%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO891^16 : 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 : n026.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 08:50:33 AM UTC 2026
% Result : Theorem 0.18s 0.27s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of formulae : 64 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 403 ( 79 equ; 0 cnn)
% Maximal formula atoms : 13 ( 6 avg)
% Number of connectives : 595 ( 17 ~; 19 |; 43 &; 456 @)
% ( 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 : 173 ( 136 ^; 33 !; 4 ?; 173 :)
% 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_18,type,
vNOT: $o > $o ).
thf(func_def_19,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vAND: $o > $o > $o ).
thf(func_def_21,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vOR: $o > $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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $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/sandbox/benchmark/theBenchmark.p',mlocal_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(f8,axiom,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( X0 @ X2 )
& ( mrel @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_def) ).
thf(f12,axiom,
! [X0: mworld,X1: mworld,X2: $i] :
( ( ( mrel @ X0 @ X1 )
& ( eiw_di @ X2 @ X0 ) )
=> ( eiw_di @ X2 @ X1 ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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(f21,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f28,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f29,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f28]) ).
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,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( X0 @ X2 )
& ( mrel @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f35,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f42,plain,
! [X0: mworld,X1: mworld,X2: $i] :
( ( ( mrel @ X0 @ X1 )
& ( eiw_di @ X2 @ X0 ) )
=> ( eiw_di @ X2 @ X1 ) ),
inference(rectify,[],[f12]) ).
thf(f43,plain,
! [X0: mworld,X1: mworld,X2: $i] :
( ( ( ( mrel @ X0 @ X1 )
= $true )
& ( ( eiw_di @ X2 @ X0 )
= $true ) )
=> ( ( eiw_di @ X2 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f45,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f46,plain,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f47,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f56,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(f57,plain,
( $true
!= ( 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 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f58,plain,
( $true
!= ( 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 ) ) ) ) ) ) ),
inference(flattening,[],[f57]) ).
thf(f61,plain,
! [X0: mworld,X1: mworld,X2: $i] :
( ( ( eiw_di @ X2 @ X1 )
= $true )
| ( ( mrel @ X0 @ X1 )
!= $true )
| ( ( eiw_di @ X2 @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f43]) ).
thf(f62,plain,
! [X0: mworld,X1: mworld,X2: $i] :
( ( ( eiw_di @ X2 @ X1 )
= $true )
| ( ( mrel @ X0 @ X1 )
!= $true )
| ( ( eiw_di @ X2 @ X0 )
!= $true ) ),
inference(flattening,[],[f61]) ).
thf(f64,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f68,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f70,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f71,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f75,plain,
! [X2: $i,X0: mworld,X1: mworld] :
( ( ( mrel @ X0 @ X1 )
!= $true )
| ( ( eiw_di @ X2 @ X1 )
= $true )
| ( ( eiw_di @ X2 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f76,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f77,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f82,plain,
( $true
!= ( 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 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f89,plain,
( $true
!= ( ^ [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] :
( ( mrel @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ ( p @ 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] : ( p @ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f82,f64,f68,f76,f70,f77,f68,f77,f71,f71,f77]) ).
thf(f90,plain,
( $true
!= ( ( !! @ $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] :
( ( mrel @ mactual @ Y1 )
& ( p @ Y0 @ Y1 ) ) ) ) )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( p @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f89]) ).
thf(f91,plain,
( $false
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
& ( p @ Y0 @ Y1 ) ) ) ) )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( p @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f90]) ).
thf(f103,plain,
( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( p @ Y1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f91]) ).
thf(f104,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
& ( p @ Y0 @ Y1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f91]) ).
thf(f105,plain,
( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
& ( p @ Y0 @ Y1 ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f104]) ).
thf(f106,plain,
( $true
= ( ( eiw_di @ sK2 @ mactual )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( p @ sK2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f105]) ).
thf(f107,plain,
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( p @ sK2 @ Y0 ) ) ) ),
inference(and_proxy_clausification,[],[f106]) ).
thf(f108,plain,
( $true
= ( eiw_di @ sK2 @ mactual ) ),
inference(and_proxy_clausification,[],[f106]) ).
thf(f109,plain,
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( p @ sK2 @ Y0 ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f107]) ).
thf(f110,plain,
( $true
= ( ( mrel @ mactual @ sK3 )
& ( p @ sK2 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f109]) ).
thf(f111,plain,
( $true
= ( p @ sK2 @ sK3 ) ),
inference(and_proxy_clausification,[],[f110]) ).
thf(f112,plain,
( $true
= ( mrel @ mactual @ sK3 ) ),
inference(and_proxy_clausification,[],[f110]) ).
thf(f113,plain,
! [X1: mworld] :
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( p @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f103]) ).
thf(f114,plain,
! [X1: mworld] :
( $false
= ( ( mrel @ mactual @ X1 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( p @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f113]) ).
thf(f115,plain,
! [X1: mworld] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( p @ Y0 @ X1 ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(and_proxy_clausification,[],[f114]) ).
thf(f116,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( p @ Y0 @ X1 ) )
@ X2 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f115]) ).
thf(f117,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( ( eiw_di @ X2 @ X1 )
& ( p @ X2 @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( p @ X2 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f117]) ).
thf(f161,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK3 ) )
| ( $false
= ( eiw_di @ sK2 @ sK3 ) ) ),
inference(constrained_superposition,[],[f111,f118]) ).
thf(f162,plain,
( ( $false
= ( mrel @ mactual @ sK3 ) )
| ( $false
= ( eiw_di @ sK2 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f161]) ).
thf(f165,plain,
( ( $true = $false )
| ( $false
= ( eiw_di @ sK2 @ sK3 ) ) ),
inference(forward_demodulation,[],[f162,f112]) ).
thf(f166,plain,
( $false
= ( eiw_di @ sK2 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f165]) ).
thf(f180,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
= ( eiw_di @ X0 @ sK3 ) )
| ( $true
!= ( eiw_di @ X0 @ mactual ) ) ),
inference(constrained_superposition,[],[f75,f112]) ).
thf(f184,plain,
! [X0: $i] :
( ( $true
!= ( eiw_di @ X0 @ mactual ) )
| ( $true
= ( eiw_di @ X0 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f180]) ).
thf(f185,plain,
( ( $true != $true )
| ( $true
= ( eiw_di @ sK2 @ sK3 ) ) ),
inference(constrained_superposition,[],[f184,f108]) ).
thf(f192,plain,
( $true
= ( eiw_di @ sK2 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f185]) ).
thf(f195,plain,
$true = $false,
inference(forward_demodulation,[],[f192,f166]) ).
thf(f196,plain,
$false,
inference(trivial_inequality_removal,[],[f195]) ).
%------------------------------------------------------------------------------
%----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/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.18 % Computer : n026.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 17:28:42 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.21 Running first-order model finding
% 0.06/0.21 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
% 0.18/0.27 % (910773)Will run a generic schedule for satisfiability detection.
% 0.18/0.27 % (910778)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1091346846_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.27 % Exception at run slice level
% 0.18/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.27 % (910779)% WARNING: option uhcvi not known.
% 0.18/0.27 % (910779)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2171595144:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.27 % (910781)dis+10_1_sil=32000:sp=arity:random_seed=1481677772:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.27 % (910780)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2675511725:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.27 % (910782)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4079875384:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.27 % (910779)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.27 % (910782)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.27 % (910779)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.18/0.27 % (910783)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=551805249:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.27 % (910783) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-910773-910783"...
% 0.18/0.27 % (910783)...printing done.
% 0.18/0.27 % (910783)Refutation found. Thanks to Tanya!
% 0.18/0.27 % SZS status Theorem for theBenchmark
% 0.18/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.27 % (910783)------------------------------
% 0.18/0.27 % (910783)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (910783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (910783)CaDiCaL version: 2.1.3
% 0.18/0.27 % (910783)Termination reason: Refutation
% 0.18/0.27 % (910783)Time elapsed: 0.005 s
% 0.18/0.27 % (910783)Peak memory usage: 12 MB
% 0.18/0.27 % (910783)Instructions burned: 18 (million)
% 0.18/0.27 % (910773)Success in time 0.045 s
% 0.18/0.27 % Vampire exiting
%------------------------------------------------------------------------------