%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET926^12 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 08:23:30 AM UTC 2026
% Result : Theorem 0.25s 0.38s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 14
% Syntax : Number of formulae : 111 ( 46 unt; 0 typ; 6 def)
% Number of atoms : 781 ( 156 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 1202 ( 68 ~; 118 |; 0 &; 937 @)
% ( 7 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 74 ( 74 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 42 usr; 13 con; 0-4 aty)
% ( 29 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 198 ( 0 sgn 30 !; 0 ?; 198 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
mrel: mworld > mworld > $o ).
thf(func_def_1,type,
mactual: mworld ).
thf(func_def_2,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_4,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_5,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
eiw_di: $i > mworld > $o ).
thf(func_def_12,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_15,type,
qmltpeq: $i > $i > mworld > $o ).
thf(func_def_16,type,
in: $i > $i > mworld > $o ).
thf(func_def_17,type,
empty: $i > mworld > $o ).
thf(func_def_18,type,
singleton: $i > $i ).
thf(func_def_19,type,
set_difference: $i > $i > $i ).
thf(func_def_20,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_25,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
vAND: $o > $o > $o ).
thf(func_def_28,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_29,type,
vIMP: $o > $o > $o ).
thf(func_def_30,type,
vIFF: $o > $o > $o ).
thf(func_def_31,type,
vNOT: $o > $o ).
thf(func_def_32,type,
vOR: $o > $o > $o ).
thf(func_def_33,type,
sK0: mworld > $i ).
thf(func_def_34,type,
sF1: $o ).
thf(func_def_35,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
db3:
!>[X0: $tType] : X0 ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f2,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_def) ).
thf(f4,axiom,
( mor
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor_def) ).
thf(f6,axiom,
( mequiv
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv_def) ).
thf(f11,axiom,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di_def) ).
thf(f24,axiom,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) @ ( mnot @ ( in @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).
thf(f25,axiom,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ empty_set ) @ ( in @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).
thf(f28,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(f29,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
thf(f32,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f37,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f38,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f39,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) ) ) ) ),
inference(rectify,[],[f29]) ).
thf(f40,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ empty_set ) @ ( in @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f25]) ).
thf(f42,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set ) @ ( in @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f41]) ).
thf(f53,plain,
( mequiv
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f54,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f57,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) @ ( mnot @ ( in @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f58,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f71,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f2]) ).
thf(f72,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f73,plain,
( mor
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f74,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f85,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f40]) ).
thf(f94,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f96,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f98,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f85]) ).
thf(f105,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f107,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set ) @ ( in @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f42]) ).
thf(f110,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f112,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f114,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f123,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f98,f114,f94,f94,f105]) ).
thf(f128,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
= ( Y3 @ Y4 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set )
@ ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f107,f114,f94,f94,f112]) ).
thf(f131,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
= ( Y3 @ Y4 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
~ ( Y2 @ Y3 )
@ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f110,f114,f94,f94,f112,f96]) ).
thf(f134,definition,
( sF1
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f135,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) )
= sF1 ),
inference(reorient_equations,[],[f134]) ).
thf(f136,plain,
sF1 != $true,
inference(definition_folding,[],[f123,f135]) ).
thf(f154,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ mactual )
= ( ~ ( in @ Y0 @ Y1 @ mactual ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f131]) ).
thf(f155,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ mactual )
= ( ~ ( in @ Y0 @ Y1 @ mactual ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ Y0 @ mactual ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ Y0 @ mactual ) ) ) ) )
= $true )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ Y0 @ mactual ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( ( eiw_di @ X2 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ X2 @ mactual ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ X2 @ mactual ) ) )
= $true )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X1: $i] :
( ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ X2 @ mactual ) ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) ) ),
inference(iff_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual )
= $true )
| ( $false
= ( ~ ( in @ X1 @ X2 @ mactual ) ) ) ),
inference(iff_proxy_clausification,[],[f161]) ).
thf(f165,plain,
! [X2: $i,X1: $i] :
( ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual )
= $true )
| ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( ( in @ X1 @ X2 @ mactual )
= $true )
| ( $false
= ( eiw_di @ X2 @ mactual ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f191,plain,
( ( sF1 = $true )
| ( $false
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f135]) ).
thf(f192,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ mactual ) ) ) ) ) ) )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f193,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ mactual ) ) ) ) )
@ sK3 ) )
| ( sF1 = $true ) ),
inference(sigma_proxy_clausification,[],[f192]) ).
thf(f194,plain,
( ( sF1 = $true )
| ( $false
= ( ( eiw_di @ sK3 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ Y0 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ Y0 ) @ ( singleton @ sK3 ) @ mactual ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f193]) ).
thf(f195,plain,
( ( sF1 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ Y0 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ Y0 ) @ ( singleton @ sK3 ) @ mactual ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f194]) ).
thf(f196,plain,
( ( sF1 = $true )
| ( ( eiw_di @ sK3 @ mactual )
= $true ) ),
inference(imp_proxy_clausification,[],[f194]) ).
thf(f197,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ Y0 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ Y0 ) @ ( singleton @ sK3 ) @ mactual ) ) )
@ sK4 ) )
| ( sF1 = $true ) ),
inference(sigma_proxy_clausification,[],[f195]) ).
thf(f198,plain,
( ( sF1 = $true )
| ( $false
= ( ( eiw_di @ sK4 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ ( singleton @ sK3 ) @ mactual ) ) ) ) ),
inference(beta-eta_normalization,[],[f197]) ).
thf(f199,plain,
( ( ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ ( singleton @ sK3 ) @ mactual ) )
= $false )
| ( sF1 = $true ) ),
inference(imp_proxy_clausification,[],[f198]) ).
thf(f200,plain,
( ( sF1 = $true )
| ( $true
= ( eiw_di @ sK4 @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f198]) ).
thf(f201,plain,
( ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ ( singleton @ sK3 ) @ mactual )
= $false )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f199]) ).
thf(f202,plain,
( ( sF1 = $true )
| ( $false
= ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ empty_set @ mactual ) ) ),
inference(or_proxy_clausification,[],[f199]) ).
thf(f250,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ mactual )
= ( in @ Y0 @ Y1 @ mactual ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f128]) ).
thf(f251,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ mactual )
= ( in @ Y0 @ Y1 @ mactual ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f250]) ).
thf(f252,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ empty_set @ mactual )
= ( in @ X1 @ Y0 @ mactual ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f251]) ).
thf(f253,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ empty_set @ mactual )
= ( in @ X1 @ Y0 @ mactual ) ) ) )
= $true )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f252]) ).
thf(f254,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ empty_set @ mactual )
= ( in @ X1 @ Y0 @ mactual ) ) )
@ X2 )
= $true )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(pi_proxy_clausification,[],[f253]) ).
thf(f255,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( ( eiw_di @ X2 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual )
= ( in @ X1 @ X2 @ mactual ) ) ) ) ),
inference(beta-eta_normalization,[],[f254]) ).
thf(f256,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual )
= ( in @ X1 @ X2 @ mactual ) )
= $true )
| ( $false
= ( eiw_di @ X2 @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f255]) ).
thf(f257,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( ( in @ X1 @ X2 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) ) ),
inference(iff_proxy_clausification,[],[f256]) ).
thf(f259,plain,
! [X2: $i,X1: $i] :
( ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual )
= $true )
| ( $false
= ( in @ X1 @ X2 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(iff_proxy_clausification,[],[f257]) ).
thf(f289,definition,
( spl6_1
<=> ( sF1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f293,definition,
( spl6_2
<=> ( ( eiw_di @ sK3 @ mactual )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f295,plain,
( ( ( eiw_di @ sK3 @ mactual )
= $true )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f293]) ).
thf(f296,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f196,f293,f289]) ).
thf(f298,definition,
( spl6_3
<=> ( $true
= ( eiw_di @ sK4 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f300,plain,
( ( $true
= ( eiw_di @ sK4 @ mactual ) )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f298]) ).
thf(f301,plain,
( spl6_3
| spl6_1 ),
inference(avatar_split_clause,[],[f200,f289,f298]) ).
thf(f303,definition,
( spl6_4
<=> ( $false
= ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ empty_set @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f305,plain,
( ( $false
= ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ empty_set @ mactual ) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f303]) ).
thf(f306,plain,
( spl6_1
| spl6_4 ),
inference(avatar_split_clause,[],[f202,f303,f289]) ).
thf(f308,definition,
( spl6_5
<=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ ( singleton @ sK3 ) @ mactual )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
thf(f310,plain,
( ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ ( singleton @ sK3 ) @ mactual )
= $false )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f308]) ).
thf(f311,plain,
( spl6_5
| spl6_1 ),
inference(avatar_split_clause,[],[f201,f289,f308]) ).
thf(f320,plain,
~ spl6_1,
inference(avatar_split_clause,[],[f136,f289]) ).
thf(f369,plain,
( ( $false
= ( eiw_di @ sK4 @ mactual ) )
| ( $false
= ( eiw_di @ sK3 @ mactual ) )
| ( $false = $true )
| ( $false
= ( in @ sK3 @ sK4 @ mactual ) )
| ~ spl6_4 ),
inference(constrained_superposition,[],[f259,f305]) ).
thf(f383,plain,
( ( $false
= ( eiw_di @ sK3 @ mactual ) )
| ( $false
= ( eiw_di @ sK4 @ mactual ) )
| ( $false
= ( in @ sK3 @ sK4 @ mactual ) )
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f369]) ).
thf(f395,plain,
( ( $false = $true )
| ( $false
= ( eiw_di @ sK4 @ mactual ) )
| ( $false
= ( in @ sK3 @ sK4 @ mactual ) )
| ~ spl6_2
| ~ spl6_4 ),
inference(forward_demodulation,[],[f383,f295]) ).
thf(f396,plain,
( ( $false
= ( in @ sK3 @ sK4 @ mactual ) )
| ( $false
= ( eiw_di @ sK4 @ mactual ) )
| ~ spl6_2
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f395]) ).
thf(f400,plain,
( ( $false
= ( in @ sK3 @ sK4 @ mactual ) )
| ( $false = $true )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4 ),
inference(forward_demodulation,[],[f396,f300]) ).
thf(f401,plain,
( ( $false
= ( in @ sK3 @ sK4 @ mactual ) )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f400]) ).
thf(f418,plain,
( ( $false
= ( eiw_di @ sK3 @ mactual ) )
| ( $true
= ( in @ sK3 @ sK4 @ mactual ) )
| ( $false = $true )
| ( $false
= ( eiw_di @ sK4 @ mactual ) )
| ~ spl6_5 ),
inference(constrained_superposition,[],[f165,f310]) ).
thf(f432,plain,
( ( $false
= ( eiw_di @ sK4 @ mactual ) )
| ( $true
= ( in @ sK3 @ sK4 @ mactual ) )
| ( $false
= ( eiw_di @ sK3 @ mactual ) )
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f418]) ).
thf(f438,plain,
( ( $false
= ( eiw_di @ sK3 @ mactual ) )
| ( $true
= ( in @ sK3 @ sK4 @ mactual ) )
| ( $false = $true )
| ~ spl6_3
| ~ spl6_5 ),
inference(forward_demodulation,[],[f432,f300]) ).
thf(f439,plain,
( ( $false
= ( eiw_di @ sK3 @ mactual ) )
| ( $true
= ( in @ sK3 @ sK4 @ mactual ) )
| ~ spl6_3
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f438]) ).
thf(f442,plain,
( ( $false = $true )
| ( $true
= ( in @ sK3 @ sK4 @ mactual ) )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_5 ),
inference(forward_demodulation,[],[f439,f295]) ).
thf(f443,plain,
( ( $true
= ( in @ sK3 @ sK4 @ mactual ) )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f442]) ).
thf(f447,plain,
( ( $false = $true )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| ~ spl6_5 ),
inference(forward_demodulation,[],[f443,f401]) ).
thf(f448,plain,
( $false
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f447]) ).
thf(f449,plain,
( ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| ~ spl6_5 ),
inference(avatar_contradiction_clause,[],[f448]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f296]) ).
cnf(s2,plain,
( spl6_1
| spl6_3 ),
inference(sat_conversion,[],[f301]) ).
cnf(s3,plain,
( spl6_1
| spl6_4 ),
inference(sat_conversion,[],[f306]) ).
cnf(s4,plain,
( spl6_1
| spl6_5 ),
inference(sat_conversion,[],[f311]) ).
cnf(s6,plain,
~ spl6_1,
inference(sat_conversion,[],[f320]) ).
cnf(s10,plain,
( ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| ~ spl6_5 ),
inference(sat_conversion,[],[f449]) ).
cnf(s11,plain,
spl6_5,
inference(rat,[],[s4,s6]) ).
cnf(s12,plain,
spl6_4,
inference(rat,[],[s3,s6]) ).
cnf(s13,plain,
spl6_3,
inference(rat,[],[s2,s6]) ).
cnf(s14,plain,
~ spl6_2,
inference(rat,[],[s10,s11,s12,s13]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s1,s14,s6]) ).
thf(f450,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET926^12 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.25 % Computer : n007.cluster.edu
% 0.12/0.25 % Model : x86_64 x86_64
% 0.12/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.25 % Memory : 8046.5625MB
% 0.12/0.25 % OS : Linux 6.8.0-71-generic
% 0.12/0.25 % CPULimit : 300
% 0.12/0.25 % WCLimit : 300
% 0.12/0.25 % DateTime : Tue Sep 29 13:39:11 UTC 2026
% 0.12/0.26 % CPUTime :
% 0.12/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.29 Running higher-order theorem proving
% 0.25/0.31 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
% 0.25/0.38 % (3373992)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.38 % (3374010)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2286173339:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.25/0.38 % (3374012)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.25/0.38 % (3374012)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
% 0.25/0.38 % (3374007)lrs+10_16_si=on:nwc=1.5:random_seed=2327978955:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.25/0.38 % (3374010)Instruction limit reached!
% 0.25/0.38 % (3374010)------------------------------
% 0.25/0.38 % (3374010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.38 % (3374010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.38 % (3374010)CaDiCaL version: 2.1.3
% 0.25/0.38 % (3374010)Termination reason: Instruction limit
% 0.25/0.38 % (3374010)Termination phase: Saturation
% 0.25/0.38 % (3374010)Time elapsed: 0.007 s
% 0.25/0.38 % (3374010)Peak memory usage: 12 MB
% 0.25/0.38 % (3374010)Instructions burned: 24 (million)
% 0.25/0.38 % (3374008)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=92698361:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.25/0.38 % (3374009)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=2486336398: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)
% 0.25/0.38 % (3374011)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2058382469:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.25/0.38 % (3374012)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=1500104175:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.25/0.38 % (3374008)Instruction limit reached!
% 0.25/0.38 % (3374008)------------------------------
% 0.25/0.38 % (3374008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.38 % (3374008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.38 % (3374008)CaDiCaL version: 2.1.3
% 0.25/0.38 % (3374008)Termination reason: Instruction limit
% 0.25/0.38 % (3374008)Termination phase: Property scanning
% 0.25/0.38 % (3374008)Time elapsed: 0.002 s
% 0.25/0.38 % (3374008)Peak memory usage: 10 MB
% 0.25/0.38 % (3374008)Instructions burned: 4 (million)
% 0.25/0.38 % (3374007)Instruction limit reached!
% 0.25/0.38 % (3374007)------------------------------
% 0.25/0.38 % (3374007)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.38 % (3374007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.38 % (3374007)CaDiCaL version: 2.1.3
% 0.25/0.38 % (3374007)Termination reason: Instruction limit
% 0.25/0.38 % (3374007)Termination phase: Saturation
% 0.25/0.38 % (3374007)Time elapsed: 0.009 s
% 0.25/0.38 % (3374007)Peak memory usage: 12 MB
% 0.25/0.38 % (3374007)Instructions burned: 19 (million)
% 0.25/0.38 % (3374025)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1223345963:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.25/0.38 % (3374025)Instruction limit reached!
% 0.25/0.38 % (3374025)------------------------------
% 0.25/0.38 % (3374025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.38 % (3374025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.38 % (3374025)CaDiCaL version: 2.1.3
% 0.25/0.38 % (3374025)Termination reason: Instruction limit
% 0.25/0.38 % (3374025)Termination phase: Preprocessing 3
% 0.25/0.38 % (3374025)Time elapsed: 0.001 s
% 0.25/0.38 % (3374025)Peak memory usage: 10 MB
% 0.25/0.38 % (3374025)Instructions burned: 4 (million)
% 0.25/0.38 % (3374006)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2826277162:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.25/0.38 % (3374012) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3373992-3374012"...
% 0.25/0.38 % (3374029)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=865972002:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.25/0.38 % (3374037)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3031253605:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.25/0.38 % (3374012)...printing done.
% 0.25/0.38 % (3374033)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.25/0.38 % (3374012)Refutation found. Thanks to Tanya!
% 0.25/0.38 % SZS status Theorem for theBenchmark
% 0.25/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.39 % (3374012)------------------------------
% 0.25/0.39 % (3374012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.39 % (3374012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.39 % (3374012)CaDiCaL version: 2.1.3
% 0.25/0.39 % (3374012)Termination reason: Refutation
% 0.25/0.39 % (3374012)Time elapsed: 0.022 s
% 0.25/0.39 % (3374012)Peak memory usage: 13 MB
% 0.25/0.39 % (3374012)Instructions burned: 42 (million)
% 0.25/0.39 % (3373992)Success in time 0.071 s
% 0.25/0.39 % Vampire exiting
%------------------------------------------------------------------------------