%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET047^1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 08:23:33 AM UTC 2026
% Result : Theorem 0.19s 0.29s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 7
% Syntax : Number of formulae : 90 ( 34 unt; 0 typ; 2 def)
% Number of atoms : 606 ( 155 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 778 ( 34 ~; 86 |; 0 &; 631 @)
% ( 4 <=>; 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 : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 33 usr; 8 con; 0-4 aty)
% ( 23 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 169 ( 0 sgn 67 !; 0 ?; 169 :)
% 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,
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_19,type,
vAND: $o > $o > $o ).
thf(func_def_20,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
vOR: $o > $o > $o ).
thf(func_def_22,type,
vIMP: $o > $o > $o ).
thf(func_def_23,type,
vIFF: $o > $o > $o ).
thf(func_def_24,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_25,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_28,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
sK2: $i > $i > $i ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_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(f9,axiom,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f23,plain,
( mequiv
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f24,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f29,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f9]) ).
thf(f30,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f29]) ).
thf(f33,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(f34,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,[],[f33]) ).
thf(f35,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( set_equal @ X0 @ X1 ) @ ( set_equal @ X1 @ X0 ) ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f36,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( set_equal @ Y0 @ Y1 ) @ ( set_equal @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f35]) ).
thf(f37,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( set_equal @ Y0 @ Y1 ) @ ( set_equal @ Y1 @ Y0 ) ) ) ) ) ),
inference(flattening,[],[f36]) ).
thf(f38,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f43,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f46,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f48,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,[],[f34]) ).
thf(f49,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,[],[f48,f38,f46,f46,f43,f46,f43]) ).
thf(f53,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 )
@ ( set_equal @ Y1 @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f49,f38,f46,f46,f43]) ).
thf(f54,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( set_equal @ Y0 @ Y1 @ mactual )
= ( set_equal @ Y1 @ Y0 @ mactual ) ) ) ) ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f55,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( set_equal @ Y0 @ Y1 @ mactual )
= ( set_equal @ Y1 @ Y0 @ mactual ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f54]) ).
thf(f56,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( set_equal @ sK0 @ Y0 @ mactual )
= ( set_equal @ Y0 @ sK0 @ mactual ) ) ) ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,plain,
( $false
= ( ^ [Y0: $i] :
( ( set_equal @ sK0 @ Y0 @ mactual )
= ( set_equal @ Y0 @ sK0 @ mactual ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f56]) ).
thf(f58,plain,
( $false
= ( ( set_equal @ sK0 @ sK1 @ mactual )
= ( set_equal @ sK1 @ sK0 @ mactual ) ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f59,plain,
( ( set_equal @ sK0 @ sK1 @ mactual )
!= ( set_equal @ sK1 @ sK0 @ mactual ) ),
inference(iff_proxy_clausification,[],[f58]) ).
thf(f60,plain,
( ( $true
= ( set_equal @ sK0 @ sK1 @ mactual ) )
| ( $true
= ( set_equal @ sK1 @ sK0 @ mactual ) ) ),
inference(xor_proxy_clausification,[],[f59]) ).
thf(f61,plain,
( ( $false
= ( set_equal @ sK0 @ sK1 @ mactual ) )
| ( $false
= ( set_equal @ sK1 @ sK0 @ mactual ) ) ),
inference(xor_proxy_clausification,[],[f59]) ).
thf(f62,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( set_equal @ Y0 @ Y1 @ mactual )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( element @ Y2 @ Y0 @ mactual )
= ( element @ Y2 @ Y1 @ mactual ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f63,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,[],[f62]) ).
thf(f64,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,[],[f63]) ).
thf(f65,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,[],[f64]) ).
thf(f66,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,[],[f65]) ).
thf(f67,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,[],[f66]) ).
thf(f68,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( set_equal @ X1 @ X2 @ mactual ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( element @ Y0 @ X1 @ mactual )
= ( element @ Y0 @ X2 @ mactual ) ) ) ) ),
inference(iff_proxy_clausification,[],[f67]) ).
thf(f69,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( set_equal @ X1 @ X2 @ mactual ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( element @ Y0 @ X1 @ mactual )
= ( element @ Y0 @ X2 @ mactual ) ) ) ) ),
inference(iff_proxy_clausification,[],[f67]) ).
thf(f70,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( set_equal @ X1 @ X2 @ mactual ) )
| ( $true
= ( ^ [Y0: $i] :
( ( element @ Y0 @ X1 @ mactual )
= ( element @ Y0 @ X2 @ mactual ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( set_equal @ X1 @ X2 @ mactual ) )
| ( $true
= ( ( element @ X3 @ X1 @ mactual )
= ( element @ X3 @ X2 @ mactual ) ) ) ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f72,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( set_equal @ X1 @ X2 @ mactual ) )
| ( ( element @ X3 @ X1 @ mactual )
= ( element @ X3 @ X2 @ mactual ) ) ),
inference(iff_proxy_clausification,[],[f71]) ).
thf(f73,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( set_equal @ X1 @ X2 @ mactual ) )
| ( $true
= ( element @ X3 @ X1 @ mactual ) )
| ( $false
= ( element @ X3 @ X2 @ mactual ) ) ),
inference(iff_proxy_clausification,[],[f72]) ).
thf(f74,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( set_equal @ X1 @ X2 @ mactual ) )
| ( $false
= ( element @ X3 @ X1 @ mactual ) )
| ( $true
= ( element @ X3 @ X2 @ mactual ) ) ),
inference(iff_proxy_clausification,[],[f72]) ).
thf(f75,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( set_equal @ X1 @ X2 @ mactual ) )
| ( $false
= ( ^ [Y0: $i] :
( ( element @ Y0 @ X1 @ mactual )
= ( element @ Y0 @ X2 @ mactual ) )
@ ( sK2 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f68]) ).
thf(f76,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( set_equal @ X1 @ X2 @ mactual ) )
| ( $false
= ( ( element @ ( sK2 @ X1 @ X2 ) @ X1 @ mactual )
= ( element @ ( sK2 @ X1 @ X2 ) @ X2 @ mactual ) ) ) ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f77,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( set_equal @ X1 @ X2 @ mactual ) )
| ( ( element @ ( sK2 @ X1 @ X2 ) @ X1 @ mactual )
!= ( element @ ( sK2 @ X1 @ X2 ) @ X2 @ mactual ) ) ),
inference(iff_proxy_clausification,[],[f76]) ).
thf(f78,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( element @ ( sK2 @ X1 @ X2 ) @ X2 @ mactual ) )
| ( $true
= ( element @ ( sK2 @ X1 @ X2 ) @ X1 @ mactual ) )
| ( $true
= ( set_equal @ X1 @ X2 @ mactual ) ) ),
inference(xor_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( element @ ( sK2 @ X1 @ X2 ) @ X2 @ mactual ) )
| ( $false
= ( element @ ( sK2 @ X1 @ X2 ) @ X1 @ mactual ) )
| ( $true
= ( set_equal @ X1 @ X2 @ mactual ) ) ),
inference(xor_proxy_clausification,[],[f77]) ).
thf(f81,definition,
( spl3_1
<=> ( $true
= ( set_equal @ sK1 @ sK0 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f82,plain,
( ( $true
!= ( set_equal @ sK1 @ sK0 @ mactual ) )
| spl3_1 ),
inference(avatar_component_clause,[],[f81]) ).
thf(f83,plain,
( ( $true
= ( set_equal @ sK1 @ sK0 @ mactual ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f81]) ).
thf(f85,definition,
( spl3_2
<=> ( $true
= ( set_equal @ sK0 @ sK1 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f86,plain,
( ( $true
!= ( set_equal @ sK0 @ sK1 @ mactual ) )
| spl3_2 ),
inference(avatar_component_clause,[],[f85]) ).
thf(f87,plain,
( ( $true
= ( set_equal @ sK0 @ sK1 @ mactual ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f85]) ).
thf(f88,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f60,f85,f81]) ).
thf(f200,plain,
( ( $true = $false )
| ( $false
= ( set_equal @ sK1 @ sK0 @ mactual ) )
| ~ spl3_2 ),
inference(forward_demodulation,[],[f61,f87]) ).
thf(f201,plain,
( ( $false
= ( set_equal @ sK1 @ sK0 @ mactual ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f200]) ).
thf(f207,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_2 ),
inference(constrained_superposition,[],[f83,f201]) ).
thf(f208,plain,
( $false
| ~ spl3_1
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f207]) ).
thf(f209,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_contradiction_clause,[],[f208]) ).
thf(f253,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( set_equal @ X2 @ X0 @ mactual ) )
| ( $true
= ( element @ ( sK2 @ X0 @ X1 ) @ X2 @ mactual ) )
| ( $true
= ( element @ ( sK2 @ X0 @ X1 ) @ X1 @ mactual ) )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) ) ),
inference(constrained_superposition,[],[f73,f78]) ).
thf(f258,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( element @ ( sK2 @ X0 @ X1 ) @ X2 @ mactual ) )
| ( $true
= ( element @ ( sK2 @ X0 @ X1 ) @ X1 @ mactual ) )
| ( $false
= ( set_equal @ X2 @ X0 @ mactual ) )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f253]) ).
thf(f1047,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true = $false )
| ( $false
= ( set_equal @ X1 @ X0 @ mactual ) )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( $false
= ( element @ ( sK2 @ X0 @ X1 ) @ X0 @ mactual ) )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) ) ),
inference(constrained_superposition,[],[f258,f79]) ).
thf(f1072,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( element @ ( sK2 @ X0 @ X1 ) @ X1 @ mactual ) )
| ( $false
= ( set_equal @ X1 @ X0 @ mactual ) )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) ) ),
inference(equality_factoring,[],[f258]) ).
thf(f1073,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( element @ ( sK2 @ X0 @ X1 ) @ X1 @ mactual ) )
| ( $false
= ( set_equal @ X1 @ X0 @ mactual ) )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f1072]) ).
thf(f1103,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( set_equal @ X1 @ X0 @ mactual ) )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( $false
= ( element @ ( sK2 @ X0 @ X1 ) @ X0 @ mactual ) ) ),
inference(duplicate_literal_removal,[],[f1047]) ).
thf(f1104,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( element @ ( sK2 @ X0 @ X1 ) @ X0 @ mactual ) )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( $false
= ( set_equal @ X1 @ X0 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f1103]) ).
thf(f1119,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( set_equal @ X1 @ X2 @ mactual ) )
| ( $true
= ( element @ ( sK2 @ X0 @ X1 ) @ X2 @ mactual ) )
| ( $false
= ( set_equal @ X1 @ X0 @ mactual ) )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) ) ),
inference(constrained_superposition,[],[f74,f1073]) ).
thf(f1134,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( element @ ( sK2 @ X0 @ X1 ) @ X2 @ mactual ) )
| ( $false
= ( set_equal @ X1 @ X2 @ mactual ) )
| ( $false
= ( set_equal @ X1 @ X0 @ mactual ) )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f1119]) ).
thf(f1219,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( $false
= ( set_equal @ X1 @ X0 @ mactual ) )
| ( $false
= ( set_equal @ X1 @ X0 @ mactual ) )
| ( $false
= ( set_equal @ X1 @ X0 @ mactual ) )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) ) ),
inference(constrained_superposition,[],[f1104,f1134]) ).
thf(f1223,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( $false
= ( set_equal @ X1 @ X0 @ mactual ) ) ),
inference(duplicate_literal_removal,[],[f1219]) ).
thf(f1224,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( set_equal @ X0 @ X1 @ mactual ) )
| ( $false
= ( set_equal @ X1 @ X0 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f1223]) ).
thf(f1283,plain,
( ( $true != $true )
| ( $false
= ( set_equal @ sK0 @ sK1 @ mactual ) )
| spl3_1 ),
inference(constrained_superposition,[],[f82,f1224]) ).
thf(f1286,plain,
( ( $false
= ( set_equal @ sK0 @ sK1 @ mactual ) )
| spl3_1 ),
inference(trivial_inequality_removal,[],[f1283]) ).
thf(f1313,plain,
( ( $true = $false )
| spl3_1
| ~ spl3_2 ),
inference(constrained_superposition,[],[f1286,f87]) ).
thf(f1317,plain,
( $false
| spl3_1
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f1313]) ).
thf(f1318,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_contradiction_clause,[],[f1317]) ).
thf(f1322,plain,
( ( $true = $false )
| ( $true
= ( set_equal @ sK0 @ sK1 @ mactual ) )
| ~ spl3_1 ),
inference(constrained_superposition,[],[f83,f1224]) ).
thf(f1325,plain,
( ( $true
= ( set_equal @ sK0 @ sK1 @ mactual ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f1322]) ).
thf(f1328,plain,
( $false
| ~ spl3_1
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f1325,f86]) ).
thf(f1329,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_contradiction_clause,[],[f1328]) ).
cnf(s11,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f88]) ).
cnf(s59,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f209]) ).
cnf(s441,plain,
( spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f1318]) ).
cnf(s450,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f1329]) ).
cnf(s451,plain,
spl3_1,
inference(rat,[],[s11,s441]) ).
cnf(s452,plain,
spl3_2,
inference(rat,[],[s450,s451]) ).
cnf(s456,plain,
$false,
inference(rat,[],[s59,s452,s451]) ).
thf(f1330,plain,
$false,
inference(avatar_sat_refutation,[],[s456]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET047^1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n018.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 13:38:42 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.29 % (72624)Will run a generic schedule for satisfiability detection.
% 0.19/0.29 % (72631)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3715465410:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.29 % (72630)% WARNING: option uhcvi not known.
% 0.19/0.29 % (72629)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2707789171_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.29 % (72630)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=620587407:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.29 % (72633)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1515316253:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.29 % (72632)dis+10_1_sil=32000:sp=arity:random_seed=2065068764:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.29 % (72634)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=309312992:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.29 % (72635)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1122260319:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.29 % (72633)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.29 % (72630)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.29 % Exception at run slice level
% 0.19/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.29 % (72630)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.29 % (72643)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=775150450:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.29 % Exception at run slice level
% 0.19/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.29 % (72631) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-72624-72631"...
% 0.19/0.29 % (72631)...printing done.
% 0.19/0.29 % (72631)Refutation found. Thanks to Tanya!
% 0.19/0.29 % SZS status Theorem for theBenchmark
% 0.19/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.29 % (72631)------------------------------
% 0.19/0.29 % (72631)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (72631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (72631)CaDiCaL version: 2.1.3
% 0.19/0.29 % (72631)Termination reason: Refutation
% 0.19/0.29 % (72631)Time elapsed: 0.032 s
% 0.19/0.29 % (72631)Peak memory usage: 13 MB
% 0.19/0.29 % (72631)Instructions burned: 120 (million)
% 0.19/0.29 % (72624)Success in time 0.059 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------