%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU461^1 : 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 : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:29:43 AM UTC 2026
% Result : Theorem 0.21s 0.34s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 4
% Syntax : Number of formulae : 62 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 638 ( 63 equ; 0 cnn)
% Maximal formula atoms : 2 ( 10 avg)
% Number of connectives : 2016 ( 11 ~; 5 |; 126 &;1378 @)
% ( 0 <=>; 172 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 252 ( 252 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 51 usr; 6 con; 0-4 aty)
% ( 324 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 406 ( 371 ^; 35 !; 0 ?; 406 :)
% 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,
vOR: $o > $o > $o ).
thf(func_def_31,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_35,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_36,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vAND: $o > $o > $o ).
thf(func_def_38,type,
vIMP: $o > $o > $o ).
thf(func_def_39,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vNOT: $o > $o ).
thf(func_def_43,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $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_52,type,
sK4: $i > $i > $o ).
thf(f1,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X3: $i,X2: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
= subrel ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',subrel) ).
thf(f13,axiom,
( trans
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X3: $i,X2: $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(f30,conjecture,
! [X0: $i > $i > $o] : ( trans @ ( tc @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_closure_is_transitive) ).
thf(f31,negated_conjecture,
~ ! [X0: $i > $i > $o] : ( trans @ ( tc @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f38,plain,
( trans
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X3 @ X2 ) )
=> ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f39,plain,
( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f40,plain,
~ ! [X0: $i > $i > $o] : ( trans @ ( tc @ X0 ) ),
inference(rectify,[],[f31]) ).
thf(f41,plain,
( ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] : ( trans @ ( tc @ Y0 ) ) ) )
= $true ),
inference(fool_elimination,[],[f40]) ).
thf(f55,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X0 @ X3 @ X2 )
=> ( X1 @ X3 @ X2 ) ) )
= subrel ),
inference(rectify,[],[f1]) ).
thf(f56,plain,
( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f83,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(f84,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,[],[f83]) ).
thf(f90,plain,
( ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] : ( trans @ ( tc @ Y0 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f41]) ).
thf(f91,plain,
( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f113,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,[],[f84]) ).
thf(f115,plain,
( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
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 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
@ Y3 )
& ( ^ [Y4: $i > $i > $o,Y5: $i > $i > $o] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
@ Y0
@ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[],[f113,f91,f115]) ).
thf(f135,plain,
( $true
= ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ 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 @ Y7 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) )
@ Y4 )
& ( ^ [Y5: $i > $i > $o,Y6: $i > $i > $o] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
@ Y1
@ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f90,f91,f122]) ).
thf(f136,plain,
( ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $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 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y1 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
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] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y1 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f136]) ).
thf(f138,plain,
( $false
= ( ^ [Y0: $i > $i > $o] :
( !! @ $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 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y1 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f137]) ).
thf(f140,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 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f142,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 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y0 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f140]) ).
thf(f143,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 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ sK1 @ Y0 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ sK1 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f142]) ).
thf(f144,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ sK1 @ Y0 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ sK1 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f143]) ).
thf(f145,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK1 @ sK2 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK1 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f146,plain,
( $false
= ( ^ [Y0: $i] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK1 @ sK2 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK1 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK2 ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK1 @ sK2 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK1 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f147]) ).
thf(f149,plain,
( $true
= ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK1 @ sK2 ) ) )
& ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f147]) ).
thf(f150,plain,
( $false
= ( ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) )
@ sK4 ) ),
inference(sigma_proxy_clausification,[],[f148]) ).
thf(f151,plain,
( $false
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK4 @ Y0 @ Y1 )
& ( sK4 @ Y2 @ Y0 ) )
=> ( sK4 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) )
=> ( sK4 @ sK3 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f150]) ).
thf(f152,plain,
( ( sK4 @ sK3 @ sK2 )
= $false ),
inference(imp_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK4 @ Y0 @ Y1 )
& ( sK4 @ Y2 @ Y0 ) )
=> ( sK4 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f151]) ).
thf(f159,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK4 @ Y0 @ Y1 )
& ( sK4 @ Y2 @ Y0 ) )
=> ( sK4 @ Y2 @ Y1 ) ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f153]) ).
thf(f172,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK4 @ Y0 @ Y1 )
& ( sK4 @ Y2 @ Y0 ) )
=> ( sK4 @ Y2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f159]) ).
thf(f173,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK4 @ X1 @ Y0 )
& ( sK4 @ Y1 @ X1 ) )
=> ( sK4 @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK4 @ X1 @ Y0 )
& ( sK4 @ Y1 @ X1 ) )
=> ( sK4 @ Y1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK4 @ X1 @ X2 )
& ( sK4 @ Y0 @ X1 ) )
=> ( sK4 @ Y0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( sK4 @ X1 @ X2 )
& ( sK4 @ Y0 @ X1 ) )
=> ( sK4 @ Y0 @ X2 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( sK4 @ X1 @ X2 )
& ( sK4 @ X3 @ X1 ) )
=> ( sK4 @ X3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f179,plain,
! [X0: $i] :
( $true
= ( ( ( sK4 @ X0 @ sK2 )
& ( sK4 @ sK3 @ X0 ) )
=> $false ) ),
inference(constrained_superposition,[],[f177,f152]) ).
thf(f184,plain,
! [X0: $i] :
( $true
= ( ~ ( ( sK4 @ X0 @ sK2 )
& ( sK4 @ sK3 @ X0 ) ) ) ),
inference(boolean_simplification,[],[f179]) ).
thf(f187,plain,
! [X0: $i] :
( ( ( sK4 @ X0 @ sK2 )
& ( sK4 @ sK3 @ X0 ) )
= $false ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f194,plain,
! [X0: $i] :
( ( $false
= ( sK4 @ sK3 @ X0 ) )
| ( $false
= ( sK4 @ X0 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f187]) ).
thf(f203,plain,
( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK1 ) ) ) ),
inference(and_proxy_clausification,[],[f149]) ).
thf(f204,plain,
( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK1 @ sK2 ) ) ) ),
inference(and_proxy_clausification,[],[f149]) ).
thf(f205,plain,
! [X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK1 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f203]) ).
thf(f206,plain,
! [X1: $i > $i > $o] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK3 @ sK1 ) )
= $true ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f208,plain,
! [X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK1 @ sK2 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f204]) ).
thf(f209,plain,
! [X1: $i > $i > $o] :
( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK1 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f208]) ).
thf(f250,plain,
( ( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK4 @ Y0 @ Y1 )
& ( sK4 @ Y2 @ Y0 ) )
=> ( sK4 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) )
=> $false ) )
| ( $false
= ( sK4 @ sK1 @ sK2 ) ) ),
inference(constrained_superposition,[],[f206,f194]) ).
thf(f253,plain,
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK4 @ Y0 @ Y1 )
& ( sK4 @ Y2 @ Y0 ) )
=> ( sK4 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( sK4 @ sK1 @ sK2 ) ) ),
inference(boolean_simplification,[],[f250]) ).
thf(f267,plain,
( ( $false
= ( sK4 @ sK1 @ sK2 ) )
| ( $true = ( ~ $true ) ) ),
inference(forward_demodulation,[],[f253,f153]) ).
thf(f268,plain,
( ( $false
= ( sK4 @ sK1 @ sK2 ) )
| ( $true = $false ) ),
inference(boolean_simplification,[],[f267]) ).
thf(f269,plain,
( $false
= ( sK4 @ sK1 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f268]) ).
thf(f280,plain,
( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK4 @ Y0 @ Y1 )
& ( sK4 @ Y2 @ Y0 ) )
=> ( sK4 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) )
=> $false ) ),
inference(constrained_superposition,[],[f209,f269]) ).
thf(f285,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK4 @ Y0 @ Y1 )
& ( sK4 @ Y2 @ Y0 ) )
=> ( sK4 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f280]) ).
thf(f293,plain,
( $true = ( ~ $true ) ),
inference(forward_demodulation,[],[f285,f153]) ).
thf(f294,plain,
$true = $false,
inference(boolean_simplification,[],[f293]) ).
thf(f295,plain,
$false,
inference(trivial_inequality_removal,[],[f294]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU461^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n007.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:39:56 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.34 % (3376420)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.34 % (3376431)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.34 % (3376431)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.34 % (3376431)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=3000375362:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.34 % (3376426)lrs+10_16_si=on:nwc=1.5:random_seed=757275142:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.34 % (3376427)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=801488120:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.34 % (3376429)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=566404731:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.34 % (3376428)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=1620957472:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.34 % (3376430)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2376125972:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.34 % (3376425)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1461341167:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.34 % (3376427)Instruction limit reached!
% 0.21/0.34 % (3376427)------------------------------
% 0.21/0.34 % (3376427)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3376427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3376427)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3376427)Termination reason: Instruction limit
% 0.21/0.34 % (3376427)Termination phase: Property scanning
% 0.21/0.34 % (3376427)Time elapsed: 0.003 s
% 0.21/0.34 % (3376427)Peak memory usage: 10 MB
% 0.21/0.34 % (3376427)Instructions burned: 6 (million)
% 0.21/0.34 % (3376426)Instruction limit reached!
% 0.21/0.34 % (3376426)------------------------------
% 0.21/0.34 % (3376426)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3376426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3376426)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3376426)Termination reason: Instruction limit
% 0.21/0.34 % (3376426)Termination phase: Saturation
% 0.21/0.34 % (3376426)Time elapsed: 0.009 s
% 0.21/0.34 % (3376426)Peak memory usage: 12 MB
% 0.21/0.34 % (3376426)Instructions burned: 19 (million)
% 0.21/0.34 % (3376429)Instruction limit reached!
% 0.21/0.34 % (3376429)------------------------------
% 0.21/0.34 % (3376429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3376429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3376429)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3376429)Termination reason: Instruction limit
% 0.21/0.34 % (3376429)Termination phase: Saturation
% 0.21/0.34 % (3376429)Time elapsed: 0.014 s
% 0.21/0.34 % (3376429)Peak memory usage: 11 MB
% 0.21/0.34 % (3376429)Instructions burned: 24 (million)
% 0.21/0.34 % (3376439)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=958835077:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.34 % (3376439)Instruction limit reached!
% 0.21/0.34 % (3376439)------------------------------
% 0.21/0.34 % (3376439)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3376439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3376439)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3376439)Termination reason: Instruction limit
% 0.21/0.34 % (3376439)Termination phase: Function definition elimination
% 0.21/0.34 % (3376439)Time elapsed: 0.003 s
% 0.21/0.34 % (3376439)Peak memory usage: 11 MB
% 0.21/0.34 % (3376439)Instructions burned: 7 (million)
% 0.21/0.34 % (3376440)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1608878349:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.34 % (3376441)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.34 % (3376440)Instruction limit reached!
% 0.21/0.34 % (3376440)------------------------------
% 0.21/0.34 % (3376440)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3376440)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3376440)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3376440)Termination reason: Instruction limit
% 0.21/0.34 % (3376440)Termination phase: Property scanning
% 0.21/0.34 % (3376440)Time elapsed: 0.002 s
% 0.21/0.34 % (3376440)Peak memory usage: 10 MB
% 0.21/0.34 % (3376440)Instructions burned: 5 (million)
% 0.21/0.34 % (3376441)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2001502161:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.34 % (3376431)Instruction limit reached!
% 0.21/0.34 % (3376431)------------------------------
% 0.21/0.34 % (3376431)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3376431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3376431)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3376431)Termination reason: Instruction limit
% 0.21/0.34 % (3376431)Termination phase: Saturation
% 0.21/0.34 % (3376431)Time elapsed: 0.042 s
% 0.21/0.34 % (3376431)Peak memory usage: 13 MB
% 0.21/0.34 % (3376431)Instructions burned: 157 (million)
% 0.21/0.34 % (3376441)Instruction limit reached!
% 0.21/0.34 % (3376441)------------------------------
% 0.21/0.34 % (3376441)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3376441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3376430)Instruction limit reached!
% 0.21/0.34 % (3376430)------------------------------
% 0.21/0.34 % (3376430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3376441)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3376430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3376441)Termination reason: Instruction limit
% 0.21/0.34 % (3376441)Termination phase: Function definition elimination
% 0.21/0.34 % (3376430)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3376430)Termination reason: Instruction limit
% 0.21/0.34 % (3376430)Termination phase: Saturation
% 0.21/0.34 % (3376430)Time elapsed: 0.037 s
% 0.21/0.34 % (3376430)Peak memory usage: 12 MB
% 0.21/0.34 % (3376441)Time elapsed: 0.003 s
% 0.21/0.34 % (3376430)Instructions burned: 76 (million)
% 0.21/0.34 % (3376441)Peak memory usage: 10 MB
% 0.21/0.34 % (3376441)Instructions burned: 7 (million)
% 0.21/0.34 % (3376425)Instruction limit reached!
% 0.21/0.34 % (3376425)------------------------------
% 0.21/0.34 % (3376425)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3376425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3376425)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3376425)Termination reason: Instruction limit
% 0.21/0.34 % (3376425)Termination phase: Saturation
% 0.21/0.34 % (3376425)Time elapsed: 0.042 s
% 0.21/0.34 % (3376425)Peak memory usage: 12 MB
% 0.21/0.34 % (3376425)Instructions burned: 87 (million)
% 0.21/0.34 % (3376447)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=1835878149:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.21/0.34 % (3376443)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2185016792:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.34 % (3376445)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.34 % (3376445)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.34 % (3376449)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.21/0.34 % (3376443)Instruction limit reached!
% 0.21/0.34 % (3376443)------------------------------
% 0.21/0.34 % (3376443)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3376443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3376443)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3376443)Termination reason: Instruction limit
% 0.21/0.34 % (3376443)Termination phase: Saturation
% 0.21/0.34 % (3376443)Time elapsed: 0.006 s
% 0.21/0.34 % (3376443)Peak memory usage: 12 MB
% 0.21/0.34 % (3376443)Instructions burned: 13 (million)
% 0.21/0.34 % (3376447) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3376420-3376447"...
% 0.21/0.34 % (3376445)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2472244610:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.21/0.34 % (3376448)lrs+10_1_si=on:cs=on:random_seed=712771942:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.21/0.34 % (3376449)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=3664230550:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.34 % (3376447)...printing done.
% 0.21/0.34 % (3376447)Refutation found. Thanks to Tanya!
% 0.21/0.34 % SZS status Theorem for theBenchmark
% 0.21/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.34 % (3376447)------------------------------
% 0.21/0.34 % (3376447)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3376447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3376447)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3376447)Termination reason: Refutation
% 0.21/0.34 % (3376447)Time elapsed: 0.011 s
% 0.21/0.34 % (3376447)Peak memory usage: 13 MB
% 0.21/0.34 % (3376447)Instructions burned: 41 (million)
% 0.21/0.34 % (3376420)Success in time 0.095 s
% 0.21/0.34 % Vampire exiting
%------------------------------------------------------------------------------