%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU496^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:29:48 AM UTC 2026
% Result : Theorem 1.20s 0.53s
% Output : Refutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 10
% Syntax : Number of formulae : 134 ( 45 unt; 0 typ; 4 def)
% Number of atoms : 1423 ( 126 equ; 0 cnn)
% Maximal formula atoms : 4 ( 10 avg)
% Number of connectives : 4445 ( 143 ~; 103 |; 255 &;2872 @)
% ( 4 <=>; 364 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 452 ( 452 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 59 usr; 14 con; 0-4 aty)
% ( 704 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 828 ( 24 sgn 53 !; 0 ?; 828 :)
% 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,
vNOT: $o > $o ).
thf(func_def_31,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_32,type,
vIMP: $o > $o > $o ).
thf(func_def_33,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_37,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vAND: $o > $o > $o ).
thf(func_def_40,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_43,type,
vOR: $o > $o > $o ).
thf(func_def_44,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
sK0: $i > $i > $o ).
thf(func_def_57,type,
sK9: $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/sandbox/benchmark/Axioms/SET009^0.ax',subrel) ).
thf(f11,axiom,
( asymm
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i] :
( ( X0 @ X1 @ X2 )
=> ~ ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',asymmetric) ).
thf(f13,axiom,
( trans
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i,X3: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET009^0.ax',transitive_closure) ).
thf(f18,axiom,
( so
= ( ^ [X0: $i > $i > $o] :
( ( asymm @ X0 )
& ( trans @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',strict_order) ).
thf(f30,conjecture,
! [X0: $i > $i > $o] :
( ( so @ X0 )
=> ( so @ ( tc @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_closure_of_strict_order_is_strict_order) ).
thf(f31,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( so @ X0 )
=> ( so @ ( tc @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f32,plain,
~ ! [X0: $i > $i > $o] :
( ( so @ X0 )
=> ( so @ ( tc @ X0 ) ) ),
inference(rectify,[],[f31]) ).
thf(f33,plain,
( $true
= ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( so @ Y0 )
=> ( so @ ( tc @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f34,plain,
( asymm
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
=> ~ ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f35,plain,
( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f39,plain,
( so
= ( ^ [X0: $i > $i > $o] :
( ( asymm @ X0 )
& ( trans @ X0 ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f40,plain,
( so
= ( ^ [Y0: $i > $i > $o] :
( ( trans @ Y0 )
& ( asymm @ Y0 ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f53,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
= subrel ),
inference(rectify,[],[f1]) ).
thf(f54,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,[],[f53]) ).
thf(f55,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(f56,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,[],[f55]) ).
thf(f86,plain,
( trans
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X1 )
& ( X0 @ X1 @ X3 ) )
=> ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f87,plain,
( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f86]) ).
thf(f90,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,[],[f54]) ).
thf(f93,plain,
( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f87]) ).
thf(f96,plain,
( so
= ( ^ [Y0: $i > $i > $o] :
( ( trans @ Y0 )
& ( asymm @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f101,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,[],[f56]) ).
thf(f111,plain,
( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f114,plain,
( $true
= ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( so @ Y0 )
=> ( so @ ( tc @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
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 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
@ 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,[],[f101,f93,f90]) ).
thf(f126,plain,
( so
= ( ^ [Y0: $i > $i > $o] :
( ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
@ Y0 )
& ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ~ ( Y1 @ Y3 @ Y2 ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f96,f93,f111]) ).
thf(f135,plain,
( $true
= ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ^ [Y1: $i > $i > $o] :
( ( ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
@ Y1 )
& ( ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
=> ~ ( Y2 @ Y4 @ Y3 ) ) ) )
@ Y1 ) )
@ Y0 )
=> ( ^ [Y1: $i > $i > $o] :
( ( ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
@ Y1 )
& ( ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
=> ~ ( Y2 @ Y4 @ Y3 ) ) ) )
@ Y1 ) )
@ ( ^ [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 @ Y8 @ Y6 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
@ 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,[],[f114,f126,f126,f122]) ).
thf(f136,plain,
( $true
= ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ~ ( Y0 @ Y2 @ 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 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y1 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
=> ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f135]) ).
thf(f137,plain,
( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ~ ( Y0 @ Y2 @ 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 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y1 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
=> ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f136]) ).
thf(f138,plain,
( $false
= ( ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ~ ( Y0 @ Y2 @ 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 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y1 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
=> ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f137]) ).
thf(f141,plain,
( $false
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ~ ( sK0 @ Y1 @ Y0 ) ) ) ) )
=> ( ( !! @ $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 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
=> ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f142,plain,
( ( ( !! @ $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 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
=> ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f143,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ~ ( sK0 @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f144,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ~ ( sK0 @ Y1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f143]) ).
thf(f145,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f143]) ).
thf(f146,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ~ ( sK0 @ Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f144]) ).
thf(f147,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
=> ~ ( sK0 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
=> ~ ( sK0 @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( sK0 @ X1 @ X2 )
=> ~ ( sK0 @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f150,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( sK0 @ X2 @ X1 ) ) )
| ( $false
= ( sK0 @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f149]) ).
thf(f158,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 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
=> ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f142]) ).
thf(f160,definition,
( spl1_1
<=> ( $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 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f162,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 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f160]) ).
thf(f164,definition,
( spl1_2
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
=> ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f166,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
=> ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f164]) ).
thf(f167,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f158,f164,f160]) ).
thf(f168,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
=> ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) )
@ sK2 ) )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f166]) ).
thf(f169,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK2 @ Y0 ) ) )
=> ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK2 ) ) ) ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f168]) ).
thf(f170,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK2 @ Y0 ) ) )
=> ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK2 ) ) ) )
@ sK3 ) )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( $false
= ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) )
=> ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
( ( $false
= ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) ) ) )
| ~ spl1_2 ),
inference(imp_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
| ~ spl1_2 ),
inference(imp_proxy_clausification,[],[f171]) ).
thf(f174,plain,
( ! [X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) )
@ X1 ) )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( ! [X1: $i > $i > $o] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y1 @ Y2 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK2 @ sK3 ) )
= $true )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f177,plain,
( ( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f178,plain,
( ! [X1: $i > $i > $o] :
( ( ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) )
@ X1 )
= $true )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( ! [X1: $i > $i > $o] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y1 @ Y2 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK3 @ sK2 ) )
= $true )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f178]) ).
thf(f181,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f150]) ).
thf(f190,plain,
( ( $false
= ( sK0 @ sK3 @ sK2 ) )
| ( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f175,f181]) ).
thf(f200,plain,
( ( $false
= ( sK0 @ sK3 @ sK2 ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f190]) ).
thf(f201,plain,
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true ) ) ) ) )
| ( $false
= ( sK0 @ sK3 @ sK2 ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f200]) ).
thf(f208,plain,
( ( $false
= ( sK0 @ sK3 @ sK2 ) )
| ( ( ~ ( $true
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true ) ) ) )
= $true )
| ~ spl1_2 ),
inference(forward_demodulation,[],[f201,f145]) ).
thf(f209,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true ) ) )
= $true )
| ( $false
= ( sK0 @ sK3 @ sK2 ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f208]) ).
thf(f213,definition,
( spl1_3
<=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
thf(f214,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true ) ) )
!= $true )
| spl1_3 ),
inference(avatar_component_clause,[],[f213]) ).
thf(f215,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true ) ) )
= $true )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f213]) ).
thf(f217,definition,
( spl1_4
<=> ( $false
= ( sK0 @ sK3 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
thf(f219,plain,
( ( $false
= ( sK0 @ sK3 @ sK2 ) )
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f217]) ).
thf(f220,plain,
( spl1_3
| spl1_4
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f209,f164,f217,f213]) ).
thf(f238,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true ) ) )
| ~ spl1_3 ),
inference(not_proxy_clausification,[],[f215]) ).
thf(f239,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true )
@ sK4 )
= $false )
| ~ spl1_3 ),
inference(sigma_proxy_clausification,[],[f238]) ).
thf(f240,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] : $true ) )
| ~ spl1_3 ),
inference(beta-eta_normalization,[],[f239]) ).
thf(f241,plain,
( ( $false
= ( ^ [Y0: $i] : $true
@ sK5 ) )
| ~ spl1_3 ),
inference(sigma_proxy_clausification,[],[f240]) ).
thf(f242,plain,
( ( $false = $true )
| ~ spl1_3 ),
inference(beta-eta_normalization,[],[f241]) ).
thf(f243,plain,
( $false
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f242]) ).
thf(f244,plain,
~ spl1_3,
inference(avatar_contradiction_clause,[],[f243]) ).
thf(f245,plain,
( ( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl1_2
| ~ spl1_4 ),
inference(constrained_superposition,[],[f179,f219]) ).
thf(f254,plain,
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl1_2
| ~ spl1_4 ),
inference(boolean_simplification,[],[f245]) ).
thf(f255,plain,
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true ) ) ) ) )
| ~ spl1_2
| ~ spl1_4 ),
inference(boolean_simplification,[],[f254]) ).
thf(f263,plain,
( ( ( ~ ( $true
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true ) ) ) )
= $true )
| ~ spl1_2
| ~ spl1_4 ),
inference(forward_demodulation,[],[f255,f145]) ).
thf(f264,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true ) ) )
= $true )
| ~ spl1_2
| ~ spl1_4 ),
inference(boolean_simplification,[],[f263]) ).
thf(f265,plain,
( $false
| ~ spl1_2
| spl1_3
| ~ spl1_4 ),
inference(forward_subsumption_resolution,[],[f264,f214]) ).
thf(f266,plain,
( ~ spl1_2
| spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f265]) ).
thf(f383,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 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) ) ) )
@ sK6 ) )
| ~ spl1_1 ),
inference(sigma_proxy_clausification,[],[f162]) ).
thf(f384,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ sK6 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ sK6 ) ) ) ) ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f383]) ).
thf(f385,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ sK6 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ sK6 ) ) ) ) )
@ sK7 ) )
| ~ spl1_1 ),
inference(sigma_proxy_clausification,[],[f384]) ).
thf(f386,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK6 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK7 @ sK6 ) ) ) ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f385]) ).
thf(f387,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK6 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK7 @ sK6 ) ) ) )
@ sK8 ) )
| ~ spl1_1 ),
inference(sigma_proxy_clausification,[],[f386]) ).
thf(f388,plain,
( ( $false
= ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK6 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f387]) ).
thf(f389,plain,
( ( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) ) )
| ~ spl1_1 ),
inference(imp_proxy_clausification,[],[f388]) ).
thf(f390,plain,
( ( $true
= ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK6 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) ) )
| ~ spl1_1 ),
inference(imp_proxy_clausification,[],[f388]) ).
thf(f391,plain,
( ( $false
= ( ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) )
@ sK9 ) )
| ~ spl1_1 ),
inference(sigma_proxy_clausification,[],[f389]) ).
thf(f392,plain,
( ( $false
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK9 @ Y2 @ Y0 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) )
=> ( sK9 @ sK7 @ sK6 ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f391]) ).
thf(f393,plain,
( ( $false
= ( sK9 @ sK7 @ sK6 ) )
| ~ spl1_1 ),
inference(imp_proxy_clausification,[],[f392]) ).
thf(f394,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK9 @ Y2 @ Y0 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl1_1 ),
inference(imp_proxy_clausification,[],[f392]) ).
thf(f400,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK9 @ Y2 @ Y0 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl1_1 ),
inference(and_proxy_clausification,[],[f394]) ).
thf(f490,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK9 @ Y2 @ Y0 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y1 @ Y0 ) ) ) )
@ X1 ) )
| ~ spl1_1 ),
inference(pi_proxy_clausification,[],[f400]) ).
thf(f491,plain,
( ! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK9 @ Y1 @ X1 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ X1 ) ) ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f490]) ).
thf(f492,plain,
( ! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK9 @ Y1 @ X1 )
& ( sK9 @ Y0 @ Y1 ) )
=> ( sK9 @ Y0 @ X1 ) ) )
@ X2 )
= $true )
| ~ spl1_1 ),
inference(pi_proxy_clausification,[],[f491]) ).
thf(f493,plain,
( ! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK9 @ Y0 @ X1 )
& ( sK9 @ X2 @ Y0 ) )
=> ( sK9 @ X2 @ X1 ) ) )
= $true )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f492]) ).
thf(f494,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( sK9 @ Y0 @ X1 )
& ( sK9 @ X2 @ Y0 ) )
=> ( sK9 @ X2 @ X1 ) )
@ X3 ) )
| ~ spl1_1 ),
inference(pi_proxy_clausification,[],[f493]) ).
thf(f495,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( sK9 @ X3 @ X1 )
& ( sK9 @ X2 @ X3 ) )
=> ( sK9 @ X2 @ X1 ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f494]) ).
thf(f497,plain,
( ! [X0: $i] :
( $true
= ( ( ( sK9 @ X0 @ sK6 )
& ( sK9 @ sK7 @ X0 ) )
=> $false ) )
| ~ spl1_1 ),
inference(constrained_superposition,[],[f495,f393]) ).
thf(f504,plain,
( ! [X0: $i] :
( $true
= ( ~ ( ( sK9 @ X0 @ sK6 )
& ( sK9 @ sK7 @ X0 ) ) ) )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f497]) ).
thf(f505,plain,
( ! [X0: $i] :
( $false
= ( ( sK9 @ X0 @ sK6 )
& ( sK9 @ sK7 @ X0 ) ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f504]) ).
thf(f512,plain,
( ! [X0: $i] :
( ( $false
= ( sK9 @ sK7 @ X0 ) )
| ( $false
= ( sK9 @ X0 @ sK6 ) ) )
| ~ spl1_1 ),
inference(and_proxy_clausification,[],[f505]) ).
thf(f521,plain,
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
= $true )
| ~ spl1_1 ),
inference(and_proxy_clausification,[],[f390]) ).
thf(f522,plain,
( ( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK6 ) ) ) )
| ~ spl1_1 ),
inference(and_proxy_clausification,[],[f390]) ).
thf(f523,plain,
( ! [X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) )
@ X1 ) )
| ~ spl1_1 ),
inference(pi_proxy_clausification,[],[f521]) ).
thf(f524,plain,
( ! [X1: $i > $i > $o] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y1 @ Y2 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK7 @ sK8 ) )
= $true )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f523]) ).
thf(f601,plain,
( ! [X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK6 ) )
@ X1 ) )
| ~ spl1_1 ),
inference(pi_proxy_clausification,[],[f522]) ).
thf(f602,plain,
( ! [X1: $i > $i > $o] :
( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y1 @ Y2 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK8 @ sK6 ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f601]) ).
thf(f773,plain,
( ( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK9 @ Y2 @ Y0 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) )
=> $false ) )
| ( ( sK9 @ sK8 @ sK6 )
= $false )
| ~ spl1_1 ),
inference(constrained_superposition,[],[f524,f512]) ).
thf(f783,plain,
( ( ( sK9 @ sK8 @ sK6 )
= $false )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK9 @ Y2 @ Y0 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f773]) ).
thf(f792,plain,
( ( ( ~ $true ) = $true )
| ( ( sK9 @ sK8 @ sK6 )
= $false )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f783,f394]) ).
thf(f793,plain,
( ( ( sK9 @ sK8 @ sK6 )
= $false )
| ( $false = $true )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f792]) ).
thf(f794,plain,
( ( ( sK9 @ sK8 @ sK6 )
= $false )
| ~ spl1_1 ),
inference(trivial_inequality_removal,[],[f793]) ).
thf(f796,plain,
( ( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK9 @ Y2 @ Y0 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl1_1 ),
inference(constrained_superposition,[],[f602,f794]) ).
thf(f806,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK9 @ Y2 @ Y0 )
& ( sK9 @ Y1 @ Y2 ) )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK9 @ Y1 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f796]) ).
thf(f816,plain,
( ( ( ~ $true ) = $true )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f806,f394]) ).
thf(f817,plain,
( ( $false = $true )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f816]) ).
thf(f818,plain,
( $false
| ~ spl1_1 ),
inference(trivial_inequality_removal,[],[f817]) ).
thf(f819,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f818]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f167]) ).
cnf(s2,plain,
( ~ spl1_2
| spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f220]) ).
cnf(s4,plain,
~ spl1_3,
inference(sat_conversion,[],[f244]) ).
cnf(s5,plain,
( ~ spl1_2
| spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f266]) ).
cnf(s6,plain,
~ spl1_1,
inference(sat_conversion,[],[f819]) ).
cnf(s8,plain,
( ~ spl1_2
| spl1_4 ),
inference(rat,[],[s2,s4]) ).
cnf(s9,plain,
spl1_2,
inference(rat,[],[s1,s6]) ).
cnf(s10,plain,
~ spl1_4,
inference(rat,[],[s5,s4,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s8,s10,s9]) ).
thf(f822,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU496^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 % Computer : n014.cluster.edu
% 0.11/0.24 % Model : x86_64 x86_64
% 0.11/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.24 % Memory : 8046.5625MB
% 0.11/0.24 % OS : Linux 6.8.0-71-generic
% 0.11/0.24 % CPULimit : 300
% 0.11/0.24 % WCLimit : 300
% 0.11/0.24 % DateTime : Tue Sep 29 13:46:09 UTC 2026
% 0.11/0.25 % CPUTime :
% 0.11/0.25 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.30 Running higher-order theorem proving
% 0.23/0.32 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.20/0.50 % (2681099)Detected a higher-order problem, will run a greedy HOL sequence.
% 1.20/0.50 % (2681109)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2460878413:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 1.20/0.50 % (2681104)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2069286134:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 1.20/0.50 % (2681110)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 1.20/0.50 % (2681110)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
% 1.20/0.50 % (2681105)lrs+10_16_si=on:nwc=1.5:random_seed=408083831:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 1.20/0.50 % (2681106)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3613199694:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 1.20/0.50 % (2681108)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=13891813:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 1.20/0.50 % (2681107)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=2529568755: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)
% 1.20/0.50 % (2681110)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=336697883:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 1.20/0.50 % (2681106)Instruction limit reached!
% 1.20/0.50 % (2681106)------------------------------
% 1.20/0.50 % (2681106)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.50 % (2681106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.50 % (2681106)CaDiCaL version: 2.1.3
% 1.20/0.50 % (2681106)Termination reason: Instruction limit
% 1.20/0.50 % (2681106)Termination phase: Property scanning
% 1.20/0.50 % (2681106)Time elapsed: 0.003 s
% 1.20/0.50 % (2681106)Peak memory usage: 9 MB
% 1.20/0.50 % (2681106)Instructions burned: 3 (million)
% 1.20/0.50 % (2681105)Instruction limit reached!
% 1.20/0.50 % (2681105)------------------------------
% 1.20/0.50 % (2681105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.50 % (2681105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.50 % (2681105)CaDiCaL version: 2.1.3
% 1.20/0.50 % (2681105)Termination reason: Instruction limit
% 1.20/0.50 % (2681105)Termination phase: Saturation
% 1.20/0.50 % (2681105)Time elapsed: 0.015 s
% 1.20/0.50 % (2681105)Peak memory usage: 11 MB
% 1.20/0.50 % (2681105)Instructions burned: 18 (million)
% 1.20/0.50 % (2681109)Instruction limit reached!
% 1.20/0.50 % (2681109)------------------------------
% 1.20/0.50 % (2681109)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.50 % (2681109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.50 % (2681109)CaDiCaL version: 2.1.3
% 1.20/0.50 % (2681109)Termination reason: Instruction limit
% 1.20/0.50 % (2681109)Termination phase: Saturation
% 1.20/0.50 % (2681109)Time elapsed: 0.033 s
% 1.20/0.50 % (2681109)Peak memory usage: 13 MB
% 1.20/0.50 % (2681109)Instructions burned: 75 (million)
% 1.20/0.50 % (2681108)Instruction limit reached!
% 1.20/0.50 % (2681108)------------------------------
% 1.20/0.50 % (2681108)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.50 % (2681108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.50 % (2681108)CaDiCaL version: 2.1.3
% 1.20/0.50 % (2681108)Termination reason: Instruction limit
% 1.20/0.50 % (2681108)Termination phase: Saturation
% 1.20/0.50 % (2681108)Time elapsed: 0.025 s
% 1.20/0.50 % (2681108)Peak memory usage: 12 MB
% 1.20/0.50 % (2681108)Instructions burned: 25 (million)
% 1.20/0.50 % (2681120)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.20/0.50 % (2681118)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1928035771:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.20/0.53 % (2681120)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4274002229:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.20/0.53 % (2681118)Instruction limit reached!
% 1.20/0.53 % (2681118)------------------------------
% 1.20/0.53 % (2681118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.53 % (2681118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.53 % (2681118)CaDiCaL version: 2.1.3
% 1.20/0.53 % (2681118)Termination reason: Instruction limit
% 1.20/0.53 % (2681118)Termination phase: shuffling
% 1.20/0.53 % (2681118)Time elapsed: 0.002 s
% 1.20/0.53 % (2681118)Peak memory usage: 10 MB
% 1.20/0.53 % (2681118)Instructions burned: 2 (million)
% 1.20/0.53 % (2681120)Instruction limit reached!
% 1.20/0.53 % (2681120)------------------------------
% 1.20/0.53 % (2681120)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.53 % (2681120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.53 % (2681120)CaDiCaL version: 2.1.3
% 1.20/0.53 % (2681120)Termination reason: Instruction limit
% 1.20/0.53 % (2681120)Termination phase: Saturation
% 1.20/0.53 % (2681120)Time elapsed: 0.004 s
% 1.20/0.53 % (2681120)Peak memory usage: 11 MB
% 1.20/0.53 % (2681120)Instructions burned: 10 (million)
% 1.20/0.53 % (2681119)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2345357819:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.20/0.53 % (2681119)Instruction limit reached!
% 1.20/0.53 % (2681119)------------------------------
% 1.20/0.53 % (2681119)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.53 % (2681119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.53 % (2681119)CaDiCaL version: 2.1.3
% 1.20/0.53 % (2681119)Termination reason: Instruction limit
% 1.20/0.53 % (2681119)Termination phase: Property scanning
% 1.20/0.53 % (2681119)Time elapsed: 0.005 s
% 1.20/0.53 % (2681119)Peak memory usage: 10 MB
% 1.20/0.53 % (2681119)Instructions burned: 6 (million)
% 1.20/0.53 % (2681124)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
% 1.20/0.53 % (2681124)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.20/0.53 % (2681121)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2007045943:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.20/0.53 % (2681124)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3200522309:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.20/0.53 % (2681104)Instruction limit reached!
% 1.20/0.53 % (2681104)------------------------------
% 1.20/0.53 % (2681104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.53 % (2681104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.53 % (2681104)CaDiCaL version: 2.1.3
% 1.20/0.53 % (2681104)Termination reason: Instruction limit
% 1.20/0.53 % (2681104)Termination phase: Saturation
% 1.20/0.53 % (2681104)Time elapsed: 0.077 s
% 1.20/0.53 % (2681104)Peak memory usage: 13 MB
% 1.20/0.53 % (2681104)Instructions burned: 88 (million)
% 1.20/0.53 % (2681121)Instruction limit reached!
% 1.20/0.53 % (2681121)------------------------------
% 1.20/0.53 % (2681121)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.53 % (2681121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.53 % (2681121)CaDiCaL version: 2.1.3
% 1.20/0.53 % (2681121)Termination reason: Instruction limit
% 1.20/0.53 % (2681121)Termination phase: Saturation
% 1.20/0.53 % (2681121)Time elapsed: 0.011 s
% 1.20/0.53 % (2681121)Peak memory usage: 12 MB
% 1.20/0.53 % (2681121)Instructions burned: 14 (million)
% 1.20/0.53 % (2681124)Instruction limit reached!
% 1.20/0.53 % (2681124)------------------------------
% 1.20/0.53 % (2681124)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.53 % (2681124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.53 % (2681124)CaDiCaL version: 2.1.3
% 1.20/0.53 % (2681124)Termination reason: Instruction limit
% 1.20/0.53 % (2681124)Termination phase: Saturation
% 1.20/0.53 % (2681124)Time elapsed: 0.014 s
% 1.20/0.53 % (2681124)Peak memory usage: 12 MB
% 1.20/0.53 % (2681124)Instructions burned: 29 (million)
% 1.20/0.53 % (2681125)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=624036847:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.20/0.53 % (2681127)lrs+10_1_si=on:cs=on:random_seed=2877324133:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.20/0.53 % (2681130)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.20/0.53 % (2681133)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1220407156:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.20/0.53 % (2681127)Instruction limit reached!
% 1.20/0.53 % (2681127)------------------------------
% 1.20/0.53 % (2681127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.53 % (2681127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.53 % (2681127)CaDiCaL version: 2.1.3
% 1.20/0.53 % (2681127)Termination reason: Instruction limit
% 1.20/0.53 % (2681127)Termination phase: Property scanning
% 1.20/0.53 % (2681127)Time elapsed: 0.008 s
% 1.20/0.53 % (2681127)Peak memory usage: 10 MB
% 1.20/0.53 % (2681127)Instructions burned: 8 (million)
% 1.20/0.53 % (2681130)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=2892377780:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.20/0.53 % (2681133)Refutation not found, incomplete strategy
% 1.20/0.53 % (2681133)------------------------------
% 1.20/0.53 % (2681133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.53 % (2681133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.53 % (2681133)CaDiCaL version: 2.1.3
% 1.20/0.53 % (2681133)Termination reason: Refutation not found, incomplete strategy
% 1.20/0.53 % (2681133)Time elapsed: 0.004 s
% 1.20/0.53 % (2681133)Peak memory usage: 12 MB
% 1.20/0.53 % (2681133)Instructions burned: 7 (million)
% 1.20/0.53 % (2681133)------------------------------
% 1.20/0.53 % (2681133)------------------------------
% 1.20/0.53 % (2681130)Instruction limit reached!
% 1.20/0.53 % (2681130)------------------------------
% 1.20/0.53 % (2681130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.53 % (2681130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.53 % (2681130)CaDiCaL version: 2.1.3
% 1.20/0.53 % (2681130)Termination reason: Instruction limit
% 1.20/0.53 % (2681130)Termination phase: Property scanning
% 1.20/0.53 % (2681130)Time elapsed: 0.003 s
% 1.20/0.53 % (2681130)Peak memory usage: 9 MB
% 1.20/0.53 % (2681130)Instructions burned: 3 (million)
% 1.20/0.53 % (2681131)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2113582888:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.20/0.53 % (2681138)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2015405139:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.20/0.53 % (2681138)Instruction limit reached!
% 1.20/0.53 % (2681138)------------------------------
% 1.20/0.53 % (2681138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.53 % (2681138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.53 % (2681138)CaDiCaL version: 2.1.3
% 1.20/0.53 % (2681138)Termination reason: Instruction limit
% 1.20/0.53 % (2681138)Termination phase: Saturation
% 1.20/0.53 % (2681138)Time elapsed: 0.006 s
% 1.20/0.53 % (2681138)Peak memory usage: 11 MB
% 1.20/0.53 % (2681138)Instructions burned: 15 (million)
% 1.20/0.53 % (2681137)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1102439993:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.20/0.53 % (2681110)Instruction limit reached!
% 1.20/0.53 % (2681110)------------------------------
% 1.20/0.53 % (2681110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.53 % (2681110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.53 % (2681110)CaDiCaL version: 2.1.3
% 1.20/0.53 % (2681110)Termination reason: Instruction limit
% 1.20/0.53 % (2681110)Termination phase: Saturation
% 1.20/0.53 % (2681110)Time elapsed: 0.131 s
% 1.20/0.53 % (2681110)Peak memory usage: 13 MB
% 1.20/0.53 % (2681110)Instructions burned: 158 (million)
% 1.20/0.53 % (2681139)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=317015512:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.20/0.53 % (2681131)Instruction limit reached!
% 1.20/0.53 % (2681131)------------------------------
% 1.20/0.53 % (2681131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.53 % (2681131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.53 % (2681131)CaDiCaL version: 2.1.3
% 1.20/0.53 % (2681131)Termination reason: Instruction limit
% 1.20/0.53 % (2681131)Termination phase: Saturation
% 1.20/0.53 % (2681131)Time elapsed: 0.032 s
% 1.20/0.53 % (2681131)Peak memory usage: 12 MB
% 1.20/0.53 % (2681131)Instructions burned: 39 (million)
% 1.20/0.53 % (2681125) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2681099-2681125"...
% 1.20/0.53 % (2681142)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=607139927:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.20/0.53 % (2681144)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=218133006:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.20/0.53 % (2681137)Instruction limit reached!
% 1.20/0.53 % (2681137)------------------------------
% 1.20/0.53 % (2681137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.53 % (2681137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.53 % (2681137)CaDiCaL version: 2.1.3
% 1.20/0.53 % (2681137)Termination reason: Instruction limit
% 1.20/0.53 % (2681137)Termination phase: Saturation
% 1.20/0.53 % (2681137)Time elapsed: 0.023 s
% 1.20/0.53 % (2681137)Peak memory usage: 12 MB
% 1.20/0.53 % (2681137)Instructions burned: 25 (million)
% 1.20/0.53 % (2681144)Instruction limit reached!
% 1.20/0.53 % (2681144)------------------------------
% 1.20/0.53 % (2681144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.53 % (2681144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.53 % (2681144)CaDiCaL version: 2.1.3
% 1.20/0.53 % (2681144)Termination reason: Instruction limit
% 1.20/0.53 % (2681144)Termination phase: Property scanning
% 1.20/0.53 % (2681144)Time elapsed: 0.001 s
% 1.20/0.53 % (2681144)Peak memory usage: 10 MB
% 1.20/0.53 % (2681144)Instructions burned: 3 (million)
% 1.20/0.53 % (2681142)Instruction limit reached!
% 1.20/0.53 % (2681142)------------------------------
% 1.20/0.53 % (2681142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.53 % (2681142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.53 % (2681142)CaDiCaL version: 2.1.3
% 1.20/0.53 % (2681142)Termination reason: Instruction limit
% 1.20/0.53 % (2681142)Termination phase: Saturation
% 1.20/0.53 % (2681142)Time elapsed: 0.008 s
% 1.20/0.53 % (2681142)Peak memory usage: 12 MB
% 1.20/0.53 % (2681142)Instructions burned: 15 (million)
% 1.20/0.53 % (2681125)...printing done.
% 1.20/0.53 % (2681125)Refutation found. Thanks to Tanya!
% 1.20/0.53 % SZS status Theorem for theBenchmark
% 1.20/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 1.20/0.53 % (2681125)------------------------------
% 1.20/0.53 % (2681125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.53 % (2681125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.53 % (2681125)CaDiCaL version: 2.1.3
% 1.20/0.53 % (2681125)Termination reason: Refutation
% 1.20/0.53 % (2681125)Time elapsed: 0.080 s
% 1.20/0.53 % (2681125)Peak memory usage: 14 MB
% 1.20/0.53 % (2681125)Instructions burned: 91 (million)
% 1.20/0.53 % (2681099)Success in time 0.197 s
% 1.20/0.53 % Vampire exiting
%------------------------------------------------------------------------------