%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO891^16 : 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 : n001.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 08:48:35 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of formulae : 65 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 410 ( 82 equ; 0 cnn)
% Maximal formula atoms : 13 ( 6 avg)
% Number of connectives : 605 ( 19 ~; 21 |; 43 &; 462 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 33 usr; 7 con; 0-4 aty)
% ( 8 !!; 28 ??; 0 @@+; 0 @@-)
% Number of variables : 178 ( 136 ^; 38 !; 4 ?; 178 :)
% 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,
qmltpeq: $i > $i > mworld > $o ).
thf(func_def_15,type,
p: $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_20,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_21,type,
vIMP: $o > $o > $o ).
thf(func_def_22,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vOR: $o > $o > $o ).
thf(func_def_25,type,
vIFF: $o > $o > $o ).
thf(func_def_26,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
vAND: $o > $o > $o ).
thf(func_def_28,type,
vNOT: $o > $o ).
thf(func_def_29,type,
sK0: mworld > $i ).
thf(func_def_30,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
sK1: $i > mworld > $i ).
thf(func_def_34,type,
sK3: mworld ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_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(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f8,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( mrel @ X1 @ X2 )
& ( X0 @ X2 ) ) )
= mdia ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_def) ).
thf(f12,axiom,
! [X1: mworld,X2: $i,X0: mworld] :
( ( ( eiw_di @ X2 @ X0 )
& ( mrel @ X0 @ X1 ) )
=> ( eiw_di @ X2 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_cumul) ).
thf(f13,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(f14,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(f19,conjecture,
( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [X0: $i] :
( mbox
@ ( mexists_di
@ ^ [X1: $i] : ( qmltpeq @ X0 @ X1 ) ) ) )
@ ( mimplies
@ ( mexists_di
@ ^ [X0: $i] : ( mdia @ ( p @ X0 ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [X0: $i] : ( p @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f20,negated_conjecture,
~ ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [X0: $i] :
( mbox
@ ( mexists_di
@ ^ [X1: $i] : ( qmltpeq @ X0 @ X1 ) ) ) )
@ ( mimplies
@ ( mexists_di
@ ^ [X0: $i] : ( mdia @ ( p @ X0 ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [X0: $i] : ( p @ X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
thf(f23,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f24,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f39,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f40,plain,
! [X0: mworld,X1: $i,X2: mworld] :
( ( ( eiw_di @ X1 @ X2 )
& ( mrel @ X2 @ X0 ) )
=> ( eiw_di @ X1 @ X0 ) ),
inference(rectify,[],[f12]) ).
thf(f41,plain,
! [X2: mworld,X0: mworld,X1: $i] :
( ( ( ( eiw_di @ X1 @ X2 )
= $true )
& ( ( mrel @ X2 @ X0 )
= $true ) )
=> ( ( eiw_di @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f40]) ).
thf(f42,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f43,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f46,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f47,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f48,plain,
~ ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [X0: $i] :
( mbox
@ ( mexists_di
@ ^ [X1: $i] : ( qmltpeq @ X0 @ X1 ) ) ) )
@ ( mimplies
@ ( mexists_di
@ ^ [X2: $i] : ( mdia @ ( p @ X2 ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [X3: $i] : ( p @ X3 ) ) ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f49,plain,
( ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mexists_di
@ ^ [Y1: $i] : ( qmltpeq @ Y0 @ Y1 ) ) ) )
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] : ( mdia @ ( p @ Y0 ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [Y0: $i] : ( p @ Y0 ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f48]) ).
thf(f50,plain,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f51,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f56,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( mrel @ X1 @ X2 )
& ( X0 @ X2 ) ) )
= mdia ),
inference(rectify,[],[f8]) ).
thf(f57,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f58,plain,
( ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mexists_di
@ ^ [Y1: $i] : ( qmltpeq @ Y0 @ Y1 ) ) ) )
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] : ( mdia @ ( p @ Y0 ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [Y0: $i] : ( p @ Y0 ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f49]) ).
thf(f61,plain,
! [X2: mworld,X0: mworld,X1: $i] :
( ( ( eiw_di @ X1 @ X0 )
= $true )
| ( ( eiw_di @ X1 @ X2 )
!= $true )
| ( ( mrel @ X2 @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f41]) ).
thf(f62,plain,
! [X2: mworld,X0: mworld,X1: $i] :
( ( ( eiw_di @ X1 @ X0 )
= $true )
| ( ( eiw_di @ X1 @ X2 )
!= $true )
| ( ( mrel @ X2 @ X0 )
!= $true ) ),
inference(flattening,[],[f61]) ).
thf(f65,plain,
! [X0: mworld,X1: mworld,X2: $i] :
( ( ( eiw_di @ X2 @ X1 )
= $true )
| ( ( eiw_di @ X2 @ X0 )
!= $true )
| ( ( mrel @ X0 @ X1 )
!= $true ) ),
inference(rectify,[],[f62]) ).
thf(f66,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f70,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f73,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f75,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f76,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f77,plain,
( ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mexists_di
@ ^ [Y1: $i] : ( qmltpeq @ Y0 @ Y1 ) ) ) )
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] : ( mdia @ ( p @ Y0 ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [Y0: $i] : ( p @ Y0 ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f58]) ).
thf(f81,plain,
! [X2: $i,X0: mworld,X1: mworld] :
( ( ( mrel @ X0 @ X1 )
!= $true )
| ( ( eiw_di @ X2 @ X0 )
!= $true )
| ( ( eiw_di @ X2 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f83,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f89,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: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
& ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] : ( qmltpeq @ Y0 @ Y1 ) ) ) )
@ ( ^ [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: mworld > $o,Y2: mworld] :
( ?? @ mworld
@ ^ [Y3: mworld] :
( ( Y1 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
@ ( p @ Y0 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] : ( p @ Y0 ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f77,f73,f70,f83,f76,f66,f70,f66,f75,f75,f66]) ).
thf(f92,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( qmltpeq @ Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( p @ Y0 @ Y1 )
& ( mrel @ mactual @ Y1 ) ) ) ) )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( p @ Y1 @ Y0 ) ) )
& ( mrel @ mactual @ Y0 ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f89]) ).
thf(f93,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( p @ Y0 @ Y1 )
& ( mrel @ mactual @ Y1 ) ) ) ) )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( p @ Y1 @ Y0 ) ) )
& ( mrel @ mactual @ Y0 ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f92]) ).
thf(f105,plain,
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( p @ Y1 @ Y0 ) ) )
& ( mrel @ mactual @ Y0 ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f93]) ).
thf(f106,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( p @ Y0 @ Y1 )
& ( mrel @ mactual @ Y1 ) ) ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f93]) ).
thf(f107,plain,
( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( p @ Y0 @ Y1 )
& ( mrel @ mactual @ Y1 ) ) ) )
@ sK2 )
= $true ),
inference(sigma_proxy_clausification,[],[f106]) ).
thf(f108,plain,
( ( ( eiw_di @ sK2 @ mactual )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ sK2 @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f107]) ).
thf(f109,plain,
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ sK2 @ Y0 )
& ( mrel @ mactual @ Y0 ) ) )
= $true ),
inference(and_proxy_clausification,[],[f108]) ).
thf(f110,plain,
( ( eiw_di @ sK2 @ mactual )
= $true ),
inference(and_proxy_clausification,[],[f108]) ).
thf(f111,plain,
( ( ^ [Y0: mworld] :
( ( p @ sK2 @ Y0 )
& ( mrel @ mactual @ Y0 ) )
@ sK3 )
= $true ),
inference(sigma_proxy_clausification,[],[f109]) ).
thf(f112,plain,
( ( ( p @ sK2 @ sK3 )
& ( mrel @ mactual @ sK3 ) )
= $true ),
inference(beta-eta_normalization,[],[f111]) ).
thf(f113,plain,
( ( mrel @ mactual @ sK3 )
= $true ),
inference(and_proxy_clausification,[],[f112]) ).
thf(f114,plain,
( ( p @ sK2 @ sK3 )
= $true ),
inference(and_proxy_clausification,[],[f112]) ).
thf(f115,plain,
! [X1: mworld] :
( $false
= ( ^ [Y0: mworld] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( p @ Y1 @ Y0 ) ) )
& ( mrel @ mactual @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f105]) ).
thf(f116,plain,
! [X1: mworld] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( p @ Y0 @ X1 ) ) )
& ( mrel @ mactual @ X1 ) )
= $false ),
inference(beta-eta_normalization,[],[f115]) ).
thf(f117,plain,
! [X1: mworld] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( p @ Y0 @ X1 ) ) )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(and_proxy_clausification,[],[f116]) ).
thf(f118,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( p @ Y0 @ X1 ) )
@ X2 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( eiw_di @ X2 @ X1 )
& ( p @ X2 @ X1 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( p @ X2 @ X1 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f119]) ).
thf(f154,plain,
! [X0: $i] :
( ( ( eiw_di @ X0 @ sK3 )
= $false )
| ( $false = $true )
| ( ( p @ X0 @ sK3 )
= $false ) ),
inference(constrained_superposition,[],[f120,f113]) ).
thf(f156,plain,
! [X0: $i] :
( ( ( p @ X0 @ sK3 )
= $false )
| ( ( eiw_di @ X0 @ sK3 )
= $false ) ),
inference(trivial_inequality_removal,[],[f154]) ).
thf(f158,plain,
( ( $false = $true )
| ( ( eiw_di @ sK2 @ sK3 )
= $false ) ),
inference(constrained_superposition,[],[f156,f114]) ).
thf(f160,plain,
( ( eiw_di @ sK2 @ sK3 )
= $false ),
inference(trivial_inequality_removal,[],[f158]) ).
thf(f172,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( eiw_di @ X0 @ mactual )
!= $true )
| ( ( eiw_di @ X0 @ sK3 )
= $true ) ),
inference(constrained_superposition,[],[f81,f113]) ).
thf(f175,plain,
! [X0: $i] :
( ( ( eiw_di @ X0 @ mactual )
!= $true )
| ( ( eiw_di @ X0 @ sK3 )
= $true ) ),
inference(trivial_inequality_removal,[],[f172]) ).
thf(f178,plain,
( ( ( eiw_di @ sK2 @ sK3 )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f175,f110]) ).
thf(f181,plain,
( ( eiw_di @ sK2 @ sK3 )
= $true ),
inference(trivial_inequality_removal,[],[f178]) ).
thf(f184,plain,
$false = $true,
inference(forward_demodulation,[],[f181,f160]) ).
thf(f185,plain,
$false,
inference(trivial_inequality_removal,[],[f184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO891^16 : 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 : n001.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 17:31:52 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.22/0.28 % (1556381)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (1556386)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2419298708:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.28 % (1556386) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1556381-1556386"...
% 0.22/0.28 % (1556392)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.28 % (1556392)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
% 0.22/0.28 % (1556386)...printing done.
% 0.22/0.28 % (1556386)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (1556386)------------------------------
% 0.22/0.28 % (1556386)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (1556386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (1556386)CaDiCaL version: 2.1.3
% 0.22/0.28 % (1556386)Termination reason: Refutation
% 0.22/0.28 % (1556386)Time elapsed: 0.005 s
% 0.22/0.28 % (1556386)Peak memory usage: 12 MB
% 0.22/0.28 % (1556386)Instructions burned: 18 (million)
% 0.22/0.28 % (1556381)Success in time 0.022 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------