%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO889^16 : 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 : n019.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 0.11s 0.26s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 8
% Syntax : Number of formulae : 87 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 732 ( 154 equ; 0 cnn)
% Maximal formula atoms : 17 ( 8 avg)
% Number of connectives : 1090 ( 7 ~; 71 |; 78 &; 825 @)
% ( 0 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 32 usr; 7 con; 0-4 aty)
% ( 25 !!; 43 ??; 0 @@+; 0 @@-)
% Number of variables : 253 ( 185 ^; 64 !; 4 ?; 253 :)
% 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,
a: $i > mworld > $o ).
thf(func_def_15,type,
b: $i > mworld > $o ).
thf(func_def_16,type,
vAND: $o > $o > $o ).
thf(func_def_17,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_23,type,
vIMP: $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_26,type,
vOR: $o > $o > $o ).
thf(func_def_27,type,
vNOT: $o > $o ).
thf(func_def_28,type,
vIFF: $o > $o > $o ).
thf(func_def_29,type,
sK0: mworld > $i ).
thf(func_def_30,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
sK1: mworld ).
thf(func_def_33,type,
sK3: mworld > $i > mworld ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f3,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(f5,axiom,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f8,axiom,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( mrel @ X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_def) ).
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,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( eiw_di @ X2 @ X1 )
& ( X0 @ X2 @ X1 ) ) )
= mexists_di ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_di_def) ).
thf(f15,conjecture,
( mlocal
@ ( mimplies
@ ( mand
@ ( mdia
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( a @ X0 ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] : ( mdia @ ( b @ X0 ) ) ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [X0: $i] : ( mdia @ ( mand @ ( a @ X0 ) @ ( b @ X0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f16,negated_conjecture,
~ ( mlocal
@ ( mimplies
@ ( mand
@ ( mdia
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( a @ X0 ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] : ( mdia @ ( b @ X0 ) ) ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [X0: $i] : ( mdia @ ( mand @ ( a @ X0 ) @ ( b @ X0 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f17,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= mand ),
inference(rectify,[],[f3]) ).
thf(f18,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f24,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f25,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f26,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f27,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f26]) ).
thf(f28,plain,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( mrel @ X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f29,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f32,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[],[f7]) ).
thf(f33,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f34,plain,
~ ( mlocal
@ ( mimplies
@ ( mand
@ ( mdia
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( a @ X0 ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( mdia @ ( b @ X1 ) ) ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [X2: $i] : ( mdia @ ( mand @ ( a @ X2 ) @ ( b @ X2 ) ) ) ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f35,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mand
@ ( mdia
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( a @ Y0 ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( mdia @ ( b @ Y0 ) ) ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [Y0: $i] : ( mdia @ ( mand @ ( a @ Y0 ) @ ( b @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f38,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( eiw_di @ X2 @ X1 )
& ( X0 @ X2 @ X1 ) ) )
= mexists_di ),
inference(rectify,[],[f14]) ).
thf(f39,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
& ( eiw_di @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f46,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mand
@ ( mdia
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( a @ Y0 ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( mdia @ ( b @ Y0 ) ) ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [Y0: $i] : ( mdia @ ( mand @ ( a @ Y0 ) @ ( b @ Y0 ) ) ) ) ) ) ) ),
inference(flattening,[],[f35]) ).
thf(f54,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f55,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f56,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f58,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f60,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
& ( eiw_di @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f63,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f64,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mand
@ ( mdia
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( a @ Y0 ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( mdia @ ( b @ Y0 ) ) ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [Y0: $i] : ( mdia @ ( mand @ ( a @ Y0 ) @ ( b @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f66,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f70,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
& ( eiw_di @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( a @ Y0 ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ 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 ) ) )
@ ( b @ Y0 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
& ( eiw_di @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( ?? @ mworld
@ ^ [Y3: mworld] :
( ( Y1 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: mworld > $o,Y2: mworld > $o,Y3: mworld] :
( ( Y1 @ Y3 )
& ( Y2 @ Y3 ) )
@ ( a @ Y0 )
@ ( b @ Y0 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f64,f58,f66,f63,f55,f60,f54,f54,f56,f55,f55,f60,f55,f63]) ).
thf(f71,plain,
( ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( a @ Y1 @ Y2 ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) )
& ( mrel @ mactual @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( b @ Y1 @ Y2 )
& ( mrel @ Y0 @ Y2 ) ) ) ) ) ) ) )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( a @ Y1 @ Y2 )
& ( b @ Y1 @ Y2 )
& ( mrel @ Y0 @ Y2 ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) )
& ( mrel @ mactual @ Y0 ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f72,plain,
( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( a @ Y1 @ Y2 )
& ( b @ Y1 @ Y2 )
& ( mrel @ Y0 @ Y2 ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) )
& ( mrel @ mactual @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f71]) ).
thf(f73,plain,
( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( a @ Y1 @ Y2 ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) )
& ( mrel @ mactual @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( b @ Y1 @ Y2 )
& ( mrel @ Y0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f71]) ).
thf(f74,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( b @ Y1 @ Y2 )
& ( mrel @ Y0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f73]) ).
thf(f75,plain,
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( a @ Y1 @ Y2 ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) )
& ( mrel @ mactual @ Y0 ) ) ) ),
inference(and_proxy_clausification,[],[f73]) ).
thf(f76,plain,
( ( ^ [Y0: mworld] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( a @ Y1 @ Y2 ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) )
& ( mrel @ mactual @ Y0 ) )
@ sK1 )
= $true ),
inference(sigma_proxy_clausification,[],[f75]) ).
thf(f77,plain,
( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( a @ Y0 @ Y1 ) ) )
& ( eiw_di @ Y0 @ sK1 ) ) )
& ( mrel @ mactual @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f76]) ).
thf(f78,plain,
( ( mrel @ mactual @ sK1 )
= $true ),
inference(and_proxy_clausification,[],[f77]) ).
thf(f79,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( a @ Y0 @ Y1 ) ) )
& ( eiw_di @ Y0 @ sK1 ) ) ) ),
inference(and_proxy_clausification,[],[f77]) ).
thf(f80,plain,
( $true
= ( ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( a @ Y0 @ Y1 ) ) )
& ( eiw_di @ Y0 @ sK1 ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f79]) ).
thf(f81,plain,
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( a @ sK2 @ Y0 ) ) )
& ( eiw_di @ sK2 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f80]) ).
thf(f82,plain,
( $true
= ( eiw_di @ sK2 @ sK1 ) ),
inference(and_proxy_clausification,[],[f81]) ).
thf(f83,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( a @ sK2 @ Y0 ) ) )
= $true ),
inference(and_proxy_clausification,[],[f81]) ).
thf(f84,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( a @ sK2 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f83]) ).
thf(f85,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ sK1 @ X1 )
=> ( a @ sK2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f84]) ).
thf(f86,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( a @ sK2 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f85]) ).
thf(f87,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( b @ Y1 @ Y2 )
& ( mrel @ Y0 @ Y2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f74]) ).
thf(f88,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( b @ Y0 @ Y1 )
& ( mrel @ X1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f87]) ).
thf(f89,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( b @ Y0 @ Y1 )
& ( mrel @ X1 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f88]) ).
thf(f90,plain,
! [X2: $i,X1: mworld] :
( ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( b @ Y0 @ Y1 )
& ( mrel @ X1 @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f89]) ).
thf(f91,plain,
! [X2: $i,X1: mworld] :
( ( ( ( eiw_di @ X2 @ X1 )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( b @ X2 @ Y0 )
& ( mrel @ X1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f90]) ).
thf(f92,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( b @ X2 @ Y0 )
& ( mrel @ X1 @ Y0 ) ) )
= $true )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f91]) ).
thf(f93,plain,
! [X2: $i,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( b @ X2 @ Y0 )
& ( mrel @ X1 @ Y0 ) )
@ ( sK3 @ X1 @ X2 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f92]) ).
thf(f94,plain,
! [X2: $i,X1: mworld] :
( ( ( ( b @ X2 @ ( sK3 @ X1 @ X2 ) )
& ( mrel @ X1 @ ( sK3 @ X1 @ X2 ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f93]) ).
thf(f95,plain,
! [X2: $i,X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK3 @ X1 @ X2 ) ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(and_proxy_clausification,[],[f94]) ).
thf(f96,plain,
! [X2: $i,X1: mworld] :
( ( $true
= ( b @ X2 @ ( sK3 @ X1 @ X2 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f94]) ).
thf(f97,plain,
! [X1: mworld] :
( $false
= ( ^ [Y0: mworld] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( a @ Y1 @ Y2 )
& ( b @ Y1 @ Y2 )
& ( mrel @ Y0 @ Y2 ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) )
& ( mrel @ mactual @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f72]) ).
thf(f98,plain,
! [X1: mworld] :
( $false
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( a @ Y0 @ Y1 )
& ( b @ Y0 @ Y1 )
& ( mrel @ X1 @ Y1 ) ) )
& ( eiw_di @ Y0 @ X1 ) ) )
& ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f97]) ).
thf(f99,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( a @ Y0 @ Y1 )
& ( b @ Y0 @ Y1 )
& ( mrel @ X1 @ Y1 ) ) )
& ( eiw_di @ Y0 @ X1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f98]) ).
thf(f100,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( a @ Y0 @ Y1 )
& ( b @ Y0 @ Y1 )
& ( mrel @ X1 @ Y1 ) ) )
& ( eiw_di @ Y0 @ X1 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f99]) ).
thf(f101,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( a @ X2 @ Y0 )
& ( b @ X2 @ Y0 )
& ( mrel @ X1 @ Y0 ) ) )
& ( eiw_di @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f100]) ).
thf(f102,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( a @ X2 @ Y0 )
& ( b @ X2 @ Y0 )
& ( mrel @ X1 @ Y0 ) ) ) )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( ^ [Y0: mworld] :
( ( a @ X2 @ Y0 )
& ( b @ X2 @ Y0 )
& ( mrel @ X1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f102]) ).
thf(f104,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( ( a @ X2 @ X3 )
& ( b @ X2 @ X3 )
& ( mrel @ X1 @ X3 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f103]) ).
thf(f105,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( ( a @ X2 @ X3 )
& ( b @ X2 @ X3 ) ) ) ),
inference(and_proxy_clausification,[],[f104]) ).
thf(f106,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( b @ X2 @ X3 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( a @ X2 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f105]) ).
thf(f124,plain,
! [X0: $i] :
( ( $false
= ( mrel @ mactual @ sK1 ) )
| ( $false
= ( eiw_di @ X0 @ sK1 ) )
| ( $false = $true )
| ( ( a @ sK2 @ ( sK3 @ sK1 @ X0 ) )
= $true ) ),
inference(constrained_superposition,[],[f95,f86]) ).
thf(f125,plain,
! [X2: $i,X0: mworld,X1: $i] :
( ( ( eiw_di @ X1 @ X0 )
= $false )
| ( $false
= ( b @ X2 @ ( sK3 @ X0 @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( a @ X2 @ ( sK3 @ X0 @ X1 ) ) )
| ( ( eiw_di @ X2 @ X0 )
= $false )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f106,f95]) ).
thf(f127,plain,
! [X0: $i] :
( ( $false
= ( mrel @ mactual @ sK1 ) )
| ( ( a @ sK2 @ ( sK3 @ sK1 @ X0 ) )
= $true )
| ( $false
= ( eiw_di @ X0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f124]) ).
thf(f128,plain,
! [X2: $i,X0: mworld,X1: $i] :
( ( $false
= ( b @ X2 @ ( sK3 @ X0 @ X1 ) ) )
| ( ( eiw_di @ X1 @ X0 )
= $false )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false = $true )
| ( $false
= ( a @ X2 @ ( sK3 @ X0 @ X1 ) ) )
| ( ( eiw_di @ X2 @ X0 )
= $false ) ),
inference(duplicate_literal_removal,[],[f125]) ).
thf(f129,plain,
! [X2: $i,X0: mworld,X1: $i] :
( ( $false
= ( b @ X2 @ ( sK3 @ X0 @ X1 ) ) )
| ( ( eiw_di @ X1 @ X0 )
= $false )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( ( eiw_di @ X2 @ X0 )
= $false )
| ( $false
= ( a @ X2 @ ( sK3 @ X0 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f128]) ).
thf(f133,plain,
! [X0: $i] :
( ( $false
= ( eiw_di @ X0 @ sK1 ) )
| ( $false = $true )
| ( ( a @ sK2 @ ( sK3 @ sK1 @ X0 ) )
= $true ) ),
inference(forward_demodulation,[],[f127,f78]) ).
thf(f134,plain,
! [X0: $i] :
( ( ( a @ sK2 @ ( sK3 @ sK1 @ X0 ) )
= $true )
| ( $false
= ( eiw_di @ X0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f133]) ).
thf(f141,plain,
! [X0: $i,X1: mworld] :
( ( $false
= ( eiw_di @ X0 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( a @ X0 @ ( sK3 @ X1 @ X0 ) ) )
| ( $false = $true )
| ( $false
= ( eiw_di @ X0 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f129,f96]) ).
thf(f143,plain,
! [X0: $i,X1: mworld] :
( ( $false = $true )
| ( $false
= ( eiw_di @ X0 @ X1 ) )
| ( $false
= ( a @ X0 @ ( sK3 @ X1 @ X0 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(duplicate_literal_removal,[],[f141]) ).
thf(f144,plain,
! [X0: $i,X1: mworld] :
( ( $false
= ( a @ X0 @ ( sK3 @ X1 @ X0 ) ) )
| ( $false
= ( eiw_di @ X0 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f143]) ).
thf(f147,plain,
( ( $false
= ( mrel @ mactual @ sK1 ) )
| ( $false
= ( eiw_di @ sK2 @ sK1 ) )
| ( $false
= ( eiw_di @ sK2 @ sK1 ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f144,f134]) ).
thf(f149,plain,
( ( $false
= ( mrel @ mactual @ sK1 ) )
| ( $false = $true )
| ( $false
= ( eiw_di @ sK2 @ sK1 ) ) ),
inference(duplicate_literal_removal,[],[f147]) ).
thf(f150,plain,
( ( $false
= ( mrel @ mactual @ sK1 ) )
| ( $false
= ( eiw_di @ sK2 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f149]) ).
thf(f153,plain,
( ( $false = $true )
| ( $false
= ( eiw_di @ sK2 @ sK1 ) ) ),
inference(forward_demodulation,[],[f150,f78]) ).
thf(f154,plain,
( $false
= ( eiw_di @ sK2 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f153]) ).
thf(f157,plain,
$false = $true,
inference(forward_demodulation,[],[f154,f82]) ).
thf(f158,plain,
$false,
inference(trivial_inequality_removal,[],[f157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO889^16 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.17 % Computer : n019.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Sep 29 17:25:48 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 Running higher-order theorem proving
% 0.11/0.23 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
% 0.11/0.26 % (1111873)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.11/0.26 % (1111878)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=249855197:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.11/0.26 % (1111878) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1111873-1111878"...
% 0.11/0.26 % (1111884)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.11/0.26 % (1111884)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
% 0.11/0.26 % (1111878)...printing done.
% 0.11/0.26 % (1111879)lrs+10_16_si=on:nwc=1.5:random_seed=1588158618:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.11/0.26 % (1111880)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=934567570:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.11/0.26 % (1111881)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=2736646566: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)
% 0.11/0.26 % (1111882)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2738316037:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.11/0.26 % (1111883)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1935519949:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.11/0.26 % (1111884)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=3897178298:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.11/0.26 % (1111880)Instruction limit reached!
% 0.11/0.26 % (1111880)------------------------------
% 0.11/0.26 % (1111880)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.26 % (1111880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.26 % (1111880)CaDiCaL version: 2.1.3
% 0.11/0.26 % (1111880)Termination reason: Instruction limit
% 0.11/0.26 % (1111880)Termination phase: Saturation
% 0.11/0.26 % (1111880)Time elapsed: 0.002 s
% 0.11/0.26 % (1111880)Peak memory usage: 10 MB
% 0.11/0.26 % (1111880)Instructions burned: 3 (million)
% 0.11/0.26 % (1111878)Refutation found. Thanks to Tanya!
% 0.11/0.26 % SZS status Theorem for theBenchmark
% 0.11/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.26 % (1111878)------------------------------
% 0.11/0.26 % (1111878)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.26 % (1111878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.26 % (1111878)CaDiCaL version: 2.1.3
% 0.11/0.26 % (1111878)Termination reason: Refutation
% 0.11/0.26 % (1111878)Time elapsed: 0.005 s
% 0.11/0.26 % (1111878)Peak memory usage: 12 MB
% 0.11/0.26 % (1111878)Instructions burned: 18 (million)
% 0.11/0.26 % (1111873)Success in time 0.025 s
% 0.11/0.26 % Vampire exiting
%------------------------------------------------------------------------------