%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU460^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 85 ( 28 unt; 0 typ; 7 def)
% Number of atoms : 486 ( 86 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 703 ( 48 ~; 101 |; 0 &; 439 @)
% ( 6 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 178 ( 178 >; 0 *; 0 +; 0 <<)
% Number of symbols : 61 ( 57 usr; 12 con; 0-4 aty)
% ( 64 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 143 ( 0 sgn 20 !; 0 ?; 143 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_2,type,
inv: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_3,type,
idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_4,type,
infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_5,type,
mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_6,type,
refl: ( $i > $i > $o ) > $o ).
thf(func_def_7,type,
irrefl: ( $i > $i > $o ) > $o ).
thf(func_def_8,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_9,type,
symm: ( $i > $i > $o ) > $o ).
thf(func_def_10,type,
antisymm: ( $i > $i > $o ) > $o ).
thf(func_def_11,type,
asymm: ( $i > $i > $o ) > $o ).
thf(func_def_12,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_13,type,
trans: ( $i > $i > $o ) > $o ).
thf(func_def_14,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_15,type,
trc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_16,type,
trsc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_17,type,
po: ( $i > $i > $o ) > $o ).
thf(func_def_18,type,
so: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
total: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
term: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
ind: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
innf: ( $i > $i > $o ) > $i > $o ).
thf(func_def_23,type,
nfof: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_24,type,
norm: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
join: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_26,type,
lconfl: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
sconfl: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
confl: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
cr: ( $i > $i > $o ) > $o ).
thf(func_def_30,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
vIMP: $o > $o > $o ).
thf(func_def_32,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_36,type,
vAND: $o > $o > $o ).
thf(func_def_37,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
vNOT: $o > $o ).
thf(func_def_39,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vOR: $o > $o > $o ).
thf(func_def_41,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_44,type,
sF0: $o ).
thf(func_def_45,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
sK1: ( $i > $i > $o ) > ( $i > $i > $o ) > $i ).
thf(func_def_48,type,
sK2: ( $i > $i > $o ) > ( $i > $i > $o ) > $i ).
thf(func_def_49,type,
sK3: $i > $i > $o ).
thf(func_def_50,type,
sK4: $i > $i > $o ).
thf(f1,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
= subrel ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',subrel) ).
thf(f5,axiom,
( ( ^ [X0: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X1: $i > $i > $o] :
( ( subrel @ X1 @ X2 )
=> ( subrel @ ( X0 @ X1 ) @ ( X0 @ X2 ) ) ) )
= mono ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',monotonic) ).
thf(f12,axiom,
( sc
= ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
| ( X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',symmetric_closure) ).
thf(f30,conjecture,
mono @ sc,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_closure_op_is_monotonic) ).
thf(f31,negated_conjecture,
~ ( mono @ sc ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f38,plain,
( ( ^ [X0: ( $i > $i > $o ) > $i > $i > $o] :
! [X1: $i > $i > $o,X2: $i > $i > $o] :
( ( subrel @ X2 @ X1 )
=> ( subrel @ ( X0 @ X2 ) @ ( X0 @ X1 ) ) ) )
= mono ),
inference(rectify,[],[f5]) ).
thf(f39,plain,
( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( subrel @ Y1 @ Y2 )
=> ( subrel @ ( Y0 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f64,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
= subrel ),
inference(rectify,[],[f1]) ).
thf(f65,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,[],[f64]) ).
thf(f75,plain,
~ ( mono @ sc ),
inference(rectify,[],[f31]) ).
thf(f76,plain,
( ( mono @ sc )
!= $true ),
inference(fool_elimination,[],[f75]) ).
thf(f77,plain,
( sc
= ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
| ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f78,plain,
( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f77]) ).
thf(f88,plain,
( ( mono @ sc )
!= $true ),
inference(flattening,[],[f76]) ).
thf(f105,plain,
( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f78]) ).
thf(f106,plain,
( ( mono @ sc )
!= $true ),
inference(cnf_transformation,[],[f88]) ).
thf(f115,plain,
( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( subrel @ Y1 @ Y2 )
=> ( subrel @ ( Y0 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f118,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,[],[f65]) ).
thf(f122,plain,
( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ^ [Y3: $i > $i > $o,Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
@ Y1
@ Y2 )
=> ( ^ [Y3: $i > $i > $o,Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
@ ( Y0 @ Y1 )
@ ( Y0 @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f115,f118,f118]) ).
thf(f136,plain,
( $true
!= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ^ [Y3: $i > $i > $o,Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
@ Y1
@ Y2 )
=> ( ^ [Y3: $i > $i > $o,Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
@ ( Y0 @ Y1 )
@ ( Y0 @ Y2 ) ) ) ) )
@ ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f106,f122,f105]) ).
thf(f137,definition,
( sF0
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ^ [Y3: $i > $i > $o,Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
@ Y1
@ Y2 )
=> ( ^ [Y3: $i > $i > $o,Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
@ ( Y0 @ Y1 )
@ ( Y0 @ Y2 ) ) ) ) )
@ ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f138,plain,
$true != sF0,
inference(definition_folding,[],[f136,f137]) ).
thf(f139,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ^ [Y3: $i > $i > $o,Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
@ Y1
@ Y2 )
=> ( ^ [Y3: $i > $i > $o,Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
@ ( Y0 @ Y1 )
@ ( Y0 @ Y2 ) ) ) ) )
@ ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(iff_proxy_clausification,[],[f137]) ).
thf(f162,plain,
( ( $true = sF0 )
| ( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y2 @ Y3 ) )
=> ( ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f163,plain,
( ( $false
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y2 @ Y3 ) )
=> ( ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
@ sK3 ) )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
( ( $false
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
@ sK4 ) )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK4 @ Y1 @ Y0 ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( ( sK4 @ Y1 @ Y0 )
| ( sK4 @ Y0 @ Y1 ) ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
( ( $true = sF0 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( ( sK4 @ Y1 @ Y0 )
| ( sK4 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK4 @ Y1 @ Y0 ) ) ) ) )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f169,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK4 @ Y1 @ Y0 ) ) )
@ X1 ) )
| ( $true = sF0 ) ),
inference(pi_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 @ X1 )
=> ( sK4 @ Y0 @ X1 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,plain,
! [X2: $i,X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ^ [Y0: $i] :
( ( sK3 @ Y0 @ X1 )
=> ( sK4 @ Y0 @ X1 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ( sK3 @ X2 @ X1 )
=> ( sK4 @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK3 @ X2 @ X1 ) )
| ( $true = sF0 )
| ( $true
= ( sK4 @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( ( sK4 @ Y1 @ Y0 )
| ( sK4 @ Y0 @ Y1 ) ) ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f167]) ).
thf(f175,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK3 @ Y0 @ sK5 )
| ( sK3 @ sK5 @ Y0 ) )
=> ( ( sK4 @ Y0 @ sK5 )
| ( sK4 @ sK5 @ Y0 ) ) ) )
= $false )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
( ( ( ^ [Y0: $i] :
( ( ( sK3 @ Y0 @ sK5 )
| ( sK3 @ sK5 @ Y0 ) )
=> ( ( sK4 @ Y0 @ sK5 )
| ( sK4 @ sK5 @ Y0 ) ) )
@ sK6 )
= $false )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( ( $false
= ( ( ( sK3 @ sK6 @ sK5 )
| ( sK3 @ sK5 @ sK6 ) )
=> ( ( sK4 @ sK6 @ sK5 )
| ( sK4 @ sK5 @ sK6 ) ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f178,plain,
( ( $true = sF0 )
| ( ( ( sK4 @ sK6 @ sK5 )
| ( sK4 @ sK5 @ sK6 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( ( $true
= ( ( sK3 @ sK6 @ sK5 )
| ( sK3 @ sK5 @ sK6 ) ) )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f177]) ).
thf(f180,plain,
( ( $true
= ( sK3 @ sK6 @ sK5 ) )
| ( $true = sF0 )
| ( $true
= ( sK3 @ sK5 @ sK6 ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( $true = sF0 )
| ( $false
= ( sK4 @ sK5 @ sK6 ) ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f182,plain,
( ( $true = sF0 )
| ( $false
= ( sK4 @ sK6 @ sK5 ) ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f198,definition,
( spl7_4
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
thf(f202,definition,
( spl7_5
<=> ! [X2: $i,X1: $i] :
( ( $false
= ( sK3 @ X2 @ X1 ) )
| ( $true
= ( sK4 @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
thf(f203,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( sK4 @ X2 @ X1 ) )
| ( $false
= ( sK3 @ X2 @ X1 ) ) )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f202]) ).
thf(f204,plain,
( spl7_4
| spl7_5 ),
inference(avatar_split_clause,[],[f173,f202,f198]) ).
thf(f206,definition,
( spl7_6
<=> ( $true
= ( sK3 @ sK6 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
thf(f208,plain,
( ( $true
= ( sK3 @ sK6 @ sK5 ) )
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f206]) ).
thf(f210,definition,
( spl7_7
<=> ( $true
= ( sK3 @ sK5 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
thf(f212,plain,
( ( $true
= ( sK3 @ sK5 @ sK6 ) )
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f210]) ).
thf(f213,plain,
( spl7_4
| spl7_6
| spl7_7 ),
inference(avatar_split_clause,[],[f180,f210,f206,f198]) ).
thf(f215,definition,
( spl7_8
<=> ( $false
= ( sK4 @ sK6 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
thf(f217,plain,
( ( $false
= ( sK4 @ sK6 @ sK5 ) )
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f215]) ).
thf(f218,plain,
( spl7_8
| spl7_4 ),
inference(avatar_split_clause,[],[f182,f198,f215]) ).
thf(f220,definition,
( spl7_9
<=> ( $false
= ( sK4 @ sK5 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_9])],[avatar_definition]) ).
thf(f222,plain,
( ( $false
= ( sK4 @ sK5 @ sK6 ) )
| ~ spl7_9 ),
inference(avatar_component_clause,[],[f220]) ).
thf(f223,plain,
( spl7_4
| spl7_9 ),
inference(avatar_split_clause,[],[f181,f220,f198]) ).
thf(f224,plain,
~ spl7_4,
inference(avatar_split_clause,[],[f138,f198]) ).
thf(f244,plain,
( ( $true = $false )
| ( ( sK3 @ sK6 @ sK5 )
= $false )
| ~ spl7_5
| ~ spl7_8 ),
inference(constrained_superposition,[],[f217,f203]) ).
thf(f245,plain,
( ( $true = $false )
| ( $false
= ( sK3 @ sK5 @ sK6 ) )
| ~ spl7_5
| ~ spl7_9 ),
inference(constrained_superposition,[],[f222,f203]) ).
thf(f247,plain,
( ( ( sK3 @ sK6 @ sK5 )
= $false )
| ~ spl7_5
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f244]) ).
thf(f248,plain,
( ( $false
= ( sK3 @ sK5 @ sK6 ) )
| ~ spl7_5
| ~ spl7_9 ),
inference(trivial_inequality_removal,[],[f245]) ).
thf(f253,plain,
( ( $true = $false )
| ~ spl7_5
| ~ spl7_6
| ~ spl7_8 ),
inference(forward_demodulation,[],[f247,f208]) ).
thf(f254,plain,
( $false
| ~ spl7_5
| ~ spl7_6
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f253]) ).
thf(f255,plain,
( ~ spl7_5
| ~ spl7_6
| ~ spl7_8 ),
inference(avatar_contradiction_clause,[],[f254]) ).
thf(f266,plain,
( ( $true = $false )
| ~ spl7_5
| ~ spl7_7
| ~ spl7_9 ),
inference(forward_demodulation,[],[f248,f212]) ).
thf(f267,plain,
( $false
| ~ spl7_5
| ~ spl7_7
| ~ spl7_9 ),
inference(trivial_inequality_removal,[],[f266]) ).
thf(f268,plain,
( ~ spl7_5
| ~ spl7_7
| ~ spl7_9 ),
inference(avatar_contradiction_clause,[],[f267]) ).
cnf(s5,plain,
( spl7_4
| spl7_5 ),
inference(sat_conversion,[],[f204]) ).
cnf(s6,plain,
( spl7_4
| spl7_6
| spl7_7 ),
inference(sat_conversion,[],[f213]) ).
cnf(s7,plain,
( spl7_4
| spl7_8 ),
inference(sat_conversion,[],[f218]) ).
cnf(s8,plain,
( spl7_4
| spl7_9 ),
inference(sat_conversion,[],[f223]) ).
cnf(s9,plain,
~ spl7_4,
inference(sat_conversion,[],[f224]) ).
cnf(s12,plain,
( ~ spl7_5
| ~ spl7_6
| ~ spl7_8 ),
inference(sat_conversion,[],[f255]) ).
cnf(s13,plain,
( ~ spl7_5
| ~ spl7_7
| ~ spl7_9 ),
inference(sat_conversion,[],[f268]) ).
cnf(s15,plain,
spl7_9,
inference(rat,[],[s8,s9]) ).
cnf(s16,plain,
spl7_8,
inference(rat,[],[s7,s9]) ).
cnf(s17,plain,
( spl7_6
| spl7_7 ),
inference(rat,[],[s6,s9]) ).
cnf(s18,plain,
spl7_5,
inference(rat,[],[s5,s9]) ).
cnf(s19,plain,
~ spl7_7,
inference(rat,[],[s13,s15,s18]) ).
cnf(s20,plain,
~ spl7_6,
inference(rat,[],[s12,s16,s18]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s17,s19,s20]) ).
thf(f269,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU460^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n004.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:41:37 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.29 % (1302512)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (1302526)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (1302526)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
% 0.21/0.29 % (1302526)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=2208050778:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (1302526) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1302512-1302526"...
% 0.21/0.29 % (1302526)...printing done.
% 0.21/0.29 % (1302522)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3212475430:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (1302525)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1490740580:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (1302520)lrs+10_16_si=on:nwc=1.5:random_seed=3414859180:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (1302519)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3520118399:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (1302526)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (1302526)------------------------------
% 0.21/0.29 % (1302526)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (1302526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (1302526)CaDiCaL version: 2.1.3
% 0.21/0.29 % (1302526)Termination reason: Refutation
% 0.21/0.29 % (1302526)Time elapsed: 0.006 s
% 0.21/0.29 % (1302526)Peak memory usage: 13 MB
% 0.21/0.29 % (1302526)Instructions burned: 19 (million)
% 0.21/0.29 % (1302512)Success in time 0.034 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------