%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET047^1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:23:12 AM UTC 2026
% Result : Theorem 0.23s 0.30s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 12
% Syntax : Number of formulae : 107 ( 35 unt; 0 typ; 7 def)
% Number of atoms : 704 ( 175 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 914 ( 56 ~; 115 |; 0 &; 706 @)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 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 : 42 ( 38 usr; 13 con; 0-4 aty)
% ( 29 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 209 ( 0 sgn 71 !; 0 ?; 209 :)
% 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,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
set_equal: $i > $i > mworld > $o ).
thf(func_def_14,type,
element: $i > $i > mworld > $o ).
thf(func_def_15,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_16,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_22,type,
vIMP: $o > $o > $o ).
thf(func_def_23,type,
vIFF: $o > $o > $o ).
thf(func_def_24,type,
vOR: $o > $o > $o ).
thf(func_def_25,type,
vAND: $o > $o > $o ).
thf(func_def_26,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
vNOT: $o > $o ).
thf(func_def_28,type,
sF0: $o ).
thf(func_def_29,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
sK3: $i > $i > $i ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f6,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) )
= mequiv ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv_def) ).
thf(f9,axiom,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) )
= mforall_di ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di_def) ).
thf(f11,axiom,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mequiv @ ( set_equal @ X0 @ X1 )
@ ( mforall_di
@ ^ [X2: $i] : ( mequiv @ ( element @ X2 @ X0 ) @ ( element @ X2 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel43_1) ).
thf(f12,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( set_equal @ X0 @ X1 ) @ ( set_equal @ X1 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel43) ).
thf(f13,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( set_equal @ X0 @ X1 ) @ ( set_equal @ X1 @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
thf(f14,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) )
= mforall_di ),
inference(rectify,[],[f9]) ).
thf(f15,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( set_equal @ X0 @ X1 ) @ ( set_equal @ X1 @ X0 ) ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f17,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( set_equal @ Y0 @ Y1 ) @ ( set_equal @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f20,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) )
= mequiv ),
inference(rectify,[],[f6]) ).
thf(f21,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f28,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mequiv @ ( set_equal @ X0 @ X1 )
@ ( mforall_di
@ ^ [X2: $i] : ( mequiv @ ( element @ X2 @ X0 ) @ ( element @ X2 @ X1 ) ) ) ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f29,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mequiv @ ( set_equal @ Y0 @ Y1 )
@ ( mforall_di
@ ^ [Y2: $i] : ( mequiv @ ( element @ Y2 @ Y0 ) @ ( element @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f28]) ).
thf(f36,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f37,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( set_equal @ Y0 @ Y1 ) @ ( set_equal @ Y1 @ Y0 ) ) ) ) ) ),
inference(flattening,[],[f17]) ).
thf(f39,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f41,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mequiv @ ( set_equal @ Y0 @ Y1 )
@ ( mforall_di
@ ^ [Y2: $i] : ( mequiv @ ( element @ Y2 @ Y0 ) @ ( element @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f29]) ).
thf(f44,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f46,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f48,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( set_equal @ Y0 @ Y1 ) @ ( set_equal @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f52,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
= ( Y3 @ Y4 ) )
@ ( set_equal @ Y0 @ Y1 )
@ ( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
= ( Y4 @ Y5 ) )
@ ( element @ Y2 @ Y0 )
@ ( element @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f41,f39,f46,f46,f44,f46,f44]) ).
thf(f53,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
= ( Y3 @ Y4 ) )
@ ( set_equal @ Y0 @ Y1 )
@ ( set_equal @ Y1 @ Y0 ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f48,f39,f46,f46,f44]) ).
thf(f54,definition,
( sF0
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
= ( Y3 @ Y4 ) )
@ ( set_equal @ Y0 @ Y1 )
@ ( set_equal @ Y1 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f55,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
= ( Y3 @ Y4 ) )
@ ( set_equal @ Y0 @ Y1 )
@ ( set_equal @ Y1 @ Y0 ) ) ) ) )
= sF0 ),
inference(reorient_equations,[],[f54]) ).
thf(f56,plain,
$true != sF0,
inference(definition_folding,[],[f53,f55]) ).
thf(f58,plain,
( ( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
= ( Y3 @ Y4 ) )
@ ( set_equal @ Y0 @ Y1 )
@ ( set_equal @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( $true = sF0 ) ),
inference(iff_proxy_clausification,[],[f55]) ).
thf(f59,plain,
( ( $true = sF0 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( set_equal @ Y0 @ Y1 @ mactual )
= ( set_equal @ Y1 @ Y0 @ mactual ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f58]) ).
thf(f60,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( set_equal @ Y0 @ Y1 @ mactual )
= ( set_equal @ Y1 @ Y0 @ mactual ) ) )
@ sK1 ) )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f59]) ).
thf(f61,plain,
( ( $true = sF0 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( set_equal @ sK1 @ Y0 @ mactual )
= ( set_equal @ Y0 @ sK1 @ mactual ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f60]) ).
thf(f62,plain,
( ( $true = sF0 )
| ( ( ^ [Y0: $i] :
( ( set_equal @ sK1 @ Y0 @ mactual )
= ( set_equal @ Y0 @ sK1 @ mactual ) )
@ sK2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f61]) ).
thf(f63,plain,
( ( $true = sF0 )
| ( ( ( set_equal @ sK1 @ sK2 @ mactual )
= ( set_equal @ sK2 @ sK1 @ mactual ) )
= $false ) ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f64,plain,
( ( ( set_equal @ sK2 @ sK1 @ mactual )
!= ( set_equal @ sK1 @ sK2 @ mactual ) )
| ( $true = sF0 ) ),
inference(iff_proxy_clausification,[],[f63]) ).
thf(f65,plain,
( ( $true
= ( set_equal @ sK2 @ sK1 @ mactual ) )
| ( $true = sF0 )
| ( $true
= ( set_equal @ sK1 @ sK2 @ mactual ) ) ),
inference(xor_proxy_clausification,[],[f64]) ).
thf(f66,plain,
( ( ( set_equal @ sK1 @ sK2 @ mactual )
= $false )
| ( ( set_equal @ sK2 @ sK1 @ mactual )
= $false )
| ( $true = sF0 ) ),
inference(xor_proxy_clausification,[],[f64]) ).
thf(f75,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( set_equal @ Y0 @ Y1 @ mactual )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( element @ Y2 @ Y0 @ mactual )
= ( element @ Y2 @ Y1 @ mactual ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f76,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( set_equal @ Y0 @ Y1 @ mactual )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( element @ Y2 @ Y0 @ mactual )
= ( element @ Y2 @ Y1 @ mactual ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f75]) ).
thf(f77,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( set_equal @ X1 @ Y0 @ mactual )
= ( !! @ $i
@ ^ [Y1: $i] :
( ( element @ Y1 @ X1 @ mactual )
= ( element @ Y1 @ Y0 @ mactual ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f76]) ).
thf(f78,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( set_equal @ X1 @ Y0 @ mactual )
= ( !! @ $i
@ ^ [Y1: $i] :
( ( element @ Y1 @ X1 @ mactual )
= ( element @ Y1 @ Y0 @ mactual ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( set_equal @ X1 @ X2 @ mactual )
= ( !! @ $i
@ ^ [Y0: $i] :
( ( element @ Y0 @ X1 @ mactual )
= ( element @ Y0 @ X2 @ mactual ) ) ) ) ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
! [X2: $i,X1: $i] :
( ( set_equal @ X1 @ X2 @ mactual )
= ( !! @ $i
@ ^ [Y0: $i] :
( ( element @ Y0 @ X1 @ mactual )
= ( element @ Y0 @ X2 @ mactual ) ) ) ),
inference(iff_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( element @ Y0 @ X1 @ mactual )
= ( element @ Y0 @ X2 @ mactual ) ) )
= $false )
| ( $true
= ( set_equal @ X1 @ X2 @ mactual ) ) ),
inference(iff_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X2: $i,X1: $i] :
( ( ( set_equal @ X1 @ X2 @ mactual )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( element @ Y0 @ X1 @ mactual )
= ( element @ Y0 @ X2 @ mactual ) ) ) ) ),
inference(iff_proxy_clausification,[],[f80]) ).
thf(f83,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( element @ Y0 @ X1 @ mactual )
= ( element @ Y0 @ X2 @ mactual ) )
@ X3 )
= $true )
| ( ( set_equal @ X1 @ X2 @ mactual )
= $false ) ),
inference(pi_proxy_clausification,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( element @ X3 @ X1 @ mactual )
= ( element @ X3 @ X2 @ mactual ) ) )
| ( ( set_equal @ X1 @ X2 @ mactual )
= $false ) ),
inference(beta-eta_normalization,[],[f83]) ).
thf(f85,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( set_equal @ X1 @ X2 @ mactual )
= $false )
| ( ( element @ X3 @ X2 @ mactual )
= ( element @ X3 @ X1 @ mactual ) ) ),
inference(iff_proxy_clausification,[],[f84]) ).
thf(f86,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( element @ X3 @ X2 @ mactual ) )
| ( ( set_equal @ X1 @ X2 @ mactual )
= $false )
| ( ( element @ X3 @ X1 @ mactual )
= $false ) ),
inference(iff_proxy_clausification,[],[f85]) ).
thf(f87,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( element @ X3 @ X1 @ mactual ) )
| ( ( set_equal @ X1 @ X2 @ mactual )
= $false )
| ( ( element @ X3 @ X2 @ mactual )
= $false ) ),
inference(iff_proxy_clausification,[],[f85]) ).
thf(f88,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( set_equal @ X1 @ X2 @ mactual ) )
| ( ( ^ [Y0: $i] :
( ( element @ Y0 @ X1 @ mactual )
= ( element @ Y0 @ X2 @ mactual ) )
@ ( sK3 @ X1 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f81]) ).
thf(f89,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( element @ ( sK3 @ X1 @ X2 ) @ X1 @ mactual )
= ( element @ ( sK3 @ X1 @ X2 ) @ X2 @ mactual ) ) )
| ( $true
= ( set_equal @ X1 @ X2 @ mactual ) ) ),
inference(beta-eta_normalization,[],[f88]) ).
thf(f90,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( set_equal @ X1 @ X2 @ mactual ) )
| ( ( element @ ( sK3 @ X1 @ X2 ) @ X2 @ mactual )
!= ( element @ ( sK3 @ X1 @ X2 ) @ X1 @ mactual ) ) ),
inference(iff_proxy_clausification,[],[f89]) ).
thf(f91,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( element @ ( sK3 @ X1 @ X2 ) @ X2 @ mactual ) )
| ( $true
= ( set_equal @ X1 @ X2 @ mactual ) )
| ( $true
= ( element @ ( sK3 @ X1 @ X2 ) @ X1 @ mactual ) ) ),
inference(xor_proxy_clausification,[],[f90]) ).
thf(f92,plain,
! [X2: $i,X1: $i] :
( ( ( element @ ( sK3 @ X1 @ X2 ) @ X2 @ mactual )
= $false )
| ( ( element @ ( sK3 @ X1 @ X2 ) @ X1 @ mactual )
= $false )
| ( $true
= ( set_equal @ X1 @ X2 @ mactual ) ) ),
inference(xor_proxy_clausification,[],[f90]) ).
thf(f94,definition,
( spl4_1
<=> ( ( set_equal @ sK1 @ sK2 @ mactual )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f96,plain,
( ( ( set_equal @ sK1 @ sK2 @ mactual )
= $false )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f94]) ).
thf(f98,definition,
( spl4_2
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f102,definition,
( spl4_3
<=> ( ( set_equal @ sK2 @ sK1 @ mactual )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f103,plain,
( ( ( set_equal @ sK2 @ sK1 @ mactual )
!= $false )
| spl4_3 ),
inference(avatar_component_clause,[],[f102]) ).
thf(f104,plain,
( ( ( set_equal @ sK2 @ sK1 @ mactual )
= $false )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f102]) ).
thf(f105,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f66,f102,f98,f94]) ).
thf(f107,definition,
( spl4_4
<=> ( $true
= ( set_equal @ sK2 @ sK1 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f109,plain,
( ( $true
= ( set_equal @ sK2 @ sK1 @ mactual ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f107]) ).
thf(f111,definition,
( spl4_5
<=> ( $true
= ( set_equal @ sK1 @ sK2 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f113,plain,
( ( $true
= ( set_equal @ sK1 @ sK2 @ mactual ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f111]) ).
thf(f114,plain,
( spl4_4
| spl4_2
| spl4_5 ),
inference(avatar_split_clause,[],[f65,f111,f98,f107]) ).
thf(f116,definition,
( spl4_6
<=> ! [X2: $i,X1: $i] :
( ( $true
= ( set_equal @ X2 @ X1 @ mactual ) )
| ( ( set_equal @ X1 @ X2 @ mactual )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f117,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( set_equal @ X2 @ X1 @ mactual ) )
| ( ( set_equal @ X1 @ X2 @ mactual )
= $false ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f116]) ).
thf(f124,plain,
~ spl4_2,
inference(avatar_split_clause,[],[f56,f98]) ).
thf(f140,plain,
( ( $true = $false )
| ~ spl4_3
| ~ spl4_4 ),
inference(forward_demodulation,[],[f109,f104]) ).
thf(f141,plain,
( $false
| ~ spl4_3
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f140]) ).
thf(f142,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f141]) ).
thf(f145,plain,
( ( ( set_equal @ sK1 @ sK2 @ mactual )
= $false )
| ( $true = $false )
| ~ spl4_3
| ~ spl4_6 ),
inference(constrained_superposition,[],[f104,f117]) ).
thf(f148,plain,
( ( ( set_equal @ sK1 @ sK2 @ mactual )
= $false )
| ~ spl4_3
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f145]) ).
thf(f152,plain,
( ( $true = $false )
| ~ spl4_3
| ~ spl4_5
| ~ spl4_6 ),
inference(forward_demodulation,[],[f148,f113]) ).
thf(f153,plain,
( $false
| ~ spl4_3
| ~ spl4_5
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f152]) ).
thf(f154,plain,
( ~ spl4_3
| ~ spl4_5
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f153]) ).
thf(f167,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( set_equal @ X1 @ X2 @ mactual )
= $false )
| ( ( element @ ( sK3 @ X0 @ X1 ) @ X0 @ mactual )
= $false )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( ( element @ ( sK3 @ X0 @ X1 ) @ X2 @ mactual )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f92,f87]) ).
thf(f186,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( element @ ( sK3 @ X0 @ X1 ) @ X2 @ mactual )
= $false )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( ( set_equal @ X1 @ X2 @ mactual )
= $false )
| ( ( element @ ( sK3 @ X0 @ X1 ) @ X0 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[],[f167]) ).
thf(f223,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( $false != $false )
| ( ( element @ ( sK3 @ X0 @ X1 ) @ X0 @ mactual )
= $false )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false ) ),
inference(equality_factoring,[],[f186]) ).
thf(f233,plain,
! [X0: $i,X1: $i] :
( ( ( element @ ( sK3 @ X0 @ X1 ) @ X0 @ mactual )
= $false )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f223]) ).
thf(f245,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( element @ ( sK3 @ X0 @ X1 ) @ X2 @ mactual )
= $false )
| ( $false
= ( set_equal @ X2 @ X0 @ mactual ) )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f86,f233]) ).
thf(f258,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( element @ ( sK3 @ X0 @ X1 ) @ X2 @ mactual )
= $false )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false )
| ( $false
= ( set_equal @ X2 @ X0 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f245]) ).
thf(f287,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( element @ ( sK3 @ X0 @ X1 ) @ X0 @ mactual )
= $true )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false ) ),
inference(constrained_superposition,[],[f91,f258]) ).
thf(f297,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( ( element @ ( sK3 @ X0 @ X1 ) @ X0 @ mactual )
= $true )
| ( $true = $false )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false ) ),
inference(duplicate_literal_removal,[],[f287]) ).
thf(f298,plain,
! [X0: $i,X1: $i] :
( ( ( element @ ( sK3 @ X0 @ X1 ) @ X0 @ mactual )
= $true )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[],[f297]) ).
thf(f311,plain,
! [X0: $i,X1: $i] :
( ( ( set_equal @ X1 @ X0 @ mactual )
= $false )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f233,f298]) ).
thf(f322,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false ) ),
inference(duplicate_literal_removal,[],[f311]) ).
thf(f323,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( ( set_equal @ X1 @ X0 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[],[f322]) ).
thf(f344,plain,
spl4_6,
inference(avatar_split_clause,[],[f323,f116]) ).
thf(f354,plain,
( ( $true = $false )
| ( ( set_equal @ sK2 @ sK1 @ mactual )
= $false )
| ~ spl4_1
| ~ spl4_6 ),
inference(constrained_superposition,[],[f117,f96]) ).
thf(f359,plain,
( ( ( set_equal @ sK2 @ sK1 @ mactual )
= $false )
| ~ spl4_1
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f354]) ).
thf(f362,plain,
( $false
| ~ spl4_1
| spl4_3
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f359,f103]) ).
thf(f363,plain,
( ~ spl4_1
| spl4_3
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f362]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f105]) ).
cnf(s2,plain,
( spl4_2
| spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f114]) ).
cnf(s5,plain,
~ spl4_2,
inference(sat_conversion,[],[f124]) ).
cnf(s7,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f142]) ).
cnf(s9,plain,
( ~ spl4_3
| ~ spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f154]) ).
cnf(s11,plain,
spl4_6,
inference(sat_conversion,[],[f344]) ).
cnf(s19,plain,
( ~ spl4_1
| spl4_3
| ~ spl4_6 ),
inference(sat_conversion,[],[f363]) ).
cnf(s20,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(rat,[],[s9,s11]) ).
cnf(s23,plain,
( spl4_4
| spl4_5 ),
inference(rat,[],[s2,s5]) ).
cnf(s24,plain,
( spl4_1
| spl4_3 ),
inference(rat,[],[s1,s5]) ).
cnf(s25,plain,
~ spl4_3,
inference(rat,[],[s23,s7,s20]) ).
cnf(s26,plain,
~ spl4_1,
inference(rat,[],[s19,s11,s25]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s24,s25,s26]) ).
thf(f364,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET047^1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n020.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
% 0.09/0.19 % DateTime : Tue Sep 29 13:37:20 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.30 % (1055796)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.30 % (1055806)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4074106622:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.30 % (1055807)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.30 % (1055807)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.23/0.30 % (1055802)lrs+10_16_si=on:nwc=1.5:random_seed=1484928128:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.30 % (1055801)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3592327154:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.30 % (1055807)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=133744130:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.30 % (1055803)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1070336401:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.30 % (1055805)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2197275486:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.30 % (1055804)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2612666222:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.23/0.30 % (1055803)Instruction limit reached!
% 0.23/0.30 % (1055803)------------------------------
% 0.23/0.30 % (1055803)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (1055803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (1055803)CaDiCaL version: 2.1.3
% 0.23/0.30 % (1055803)Termination reason: Instruction limit
% 0.23/0.30 % (1055803)Termination phase: Saturation
% 0.23/0.30 % (1055803)Time elapsed: 0.002 s
% 0.23/0.30 % (1055803)Peak memory usage: 11 MB
% 0.23/0.30 % (1055803)Instructions burned: 3 (million)
% 0.23/0.30 % (1055802)Instruction limit reached!
% 0.23/0.30 % (1055802)------------------------------
% 0.23/0.30 % (1055802)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (1055802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (1055802)CaDiCaL version: 2.1.3
% 0.23/0.30 % (1055802)Termination reason: Instruction limit
% 0.23/0.30 % (1055802)Termination phase: Saturation
% 0.23/0.30 % (1055802)Time elapsed: 0.010 s
% 0.23/0.30 % (1055802)Peak memory usage: 12 MB
% 0.23/0.30 % (1055802)Instructions burned: 20 (million)
% 0.23/0.30 % (1055807) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1055796-1055807"...
% 0.23/0.30 % (1055806)Instruction limit reached!
% 0.23/0.30 % (1055806)------------------------------
% 0.23/0.30 % (1055806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (1055806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (1055806)CaDiCaL version: 2.1.3
% 0.23/0.30 % (1055806)Termination reason: Instruction limit
% 0.23/0.30 % (1055806)Termination phase: Saturation
% 0.23/0.30 % (1055806)Time elapsed: 0.020 s
% 0.23/0.30 % (1055806)Peak memory usage: 12 MB
% 0.23/0.30 % (1055806)Instructions burned: 77 (million)
% 0.23/0.30 % (1055805)Instruction limit reached!
% 0.23/0.30 % (1055805)------------------------------
% 0.23/0.30 % (1055805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (1055805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (1055805)CaDiCaL version: 2.1.3
% 0.23/0.30 % (1055805)Termination reason: Instruction limit
% 0.23/0.30 % (1055805)Termination phase: Saturation
% 0.23/0.30 % (1055805)Time elapsed: 0.014 s
% 0.23/0.30 % (1055805)Peak memory usage: 11 MB
% 0.23/0.30 % (1055805)Instructions burned: 24 (million)
% 0.23/0.30 % (1055807)...printing done.
% 0.23/0.30 % (1055807)Refutation found. Thanks to Tanya!
% 0.23/0.30 % SZS status Theorem for theBenchmark
% 0.23/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.30 % (1055807)------------------------------
% 0.23/0.30 % (1055807)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (1055807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (1055807)CaDiCaL version: 2.1.3
% 0.23/0.30 % (1055807)Termination reason: Refutation
% 0.23/0.30 % (1055807)Time elapsed: 0.015 s
% 0.23/0.30 % (1055807)Peak memory usage: 13 MB
% 0.23/0.30 % (1055807)Instructions burned: 28 (million)
% 0.23/0.30 % (1055796)Success in time 0.053 s
% 0.23/0.30 % Vampire exiting
%------------------------------------------------------------------------------