%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET926^11 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 0.06s 0.19s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 80 ( 50 unt; 0 typ; 0 def)
% Number of atoms : 597 ( 131 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 944 ( 21 ~; 53 |; 0 &; 808 @)
% ( 2 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 36 usr; 7 con; 0-4 aty)
% ( 23 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 162 ( 132 ^; 30 !; 0 ?; 162 :)
% 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
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,
vIMP: $o > $o > $o ).
thf(func_def_29,type,
vPI:
!>[X0: $tType] : ( ( X0 > $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,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db3:
!>[X0: $tType] : X0 ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(f2,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot_def) ).
thf(f4,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor_def) ).
thf(f6,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) )
= mequiv ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv_def) ).
thf(f12,axiom,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_di ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_di_def) ).
thf(f25,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/sandbox/benchmark/theBenchmark.p',l34_zfmisc_1) ).
thf(f26,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/sandbox/benchmark/theBenchmark.p',l36_zfmisc_1) ).
thf(f29,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/sandbox/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(f30,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)],[f29]) ).
thf(f37,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,[],[f30]) ).
thf(f38,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,[],[f37]) ).
thf(f51,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f52,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) )
= mequiv ),
inference(rectify,[],[f6]) ).
thf(f53,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f52]) ).
thf(f60,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f2]) ).
thf(f61,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f60]) ).
thf(f66,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ empty_set ) @ ( in @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f26]) ).
thf(f67,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,[],[f66]) ).
thf(f68,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_di ),
inference(rectify,[],[f12]) ).
thf(f69,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f70,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f71,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f70]) ).
thf(f74,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,[],[f25]) ).
thf(f75,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f74]) ).
thf(f88,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,[],[f38]) ).
thf(f98,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f101,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f104,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f110,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f75]) ).
thf(f111,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f115,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,[],[f67]) ).
thf(f117,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,[],[f88]) ).
thf(f119,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f132,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 ) @ ( singleton @ Y0 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
~ ( Y2 @ Y3 )
@ ( in @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f110,f101,f111,f111,f104,f98]) ).
thf(f136,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 )
@ ( in @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f115,f101,f111,f111,f104]) ).
thf(f137,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] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f117,f101,f111,f111,f119]) ).
thf(f177,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 )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ mactual ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f137]) ).
thf(f178,plain,
( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ mactual ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( ( ( eiw_di @ sK2 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ Y0 ) @ ( singleton @ sK2 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ Y0 ) @ empty_set @ mactual ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f178]) ).
thf(f180,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ Y0 ) @ ( singleton @ sK2 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ Y0 ) @ empty_set @ mactual ) ) ) ) ),
inference(imp_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( eiw_di @ sK2 @ mactual )
= $true ),
inference(imp_proxy_clausification,[],[f179]) ).
thf(f182,plain,
( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ Y0 ) @ ( singleton @ sK2 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ Y0 ) @ empty_set @ mactual ) ) )
@ sK3 )
= $false ),
inference(sigma_proxy_clausification,[],[f180]) ).
thf(f183,plain,
( $false
= ( ( eiw_di @ sK3 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ sK3 ) @ ( singleton @ sK2 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ sK3 ) @ empty_set @ mactual ) ) ) ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f184,plain,
( ( ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ sK3 ) @ ( singleton @ sK2 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ sK3 ) @ empty_set @ mactual ) )
= $false ),
inference(imp_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( ( eiw_di @ sK3 @ mactual )
= $true ),
inference(imp_proxy_clausification,[],[f183]) ).
thf(f186,plain,
( $false
= ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ sK3 ) @ empty_set @ mactual ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f187,plain,
( $false
= ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ sK3 ) @ ( singleton @ sK2 ) @ mactual ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f200,plain,
( ( !! @ $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 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f132]) ).
thf(f201,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,[],[f200]) ).
thf(f202,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,[],[f201]) ).
thf(f203,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ Y0 @ mactual ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X2: $i,X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ Y0 @ mactual ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X2: $i,X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( ( eiw_di @ X2 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ X2 @ mactual ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f204]) ).
thf(f206,plain,
! [X2: $i,X1: $i] :
( ( ( eiw_di @ X2 @ mactual )
= $false )
| ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ X2 @ mactual ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( ( ( eiw_di @ X2 @ mactual )
= $false )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ X2 @ mactual ) ) )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(iff_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X2: $i,X1: $i] :
( ( ( eiw_di @ X2 @ mactual )
= $false )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual )
= $true )
| ( ( eiw_di @ X1 @ mactual )
= $false )
| ( $false
= ( ~ ( in @ X1 @ X2 @ mactual ) ) ) ),
inference(iff_proxy_clausification,[],[f207]) ).
thf(f211,plain,
! [X2: $i,X1: $i] :
( ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual )
= $true )
| ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( eiw_di @ X2 @ mactual )
= $false )
| ( ( in @ X1 @ X2 @ mactual )
= $true ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f266,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,[],[f136]) ).
thf(f267,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,[],[f266]) ).
thf(f268,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,[],[f267]) ).
thf(f269,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ empty_set @ mactual )
= ( in @ X1 @ Y0 @ mactual ) ) ) )
= $true )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(imp_proxy_clausification,[],[f268]) ).
thf(f270,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ empty_set @ mactual )
= ( in @ X1 @ Y0 @ mactual ) ) )
@ X2 ) )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(pi_proxy_clausification,[],[f269]) ).
thf(f271,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( eiw_di @ X2 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual )
= ( in @ X1 @ X2 @ mactual ) ) ) )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(beta-eta_normalization,[],[f270]) ).
thf(f272,plain,
! [X2: $i,X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( eiw_di @ X2 @ mactual )
= $false )
| ( ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual )
= ( in @ X1 @ X2 @ mactual ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f271]) ).
thf(f273,plain,
! [X2: $i,X1: $i] :
( ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual )
= ( in @ X1 @ X2 @ mactual ) )
| ( ( eiw_di @ X2 @ mactual )
= $false )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(iff_proxy_clausification,[],[f272]) ).
thf(f274,plain,
! [X2: $i,X1: $i] :
( ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual )
= $true )
| ( ( in @ X1 @ X2 @ mactual )
= $false )
| ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( eiw_di @ X2 @ mactual )
= $false ) ),
inference(iff_proxy_clausification,[],[f273]) ).
thf(f362,plain,
( ( $false = $true )
| ( $false
= ( in @ sK2 @ sK3 @ mactual ) )
| ( ( eiw_di @ sK2 @ mactual )
= $false )
| ( ( eiw_di @ sK3 @ mactual )
= $false ) ),
inference(constrained_superposition,[],[f186,f274]) ).
thf(f369,plain,
( ( ( eiw_di @ sK3 @ mactual )
= $false )
| ( $false
= ( in @ sK2 @ sK3 @ mactual ) )
| ( ( eiw_di @ sK2 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[],[f362]) ).
thf(f374,plain,
( ( ( eiw_di @ sK2 @ mactual )
= $false )
| ( $false
= ( in @ sK2 @ sK3 @ mactual ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f369,f185]) ).
thf(f375,plain,
( ( $false
= ( in @ sK2 @ sK3 @ mactual ) )
| ( ( eiw_di @ sK2 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[],[f374]) ).
thf(f378,plain,
( ( $false
= ( in @ sK2 @ sK3 @ mactual ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f375,f181]) ).
thf(f379,plain,
( $false
= ( in @ sK2 @ sK3 @ mactual ) ),
inference(trivial_inequality_removal,[],[f378]) ).
thf(f394,plain,
( ( ( eiw_di @ sK3 @ mactual )
= $false )
| ( $false = $true )
| ( ( eiw_di @ sK2 @ mactual )
= $false )
| ( $true
= ( in @ sK2 @ sK3 @ mactual ) ) ),
inference(constrained_superposition,[],[f211,f187]) ).
thf(f405,plain,
( ( ( eiw_di @ sK2 @ mactual )
= $false )
| ( ( eiw_di @ sK3 @ mactual )
= $false )
| ( $true
= ( in @ sK2 @ sK3 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f394]) ).
thf(f414,plain,
( ( $false = $true )
| ( ( eiw_di @ sK3 @ mactual )
= $false )
| ( $true
= ( in @ sK2 @ sK3 @ mactual ) ) ),
inference(forward_demodulation,[],[f405,f181]) ).
thf(f415,plain,
( ( $true
= ( in @ sK2 @ sK3 @ mactual ) )
| ( ( eiw_di @ sK3 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[],[f414]) ).
thf(f418,plain,
( ( ( eiw_di @ sK3 @ mactual )
= $false )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f415,f379]) ).
thf(f419,plain,
( ( eiw_di @ sK3 @ mactual )
= $false ),
inference(trivial_inequality_removal,[],[f418]) ).
thf(f422,plain,
$false = $true,
inference(forward_demodulation,[],[f419,f185]) ).
thf(f423,plain,
$false,
inference(trivial_inequality_removal,[],[f422]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET926^11 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 13:41:04 UTC 2026
% 0.06/0.11 % CPUTime :
% 0.06/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.13 Running higher-order theorem proving
% 0.06/0.14 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
% 0.06/0.19 % (118717)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.06/0.19 % (118722)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2413699990:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.06/0.19 % (118724)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3590235822:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.06/0.19 % (118723)lrs+10_16_si=on:nwc=1.5:random_seed=2881273530:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.06/0.19 % (118724)Instruction limit reached!
% 0.06/0.19 % (118724)------------------------------
% 0.06/0.19 % (118724)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.19 % (118724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.19 % (118724)CaDiCaL version: 2.1.3
% 0.06/0.19 % (118724)Termination reason: Instruction limit
% 0.06/0.19 % (118724)Termination phase: Property scanning
% 0.06/0.19 % (118724)Time elapsed: 0.001 s
% 0.06/0.19 % (118724)Peak memory usage: 9 MB
% 0.06/0.19 % (118724)Instructions burned: 4 (million)
% 0.06/0.19 % (118723)Instruction limit reached!
% 0.06/0.19 % (118723)------------------------------
% 0.06/0.19 % (118723)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.19 % (118723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.19 % (118723)CaDiCaL version: 2.1.3
% 0.06/0.19 % (118723)Termination reason: Instruction limit
% 0.06/0.19 % (118723)Termination phase: Saturation
% 0.06/0.19 % (118723)Time elapsed: 0.005 s
% 0.06/0.19 % (118723)Peak memory usage: 11 MB
% 0.06/0.19 % (118723)Instructions burned: 21 (million)
% 0.06/0.19 % (118725)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=684267167: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)
% 0.06/0.19 % (118722) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-118717-118722"...
% 0.06/0.19 % (118728)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.06/0.19 % (118728)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
% 0.06/0.19 % (118732)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4116777723:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.06/0.19 % (118722)...printing done.
% 0.06/0.19 % (118732)Instruction limit reached!
% 0.06/0.19 % (118732)------------------------------
% 0.06/0.19 % (118732)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.19 % (118732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.19 % (118732)CaDiCaL version: 2.1.3
% 0.06/0.19 % (118732)Termination reason: Instruction limit
% 0.06/0.19 % (118732)Termination phase: Property scanning
% 0.06/0.19 % (118722)Refutation found. Thanks to Tanya!
% 0.06/0.19 % SZS status Theorem for theBenchmark
% 0.06/0.19 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.19 % (118722)------------------------------
% 0.06/0.19 % (118722)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.19 % (118722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.19 % (118722)CaDiCaL version: 2.1.3
% 0.06/0.19 % (118722)Termination reason: Refutation
% 0.06/0.19 % (118722)Time elapsed: 0.012 s
% 0.06/0.19 % (118722)Peak memory usage: 12 MB
% 0.06/0.19 % (118722)Instructions burned: 44 (million)
% 0.06/0.19 % (118717)Success in time 0.043 s
% 0.06/0.19 % Vampire exiting
%------------------------------------------------------------------------------