%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU469^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:29:44 AM UTC 2026
% Result : Theorem 0.22s 0.33s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 13
% Syntax : Number of formulae : 133 ( 43 unt; 0 typ; 6 def)
% Number of atoms : 1356 ( 182 equ; 0 cnn)
% Maximal formula atoms : 4 ( 10 avg)
% Number of connectives : 3761 ( 146 ~; 197 |; 217 &;2345 @)
% ( 6 <=>; 284 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 442 ( 442 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 58 usr; 13 con; 0-4 aty)
% ( 566 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 696 ( 8 sgn 38 !; 0 ?; 696 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_2,type,
inv: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_3,type,
idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_4,type,
infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_5,type,
mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_6,type,
refl: ( $i > $i > $o ) > $o ).
thf(func_def_7,type,
irrefl: ( $i > $i > $o ) > $o ).
thf(func_def_8,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_9,type,
symm: ( $i > $i > $o ) > $o ).
thf(func_def_10,type,
antisymm: ( $i > $i > $o ) > $o ).
thf(func_def_11,type,
asymm: ( $i > $i > $o ) > $o ).
thf(func_def_12,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_13,type,
trans: ( $i > $i > $o ) > $o ).
thf(func_def_14,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_15,type,
trc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_16,type,
trsc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_17,type,
po: ( $i > $i > $o ) > $o ).
thf(func_def_18,type,
so: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
total: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
term: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
ind: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
innf: ( $i > $i > $o ) > $i > $o ).
thf(func_def_23,type,
nfof: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_24,type,
norm: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
join: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_26,type,
lconfl: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
sconfl: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
confl: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
cr: ( $i > $i > $o ) > $o ).
thf(func_def_30,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
vIMP: $o > $o > $o ).
thf(func_def_32,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_37,type,
vAND: $o > $o > $o ).
thf(func_def_38,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_39,type,
vNOT: $o > $o ).
thf(func_def_40,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
vOR: $o > $o > $o ).
thf(func_def_44,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
sK0: $i > $i > $o ).
thf(func_def_53,type,
sK5: $i > $i > $o ).
thf(f1,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
= subrel ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',subrel) ).
thf(f6,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= refl ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',reflexive) ).
thf(f8,axiom,
( rc
= ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',reflexive_closure) ).
thf(f13,axiom,
( trans
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X3: $i,X1: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',transitive) ).
thf(f14,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
! [X3: $i > $i > $o] :
( ( ( subrel @ X0 @ X3 )
& ( trans @ X3 ) )
=> ( X3 @ X1 @ X2 ) ) )
= tc ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',transitive_closure) ).
thf(f15,axiom,
( ( ^ [X0: $i > $i > $o] : ( rc @ ( tc @ X0 ) ) )
= trc ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',transitive_reflexive_closure) ).
thf(f30,conjecture,
! [X0: $i > $i > $o] :
( ( trans @ ( trc @ X0 ) )
& ( refl @ ( trc @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_reflexive_closure_is_transitive_reflexive) ).
thf(f31,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( trans @ ( trc @ X0 ) )
& ( refl @ ( trc @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f34,plain,
( trans
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X3 @ X1 ) )
=> ( X0 @ X3 @ X2 ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f35,plain,
( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f46,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= refl ),
inference(rectify,[],[f6]) ).
thf(f47,plain,
( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f48,plain,
( ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
! [X3: $i > $i > $o] :
( ( ( subrel @ X0 @ X3 )
& ( trans @ X3 ) )
=> ( X3 @ X1 @ X2 ) ) )
= tc ),
inference(rectify,[],[f14]) ).
thf(f49,plain,
( tc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( trans @ Y3 )
& ( subrel @ Y0 @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f53,plain,
( trc
= ( ^ [Y0: $i > $i > $o] : ( rc @ ( tc @ Y0 ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f54,plain,
( rc
= ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f55,plain,
( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f56,plain,
~ ! [X0: $i > $i > $o] :
( ( trans @ ( trc @ X0 ) )
& ( refl @ ( trc @ X0 ) ) ),
inference(rectify,[],[f31]) ).
thf(f57,plain,
( ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( refl @ ( trc @ Y0 ) )
& ( trans @ ( trc @ Y0 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f56]) ).
thf(f74,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
= subrel ),
inference(rectify,[],[f1]) ).
thf(f75,plain,
( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f74]) ).
thf(f90,plain,
( tc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( trans @ Y3 )
& ( subrel @ Y0 @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f92,plain,
( trc
= ( ^ [Y0: $i > $i > $o] : ( rc @ ( tc @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f102,plain,
( ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( refl @ ( trc @ Y0 ) )
& ( trans @ ( trc @ Y0 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f57]) ).
thf(f103,plain,
( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f105,plain,
( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f110,plain,
( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f113,plain,
( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f122,plain,
( tc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
@ Y3 )
& ( ^ [Y4: $i > $i > $o,Y5: $i > $i > $o] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
@ Y0
@ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[],[f90,f113,f110]) ).
thf(f123,plain,
( trc
= ( ^ [Y0: $i > $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i,Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ( Y2 = Y3 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i,Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( ^ [Y5: $i > $i > $o] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
@ Y4 )
& ( ^ [Y5: $i > $i > $o,Y6: $i > $i > $o] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
@ Y1
@ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f92,f105,f122]) ).
thf(f135,plain,
( $true
= ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 @ Y2 ) )
@ ( ^ [Y1: $i > $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i,Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
| ( Y3 = Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i,Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( ( ^ [Y6: $i > $i > $o] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
@ Y5 )
& ( ^ [Y6: $i > $i > $o,Y7: $i > $i > $o] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
@ Y2
@ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
@ Y1 ) )
@ Y0 ) )
& ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
@ ( ^ [Y1: $i > $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i,Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
| ( Y3 = Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i,Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( ( ^ [Y6: $i > $i > $o] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
@ Y5 )
& ( ^ [Y6: $i > $i > $o,Y7: $i > $i > $o] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
@ Y2
@ Y5 ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
@ Y1 ) )
@ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f102,f103,f123,f113,f123]) ).
thf(f136,plain,
( ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y1 ) ) )
| ( Y1 = Y1 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) )
| ( Y1 = Y3 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( Y3 = Y2 ) ) )
=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f135]) ).
thf(f137,plain,
( $true
= ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y1 ) ) )
| $true ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) )
| ( Y1 = Y3 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( Y3 = Y2 ) ) )
=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f136]) ).
thf(f138,plain,
( $true
= ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : $true )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) )
| ( Y1 = Y3 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( Y3 = Y2 ) ) )
=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f137]) ).
thf(f139,plain,
( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : $true )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) )
| ( Y1 = Y3 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( Y3 = Y2 ) ) )
=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f138]) ).
thf(f140,plain,
( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : $true )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) )
| ( Y1 = Y3 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( Y3 = Y2 ) ) )
=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) ) ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f139]) ).
thf(f143,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] : $true )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
| ( Y0 = Y2 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( Y2 = Y1 ) ) )
=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
| ( Y0 = Y1 ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f144,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
| ( Y0 = Y2 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( Y2 = Y1 ) ) )
=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
| ( Y0 = Y1 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] : $true )
= $false ) ),
inference(and_proxy_clausification,[],[f143]) ).
thf(f146,definition,
( spl1_1
<=> ( ( !! @ $i
@ ^ [Y0: $i] : $true )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f148,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] : $true )
= $false )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f146]) ).
thf(f150,definition,
( spl1_2
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
| ( Y0 = Y2 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( Y2 = Y1 ) ) )
=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
| ( Y0 = Y1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f152,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
| ( Y0 = Y2 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( Y2 = Y1 ) ) )
=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
| ( Y0 = Y1 ) ) ) ) ) ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f150]) ).
thf(f153,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f144,f150,f146]) ).
thf(f154,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
| ( Y0 = Y2 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( Y2 = Y1 ) ) )
=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
| ( Y0 = Y1 ) ) ) ) )
@ sK2 ) )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f152]) ).
thf(f155,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK2 @ Y1 ) ) )
| ( sK2 = Y1 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( Y1 = Y0 ) ) )
=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK2 @ Y0 ) ) )
| ( sK2 = Y0 ) ) ) ) )
= $false )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK2 @ Y1 ) ) )
| ( sK2 = Y1 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( Y1 = Y0 ) ) )
=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK2 @ Y0 ) ) )
| ( sK2 = Y0 ) ) ) )
@ sK3 )
= $false )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK2 @ Y0 ) ) )
| ( sK2 = Y0 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK3 ) ) )
| ( Y0 = sK3 ) ) )
=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK2 @ sK3 ) ) )
| ( sK2 = sK3 ) ) ) )
= $false )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK2 @ Y0 ) ) )
| ( sK2 = Y0 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK3 ) ) )
| ( Y0 = sK3 ) ) )
=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK2 @ sK3 ) ) )
| ( sK2 = sK3 ) ) )
@ sK4 ) )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( ( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) )
| ( sK2 = sK4 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) )
| ( sK4 = sK3 ) ) )
=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) )
| ( sK2 = sK3 ) ) )
= $false )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) )
| ( sK2 = sK3 ) )
= $false )
| ~ spl1_2 ),
inference(imp_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( $true
= ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) )
| ( sK2 = sK4 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) )
| ( sK4 = sK3 ) ) ) )
| ~ spl1_2 ),
inference(imp_proxy_clausification,[],[f159]) ).
thf(f163,plain,
( ( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f171,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) )
@ sK5 )
= $false )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f163]) ).
thf(f172,plain,
( ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK5 @ Y0 @ Y2 )
& ( sK5 @ Y2 @ Y1 ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK5 @ Y1 @ Y0 ) ) ) ) )
=> ( sK5 @ sK2 @ sK3 ) )
= $false )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
( ( $false
= ( sK5 @ sK2 @ sK3 ) )
| ~ spl1_2 ),
inference(imp_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK5 @ Y0 @ Y2 )
& ( sK5 @ Y2 @ Y1 ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK5 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl1_2 ),
inference(imp_proxy_clausification,[],[f172]) ).
thf(f179,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK5 @ Y1 @ Y0 ) ) ) )
= $true )
| ~ spl1_2 ),
inference(and_proxy_clausification,[],[f174]) ).
thf(f180,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK5 @ Y0 @ Y2 )
& ( sK5 @ Y2 @ Y1 ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl1_2 ),
inference(and_proxy_clausification,[],[f174]) ).
thf(f193,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK5 @ Y0 @ Y2 )
& ( sK5 @ Y2 @ Y1 ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) )
@ X1 )
= $true )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f180]) ).
thf(f194,plain,
( ! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK5 @ X1 @ Y1 )
& ( sK5 @ Y1 @ Y0 ) )
=> ( sK5 @ X1 @ Y0 ) ) ) )
= $true )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f193]) ).
thf(f195,plain,
( ! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK5 @ X1 @ Y1 )
& ( sK5 @ Y1 @ Y0 ) )
=> ( sK5 @ X1 @ Y0 ) ) )
@ X2 )
= $true )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f194]) ).
thf(f196,plain,
( ! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK5 @ X1 @ Y0 )
& ( sK5 @ Y0 @ X2 ) )
=> ( sK5 @ X1 @ X2 ) ) )
= $true )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f195]) ).
thf(f197,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( sK5 @ X1 @ Y0 )
& ( sK5 @ Y0 @ X2 ) )
=> ( sK5 @ X1 @ X2 ) )
@ X3 ) )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f196]) ).
thf(f198,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( sK5 @ X1 @ X3 )
& ( sK5 @ X3 @ X2 ) )
=> ( sK5 @ X1 @ X2 ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f197]) ).
thf(f200,plain,
( ! [X0: $i] :
( $true
= ( ( ( sK5 @ sK2 @ X0 )
& ( sK5 @ X0 @ sK3 ) )
=> $false ) )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f198,f173]) ).
thf(f205,plain,
( ! [X0: $i] :
( ( ~ ( ( sK5 @ sK2 @ X0 )
& ( sK5 @ X0 @ sK3 ) ) )
= $true )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f200]) ).
thf(f208,plain,
( ! [X0: $i] :
( ( ( sK5 @ sK2 @ X0 )
& ( sK5 @ X0 @ sK3 ) )
= $false )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f205]) ).
thf(f215,plain,
( ! [X0: $i] :
( ( $false
= ( sK5 @ sK2 @ X0 ) )
| ( $false
= ( sK5 @ X0 @ sK3 ) ) )
| ~ spl1_2 ),
inference(and_proxy_clausification,[],[f208]) ).
thf(f224,plain,
( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) )
| ( sK4 = sK3 ) )
= $true )
| ~ spl1_2 ),
inference(and_proxy_clausification,[],[f161]) ).
thf(f225,plain,
( ( $true
= ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) )
| ( sK2 = sK4 ) ) )
| ~ spl1_2 ),
inference(and_proxy_clausification,[],[f161]) ).
thf(f226,plain,
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) )
= $true )
| ( $true
= ( sK4 = sK3 ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f224]) ).
thf(f228,definition,
( spl1_3
<=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
thf(f230,plain,
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) ) )
= $true )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f228]) ).
thf(f232,definition,
( spl1_4
<=> ( $true
= ( sK4 = sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
thf(f234,plain,
( ( $true
= ( sK4 = sK3 ) )
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f232]) ).
thf(f235,plain,
( spl1_3
| spl1_4
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f226,f150,f232,f228]) ).
thf(f236,plain,
( ! [X1: $i > $i > $o] :
( ( ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK3 ) )
@ X1 )
= $true )
| ~ spl1_3 ),
inference(pi_proxy_clausification,[],[f230]) ).
thf(f237,plain,
( ! [X1: $i > $i > $o] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X1 @ Y0 @ Y2 )
& ( X1 @ Y2 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK4 @ sK3 ) )
= $true )
| ~ spl1_3 ),
inference(beta-eta_normalization,[],[f236]) ).
thf(f239,plain,
( ( ( sK2 = sK4 )
= $true )
| ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) )
= $true )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f225]) ).
thf(f241,definition,
( spl1_5
<=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
thf(f243,plain,
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) ) )
= $true )
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f241]) ).
thf(f245,definition,
( spl1_6
<=> ( ( sK2 = sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
thf(f247,plain,
( ( ( sK2 = sK4 )
= $true )
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f245]) ).
thf(f248,plain,
( spl1_5
| spl1_6
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f239,f150,f245,f241]) ).
thf(f249,plain,
( ! [X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK4 ) )
@ X1 ) )
| ~ spl1_5 ),
inference(pi_proxy_clausification,[],[f243]) ).
thf(f250,plain,
( ! [X1: $i > $i > $o] :
( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X1 @ Y0 @ Y2 )
& ( X1 @ Y2 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK2 @ sK4 ) ) )
| ~ spl1_5 ),
inference(beta-eta_normalization,[],[f249]) ).
thf(f291,plain,
( ( $false
= ( sK5 @ sK4 @ sK3 ) )
| ( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK5 @ Y0 @ Y2 )
& ( sK5 @ Y2 @ Y1 ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK5 @ Y1 @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl1_2
| ~ spl1_5 ),
inference(constrained_superposition,[],[f250,f215]) ).
thf(f300,plain,
( ( $false
= ( sK5 @ sK4 @ sK3 ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK5 @ Y0 @ Y2 )
& ( sK5 @ Y2 @ Y1 ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK5 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl1_2
| ~ spl1_5 ),
inference(boolean_simplification,[],[f291]) ).
thf(f308,plain,
( ( ( ~ $true ) = $true )
| ( $false
= ( sK5 @ sK4 @ sK3 ) )
| ~ spl1_2
| ~ spl1_5 ),
inference(forward_demodulation,[],[f300,f174]) ).
thf(f309,plain,
( ( $true = $false )
| ( $false
= ( sK5 @ sK4 @ sK3 ) )
| ~ spl1_2
| ~ spl1_5 ),
inference(boolean_simplification,[],[f308]) ).
thf(f310,plain,
( ( $false
= ( sK5 @ sK4 @ sK3 ) )
| ~ spl1_2
| ~ spl1_5 ),
inference(trivial_inequality_removal,[],[f309]) ).
thf(f321,plain,
( ( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK5 @ Y0 @ Y2 )
& ( sK5 @ Y2 @ Y1 ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK5 @ Y1 @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl1_2
| ~ spl1_3
| ~ spl1_5 ),
inference(constrained_superposition,[],[f237,f310]) ).
thf(f328,plain,
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK5 @ Y0 @ Y2 )
& ( sK5 @ Y2 @ Y1 ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK5 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl1_2
| ~ spl1_3
| ~ spl1_5 ),
inference(boolean_simplification,[],[f321]) ).
thf(f334,plain,
( ( ( ~ $true ) = $true )
| ~ spl1_2
| ~ spl1_3
| ~ spl1_5 ),
inference(forward_demodulation,[],[f328,f174]) ).
thf(f335,plain,
( ( $true = $false )
| ~ spl1_2
| ~ spl1_3
| ~ spl1_5 ),
inference(boolean_simplification,[],[f334]) ).
thf(f336,plain,
( $false
| ~ spl1_2
| ~ spl1_3
| ~ spl1_5 ),
inference(trivial_inequality_removal,[],[f335]) ).
thf(f337,plain,
( ~ spl1_2
| ~ spl1_3
| ~ spl1_5 ),
inference(avatar_contradiction_clause,[],[f336]) ).
thf(f338,plain,
( ( sK2 = sK4 )
| ~ spl1_6 ),
inference(equality_proxy_clausification,[],[f247]) ).
thf(f350,plain,
( ( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK2 ) ) )
| ( sK2 = sK2 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) )
| ( sK2 = sK3 ) ) )
= $true )
| ~ spl1_2
| ~ spl1_6 ),
inference(constrained_superposition,[],[f161,f338]) ).
thf(f364,plain,
( ( $true
= ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK2 ) ) )
| $true )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) )
| ( sK2 = sK3 ) ) ) )
| ~ spl1_2
| ~ spl1_6 ),
inference(boolean_simplification,[],[f350]) ).
thf(f365,plain,
( ( $true
= ( $true
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) )
| ( sK2 = sK3 ) ) ) )
| ~ spl1_2
| ~ spl1_6 ),
inference(boolean_simplification,[],[f364]) ).
thf(f366,plain,
( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) )
| ( sK2 = sK3 ) )
= $true )
| ~ spl1_2
| ~ spl1_6 ),
inference(boolean_simplification,[],[f365]) ).
thf(f370,plain,
( ( $true = $false )
| ~ spl1_2
| ~ spl1_6 ),
inference(forward_demodulation,[],[f366,f160]) ).
thf(f371,plain,
( $false
| ~ spl1_2
| ~ spl1_6 ),
inference(trivial_inequality_removal,[],[f370]) ).
thf(f372,plain,
( ~ spl1_2
| ~ spl1_6 ),
inference(avatar_contradiction_clause,[],[f371]) ).
thf(f373,plain,
( ( $false
= ( ^ [Y0: $i] : $true
@ sK6 ) )
| ~ spl1_1 ),
inference(sigma_proxy_clausification,[],[f148]) ).
thf(f374,plain,
( ( $true = $false )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f373]) ).
thf(f375,plain,
( $false
| ~ spl1_1 ),
inference(trivial_inequality_removal,[],[f374]) ).
thf(f376,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f375]) ).
thf(f507,plain,
( ( sK3 = sK4 )
| ~ spl1_4 ),
inference(equality_proxy_clausification,[],[f234]) ).
thf(f642,plain,
( ! [X0: $i > $i > $o] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X0 @ Y0 @ Y2 )
& ( X0 @ Y2 @ Y1 ) )
=> ( X0 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( X0 @ Y1 @ Y0 ) ) ) ) )
=> ( X0 @ sK2 @ sK3 ) )
= $true )
| ~ spl1_4
| ~ spl1_5 ),
inference(constrained_superposition,[],[f250,f507]) ).
thf(f644,plain,
( ( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK5 @ Y0 @ Y2 )
& ( sK5 @ Y2 @ Y1 ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK5 @ Y1 @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl1_2
| ~ spl1_4
| ~ spl1_5 ),
inference(constrained_superposition,[],[f642,f173]) ).
thf(f650,plain,
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK5 @ Y0 @ Y2 )
& ( sK5 @ Y2 @ Y1 ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK5 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl1_2
| ~ spl1_4
| ~ spl1_5 ),
inference(boolean_simplification,[],[f644]) ).
thf(f651,plain,
( ( $true
= ( ~ ( $true
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK5 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl1_2
| ~ spl1_4
| ~ spl1_5 ),
inference(forward_demodulation,[],[f650,f180]) ).
thf(f652,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK5 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl1_2
| ~ spl1_4
| ~ spl1_5 ),
inference(boolean_simplification,[],[f651]) ).
thf(f653,plain,
( ( ( ~ $true ) = $true )
| ~ spl1_2
| ~ spl1_4
| ~ spl1_5 ),
inference(forward_demodulation,[],[f652,f179]) ).
thf(f654,plain,
( ( $true = $false )
| ~ spl1_2
| ~ spl1_4
| ~ spl1_5 ),
inference(boolean_simplification,[],[f653]) ).
thf(f655,plain,
( $false
| ~ spl1_2
| ~ spl1_4
| ~ spl1_5 ),
inference(trivial_inequality_removal,[],[f654]) ).
thf(f656,plain,
( ~ spl1_2
| ~ spl1_4
| ~ spl1_5 ),
inference(avatar_contradiction_clause,[],[f655]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f153]) ).
cnf(s2,plain,
( ~ spl1_2
| spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f235]) ).
cnf(s3,plain,
( ~ spl1_2
| spl1_5
| spl1_6 ),
inference(sat_conversion,[],[f248]) ).
cnf(s4,plain,
( ~ spl1_2
| ~ spl1_3
| ~ spl1_5 ),
inference(sat_conversion,[],[f337]) ).
cnf(s7,plain,
( ~ spl1_2
| ~ spl1_6 ),
inference(sat_conversion,[],[f372]) ).
cnf(s8,plain,
~ spl1_1,
inference(sat_conversion,[],[f376]) ).
cnf(s10,plain,
( ~ spl1_2
| ~ spl1_4
| ~ spl1_5 ),
inference(sat_conversion,[],[f656]) ).
cnf(s11,plain,
spl1_2,
inference(rat,[],[s1,s8]) ).
cnf(s12,plain,
~ spl1_6,
inference(rat,[],[s7,s11]) ).
cnf(s13,plain,
spl1_5,
inference(rat,[],[s3,s12,s11]) ).
cnf(s14,plain,
~ spl1_4,
inference(rat,[],[s10,s11,s13]) ).
cnf(s15,plain,
~ spl1_3,
inference(rat,[],[s4,s11,s13]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s2,s11,s14,s15]) ).
thf(f657,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU469^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n019.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 13:42:33 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.33 % (783732)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.33 % (783737)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2930467528:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.33 % (783739)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=38962781:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.33 % (783741)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2384417306:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.33 % (783739)Instruction limit reached!
% 0.22/0.33 % (783739)------------------------------
% 0.22/0.33 % (783739)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (783739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (783739)CaDiCaL version: 2.1.3
% 0.22/0.33 % (783739)Termination reason: Instruction limit
% 0.22/0.33 % (783739)Termination phase: Preprocessing 1
% 0.22/0.33 % (783739)Time elapsed: 0.002 s
% 0.22/0.33 % (783739)Peak memory usage: 10 MB
% 0.22/0.33 % (783739)Instructions burned: 4 (million)
% 0.22/0.33 % (783743)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.33 % (783743)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.33 % (783740)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=4262856921:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.33 % (783741)Instruction limit reached!
% 0.22/0.33 % (783741)------------------------------
% 0.22/0.33 % (783741)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (783741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (783741)CaDiCaL version: 2.1.3
% 0.22/0.33 % (783741)Termination reason: Instruction limit
% 0.22/0.33 % (783741)Termination phase: Saturation
% 0.22/0.33 % (783741)Time elapsed: 0.013 s
% 0.22/0.33 % (783741)Peak memory usage: 12 MB
% 0.22/0.33 % (783741)Instructions burned: 24 (million)
% 0.22/0.33 % (783743)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2381928769:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.33 % (783737)Instruction limit reached!
% 0.22/0.33 % (783737)------------------------------
% 0.22/0.33 % (783737)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (783737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (783737)CaDiCaL version: 2.1.3
% 0.22/0.33 % (783737)Termination reason: Instruction limit
% 0.22/0.33 % (783737)Termination phase: Saturation
% 0.22/0.33 % (783737)Time elapsed: 0.023 s
% 0.22/0.33 % (783737)Peak memory usage: 12 MB
% 0.22/0.33 % (783737)Instructions burned: 91 (million)
% 0.22/0.33 % (783738)lrs+10_16_si=on:nwc=1.5:random_seed=3832115750:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.33 % (783742)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1268931916:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.33 % (783747)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=491411733:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.33 % (783747)Instruction limit reached!
% 0.22/0.33 % (783747)------------------------------
% 0.22/0.33 % (783747)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (783747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (783747)CaDiCaL version: 2.1.3
% 0.22/0.33 % (783747)Termination reason: Instruction limit
% 0.22/0.33 % (783747)Termination phase: Property scanning
% 0.22/0.33 % (783747)Time elapsed: 0.002 s
% 0.22/0.33 % (783747)Peak memory usage: 10 MB
% 0.22/0.33 % (783747)Instructions burned: 3 (million)
% 0.22/0.33 % (783738)Instruction limit reached!
% 0.22/0.33 % (783738)------------------------------
% 0.22/0.33 % (783738)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (783738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (783738)CaDiCaL version: 2.1.3
% 0.22/0.33 % (783750)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4165075553:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.33 % (783738)Termination reason: Instruction limit
% 0.22/0.33 % (783738)Termination phase: Saturation
% 0.22/0.33 % (783738)Time elapsed: 0.009 s
% 0.22/0.33 % (783738)Peak memory usage: 11 MB
% 0.22/0.33 % (783738)Instructions burned: 20 (million)
% 0.22/0.33 % (783750)Instruction limit reached!
% 0.22/0.33 % (783750)------------------------------
% 0.22/0.33 % (783750)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (783750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (783750)CaDiCaL version: 2.1.3
% 0.22/0.33 % (783750)Termination reason: Instruction limit
% 0.22/0.33 % (783750)Termination phase: Property scanning
% 0.22/0.33 % (783750)Time elapsed: 0.001 s
% 0.22/0.33 % (783750)Peak memory usage: 10 MB
% 0.22/0.33 % (783750)Instructions burned: 6 (million)
% 0.22/0.33 % (783758)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3648101525:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.22/0.33 % (783757)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.33 % (783757)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.33 % (783752)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.33 % (783757)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3379729289:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.22/0.33 % (783752)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3443821373:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.33 % (783752)Instruction limit reached!
% 0.22/0.33 % (783752)------------------------------
% 0.22/0.33 % (783752)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (783752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (783752)CaDiCaL version: 2.1.3
% 0.22/0.33 % (783752)Termination reason: Instruction limit
% 0.22/0.33 % (783752)Termination phase: Function definition elimination
% 0.22/0.33 % (783752)Time elapsed: 0.005 s
% 0.22/0.33 % (783752)Peak memory usage: 10 MB
% 0.22/0.33 % (783752)Instructions burned: 7 (million)
% 0.22/0.33 % (783755)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=262976716:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.22/0.33 % (783742)Instruction limit reached!
% 0.22/0.33 % (783742)------------------------------
% 0.22/0.33 % (783742)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (783742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (783742)CaDiCaL version: 2.1.3
% 0.22/0.33 % (783742)Termination reason: Instruction limit
% 0.22/0.33 % (783742)Termination phase: Saturation
% 0.22/0.33 % (783742)Time elapsed: 0.036 s
% 0.22/0.33 % (783742)Peak memory usage: 12 MB
% 0.22/0.33 % (783742)Instructions burned: 77 (million)
% 0.22/0.33 % (783758) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-783732-783758"...
% 0.22/0.33 % (783757)Instruction limit reached!
% 0.22/0.33 % (783757)------------------------------
% 0.22/0.33 % (783757)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (783757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (783757)CaDiCaL version: 2.1.3
% 0.22/0.33 % (783757)Termination reason: Instruction limit
% 0.22/0.33 % (783757)Termination phase: Saturation
% 0.22/0.33 % (783757)Time elapsed: 0.013 s
% 0.22/0.33 % (783757)Peak memory usage: 11 MB
% 0.22/0.33 % (783757)Instructions burned: 29 (million)
% 0.22/0.33 % (783758)...printing done.
% 0.22/0.33 % (783755)Instruction limit reached!
% 0.22/0.33 % (783755)------------------------------
% 0.22/0.33 % (783755)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (783755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (783755)CaDiCaL version: 2.1.3
% 0.22/0.33 % (783755)Termination reason: Instruction limit
% 0.22/0.33 % (783755)Termination phase: Saturation
% 0.22/0.33 % (783755)Time elapsed: 0.010 s
% 0.22/0.33 % (783755)Peak memory usage: 11 MB
% 0.22/0.33 % (783755)Instructions burned: 12 (million)
% 0.22/0.33 % (783758)Refutation found. Thanks to Tanya!
% 0.22/0.33 % SZS status Theorem for theBenchmark
% 0.22/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.33 % (783758)------------------------------
% 0.22/0.33 % (783758)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (783758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (783758)CaDiCaL version: 2.1.3
% 0.22/0.33 % (783758)Termination reason: Refutation
% 0.22/0.33 % (783758)Time elapsed: 0.023 s
% 0.22/0.33 % (783758)Peak memory usage: 13 MB
% 0.22/0.33 % (783758)Instructions burned: 92 (million)
% 0.22/0.33 % (783732)Success in time 0.094 s
% 0.22/0.33 % Vampire exiting
%------------------------------------------------------------------------------