%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET574^20 : 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 : n026.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 08:23:37 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 8
% Syntax : Number of formulae : 77 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 643 ( 131 equ; 0 cnn)
% Maximal formula atoms : 9 ( 8 avg)
% Number of connectives : 946 ( 7 ~; 50 |; 45 &; 755 @)
% ( 2 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 65 ( 65 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 34 usr; 8 con; 0-4 aty)
% ( 24 !!; 12 ??; 0 @@+; 0 @@-)
% Number of variables : 194 ( 159 ^; 33 !; 2 ?; 194 :)
% 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_14,type,
intersect: $i > $i > mworld > $o ).
thf(func_def_15,type,
member: $i > $i > mworld > $o ).
thf(func_def_16,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_18,type,
vNOT: $o > $o ).
thf(func_def_19,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vAND: $o > $o > $o ).
thf(func_def_21,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vOR: $o > $o > $o ).
thf(func_def_23,type,
vIMP: $o > $o > $o ).
thf(func_def_24,type,
vIFF: $o > $o > $o ).
thf(func_def_25,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_29,type,
sK0: mworld > $i ).
thf(func_def_30,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
sK4: $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(f13,axiom,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_di_def) ).
thf(f14,axiom,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mequiv @ ( intersect @ X0 @ X1 )
@ ( mexists_di
@ ^ [X2: $i] : ( mand @ ( member @ X2 @ X0 ) @ ( member @ X2 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
thf(f16,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X2: $i] : ( mimplies @ ( mand @ ( member @ X0 @ X1 ) @ ( member @ X0 @ X2 ) ) @ ( intersect @ X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th13) ).
thf(f17,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X2: $i] : ( mimplies @ ( mand @ ( member @ X0 @ X1 ) @ ( member @ X0 @ X2 ) ) @ ( intersect @ X1 @ X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
thf(f18,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f21,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f22,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f25,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f26,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f25]) ).
thf(f27,plain,
( mequiv
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f28,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f39,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f40,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f42,plain,
( mexists_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 @ ( intersect @ X0 @ X1 )
@ ( mexists_di
@ ^ [X2: $i] : ( mand @ ( member @ X2 @ X0 ) @ ( member @ X2 @ X1 ) ) ) ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f44,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mequiv @ ( intersect @ Y0 @ Y1 )
@ ( mexists_di
@ ^ [Y2: $i] : ( mand @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f43]) ).
thf(f47,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X2: $i] : ( mimplies @ ( mand @ ( member @ X0 @ X1 ) @ ( member @ X0 @ X2 ) ) @ ( intersect @ X1 @ X2 ) ) ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f48,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( mand @ ( member @ Y0 @ Y1 ) @ ( member @ Y0 @ Y2 ) ) @ ( intersect @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f49,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( mand @ ( member @ Y0 @ Y1 ) @ ( member @ Y0 @ Y2 ) ) @ ( intersect @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(flattening,[],[f48]) ).
thf(f53,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f55,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f57,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f58,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f64,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f65,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f66,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mequiv @ ( intersect @ Y0 @ Y1 )
@ ( mexists_di
@ ^ [Y2: $i] : ( mand @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f68,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( mand @ ( member @ Y0 @ Y1 ) @ ( member @ Y0 @ Y2 ) ) @ ( intersect @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f71,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 ) )
@ ( intersect @ Y0 @ Y1 )
@ ( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
& ( Y2 @ Y4 @ Y3 ) ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
& ( Y4 @ Y5 ) )
@ ( member @ Y2 @ Y0 )
@ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f66,f53,f64,f64,f58,f65,f55]) ).
thf(f73,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: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] :
( ( eiw_di @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
& ( Y4 @ Y5 ) )
@ ( member @ Y0 @ Y1 )
@ ( member @ Y0 @ Y2 ) )
@ ( intersect @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f68,f53,f64,f64,f64,f57,f55]) ).
thf(f74,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ mactual )
=> ( ( ( member @ Y0 @ Y1 @ mactual )
& ( member @ Y0 @ Y2 @ mactual ) )
=> ( intersect @ Y1 @ Y2 @ mactual ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f73]) ).
thf(f75,plain,
( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ mactual )
=> ( ( ( member @ Y0 @ Y1 @ mactual )
& ( member @ Y0 @ Y2 @ mactual ) )
=> ( intersect @ Y1 @ Y2 @ mactual ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f74]) ).
thf(f76,plain,
( $false
= ( ( eiw_di @ sK1 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( ( member @ sK1 @ Y0 @ mactual )
& ( member @ sK1 @ Y1 @ mactual ) )
=> ( intersect @ Y0 @ Y1 @ mactual ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f77,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( ( member @ sK1 @ Y0 @ mactual )
& ( member @ sK1 @ Y1 @ mactual ) )
=> ( intersect @ Y0 @ Y1 @ mactual ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f76]) ).
thf(f78,plain,
( $true
= ( eiw_di @ sK1 @ mactual ) ),
inference(imp_proxy_clausification,[],[f76]) ).
thf(f79,plain,
( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( ( member @ sK1 @ Y0 @ mactual )
& ( member @ sK1 @ Y1 @ mactual ) )
=> ( intersect @ Y0 @ Y1 @ mactual ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f77]) ).
thf(f80,plain,
( $false
= ( ( eiw_di @ sK2 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ( member @ sK1 @ sK2 @ mactual )
& ( member @ sK1 @ Y0 @ mactual ) )
=> ( intersect @ sK2 @ Y0 @ mactual ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f79]) ).
thf(f81,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ( member @ sK1 @ sK2 @ mactual )
& ( member @ sK1 @ Y0 @ mactual ) )
=> ( intersect @ sK2 @ Y0 @ mactual ) ) ) ) ),
inference(imp_proxy_clausification,[],[f80]) ).
thf(f82,plain,
( $true
= ( eiw_di @ sK2 @ mactual ) ),
inference(imp_proxy_clausification,[],[f80]) ).
thf(f83,plain,
( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ( member @ sK1 @ sK2 @ mactual )
& ( member @ sK1 @ Y0 @ mactual ) )
=> ( intersect @ sK2 @ Y0 @ mactual ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f81]) ).
thf(f84,plain,
( $false
= ( ( eiw_di @ sK3 @ mactual )
=> ( ( ( member @ sK1 @ sK2 @ mactual )
& ( member @ sK1 @ sK3 @ mactual ) )
=> ( intersect @ sK2 @ sK3 @ mactual ) ) ) ),
inference(beta-eta_normalization,[],[f83]) ).
thf(f85,plain,
( $false
= ( ( ( member @ sK1 @ sK2 @ mactual )
& ( member @ sK1 @ sK3 @ mactual ) )
=> ( intersect @ sK2 @ sK3 @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f84]) ).
thf(f86,plain,
( $true
= ( eiw_di @ sK3 @ mactual ) ),
inference(imp_proxy_clausification,[],[f84]) ).
thf(f87,plain,
( $false
= ( intersect @ sK2 @ sK3 @ mactual ) ),
inference(imp_proxy_clausification,[],[f85]) ).
thf(f88,plain,
( $true
= ( ( member @ sK1 @ sK2 @ mactual )
& ( member @ sK1 @ sK3 @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f85]) ).
thf(f89,plain,
( $true
= ( member @ sK1 @ sK3 @ mactual ) ),
inference(and_proxy_clausification,[],[f88]) ).
thf(f90,plain,
( $true
= ( member @ sK1 @ sK2 @ mactual ) ),
inference(and_proxy_clausification,[],[f88]) ).
thf(f99,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( intersect @ Y0 @ Y1 @ mactual )
= ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ mactual )
& ( member @ Y2 @ Y0 @ mactual )
& ( member @ Y2 @ Y1 @ mactual ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f100,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( intersect @ Y0 @ Y1 @ mactual )
= ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ mactual )
& ( member @ Y2 @ Y0 @ mactual )
& ( member @ Y2 @ Y1 @ mactual ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f99]) ).
thf(f101,plain,
! [X1: $i] :
( $true
= ( ( eiw_di @ X1 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( intersect @ X1 @ Y0 @ mactual )
= ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
& ( member @ Y1 @ X1 @ mactual )
& ( member @ Y1 @ Y0 @ mactual ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f100]) ).
thf(f102,plain,
! [X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( intersect @ X1 @ Y0 @ mactual )
= ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
& ( member @ Y1 @ X1 @ mactual )
& ( member @ Y1 @ Y0 @ mactual ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( intersect @ X1 @ Y0 @ mactual )
= ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
& ( member @ Y1 @ X1 @ mactual )
& ( member @ Y1 @ Y0 @ mactual ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f102]) ).
thf(f104,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( ( eiw_di @ X2 @ mactual )
=> ( ( intersect @ X1 @ X2 @ mactual )
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( member @ Y0 @ X1 @ mactual )
& ( member @ Y0 @ X2 @ mactual ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f103]) ).
thf(f105,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $true
= ( ( intersect @ X1 @ X2 @ mactual )
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( member @ Y0 @ X1 @ mactual )
& ( member @ Y0 @ X2 @ mactual ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f104]) ).
thf(f106,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( ( intersect @ X1 @ X2 @ mactual )
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( member @ Y0 @ X1 @ mactual )
& ( member @ Y0 @ X2 @ mactual ) ) ) ) ),
inference(iff_proxy_clausification,[],[f105]) ).
thf(f107,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $true
= ( intersect @ X1 @ X2 @ mactual ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( member @ Y0 @ X1 @ mactual )
& ( member @ Y0 @ X2 @ mactual ) ) ) ) ),
inference(iff_proxy_clausification,[],[f106]) ).
thf(f115,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $true
= ( intersect @ X1 @ X2 @ mactual ) )
| ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( member @ Y0 @ X1 @ mactual )
& ( member @ Y0 @ X2 @ mactual ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f107]) ).
thf(f116,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $true
= ( intersect @ X1 @ X2 @ mactual ) )
| ( $false
= ( ( eiw_di @ X3 @ mactual )
& ( member @ X3 @ X1 @ mactual )
& ( member @ X3 @ X2 @ mactual ) ) ) ),
inference(beta-eta_normalization,[],[f115]) ).
thf(f117,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $true
= ( intersect @ X1 @ X2 @ mactual ) )
| ( $false
= ( ( member @ X3 @ X1 @ mactual )
& ( member @ X3 @ X2 @ mactual ) ) )
| ( $false
= ( eiw_di @ X3 @ mactual ) ) ),
inference(and_proxy_clausification,[],[f116]) ).
thf(f118,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( intersect @ X1 @ X2 @ mactual ) )
| ( $false
= ( member @ X3 @ X2 @ mactual ) )
| ( $false
= ( member @ X3 @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $false
= ( eiw_di @ X3 @ mactual ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(and_proxy_clausification,[],[f117]) ).
thf(f162,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( intersect @ sK2 @ X0 @ mactual ) )
| ( $false
= ( member @ sK1 @ X0 @ mactual ) )
| ( $false
= ( eiw_di @ X0 @ mactual ) )
| ( $false
= ( eiw_di @ sK1 @ mactual ) )
| ( $false
= ( eiw_di @ sK2 @ mactual ) ) ),
inference(constrained_superposition,[],[f90,f118]) ).
thf(f169,plain,
! [X0: $i] :
( ( $true
= ( intersect @ sK2 @ X0 @ mactual ) )
| ( $false
= ( member @ sK1 @ X0 @ mactual ) )
| ( $false
= ( eiw_di @ X0 @ mactual ) )
| ( $false
= ( eiw_di @ sK1 @ mactual ) )
| ( $false
= ( eiw_di @ sK2 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f162]) ).
thf(f183,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( intersect @ sK2 @ X0 @ mactual ) )
| ( $false
= ( member @ sK1 @ X0 @ mactual ) )
| ( $false
= ( eiw_di @ X0 @ mactual ) )
| ( $false
= ( eiw_di @ sK2 @ mactual ) ) ),
inference(forward_demodulation,[],[f169,f78]) ).
thf(f184,plain,
! [X0: $i] :
( ( $true
= ( intersect @ sK2 @ X0 @ mactual ) )
| ( $false
= ( member @ sK1 @ X0 @ mactual ) )
| ( $false
= ( eiw_di @ X0 @ mactual ) )
| ( $false
= ( eiw_di @ sK2 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f183]) ).
thf(f199,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( intersect @ sK2 @ X0 @ mactual ) )
| ( $false
= ( member @ sK1 @ X0 @ mactual ) )
| ( $false
= ( eiw_di @ X0 @ mactual ) ) ),
inference(forward_demodulation,[],[f184,f82]) ).
thf(f200,plain,
! [X0: $i] :
( ( $false
= ( member @ sK1 @ X0 @ mactual ) )
| ( $true
= ( intersect @ sK2 @ X0 @ mactual ) )
| ( $false
= ( eiw_di @ X0 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f199]) ).
thf(f319,plain,
( ( $true = $false )
| ( $true
= ( intersect @ sK2 @ sK3 @ mactual ) )
| ( $false
= ( eiw_di @ sK3 @ mactual ) ) ),
inference(constrained_superposition,[],[f89,f200]) ).
thf(f320,plain,
( ( $true
= ( intersect @ sK2 @ sK3 @ mactual ) )
| ( $false
= ( eiw_di @ sK3 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f319]) ).
thf(f325,plain,
( ( $true = $false )
| ( $false
= ( eiw_di @ sK3 @ mactual ) ) ),
inference(forward_demodulation,[],[f320,f87]) ).
thf(f326,plain,
( $false
= ( eiw_di @ sK3 @ mactual ) ),
inference(trivial_inequality_removal,[],[f325]) ).
thf(f331,plain,
$true = $false,
inference(constrained_superposition,[],[f86,f326]) ).
thf(f333,plain,
$false,
inference(trivial_inequality_removal,[],[f331]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET574^20 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n026.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:40:12 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.20/0.28 % (599115)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (599126)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1248078848:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.28 % (599121)% WARNING: option uhcvi not known.
% 0.20/0.28 % (599120)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=926250383_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (599121)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=859497121:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (599123)dis+10_1_sil=32000:sp=arity:random_seed=2076276791:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (599122)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1559804550:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (599124)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1628915197:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (599125)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2195722850:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (599121)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (599124)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % Exception at run slice level
% 0.20/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.28 % (599121)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.28 % (599123) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-599115-599123"...
% 0.20/0.28 % (599124) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-599115-599124"...
% 0.20/0.28 % (599123)...printing done.
% 0.20/0.28 % (599123)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (599123)------------------------------
% 0.20/0.28 % (599123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (599123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (599123)CaDiCaL version: 2.1.3
% 0.20/0.28 % (599123)Termination reason: Refutation
% 0.20/0.28 % (599123)Time elapsed: 0.017 s
% 0.20/0.28 % (599123)Peak memory usage: 12 MB
% 0.20/0.28 % (599123)Instructions burned: 33 (million)
% 0.20/0.28 % (599115)Success in time 0.052 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------