%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET926^20 : 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 : n005.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 0.23s 0.32s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 80 ( 50 unt; 0 typ; 0 def)
% Number of atoms : 599 ( 131 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 946 ( 21 ~; 53 |; 0 &; 810 @)
% ( 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,
vIFF: $o > $o > $o ).
thf(func_def_27,type,
vIMP: $o > $o > $o ).
thf(func_def_28,type,
vNOT: $o > $o ).
thf(func_def_29,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_30,type,
vOR: $o > $o > $o ).
thf(func_def_31,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_32,type,
vAND: $o > $o > $o ).
thf(func_def_33,type,
sK0: mworld > $i ).
thf(func_def_34,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db4:
!>[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,
( mor
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor_def) ).
thf(f6,axiom,
( mequiv
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
<=> ( X0 @ X2 ) ) ) ),
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(f33,plain,
( mequiv
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
<=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f34,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f39,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f2]) ).
thf(f40,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_di ),
inference(rectify,[],[f12]) ).
thf(f42,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f43,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(f44,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,[],[f43]) ).
thf(f49,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(f50,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set ) @ ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f51,plain,
( mor
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f52,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f73,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(f74,plain,
( $true
!= ( 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 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f85,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f88,plain,
( $true
!= ( 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 ) ) ) ) ) ) ),
inference(flattening,[],[f74]) ).
thf(f92,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set ) @ ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f94,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f95,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f96,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f99,plain,
( $true
!= ( 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 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f100,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,[],[f44]) ).
thf(f106,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f85]) ).
thf(f119,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f123,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] :
( ( Y3 @ Y4 )
= ( Y2 @ Y4 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set )
@ ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f92,f106,f96,f96,f94]) ).
thf(f126,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] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f99,f106,f96,f96,f119]) ).
thf(f127,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] :
( ( Y3 @ Y4 )
= ( Y2 @ Y4 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
~ ( Y2 @ Y3 )
@ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f100,f106,f96,f96,f94,f95]) ).
thf(f139,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( in @ Y0 @ Y1 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ mactual ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f123]) ).
thf(f140,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( in @ Y0 @ Y1 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ mactual ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X1: $i] :
( $true
= ( ( eiw_di @ X1 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( in @ X1 @ Y0 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ empty_set @ mactual ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f142,plain,
! [X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( in @ X1 @ Y0 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ empty_set @ mactual ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f143,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( in @ X1 @ Y0 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ empty_set @ mactual ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f142]) ).
thf(f144,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( eiw_di @ X2 @ mactual )
=> ( ( in @ X1 @ X2 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual ) ) ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f145,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( ( in @ X1 @ X2 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual ) ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual )
= ( in @ X1 @ X2 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) ) ),
inference(iff_proxy_clausification,[],[f145]) ).
thf(f147,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $false
= ( in @ X1 @ X2 @ mactual ) ) ),
inference(iff_proxy_clausification,[],[f146]) ).
thf(f173,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,[],[f126]) ).
thf(f174,plain,
( ( ^ [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 ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( $false
= ( ( eiw_di @ sK1 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ Y0 ) @ ( singleton @ sK1 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ Y0 ) @ empty_set @ mactual ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ Y0 ) @ ( singleton @ sK1 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ Y0 ) @ empty_set @ mactual ) ) ) ) ),
inference(imp_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( $true
= ( eiw_di @ sK1 @ mactual ) ),
inference(imp_proxy_clausification,[],[f175]) ).
thf(f178,plain,
( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ Y0 ) @ ( singleton @ sK1 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ Y0 ) @ empty_set @ mactual ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f176]) ).
thf(f179,plain,
( $false
= ( ( eiw_di @ sK2 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ sK2 ) @ ( singleton @ sK1 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ sK2 ) @ empty_set @ mactual ) ) ) ),
inference(beta-eta_normalization,[],[f178]) ).
thf(f180,plain,
( ( ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ sK2 ) @ ( singleton @ sK1 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ sK2 ) @ empty_set @ mactual ) )
= $false ),
inference(imp_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( $true
= ( eiw_di @ sK2 @ mactual ) ),
inference(imp_proxy_clausification,[],[f179]) ).
thf(f182,plain,
( ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ sK2 ) @ empty_set @ mactual )
= $false ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f183,plain,
( ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ sK2 ) @ ( singleton @ sK1 ) @ mactual )
= $false ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f228,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( ~ ( in @ Y0 @ Y1 @ mactual ) )
= ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ mactual ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f127]) ).
thf(f229,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( ~ ( in @ Y0 @ Y1 @ mactual ) )
= ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ mactual ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X1: $i] :
( $true
= ( ( eiw_di @ X1 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ~ ( in @ X1 @ Y0 @ mactual ) )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ ( singleton @ X1 ) @ mactual ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f229]) ).
thf(f231,plain,
! [X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ~ ( in @ X1 @ Y0 @ mactual ) )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ ( singleton @ X1 ) @ mactual ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ~ ( in @ X1 @ Y0 @ mactual ) )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ ( singleton @ X1 ) @ mactual ) ) )
@ X2 ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(pi_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( ( eiw_di @ X2 @ mactual )
=> ( ( ~ ( in @ X1 @ X2 @ mactual ) )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) ) ) ) ),
inference(beta-eta_normalization,[],[f232]) ).
thf(f234,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $true
= ( ( ~ ( in @ X1 @ X2 @ mactual ) )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f233]) ).
thf(f235,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ X2 @ mactual ) ) ) ),
inference(iff_proxy_clausification,[],[f234]) ).
thf(f236,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $false
= ( ~ ( in @ X1 @ X2 @ mactual ) ) ) ),
inference(iff_proxy_clausification,[],[f235]) ).
thf(f239,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $true
= ( in @ X1 @ X2 @ mactual ) ) ),
inference(not_proxy_clausification,[],[f236]) ).
thf(f361,plain,
( ( $true = $false )
| ( ( in @ sK1 @ sK2 @ mactual )
= $false )
| ( $false
= ( eiw_di @ sK2 @ mactual ) )
| ( $false
= ( eiw_di @ sK1 @ mactual ) ) ),
inference(constrained_superposition,[],[f182,f147]) ).
thf(f368,plain,
( ( $false
= ( eiw_di @ sK1 @ mactual ) )
| ( $false
= ( eiw_di @ sK2 @ mactual ) )
| ( ( in @ sK1 @ sK2 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[],[f361]) ).
thf(f377,plain,
( ( ( in @ sK1 @ sK2 @ mactual )
= $false )
| ( $true = $false )
| ( $false
= ( eiw_di @ sK2 @ mactual ) ) ),
inference(forward_demodulation,[],[f368,f177]) ).
thf(f378,plain,
( ( ( in @ sK1 @ sK2 @ mactual )
= $false )
| ( $false
= ( eiw_di @ sK2 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f377]) ).
thf(f391,plain,
( ( $true = $false )
| ( ( in @ sK1 @ sK2 @ mactual )
= $false ) ),
inference(forward_demodulation,[],[f378,f181]) ).
thf(f392,plain,
( ( in @ sK1 @ sK2 @ mactual )
= $false ),
inference(trivial_inequality_removal,[],[f391]) ).
thf(f412,plain,
( ( $false
= ( eiw_di @ sK1 @ mactual ) )
| ( $true
= ( in @ sK1 @ sK2 @ mactual ) )
| ( $true = $false )
| ( $false
= ( eiw_di @ sK2 @ mactual ) ) ),
inference(constrained_superposition,[],[f183,f239]) ).
thf(f422,plain,
( ( $false
= ( eiw_di @ sK1 @ mactual ) )
| ( $false
= ( eiw_di @ sK2 @ mactual ) )
| ( $true
= ( in @ sK1 @ sK2 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f412]) ).
thf(f427,plain,
( ( $false
= ( eiw_di @ sK2 @ mactual ) )
| ( $true = $false )
| ( $true
= ( in @ sK1 @ sK2 @ mactual ) ) ),
inference(forward_demodulation,[],[f422,f177]) ).
thf(f428,plain,
( ( $false
= ( eiw_di @ sK2 @ mactual ) )
| ( $true
= ( in @ sK1 @ sK2 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f427]) ).
thf(f431,plain,
( ( $true
= ( in @ sK1 @ sK2 @ mactual ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f428,f181]) ).
thf(f432,plain,
( $true
= ( in @ sK1 @ sK2 @ mactual ) ),
inference(trivial_inequality_removal,[],[f431]) ).
thf(f435,plain,
$true = $false,
inference(forward_demodulation,[],[f432,f392]) ).
thf(f436,plain,
$false,
inference(trivial_inequality_removal,[],[f435]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET926^20 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n005.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:41:01 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.25 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
% 0.23/0.32 % (1682163)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.32 % (1682171)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=1298314880: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)
% 0.23/0.32 % (1682174)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.32 % (1682174)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
% 0.23/0.32 % (1682168)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3649927190:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.32 % (1682169)lrs+10_16_si=on:nwc=1.5:random_seed=1146275293:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.32 % (1682170)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=40276801:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.32 % (1682173)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1451474920:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.32 % (1682172)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1400242467:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.32 % (1682174)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=2580912388:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.32 % (1682170)Instruction limit reached!
% 0.23/0.32 % (1682170)------------------------------
% 0.23/0.32 % (1682170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (1682170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (1682170)CaDiCaL version: 2.1.3
% 0.23/0.32 % (1682170)Termination reason: Instruction limit
% 0.23/0.32 % (1682170)Termination phase: Function definition elimination
% 0.23/0.32 % (1682170)Time elapsed: 0.003 s
% 0.23/0.32 % (1682170)Peak memory usage: 10 MB
% 0.23/0.32 % (1682170)Instructions burned: 7 (million)
% 0.23/0.32 % (1682169)Instruction limit reached!
% 0.23/0.32 % (1682169)------------------------------
% 0.23/0.32 % (1682169)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (1682169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (1682169)CaDiCaL version: 2.1.3
% 0.23/0.32 % (1682169)Termination reason: Instruction limit
% 0.23/0.32 % (1682169)Termination phase: Saturation
% 0.23/0.32 % (1682169)Time elapsed: 0.009 s
% 0.23/0.32 % (1682169)Peak memory usage: 11 MB
% 0.23/0.32 % (1682169)Instructions burned: 20 (million)
% 0.23/0.32 % (1682172)Instruction limit reached!
% 0.23/0.32 % (1682172)------------------------------
% 0.23/0.32 % (1682172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (1682172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (1682172)CaDiCaL version: 2.1.3
% 0.23/0.32 % (1682172)Termination reason: Instruction limit
% 0.23/0.32 % (1682172)Termination phase: Saturation
% 0.23/0.32 % (1682172)Time elapsed: 0.013 s
% 0.23/0.32 % (1682172)Peak memory usage: 12 MB
% 0.23/0.32 % (1682172)Instructions burned: 25 (million)
% 0.23/0.32 % (1682168) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1682163-1682168"...
% 0.23/0.32 % (1682168)...printing done.
% 0.23/0.32 % (1682168)Refutation found. Thanks to Tanya!
% 0.23/0.32 % SZS status Theorem for theBenchmark
% 0.23/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.32 % (1682168)------------------------------
% 0.23/0.32 % (1682168)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (1682168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (1682168)CaDiCaL version: 2.1.3
% 0.23/0.32 % (1682168)Termination reason: Refutation
% 0.23/0.32 % (1682168)Time elapsed: 0.022 s
% 0.23/0.32 % (1682168)Peak memory usage: 12 MB
% 0.23/0.32 % (1682168)Instructions burned: 44 (million)
% 0.23/0.32 % (1682163)Success in time 0.063 s
% 0.23/0.32 % Vampire exiting
%------------------------------------------------------------------------------