) ).
thf(f1005,plain,
! [X0: $i] :
( ( $false
= ( p5 @ ( sK18 @ X0 ) ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $false
= ( p5 @ ( sK16 @ X0 ) ) )
| ( $true
= ( p4 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1004]) ).
thf(f1034,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( p5 @ ( sK18 @ X0 ) ) )
| ( $false
= ( p5 @ ( sK16 @ X0 ) ) )
| ( $true
= ( p4 @ X0 ) ) ),
inference(constrained_superposition,[],[f92,f1005]) ).
thf(f1042,plain,
! [X0: $i] :
( ( $false
= ( p5 @ ( sK18 @ X0 ) ) )
| ( $false
= ( p5 @ ( sK16 @ X0 ) ) )
| ( $true
= ( p4 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1034]) ).
thf(f1052,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( p5 @ ( sK16 @ X0 ) ) )
| ( $true
= ( p4 @ X0 ) ) ),
inference(constrained_superposition,[],[f974,f1042]) ).
thf(f1053,plain,
! [X0: $i] :
( ( $false
= ( p5 @ ( sK16 @ X0 ) ) )
| ( $true
= ( p4 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1052]) ).
thf(f1058,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p4 @ X0 ) ) ),
inference(constrained_superposition,[],[f974,f1053]) ).
thf(f1059,plain,
! [X0: $i] :
( $true
= ( p4 @ X0 ) ),
inference(trivial_inequality_removal,[],[f1058]) ).
thf(f1089,plain,
! [X0: $i] :
( ( $false != $false )
| ( $false
= ( p4 @ ( sK21 @ X0 ) ) )
| ( $false
= ( p4 @ ( sK19 @ X0 ) ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p3 @ X0 ) ) ),
inference(equality_factoring,[],[f337]) ).
thf(f1090,plain,
! [X0: $i] :
( ( $false
= ( p4 @ ( sK21 @ X0 ) ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $false
= ( p4 @ ( sK19 @ X0 ) ) )
| ( $true
= ( p3 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1089]) ).
thf(f1119,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( p4 @ ( sK21 @ X0 ) ) )
| ( $false
= ( p4 @ ( sK19 @ X0 ) ) )
| ( $true
= ( p3 @ X0 ) ) ),
inference(constrained_superposition,[],[f92,f1090]) ).
thf(f1127,plain,
! [X0: $i] :
( ( $false
= ( p4 @ ( sK21 @ X0 ) ) )
| ( $false
= ( p4 @ ( sK19 @ X0 ) ) )
| ( $true
= ( p3 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1119]) ).
thf(f1137,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( p4 @ ( sK19 @ X0 ) ) )
| ( $true
= ( p3 @ X0 ) ) ),
inference(constrained_superposition,[],[f1059,f1127]) ).
thf(f1138,plain,
! [X0: $i] :
( ( $false
= ( p4 @ ( sK19 @ X0 ) ) )
| ( $true
= ( p3 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1137]) ).
thf(f1143,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p3 @ X0 ) ) ),
inference(constrained_superposition,[],[f1059,f1138]) ).
thf(f1144,plain,
! [X0: $i] :
( $true
= ( p3 @ X0 ) ),
inference(trivial_inequality_removal,[],[f1143]) ).
thf(f1174,plain,
! [X0: $i] :
( ( $false != $false )
| ( $false
= ( p3 @ ( sK24 @ X0 ) ) )
| ( $false
= ( p3 @ ( sK22 @ X0 ) ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p2 @ X0 ) ) ),
inference(equality_factoring,[],[f364]) ).
thf(f1175,plain,
! [X0: $i] :
( ( $false
= ( p3 @ ( sK24 @ X0 ) ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $false
= ( p3 @ ( sK22 @ X0 ) ) )
| ( $true
= ( p2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1174]) ).
thf(f1204,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( p3 @ ( sK24 @ X0 ) ) )
| ( $false
= ( p3 @ ( sK22 @ X0 ) ) )
| ( $true
= ( p2 @ X0 ) ) ),
inference(constrained_superposition,[],[f92,f1175]) ).
thf(f1212,plain,
! [X0: $i] :
( ( $false
= ( p3 @ ( sK24 @ X0 ) ) )
| ( $false
= ( p3 @ ( sK22 @ X0 ) ) )
| ( $true
= ( p2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1204]) ).
thf(f1222,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( p3 @ ( sK22 @ X0 ) ) )
| ( $true
= ( p2 @ X0 ) ) ),
inference(constrained_superposition,[],[f1144,f1212]) ).
thf(f1223,plain,
! [X0: $i] :
( ( $false
= ( p3 @ ( sK22 @ X0 ) ) )
| ( $true
= ( p2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1222]) ).
thf(f1228,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p2 @ X0 ) ) ),
inference(constrained_superposition,[],[f1144,f1223]) ).
thf(f1229,plain,
! [X0: $i] :
( $true
= ( p2 @ X0 ) ),
inference(trivial_inequality_removal,[],[f1228]) ).
thf(f1259,plain,
! [X0: $i] :
( ( $false != $false )
| ( $false
= ( p2 @ ( sK27 @ X0 ) ) )
| ( $false
= ( p2 @ ( sK25 @ X0 ) ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p1 @ X0 ) ) ),
inference(equality_factoring,[],[f391]) ).
thf(f1260,plain,
! [X0: $i] :
( ( $false
= ( p2 @ ( sK27 @ X0 ) ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $false
= ( p2 @ ( sK25 @ X0 ) ) )
| ( $true
= ( p1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1259]) ).
thf(f1289,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( p2 @ ( sK27 @ X0 ) ) )
| ( $false
= ( p2 @ ( sK25 @ X0 ) ) )
| ( $true
= ( p1 @ X0 ) ) ),
inference(constrained_superposition,[],[f92,f1260]) ).
thf(f1297,plain,
! [X0: $i] :
( ( $false
= ( p2 @ ( sK27 @ X0 ) ) )
| ( $false
= ( p2 @ ( sK25 @ X0 ) ) )
| ( $true
= ( p1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1289]) ).
thf(f1328,plain,
! [X0: $i] :
( ( $false != $false )
| ( $false
= ( p1 @ ( sK30 @ X0 ) ) )
| ( $false
= ( p1 @ ( sK28 @ X0 ) ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( p0 @ X0 ) ) ),
inference(equality_factoring,[],[f418]) ).
thf(f1329,plain,
! [X0: $i] :
( ( $false
= ( p1 @ ( sK30 @ X0 ) ) )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $false
= ( p1 @ ( sK28 @ X0 ) ) )
| ( $true
= ( p0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1328]) ).
thf(f1349,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( p2 @ ( sK25 @ X0 ) ) )
| ( $true
= ( p1 @ X0 ) ) ),
inference(constrained_superposition,[],[f1229,f1297]) ).
thf(f1350,plain,
! [X0: $i] :
( ( $false
= ( p2 @ ( sK25 @ X0 ) ) )
| ( $true
= ( p1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1349]) ).
thf(f1355,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p1 @ X0 ) ) ),
inference(constrained_superposition,[],[f1229,f1350]) ).
thf(f1356,plain,
! [X0: $i] :
( $true
= ( p1 @ X0 ) ),
inference(trivial_inequality_removal,[],[f1355]) ).
thf(f1374,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( p1 @ ( sK30 @ X0 ) ) )
| ( $false
= ( p1 @ ( sK28 @ X0 ) ) )
| ( $true
= ( p0 @ X0 ) ) ),
inference(constrained_superposition,[],[f92,f1329]) ).
thf(f1382,plain,
! [X0: $i] :
( ( $false
= ( p1 @ ( sK30 @ X0 ) ) )
| ( $false
= ( p1 @ ( sK28 @ X0 ) ) )
| ( $true
= ( p0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1374]) ).
thf(f1392,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( p1 @ ( sK28 @ X0 ) ) )
| ( $true
= ( p0 @ X0 ) ) ),
inference(constrained_superposition,[],[f1356,f1382]) ).
thf(f1393,plain,
! [X0: $i] :
( ( $false
= ( p1 @ ( sK28 @ X0 ) ) )
| ( $true
= ( p0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1392]) ).
thf(f1398,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p0 @ X0 ) ) ),
inference(constrained_superposition,[],[f1356,f1393]) ).
thf(f1399,plain,
! [X0: $i] :
( $true
= ( p0 @ X0 ) ),
inference(trivial_inequality_removal,[],[f1398]) ).
thf(f1403,plain,
$true = $false,
inference(constrained_superposition,[],[f149,f1399]) ).
thf(f1404,plain,
$false,
inference(trivial_inequality_removal,[],[f1403]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYO068^4.010 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.29 % Computer : n007.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8046.5625MB
% 0.11/0.29 % OS : Linux 6.8.0-71-generic
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Sep 29 16:27:26 UTC 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.30/0.35 Running first-order model finding
% 0.30/0.35 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.33/0.46 % (3589294)Will run a generic schedule for satisfiability detection.
% 0.33/0.46 % (3589305)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3767568327:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.33/0.46 % (3589300)% WARNING: option uhcvi not known.
% 0.33/0.46 % (3589299)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2400992253_2999 on theBenchmark for (2999ds/0Mi)
% 0.33/0.46 % (3589300)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=185600015:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.33/0.46 % (3589302)dis+10_1_sil=32000:sp=arity:random_seed=530881817:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.33/0.46 % (3589304)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3930041040:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.33/0.46 % (3589301)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1133185438:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.33/0.46 % (3589303)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3310444295:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.33/0.46 % (3589300)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.33/0.46 % (3589303)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.33/0.46 % Exception at run slice level
% 0.33/0.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.33/0.46 % (3589300)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.33/0.46 % (3589305) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3589294-3589305"...
% 0.33/0.46 % (3589313)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1665590327:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.33/0.46 % Exception at run slice level
% 0.33/0.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.33/0.46 % (3589305)...printing done.
% 0.33/0.46 % (3589305)Refutation found. Thanks to Tanya!
% 0.33/0.46 % SZS status Theorem for theBenchmark
% 0.33/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.33/0.46 % (3589305)------------------------------
% 0.33/0.46 % (3589305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.46 % (3589305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.46 % (3589305)CaDiCaL version: 2.1.3
% 0.33/0.46 % (3589305)Termination reason: Refutation
% 0.33/0.46 % (3589305)Time elapsed: 0.068 s
% 0.33/0.46 % (3589305)Peak memory usage: 13 MB
% 0.33/0.46 % (3589305)Instructions burned: 156 (million)
% 0.33/0.46 % (3589294)Success in time 0.106 s
% 0.33/0.46 % Vampire exiting
%------------------------------------------------------------------------------