%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET044^23 : 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 : n008.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 08:23:11 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 9
% Syntax : Number of formulae : 91 ( 44 unt; 0 typ; 2 def)
% Number of atoms : 709 ( 171 equ; 0 cnn)
% Maximal formula atoms : 15 ( 7 avg)
% Number of connectives : 990 ( 47 ~; 84 |; 18 &; 767 @)
% ( 4 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 58 ( 58 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 33 usr; 8 con; 0-4 aty)
% ( 22 !!; 12 ??; 0 @@+; 0 @@-)
% Number of variables : 188 ( 0 sgn 37 !; 2 ?; 188 :)
% 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,
element: $i > $i > mworld > $o ).
thf(func_def_15,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_17,type,
vNOT: $o > $o ).
thf(func_def_18,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
vIFF: $o > $o > $o ).
thf(func_def_22,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_24,type,
vIMP: $o > $o > $o ).
thf(func_def_25,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vAND: $o > $o > $o ).
thf(func_def_27,type,
vOR: $o > $o > $o ).
thf(func_def_28,type,
sK0: mworld > $i ).
thf(func_def_29,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
sK2: $i > $i ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
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(f5,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def) ).
thf(f6,axiom,
( mequiv
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv_def) ).
thf(f13,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(f14,axiom,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_di_def) ).
thf(f15,conjecture,
( mlocal
@ ( mimplies
@ ( mexists_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( element @ X1 @ X0 ) @ ( element @ X1 @ X1 ) ) ) )
@ ( mnot
@ ( mforall_di
@ ^ [X2: $i] :
( mexists_di
@ ^ [X3: $i] :
( mforall_di
@ ^ [X4: $i] : ( mequiv @ ( element @ X4 @ X3 ) @ ( mnot @ ( element @ X4 @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel40) ).
thf(f16,negated_conjecture,
~ ( mlocal
@ ( mimplies
@ ( mexists_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( element @ X1 @ X0 ) @ ( element @ X1 @ X1 ) ) ) )
@ ( mnot
@ ( mforall_di
@ ^ [X2: $i] :
( mexists_di
@ ^ [X3: $i] :
( mforall_di
@ ^ [X4: $i] : ( mequiv @ ( element @ X4 @ X3 ) @ ( mnot @ ( element @ X4 @ X2 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f17,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f18,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f2]) ).
thf(f19,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f22,plain,
( mequiv
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f23,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f30,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[],[f5]) ).
thf(f31,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f32,plain,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f33,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f40,plain,
~ ( mlocal
@ ( mimplies
@ ( mexists_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( element @ X1 @ X0 ) @ ( element @ X1 @ X1 ) ) ) )
@ ( mnot
@ ( mforall_di
@ ^ [X2: $i] :
( mexists_di
@ ^ [X3: $i] :
( mforall_di
@ ^ [X4: $i] : ( mequiv @ ( element @ X4 @ X3 ) @ ( mnot @ ( element @ X4 @ X2 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f41,plain,
( ( mlocal
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( element @ Y1 @ Y0 ) @ ( element @ Y1 @ Y1 ) ) ) )
@ ( mnot
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mequiv @ ( element @ Y2 @ Y1 ) @ ( mnot @ ( element @ Y2 @ Y0 ) ) ) ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f40]) ).
thf(f44,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_di ),
inference(rectify,[],[f13]) ).
thf(f45,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f46,plain,
( ( mlocal
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( element @ Y1 @ Y0 ) @ ( element @ Y1 @ Y1 ) ) ) )
@ ( mnot
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mequiv @ ( element @ Y2 @ Y1 ) @ ( mnot @ ( element @ Y2 @ Y0 ) ) ) ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f41]) ).
thf(f53,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f54,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f55,plain,
( ( mlocal
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( element @ Y1 @ Y0 ) @ ( element @ Y1 @ Y1 ) ) ) )
@ ( mnot
@ ( mforall_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mequiv @ ( element @ Y2 @ Y1 ) @ ( mnot @ ( element @ Y2 @ Y0 ) ) ) ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f46]) ).
thf(f56,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f60,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f63,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f64,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f70,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [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 ) )
@ ( element @ Y1 @ Y0 )
@ ( element @ Y1 @ Y1 ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [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 ) )
@ ( element @ Y2 @ Y1 )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
~ ( Y3 @ Y4 )
@ ( element @ Y2 @ Y0 ) ) ) ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f55,f60,f64,f63,f53,f56,f54,f53,f63,f53,f56,f54]) ).
thf(f71,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( element @ Y1 @ Y0 @ mactual )
= ( element @ Y1 @ Y1 @ mactual ) ) ) ) ) )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ mactual )
=> ( ( element @ Y2 @ Y1 @ mactual )
= ( ~ ( element @ Y2 @ Y0 @ mactual ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f72,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ mactual )
=> ( ( element @ Y2 @ Y1 @ mactual )
= ( ~ ( element @ Y2 @ Y0 @ mactual ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f71]) ).
thf(f73,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( element @ Y1 @ Y0 @ mactual )
= ( element @ Y1 @ Y1 @ mactual ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f71]) ).
thf(f74,plain,
( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( element @ Y1 @ Y0 @ mactual )
= ( element @ Y1 @ Y1 @ mactual ) ) ) ) )
@ sK1 )
= $true ),
inference(sigma_proxy_clausification,[],[f73]) ).
thf(f75,plain,
( ( ( eiw_di @ sK1 @ mactual )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( element @ Y0 @ sK1 @ mactual )
= ( element @ Y0 @ Y0 @ mactual ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f74]) ).
thf(f76,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( element @ Y0 @ sK1 @ mactual )
= ( element @ Y0 @ Y0 @ mactual ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f75]) ).
thf(f77,plain,
( ( eiw_di @ sK1 @ mactual )
= $true ),
inference(and_proxy_clausification,[],[f75]) ).
thf(f78,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( element @ Y0 @ sK1 @ mactual )
= ( element @ Y0 @ Y0 @ mactual ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f76]) ).
thf(f79,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
=> ( ( element @ X1 @ sK1 @ mactual )
= ( element @ X1 @ X1 @ mactual ) ) )
= $true ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( $true
= ( ( element @ X1 @ sK1 @ mactual )
= ( element @ X1 @ X1 @ mactual ) ) ) ),
inference(imp_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X1: $i] :
( ( ( element @ X1 @ X1 @ mactual )
= ( element @ X1 @ sK1 @ mactual ) )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(iff_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X1: $i] :
( ( $false
= ( element @ X1 @ sK1 @ mactual ) )
| ( ( element @ X1 @ X1 @ mactual )
= $true )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(iff_proxy_clausification,[],[f81]) ).
thf(f83,plain,
! [X1: $i] :
( ( $true
= ( element @ X1 @ sK1 @ mactual ) )
| ( ( element @ X1 @ X1 @ mactual )
= $false )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(iff_proxy_clausification,[],[f81]) ).
thf(f84,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ mactual )
=> ( ( element @ Y2 @ Y1 @ mactual )
= ( ~ ( element @ Y2 @ Y0 @ mactual ) ) ) ) ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f72]) ).
thf(f85,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ mactual )
=> ( ( element @ Y2 @ Y1 @ mactual )
= ( ~ ( element @ Y2 @ Y0 @ mactual ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f84]) ).
thf(f86,plain,
! [X1: $i] :
( $true
= ( ( eiw_di @ X1 @ mactual )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( element @ Y1 @ Y0 @ mactual )
= ( ~ ( element @ Y1 @ X1 @ mactual ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f85]) ).
thf(f87,plain,
! [X1: $i] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( element @ Y1 @ Y0 @ mactual )
= ( ~ ( element @ Y1 @ X1 @ mactual ) ) ) ) ) ) )
= $true )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(imp_proxy_clausification,[],[f86]) ).
thf(f88,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( element @ Y1 @ Y0 @ mactual )
= ( ~ ( element @ Y1 @ X1 @ mactual ) ) ) ) ) )
@ ( sK2 @ X1 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f87]) ).
thf(f89,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( ( eiw_di @ ( sK2 @ X1 ) @ mactual )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( element @ Y0 @ ( sK2 @ X1 ) @ mactual )
= ( ~ ( element @ Y0 @ X1 @ mactual ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f88]) ).
thf(f90,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( element @ Y0 @ ( sK2 @ X1 ) @ mactual )
= ( ~ ( element @ Y0 @ X1 @ mactual ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f89]) ).
thf(f91,plain,
! [X1: $i] :
( ( ( eiw_di @ ( sK2 @ X1 ) @ mactual )
= $true )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(and_proxy_clausification,[],[f89]) ).
thf(f92,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( element @ Y0 @ ( sK2 @ X1 ) @ mactual )
= ( ~ ( element @ Y0 @ X1 @ mactual ) ) ) )
@ X2 )
= $true )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(pi_proxy_clausification,[],[f90]) ).
thf(f93,plain,
! [X2: $i,X1: $i] :
( ( ( ( eiw_di @ X2 @ mactual )
=> ( ( element @ X2 @ ( sK2 @ X1 ) @ mactual )
= ( ~ ( element @ X2 @ X1 @ mactual ) ) ) )
= $true )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f94,plain,
! [X2: $i,X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( eiw_di @ X2 @ mactual )
= $false )
| ( ( ( element @ X2 @ ( sK2 @ X1 ) @ mactual )
= ( ~ ( element @ X2 @ X1 @ mactual ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f93]) ).
thf(f95,plain,
! [X2: $i,X1: $i] :
( ( ( element @ X2 @ ( sK2 @ X1 ) @ mactual )
= ( ~ ( element @ X2 @ X1 @ mactual ) ) )
| ( ( eiw_di @ X2 @ mactual )
= $false )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(iff_proxy_clausification,[],[f94]) ).
thf(f96,plain,
! [X2: $i,X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( ~ ( element @ X2 @ X1 @ mactual ) )
= $false )
| ( ( element @ X2 @ ( sK2 @ X1 ) @ mactual )
= $true )
| ( ( eiw_di @ X2 @ mactual )
= $false ) ),
inference(iff_proxy_clausification,[],[f95]) ).
thf(f97,plain,
! [X2: $i,X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( element @ X2 @ ( sK2 @ X1 ) @ mactual )
= $false )
| ( ( ~ ( element @ X2 @ X1 @ mactual ) )
= $true )
| ( ( eiw_di @ X2 @ mactual )
= $false ) ),
inference(iff_proxy_clausification,[],[f95]) ).
thf(f98,plain,
! [X2: $i,X1: $i] :
( ( ( element @ X2 @ ( sK2 @ X1 ) @ mactual )
= $false )
| ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( element @ X2 @ X1 @ mactual )
= $false )
| ( ( eiw_di @ X2 @ mactual )
= $false ) ),
inference(not_proxy_clausification,[],[f97]) ).
thf(f99,plain,
! [X2: $i,X1: $i] :
( ( ( element @ X2 @ ( sK2 @ X1 ) @ mactual )
= $true )
| ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( element @ X2 @ X1 @ mactual )
= $true )
| ( ( eiw_di @ X2 @ mactual )
= $false ) ),
inference(not_proxy_clausification,[],[f96]) ).
thf(f110,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( element @ ( sK2 @ X0 ) @ sK1 @ mactual )
= $false )
| ( ( element @ ( sK2 @ X0 ) @ X0 @ mactual )
= $false )
| ( $false
= ( eiw_di @ ( sK2 @ X0 ) @ mactual ) )
| ( ( eiw_di @ X0 @ mactual )
= $false )
| ( $false
= ( eiw_di @ ( sK2 @ X0 ) @ mactual ) ) ),
inference(constrained_superposition,[],[f98,f82]) ).
thf(f112,plain,
! [X0: $i] :
( ( ( element @ ( sK2 @ X0 ) @ X0 @ mactual )
= $false )
| ( $true = $false )
| ( $false
= ( eiw_di @ ( sK2 @ X0 ) @ mactual ) )
| ( ( eiw_di @ X0 @ mactual )
= $false )
| ( ( element @ ( sK2 @ X0 ) @ sK1 @ mactual )
= $false ) ),
inference(duplicate_literal_removal,[],[f110]) ).
thf(f113,plain,
! [X0: $i] :
( ( ( element @ ( sK2 @ X0 ) @ sK1 @ mactual )
= $false )
| ( ( element @ ( sK2 @ X0 ) @ X0 @ mactual )
= $false )
| ( ( eiw_di @ X0 @ mactual )
= $false )
| ( $false
= ( eiw_di @ ( sK2 @ X0 ) @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f112]) ).
thf(f118,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( eiw_di @ ( sK2 @ X0 ) @ mactual ) )
| ( ( element @ ( sK2 @ X0 ) @ sK1 @ mactual )
= $true )
| ( ( eiw_di @ X0 @ mactual )
= $false )
| ( $false
= ( eiw_di @ ( sK2 @ X0 ) @ mactual ) )
| ( ( element @ ( sK2 @ X0 ) @ X0 @ mactual )
= $true ) ),
inference(constrained_superposition,[],[f83,f99]) ).
thf(f122,plain,
! [X0: $i] :
( ( ( element @ ( sK2 @ X0 ) @ sK1 @ mactual )
= $true )
| ( ( element @ ( sK2 @ X0 ) @ X0 @ mactual )
= $true )
| ( $true = $false )
| ( ( eiw_di @ X0 @ mactual )
= $false )
| ( $false
= ( eiw_di @ ( sK2 @ X0 ) @ mactual ) ) ),
inference(duplicate_literal_removal,[],[f118]) ).
thf(f123,plain,
! [X0: $i] :
( ( ( element @ ( sK2 @ X0 ) @ sK1 @ mactual )
= $true )
| ( ( element @ ( sK2 @ X0 ) @ X0 @ mactual )
= $true )
| ( $false
= ( eiw_di @ ( sK2 @ X0 ) @ mactual ) )
| ( ( eiw_di @ X0 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[],[f122]) ).
thf(f128,plain,
( ( $false != $false )
| ( ( element @ ( sK2 @ sK1 ) @ sK1 @ mactual )
= $false )
| ( ( eiw_di @ ( sK2 @ sK1 ) @ mactual )
= $false )
| ( ( eiw_di @ sK1 @ mactual )
= $false ) ),
inference(equality_factoring,[],[f113]) ).
thf(f135,plain,
( ( ( eiw_di @ ( sK2 @ sK1 ) @ mactual )
= $false )
| ( ( eiw_di @ sK1 @ mactual )
= $false )
| ( ( element @ ( sK2 @ sK1 ) @ sK1 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[],[f128]) ).
thf(f138,plain,
( ( $true = $false )
| ( ( eiw_di @ ( sK2 @ sK1 ) @ mactual )
= $false )
| ( ( element @ ( sK2 @ sK1 ) @ sK1 @ mactual )
= $false ) ),
inference(forward_demodulation,[],[f135,f77]) ).
thf(f139,plain,
( ( ( element @ ( sK2 @ sK1 ) @ sK1 @ mactual )
= $false )
| ( ( eiw_di @ ( sK2 @ sK1 ) @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[],[f138]) ).
thf(f141,definition,
( spl3_1
<=> ( ( eiw_di @ ( sK2 @ sK1 ) @ mactual )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f143,plain,
( ( ( eiw_di @ ( sK2 @ sK1 ) @ mactual )
= $false )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f141]) ).
thf(f145,definition,
( spl3_2
<=> ( ( element @ ( sK2 @ sK1 ) @ sK1 @ mactual )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f147,plain,
( ( ( element @ ( sK2 @ sK1 ) @ sK1 @ mactual )
= $false )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f145]) ).
thf(f149,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f139,f145,f141]) ).
thf(f154,plain,
( ( ( eiw_di @ sK1 @ mactual )
= $false )
| ( ( eiw_di @ ( sK2 @ sK1 ) @ mactual )
= $false )
| ( $true = $false )
| ( $true = $false )
| ~ spl3_2 ),
inference(constrained_superposition,[],[f123,f147]) ).
thf(f161,plain,
( ( $true = $false )
| ( ( eiw_di @ sK1 @ mactual )
= $false )
| ( ( eiw_di @ ( sK2 @ sK1 ) @ mactual )
= $false )
| ~ spl3_2 ),
inference(duplicate_literal_removal,[],[f154]) ).
thf(f162,plain,
( ( ( eiw_di @ sK1 @ mactual )
= $false )
| ( ( eiw_di @ ( sK2 @ sK1 ) @ mactual )
= $false )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f161]) ).
thf(f176,plain,
( ( ( eiw_di @ ( sK2 @ sK1 ) @ mactual )
= $false )
| ( $true = $false )
| ~ spl3_2 ),
inference(forward_demodulation,[],[f162,f77]) ).
thf(f177,plain,
( ( ( eiw_di @ ( sK2 @ sK1 ) @ mactual )
= $false )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f176]) ).
thf(f184,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f177,f145,f141]) ).
thf(f187,plain,
( ( $true = $false )
| ( ( eiw_di @ sK1 @ mactual )
= $false )
| ~ spl3_1 ),
inference(constrained_superposition,[],[f143,f91]) ).
thf(f190,plain,
( ( ( eiw_di @ sK1 @ mactual )
= $false )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f187]) ).
thf(f194,plain,
( ( $true = $false )
| ~ spl3_1 ),
inference(forward_demodulation,[],[f190,f77]) ).
thf(f195,plain,
( $false
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f194]) ).
thf(f196,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f195]) ).
cnf(s2,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f149]) ).
cnf(s3,plain,
( spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f184]) ).
cnf(s8,plain,
~ spl3_1,
inference(sat_conversion,[],[f196]) ).
cnf(s9,plain,
~ spl3_2,
inference(rat,[],[s3,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s2,s9,s8]) ).
thf(f197,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET044^23 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n008.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:36:40 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.20/0.27 % (3156982)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (3156987)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1780284725:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.27 % (3156987) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3156982-3156987"...
% 0.20/0.27 % (3156993)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.27 % (3156993)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
% 0.20/0.27 % (3156987)...printing done.
% 0.20/0.27 % (3156987)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (3156987)------------------------------
% 0.20/0.28 % (3156987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3156987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3156987)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3156987)Termination reason: Refutation
% 0.20/0.28 % (3156987)Time elapsed: 0.006 s
% 0.20/0.28 % (3156987)Peak memory usage: 13 MB
% 0.20/0.28 % (3156987)Instructions burned: 19 (million)
% 0.20/0.28 % (3156982)Success in time 0.033 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------