%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET926^8 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 08:23:51 AM UTC 2026
% Result : Theorem 0.39s 0.28s
% Output : Refutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of formulae : 98 ( 54 unt; 0 typ; 4 def)
% Number of atoms : 615 ( 125 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 973 ( 42 ~; 67 |; 0 &; 798 @)
% ( 6 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 40 usr; 11 con; 0-4 aty)
% ( 23 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 162 ( 0 sgn 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_22,type,
vNOT: $o > $o ).
thf(func_def_23,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vAND: $o > $o > $o ).
thf(func_def_25,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
vOR: $o > $o > $o ).
thf(func_def_27,type,
vIMP: $o > $o > $o ).
thf(func_def_28,type,
vIFF: $o > $o > $o ).
thf(func_def_29,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_30,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
sK0: mworld > $i ).
thf(func_def_34,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db4:
!>[X0: $tType] : X0 ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f2,axiom,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
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(f30,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f31,plain,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f32,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f31]) ).
thf(f35,plain,
( mor
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f36,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f35]) ).
thf(f39,plain,
( mequiv
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f40,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f49,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f50,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f75,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(f76,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,[],[f75]) ).
thf(f77,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(f78,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,[],[f77]) ).
thf(f83,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(f84,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,[],[f83]) ).
thf(f85,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,[],[f84]) ).
thf(f87,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f88,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f90,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f92,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f97,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
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,[],[f76]) ).
thf(f111,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,[],[f78]) ).
thf(f114,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,[],[f85]) ).
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 ) @ ( singleton @ Y0 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
~ ( Y2 @ Y3 )
@ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f110,f87,f97,f97,f92,f88]) ).
thf(f129,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,[],[f111,f87,f97,f97,f92]) ).
thf(f132,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 )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f114,f87,f97,f97,f90]) ).
thf(f133,plain,
( $true
!= ( !! @ $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 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f132]) ).
thf(f134,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 ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f133]) ).
thf(f135,plain,
( $false
= ( ( eiw_di @ sK1 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ Y0 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ Y0 ) @ ( singleton @ sK1 ) @ mactual ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f136,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ Y0 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ Y0 ) @ ( singleton @ sK1 ) @ mactual ) ) ) ) ),
inference(imp_proxy_clausification,[],[f135]) ).
thf(f137,plain,
( $true
= ( eiw_di @ sK1 @ mactual ) ),
inference(imp_proxy_clausification,[],[f135]) ).
thf(f138,plain,
( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ Y0 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ Y0 ) @ ( singleton @ sK1 ) @ mactual ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f136]) ).
thf(f139,plain,
( $false
= ( ( eiw_di @ sK2 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ sK2 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ sK2 ) @ ( singleton @ sK1 ) @ mactual ) ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
( $false
= ( ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ sK2 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ sK2 ) @ ( singleton @ sK1 ) @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f139]) ).
thf(f141,plain,
( $true
= ( eiw_di @ sK2 @ mactual ) ),
inference(imp_proxy_clausification,[],[f139]) ).
thf(f142,plain,
( $false
= ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ sK2 ) @ ( singleton @ sK1 ) @ mactual ) ),
inference(or_proxy_clausification,[],[f140]) ).
thf(f143,plain,
( $false
= ( qmltpeq @ ( set_difference @ ( singleton @ sK1 ) @ sK2 ) @ empty_set @ mactual ) ),
inference(or_proxy_clausification,[],[f140]) ).
thf(f155,plain,
( $true
= ( !! @ $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 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f129]) ).
thf(f156,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,[],[f155]) ).
thf(f157,plain,
! [X1: $i] :
( $true
= ( ( eiw_di @ X1 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ empty_set @ mactual )
= ( in @ X1 @ Y0 @ mactual ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ empty_set @ mactual )
= ( in @ X1 @ Y0 @ mactual ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ empty_set @ mactual )
= ( in @ X1 @ Y0 @ mactual ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f158]) ).
thf(f160,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,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $true
= ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual )
= ( in @ X1 @ X2 @ mactual ) ) ) ),
inference(imp_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual )
= ( in @ X1 @ X2 @ mactual ) ) ),
inference(iff_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual ) )
| ( $false
= ( in @ X1 @ X2 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(iff_proxy_clausification,[],[f162]) ).
thf(f165,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,[],[f128]) ).
thf(f166,plain,
! [X1: $i] :
( $true
= ( ^ [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 ) ),
inference(pi_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( $true
= ( ( eiw_di @ X1 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ Y0 @ mactual ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ Y0 @ mactual ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f167]) ).
thf(f169,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,[],[f168]) ).
thf(f170,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,[],[f169]) ).
thf(f171,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $true
= ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ X2 @ mactual ) ) ) ) ),
inference(imp_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ X2 @ mactual ) ) ) ),
inference(iff_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) )
| ( $false
= ( ~ ( in @ X1 @ X2 @ mactual ) ) ) ),
inference(iff_proxy_clausification,[],[f172]) ).
thf(f176,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X2 @ mactual ) )
| ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f395,plain,
( ( $true = $false )
| ( $false
= ( in @ sK1 @ sK2 @ mactual ) )
| ( $false
= ( eiw_di @ sK2 @ mactual ) )
| ( $false
= ( eiw_di @ sK1 @ mactual ) ) ),
inference(constrained_superposition,[],[f163,f143]) ).
thf(f412,plain,
( ( $false
= ( in @ sK1 @ sK2 @ mactual ) )
| ( $false
= ( eiw_di @ sK2 @ mactual ) )
| ( $false
= ( eiw_di @ sK1 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f395]) ).
thf(f426,definition,
( spl5_9
<=> ( $false
= ( eiw_di @ sK1 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
thf(f428,plain,
( ( $false
= ( eiw_di @ sK1 @ mactual ) )
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f426]) ).
thf(f430,definition,
( spl5_10
<=> ( $false
= ( eiw_di @ sK2 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
thf(f432,plain,
( ( $false
= ( eiw_di @ sK2 @ mactual ) )
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f430]) ).
thf(f434,definition,
( spl5_11
<=> ( $false
= ( in @ sK1 @ sK2 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[spl5_11])],[avatar_definition]) ).
thf(f436,plain,
( ( $false
= ( in @ sK1 @ sK2 @ mactual ) )
| ~ spl5_11 ),
inference(avatar_component_clause,[],[f434]) ).
thf(f440,plain,
( spl5_9
| spl5_10
| spl5_11 ),
inference(avatar_split_clause,[],[f412,f434,f430,f426]) ).
thf(f443,plain,
( ( $true = $false )
| ~ spl5_9 ),
inference(constrained_superposition,[],[f428,f137]) ).
thf(f449,plain,
( $false
| ~ spl5_9 ),
inference(trivial_inequality_removal,[],[f443]) ).
thf(f450,plain,
~ spl5_9,
inference(avatar_contradiction_clause,[],[f449]) ).
thf(f453,plain,
( ( $true = $false )
| ~ spl5_10 ),
inference(constrained_superposition,[],[f432,f141]) ).
thf(f459,plain,
( $false
| ~ spl5_10 ),
inference(trivial_inequality_removal,[],[f453]) ).
thf(f460,plain,
~ spl5_10,
inference(avatar_contradiction_clause,[],[f459]) ).
thf(f561,plain,
( ( $true = $false )
| ( $true
= ( in @ sK1 @ sK2 @ mactual ) )
| ( $false
= ( eiw_di @ sK2 @ mactual ) )
| ( $false
= ( eiw_di @ sK1 @ mactual ) ) ),
inference(constrained_superposition,[],[f176,f142]) ).
thf(f600,plain,
( ( $true
= ( in @ sK1 @ sK2 @ mactual ) )
| ( $false
= ( eiw_di @ sK2 @ mactual ) )
| ( $false
= ( eiw_di @ sK1 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f561]) ).
thf(f614,definition,
( spl5_12
<=> ( $true
= ( in @ sK1 @ sK2 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[spl5_12])],[avatar_definition]) ).
thf(f616,plain,
( ( $true
= ( in @ sK1 @ sK2 @ mactual ) )
| ~ spl5_12 ),
inference(avatar_component_clause,[],[f614]) ).
thf(f618,plain,
( spl5_9
| spl5_10
| spl5_12 ),
inference(avatar_split_clause,[],[f600,f614,f430,f426]) ).
thf(f619,plain,
( ( $true = $false )
| ~ spl5_11
| ~ spl5_12 ),
inference(constrained_superposition,[],[f616,f436]) ).
thf(f623,plain,
( $false
| ~ spl5_11
| ~ spl5_12 ),
inference(trivial_inequality_removal,[],[f619]) ).
thf(f624,plain,
( ~ spl5_11
| ~ spl5_12 ),
inference(avatar_contradiction_clause,[],[f623]) ).
cnf(s10,plain,
( spl5_9
| spl5_10
| spl5_11 ),
inference(sat_conversion,[],[f440]) ).
cnf(s12,plain,
~ spl5_9,
inference(sat_conversion,[],[f450]) ).
cnf(s14,plain,
~ spl5_10,
inference(sat_conversion,[],[f460]) ).
cnf(s16,plain,
( spl5_9
| spl5_10
| spl5_12 ),
inference(sat_conversion,[],[f618]) ).
cnf(s18,plain,
( ~ spl5_11
| ~ spl5_12 ),
inference(sat_conversion,[],[f624]) ).
cnf(s19,plain,
spl5_12,
inference(rat,[],[s16,s14,s12]) ).
cnf(s20,plain,
~ spl5_11,
inference(rat,[],[s18,s19]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s10,s20,s14,s12]) ).
thf(f625,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET926^8 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n005.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:41:02 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.28 % (1682463)Will run a generic schedule for satisfiability detection.
% 0.39/0.28 % (1682468)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4188098326_2999 on theBenchmark for (2999ds/0Mi)
% 0.39/0.28 % Exception at run slice level
% 0.39/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.39/0.28 % (1682469)% WARNING: option uhcvi not known.
% 0.39/0.28 % (1682472)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2940968135:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.39/0.28 % (1682470)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3706627529:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.39/0.28 % (1682471)dis+10_1_sil=32000:sp=arity:random_seed=2717200570:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.39/0.28 % (1682474)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2933821445:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.39/0.28 % (1682473)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1620293809:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.39/0.28 % (1682469)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=564469674:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.39/0.28 % (1682472)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.39/0.28 % (1682469)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.39/0.28 % (1682476)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2724031615:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.39/0.28 % (1682469)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.39/0.28 % Exception at run slice level
% 0.39/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.39/0.28 % (1682484)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1953908888:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.39/0.28 % (1682474) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1682463-1682474"...
% 0.39/0.28 % (1682470) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1682463-1682470"...
% 0.39/0.28 % (1682474)...printing done.
% 0.39/0.28 % (1682474)Refutation found. Thanks to Tanya!
% 0.39/0.28 % SZS status Theorem for theBenchmark
% 0.39/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.39/0.28 % (1682474)------------------------------
% 0.39/0.28 % (1682474)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.28 % (1682474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.28 % (1682474)CaDiCaL version: 2.1.3
% 0.39/0.28 % (1682474)Termination reason: Refutation
% 0.39/0.28 % (1682474)Time elapsed: 0.030 s
% 0.39/0.28 % (1682474)Peak memory usage: 13 MB
% 0.39/0.28 % (1682474)Instructions burned: 60 (million)
% 0.39/0.28 % (1682463)Success in time 0.055 s
% 0.39/0.28 % Vampire exiting
%------------------------------------------------------------------------------