%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET019^4 : 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 : n014.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 08:23:32 AM UTC 2026
% Result : Theorem 0.20s 0.31s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 64 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 475 ( 98 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 657 ( 7 ~; 30 |; 23 &; 541 @)
% ( 2 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 45 usr; 6 con; 0-4 aty)
% ( 16 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 130 ( 113 ^; 17 !; 0 ?; 130 :)
% 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,
equal_set: $i > $i > mworld > $o ).
thf(func_def_17,type,
member: $i > $i > mworld > $o ).
thf(func_def_18,type,
subset: $i > $i > mworld > $o ).
thf(func_def_19,type,
singleton: $i > $i ).
thf(func_def_20,type,
product: $i > $i ).
thf(func_def_21,type,
unordered_pair: $i > $i > $i ).
thf(func_def_22,type,
intersection: $i > $i > $i ).
thf(func_def_23,type,
difference: $i > $i > $i ).
thf(func_def_24,type,
sum: $i > $i ).
thf(func_def_25,type,
union: $i > $i > $i ).
thf(func_def_26,type,
power_set: $i > $i ).
thf(func_def_27,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_29,type,
vNOT: $o > $o ).
thf(func_def_30,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
vAND: $o > $o > $o ).
thf(func_def_32,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
vOR: $o > $o > $o ).
thf(func_def_34,type,
vIMP: $o > $o > $o ).
thf(func_def_35,type,
vIFF: $o > $o > $o ).
thf(func_def_36,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_40,type,
sK0: mworld > $i ).
thf(func_def_41,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
sK3: $i > $i > $i ).
thf(func_def_46,type,
sK4: $i > $i > $i ).
thf(func_def_47,type,
sK5: $i > $i > $i ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f3,axiom,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(f5,axiom,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_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(f12,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(f36,axiom,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( equal_set @ X0 @ X1 ) @ ( mand @ ( subset @ X0 @ X1 ) @ ( subset @ X1 @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set_0) ).
thf(f46,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mimplies @ ( mand @ ( subset @ X0 @ X1 ) @ ( subset @ X1 @ X0 ) ) @ ( equal_set @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI02) ).
thf(f47,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mimplies @ ( mand @ ( subset @ X0 @ X1 ) @ ( subset @ X1 @ X0 ) ) @ ( equal_set @ X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
thf(f48,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f51,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f52,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f55,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f56,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f57,plain,
( mequiv
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f58,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f69,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f70,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f117,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( equal_set @ X0 @ X1 ) @ ( mand @ ( subset @ X0 @ X1 ) @ ( subset @ X1 @ X0 ) ) ) ) ) ),
inference(rectify,[],[f36]) ).
thf(f118,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( equal_set @ Y0 @ Y1 ) @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f117]) ).
thf(f137,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mimplies @ ( mand @ ( subset @ X0 @ X1 ) @ ( subset @ X1 @ X0 ) ) @ ( equal_set @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f47]) ).
thf(f138,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mimplies @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) @ ( equal_set @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f137]) ).
thf(f139,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mimplies @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) @ ( equal_set @ Y0 @ Y1 ) ) ) ) ) ),
inference(flattening,[],[f138]) ).
thf(f143,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f145,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f147,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f148,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f154,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f178,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( equal_set @ Y0 @ Y1 ) @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f118]) ).
thf(f188,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mimplies @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) @ ( equal_set @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f139]) ).
thf(f213,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 ) )
@ ( equal_set @ Y0 @ Y1 )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ ( subset @ Y0 @ Y1 )
@ ( subset @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f178,f143,f154,f154,f148,f145]) ).
thf(f223,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 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ ( subset @ Y0 @ Y1 )
@ ( subset @ Y1 @ Y0 ) )
@ ( equal_set @ Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f188,f143,f154,f154,f147,f145]) ).
thf(f224,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( ( subset @ Y0 @ Y1 @ mactual )
& ( subset @ Y1 @ Y0 @ mactual ) )
=> ( equal_set @ Y0 @ Y1 @ mactual ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f223]) ).
thf(f225,plain,
( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( ( subset @ Y0 @ Y1 @ mactual )
& ( subset @ Y1 @ Y0 @ mactual ) )
=> ( equal_set @ Y0 @ Y1 @ mactual ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f224]) ).
thf(f226,plain,
( $false
= ( ( eiw_di @ sK1 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ( subset @ sK1 @ Y0 @ mactual )
& ( subset @ Y0 @ sK1 @ mactual ) )
=> ( equal_set @ sK1 @ Y0 @ mactual ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f225]) ).
thf(f227,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ( subset @ sK1 @ Y0 @ mactual )
& ( subset @ Y0 @ sK1 @ mactual ) )
=> ( equal_set @ sK1 @ Y0 @ mactual ) ) ) ) ),
inference(imp_proxy_clausification,[],[f226]) ).
thf(f228,plain,
( $true
= ( eiw_di @ sK1 @ mactual ) ),
inference(imp_proxy_clausification,[],[f226]) ).
thf(f229,plain,
( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ( subset @ sK1 @ Y0 @ mactual )
& ( subset @ Y0 @ sK1 @ mactual ) )
=> ( equal_set @ sK1 @ Y0 @ mactual ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f227]) ).
thf(f230,plain,
( $false
= ( ( eiw_di @ sK2 @ mactual )
=> ( ( ( subset @ sK1 @ sK2 @ mactual )
& ( subset @ sK2 @ sK1 @ mactual ) )
=> ( equal_set @ sK1 @ sK2 @ mactual ) ) ) ),
inference(beta-eta_normalization,[],[f229]) ).
thf(f231,plain,
( $false
= ( ( ( subset @ sK1 @ sK2 @ mactual )
& ( subset @ sK2 @ sK1 @ mactual ) )
=> ( equal_set @ sK1 @ sK2 @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f230]) ).
thf(f232,plain,
( $true
= ( eiw_di @ sK2 @ mactual ) ),
inference(imp_proxy_clausification,[],[f230]) ).
thf(f233,plain,
( $false
= ( equal_set @ sK1 @ sK2 @ mactual ) ),
inference(imp_proxy_clausification,[],[f231]) ).
thf(f234,plain,
( $true
= ( ( subset @ sK1 @ sK2 @ mactual )
& ( subset @ sK2 @ sK1 @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f231]) ).
thf(f235,plain,
( $true
= ( subset @ sK2 @ sK1 @ mactual ) ),
inference(and_proxy_clausification,[],[f234]) ).
thf(f236,plain,
( $true
= ( subset @ sK1 @ sK2 @ mactual ) ),
inference(and_proxy_clausification,[],[f234]) ).
thf(f368,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( equal_set @ Y0 @ Y1 @ mactual )
= ( ( subset @ Y0 @ Y1 @ mactual )
& ( subset @ Y1 @ Y0 @ mactual ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f213]) ).
thf(f369,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( equal_set @ Y0 @ Y1 @ mactual )
= ( ( subset @ Y0 @ Y1 @ mactual )
& ( subset @ Y1 @ Y0 @ mactual ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f368]) ).
thf(f370,plain,
! [X1: $i] :
( $true
= ( ( eiw_di @ X1 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( equal_set @ X1 @ Y0 @ mactual )
= ( ( subset @ X1 @ Y0 @ mactual )
& ( subset @ Y0 @ X1 @ mactual ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f369]) ).
thf(f371,plain,
! [X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( equal_set @ X1 @ Y0 @ mactual )
= ( ( subset @ X1 @ Y0 @ mactual )
& ( subset @ Y0 @ X1 @ mactual ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f370]) ).
thf(f372,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( equal_set @ X1 @ Y0 @ mactual )
= ( ( subset @ X1 @ Y0 @ mactual )
& ( subset @ Y0 @ X1 @ mactual ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f371]) ).
thf(f373,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( ( eiw_di @ X2 @ mactual )
=> ( ( equal_set @ X1 @ X2 @ mactual )
= ( ( subset @ X1 @ X2 @ mactual )
& ( subset @ X2 @ X1 @ mactual ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f372]) ).
thf(f374,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $true
= ( ( equal_set @ X1 @ X2 @ mactual )
= ( ( subset @ X1 @ X2 @ mactual )
& ( subset @ X2 @ X1 @ mactual ) ) ) ) ),
inference(imp_proxy_clausification,[],[f373]) ).
thf(f375,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( ( equal_set @ X1 @ X2 @ mactual )
= ( ( subset @ X1 @ X2 @ mactual )
& ( subset @ X2 @ X1 @ mactual ) ) ) ),
inference(iff_proxy_clausification,[],[f374]) ).
thf(f376,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $true
= ( equal_set @ X1 @ X2 @ mactual ) )
| ( $false
= ( ( subset @ X1 @ X2 @ mactual )
& ( subset @ X2 @ X1 @ mactual ) ) ) ),
inference(iff_proxy_clausification,[],[f375]) ).
thf(f380,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( equal_set @ X1 @ X2 @ mactual ) )
| ( $false
= ( subset @ X2 @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( subset @ X1 @ X2 @ mactual ) ) ),
inference(and_proxy_clausification,[],[f376]) ).
thf(f1319,plain,
( ( $true = $false )
| ( $false
= ( subset @ sK2 @ sK1 @ mactual ) )
| ( $false
= ( eiw_di @ sK2 @ mactual ) )
| ( $false
= ( eiw_di @ sK1 @ mactual ) )
| ( $false
= ( subset @ sK1 @ sK2 @ mactual ) ) ),
inference(constrained_superposition,[],[f233,f380]) ).
thf(f1323,plain,
( ( $false
= ( subset @ sK2 @ sK1 @ mactual ) )
| ( $false
= ( eiw_di @ sK2 @ mactual ) )
| ( $false
= ( eiw_di @ sK1 @ mactual ) )
| ( $false
= ( subset @ sK1 @ sK2 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f1319]) ).
thf(f1328,plain,
( ( $true = $false )
| ( $false
= ( eiw_di @ sK2 @ mactual ) )
| ( $false
= ( eiw_di @ sK1 @ mactual ) )
| ( $false
= ( subset @ sK1 @ sK2 @ mactual ) ) ),
inference(forward_demodulation,[],[f1323,f235]) ).
thf(f1329,plain,
( ( $false
= ( eiw_di @ sK2 @ mactual ) )
| ( $false
= ( eiw_di @ sK1 @ mactual ) )
| ( $false
= ( subset @ sK1 @ sK2 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f1328]) ).
thf(f1332,plain,
( ( $true = $false )
| ( $false
= ( eiw_di @ sK1 @ mactual ) )
| ( $false
= ( subset @ sK1 @ sK2 @ mactual ) ) ),
inference(forward_demodulation,[],[f1329,f232]) ).
thf(f1333,plain,
( ( $false
= ( eiw_di @ sK1 @ mactual ) )
| ( $false
= ( subset @ sK1 @ sK2 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f1332]) ).
thf(f1336,plain,
( ( $true = $false )
| ( $false
= ( subset @ sK1 @ sK2 @ mactual ) ) ),
inference(forward_demodulation,[],[f1333,f228]) ).
thf(f1337,plain,
( $false
= ( subset @ sK1 @ sK2 @ mactual ) ),
inference(trivial_inequality_removal,[],[f1336]) ).
thf(f1344,plain,
$true = $false,
inference(constrained_superposition,[],[f236,f1337]) ).
thf(f1345,plain,
$false,
inference(trivial_inequality_removal,[],[f1344]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET019^4 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n014.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:35:15 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.20/0.31 % (2655471)Will run a generic schedule for satisfiability detection.
% 0.20/0.31 % (2655478)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1162699546:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.31 % (2655477)% WARNING: option uhcvi not known.
% 0.20/0.31 % (2655476)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2121309585_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.31 % (2655477)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2467576845:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.31 % (2655479)dis+10_1_sil=32000:sp=arity:random_seed=689856249:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.31 % (2655480)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1043289776:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.31 % (2655477)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.31 % (2655480)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.31 % Exception at run slice level
% 0.20/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.31 % (2655477)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.31 % (2655482)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=12605141:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.31 % (2655481)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3266080572:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.31 % (2655478) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2655471-2655478"...
% 0.20/0.31 % (2655478)...printing done.
% 0.20/0.31 % (2655478)Refutation found. Thanks to Tanya!
% 0.20/0.31 % SZS status Theorem for theBenchmark
% 0.20/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.31 % (2655478)------------------------------
% 0.20/0.31 % (2655478)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (2655478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (2655478)CaDiCaL version: 2.1.3
% 0.20/0.31 % (2655478)Termination reason: Refutation
% 0.20/0.31 % (2655478)Time elapsed: 0.034 s
% 0.20/0.31 % (2655478)Peak memory usage: 13 MB
% 0.20/0.31 % (2655478)Instructions burned: 128 (million)
% 0.20/0.31 % (2655471)Success in time 0.069 s
% 0.20/0.31 % Vampire exiting
%------------------------------------------------------------------------------