%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO900^11 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:48:36 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 95 ( 30 unt; 0 typ; 7 def)
% Number of atoms : 621 ( 115 equ; 0 cnn)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 839 ( 81 ~; 107 |; 3 &; 517 @)
% ( 6 <=>; 79 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 37 usr; 15 con; 0-4 aty)
% ( 46 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 185 ( 0 sgn 34 !; 0 ?; 185 :)
% 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,
p: mworld > $o ).
thf(func_def_12,type,
q: mworld > $o ).
thf(func_def_13,type,
vAND: $o > $o > $o ).
thf(func_def_14,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_18,type,
vNOT: $o > $o ).
thf(func_def_19,type,
vOR: $o > $o > $o ).
thf(func_def_22,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_23,type,
vIMP: $o > $o > $o ).
thf(func_def_24,type,
vIFF: $o > $o > $o ).
thf(func_def_25,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
sF0: $o ).
thf(func_def_27,type,
sK1: mworld > mworld ).
thf(func_def_28,type,
sK2: mworld > mworld ).
thf(func_def_29,type,
sK3: mworld ).
thf(func_def_30,type,
sK4: mworld ).
thf(func_def_31,type,
sK5: mworld ).
thf(func_def_32,type,
sK6: mworld ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(f4,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor_def) ).
thf(f5,axiom,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def) ).
thf(f10,axiom,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( ( mrel @ X0 @ X1 )
& ( mrel @ X0 @ X2 ) )
=> ( mrel @ X2 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_euclidean) ).
thf(f11,conjecture,
mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f12,negated_conjecture,
~ ( mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
thf(f17,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f18,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f23,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f24,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f27,plain,
~ ( mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f28,plain,
( ( mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f27]) ).
thf(f29,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f30,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X1 @ X2 )
& ( mrel @ X1 @ X0 ) )
=> ( mrel @ X0 @ X2 ) ),
inference(rectify,[],[f10]) ).
thf(f31,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( ( $true
= ( mrel @ X1 @ X0 ) )
& ( ( mrel @ X1 @ X2 )
= $true ) )
=> ( ( mrel @ X0 @ X2 )
= $true ) ),
inference(fool_elimination,[],[f30]) ).
thf(f32,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
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 @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) )
!= $true ),
inference(flattening,[],[f28]) ).
thf(f35,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( ( mrel @ X0 @ X2 )
= $true )
| ( $true
!= ( mrel @ X1 @ X0 ) )
| ( ( mrel @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f31]) ).
thf(f36,plain,
! [X1: mworld,X0: mworld,X2: mworld] :
( ( ( mrel @ X1 @ X2 )
!= $true )
| ( ( mrel @ X0 @ X2 )
= $true )
| ( $true
!= ( mrel @ X1 @ X0 ) ) ),
inference(flattening,[],[f35]) ).
thf(f37,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X0 @ X2 )
!= $true )
| ( ( mrel @ X1 @ X2 )
= $true )
| ( ( mrel @ X0 @ X1 )
!= $true ) ),
inference(rectify,[],[f36]) ).
thf(f38,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $true )
| ( ( mrel @ X0 @ X2 )
!= $true )
| ( ( mrel @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f40,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f41,plain,
( ( mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f34]) ).
thf(f43,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f44,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f46,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f51,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p ) ) ) ) ) ),
inference(definition_unfolding,[],[f41,f40,f44,f43,f46,f43,f43,f43,f46,f43,f43]) ).
thf(f52,definition,
( sF0
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f53,plain,
$true != sF0,
inference(definition_folding,[],[f51,f52]) ).
thf(f54,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f52]) ).
thf(f82,plain,
( ( $true = sF0 )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f54]) ).
thf(f83,plain,
( ( $true = sF0 )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f82]) ).
thf(f84,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f82]) ).
thf(f85,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f84]) ).
thf(f86,plain,
( ( $true = sF0 )
| ( $false
= ( ( mrel @ mactual @ sK3 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( p @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f85]) ).
thf(f87,plain,
( ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( p @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) ) ) )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f86]) ).
thf(f88,plain,
( ( $true = sF0 )
| ( $true
= ( mrel @ mactual @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f86]) ).
thf(f90,plain,
( ( $true = sF0 )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f87]) ).
thf(f91,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( p @ Y0 ) )
@ X1 ) )
| ( $true = sF0 ) ),
inference(pi_proxy_clausification,[],[f90]) ).
thf(f92,plain,
! [X1: mworld] :
( ( $true = sF0 )
| ( $true
= ( ( mrel @ sK3 @ X1 )
=> ( p @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f91]) ).
thf(f93,plain,
! [X1: mworld] :
( ( $true = sF0 )
| ( $false
= ( mrel @ sK3 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f92]) ).
thf(f98,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f83]) ).
thf(f99,plain,
( ( $true = sF0 )
| ( ( ( mrel @ mactual @ sK5 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( q @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( p @ Y0 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f98]) ).
thf(f100,plain,
( ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( q @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( p @ Y0 ) ) ) ) )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f99]) ).
thf(f101,plain,
( ( $true
= ( mrel @ mactual @ sK5 ) )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f99]) ).
thf(f102,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f100]) ).
thf(f107,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK5 @ Y0 )
=> ( p @ Y0 ) )
@ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f102]) ).
thf(f108,plain,
( ( $false
= ( ( mrel @ sK5 @ sK6 )
=> ( p @ sK6 ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f107]) ).
thf(f109,plain,
( ( $true = sF0 )
| ( $false
= ( p @ sK6 ) ) ),
inference(imp_proxy_clausification,[],[f108]) ).
thf(f110,plain,
( ( $true
= ( mrel @ sK5 @ sK6 ) )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f108]) ).
thf(f132,definition,
( spl7_6
<=> ( $true
= ( mrel @ mactual @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
thf(f134,plain,
( ( $true
= ( mrel @ mactual @ sK3 ) )
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f132]) ).
thf(f136,definition,
( spl7_7
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
thf(f139,plain,
( spl7_6
| spl7_7 ),
inference(avatar_split_clause,[],[f88,f136,f132]) ).
thf(f141,definition,
( spl7_8
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ sK3 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
thf(f142,plain,
( ! [X1: mworld] :
( ( $false
= ( mrel @ sK3 @ X1 ) )
| ( $true
= ( p @ X1 ) ) )
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f141]) ).
thf(f143,plain,
( spl7_7
| spl7_8 ),
inference(avatar_split_clause,[],[f93,f141,f136]) ).
thf(f155,definition,
( spl7_11
<=> ( $true
= ( mrel @ mactual @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_11])],[avatar_definition]) ).
thf(f157,plain,
( ( $true
= ( mrel @ mactual @ sK5 ) )
| ~ spl7_11 ),
inference(avatar_component_clause,[],[f155]) ).
thf(f158,plain,
( spl7_11
| spl7_7 ),
inference(avatar_split_clause,[],[f101,f136,f155]) ).
thf(f164,definition,
( spl7_13
<=> ( $true
= ( mrel @ sK5 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_13])],[avatar_definition]) ).
thf(f166,plain,
( ( $true
= ( mrel @ sK5 @ sK6 ) )
| ~ spl7_13 ),
inference(avatar_component_clause,[],[f164]) ).
thf(f167,plain,
( spl7_13
| spl7_7 ),
inference(avatar_split_clause,[],[f110,f136,f164]) ).
thf(f169,definition,
( spl7_14
<=> ( $false
= ( p @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_14])],[avatar_definition]) ).
thf(f171,plain,
( ( $false
= ( p @ sK6 ) )
| ~ spl7_14 ),
inference(avatar_component_clause,[],[f169]) ).
thf(f172,plain,
( spl7_7
| spl7_14 ),
inference(avatar_split_clause,[],[f109,f169,f136]) ).
thf(f173,plain,
~ spl7_7,
inference(avatar_split_clause,[],[f53,f136]) ).
thf(f189,plain,
( ! [X0: mworld,X1: mworld] :
( ( $false = $true )
| ( ( mrel @ X1 @ sK3 )
!= $true )
| ( $true
= ( p @ X0 ) )
| ( $true
!= ( mrel @ X1 @ X0 ) ) )
| ~ spl7_8 ),
inference(constrained_superposition,[],[f142,f38]) ).
thf(f197,plain,
( ! [X0: mworld,X1: mworld] :
( ( $true
!= ( mrel @ X1 @ X0 ) )
| ( ( mrel @ X1 @ sK3 )
!= $true )
| ( $true
= ( p @ X0 ) ) )
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f189]) ).
thf(f223,plain,
( ( $true
!= ( mrel @ sK5 @ sK3 ) )
| ( $true
= ( p @ sK6 ) )
| ( $true != $true )
| ~ spl7_8
| ~ spl7_13 ),
inference(constrained_superposition,[],[f197,f166]) ).
thf(f232,plain,
( ( $true
!= ( mrel @ sK5 @ sK3 ) )
| ( $true
= ( p @ sK6 ) )
| ~ spl7_8
| ~ spl7_13 ),
inference(trivial_inequality_removal,[],[f223]) ).
thf(f235,plain,
( ( $true
!= ( mrel @ sK5 @ sK3 ) )
| ( $false = $true )
| ~ spl7_8
| ~ spl7_13
| ~ spl7_14 ),
inference(forward_demodulation,[],[f232,f171]) ).
thf(f236,plain,
( ( $true
!= ( mrel @ sK5 @ sK3 ) )
| ~ spl7_8
| ~ spl7_13
| ~ spl7_14 ),
inference(trivial_inequality_removal,[],[f235]) ).
thf(f238,plain,
( ! [X0: mworld] :
( ( $true
!= ( mrel @ X0 @ sK3 ) )
| ( $true != $true )
| ( ( mrel @ X0 @ sK5 )
!= $true ) )
| ~ spl7_8
| ~ spl7_13
| ~ spl7_14 ),
inference(constrained_superposition,[],[f236,f38]) ).
thf(f240,plain,
( ! [X0: mworld] :
( ( $true
!= ( mrel @ X0 @ sK3 ) )
| ( ( mrel @ X0 @ sK5 )
!= $true ) )
| ~ spl7_8
| ~ spl7_13
| ~ spl7_14 ),
inference(trivial_inequality_removal,[],[f238]) ).
thf(f282,plain,
( ( $true
!= ( mrel @ mactual @ sK5 ) )
| ( $true != $true )
| ~ spl7_6
| ~ spl7_8
| ~ spl7_13
| ~ spl7_14 ),
inference(constrained_superposition,[],[f240,f134]) ).
thf(f293,plain,
( ( $true
!= ( mrel @ mactual @ sK5 ) )
| ~ spl7_6
| ~ spl7_8
| ~ spl7_13
| ~ spl7_14 ),
inference(trivial_inequality_removal,[],[f282]) ).
thf(f294,plain,
( $false
| ~ spl7_6
| ~ spl7_8
| ~ spl7_11
| ~ spl7_13
| ~ spl7_14 ),
inference(forward_subsumption_resolution,[],[f293,f157]) ).
thf(f295,plain,
( ~ spl7_6
| ~ spl7_8
| ~ spl7_11
| ~ spl7_13
| ~ spl7_14 ),
inference(avatar_contradiction_clause,[],[f294]) ).
cnf(s5,plain,
( spl7_6
| spl7_7 ),
inference(sat_conversion,[],[f139]) ).
cnf(s6,plain,
( spl7_7
| spl7_8 ),
inference(sat_conversion,[],[f143]) ).
cnf(s9,plain,
( spl7_7
| spl7_11 ),
inference(sat_conversion,[],[f158]) ).
cnf(s11,plain,
( spl7_7
| spl7_13 ),
inference(sat_conversion,[],[f167]) ).
cnf(s12,plain,
( spl7_7
| spl7_14 ),
inference(sat_conversion,[],[f172]) ).
cnf(s13,plain,
~ spl7_7,
inference(sat_conversion,[],[f173]) ).
cnf(s14,plain,
( ~ spl7_6
| ~ spl7_8
| ~ spl7_11
| ~ spl7_13
| ~ spl7_14 ),
inference(sat_conversion,[],[f295]) ).
cnf(s15,plain,
spl7_14,
inference(rat,[],[s12,s13]) ).
cnf(s16,plain,
spl7_13,
inference(rat,[],[s11,s13]) ).
cnf(s18,plain,
spl7_11,
inference(rat,[],[s9,s13]) ).
cnf(s21,plain,
spl7_8,
inference(rat,[],[s6,s13]) ).
cnf(s22,plain,
~ spl7_6,
inference(rat,[],[s14,s15,s16,s18,s21]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s5,s13,s22]) ).
thf(f296,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO900^11 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n002.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 17:29:07 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.26 % (1600952)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.26 % (1600964)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.26 % (1600964)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
% 0.08/0.26 % (1600964)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=2295892190:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.08/0.26 % (1600964) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1600952-1600964"...
% 0.08/0.26 % (1600958)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4154305577:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.26 % (1600959)lrs+10_16_si=on:nwc=1.5:random_seed=3943301203:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.26 % (1600964)...printing done.
% 0.08/0.26 % (1600963)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=665908904:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.26 % (1600960)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3247757197:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.08/0.26 % (1600964)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (1600964)------------------------------
% 0.21/0.27 % (1600964)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (1600964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (1600964)CaDiCaL version: 2.1.3
% 0.21/0.27 % (1600964)Termination reason: Refutation
% 0.21/0.27 % (1600964)Time elapsed: 0.005 s
% 0.21/0.27 % (1600964)Peak memory usage: 13 MB
% 0.21/0.27 % (1600964)Instructions burned: 17 (million)
% 0.21/0.27 % (1600952)Success in time 0.036 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------