%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO889^16 : 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 : 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 08:50:33 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 10
% Syntax : Number of formulae : 97 ( 56 unt; 0 typ; 2 def)
% Number of atoms : 745 ( 152 equ; 0 cnn)
% Maximal formula atoms : 17 ( 7 avg)
% Number of connectives : 1101 ( 17 ~; 76 |; 78 &; 819 @)
% ( 2 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 34 usr; 9 con; 0-4 aty)
% ( 25 !!; 43 ??; 0 @@+; 0 @@-)
% Number of variables : 251 ( 0 sgn 62 !; 4 ?; 251 :)
% 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,
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,
sK1: mworld ).
thf(func_def_33,type,
sK3: mworld > $i > mworld ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(f3,axiom,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand_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(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(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/sandbox/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,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f20,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f21,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f20]) ).
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(f28,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f29,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f30,plain,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( X0 @ X2 )
& ( mrel @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f31,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f40,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f41,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f42,plain,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f43,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f44,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(f45,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,[],[f44]) ).
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,[],[f45]) ).
thf(f52,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f54,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f56,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f58,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f59,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f64,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f65,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f66,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(f69,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] :
( ( 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] :
( ( 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] :
( ( mrel @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ ( b @ 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] :
( ( mrel @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: mworld > $o,Y2: mworld > $o,Y3: mworld] :
( ( Y1 @ Y3 )
& ( Y2 @ Y3 ) )
@ ( a @ Y0 )
@ ( b @ Y0 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f66,f52,f56,f54,f59,f65,f58,f58,f64,f59,f59,f65,f59,f54]) ).
thf(f70,plain,
( $true
!= ( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( a @ Y1 @ Y2 ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
& ( b @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
& ( a @ Y1 @ Y2 )
& ( b @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f71,plain,
( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
& ( a @ Y1 @ Y2 )
& ( b @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f70]) ).
thf(f72,plain,
( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( a @ Y1 @ Y2 ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
& ( b @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f70]) ).
thf(f73,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
& ( b @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f72]) ).
thf(f74,plain,
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( a @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f72]) ).
thf(f75,plain,
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( a @ Y1 @ Y2 ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f74]) ).
thf(f76,plain,
( $true
= ( ( mrel @ mactual @ sK1 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( a @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f77,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( a @ Y0 @ Y1 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f76]) ).
thf(f78,plain,
( $true
= ( mrel @ mactual @ sK1 ) ),
inference(and_proxy_clausification,[],[f76]) ).
thf(f79,plain,
( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( a @ Y0 @ Y1 ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f77]) ).
thf(f80,plain,
( $true
= ( ( eiw_di @ sK2 @ sK1 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( a @ sK2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f79]) ).
thf(f81,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( a @ sK2 @ Y0 ) ) ) ),
inference(and_proxy_clausification,[],[f80]) ).
thf(f82,plain,
( $true
= ( eiw_di @ sK2 @ sK1 ) ),
inference(and_proxy_clausification,[],[f80]) ).
thf(f83,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( a @ sK2 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f81]) ).
thf(f84,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ sK1 @ X1 )
=> ( a @ sK2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f83]) ).
thf(f85,plain,
! [X1: mworld] :
( ( $true
= ( a @ sK2 @ X1 ) )
| ( $false
= ( mrel @ sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f84]) ).
thf(f86,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
& ( b @ Y1 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f73]) ).
thf(f87,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
& ( b @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f86]) ).
thf(f88,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
& ( b @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f87]) ).
thf(f89,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
& ( b @ Y0 @ Y1 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f88]) ).
thf(f90,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( eiw_di @ X2 @ X1 )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( b @ X2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f89]) ).
thf(f91,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( b @ X2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f90]) ).
thf(f92,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( b @ X2 @ Y0 ) )
@ ( sK3 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f91]) ).
thf(f93,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $true
= ( ( mrel @ X1 @ ( sK3 @ X1 @ X2 ) )
& ( b @ X2 @ ( sK3 @ X1 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f94,plain,
! [X2: $i,X1: mworld] :
( ( $true
= ( b @ X2 @ ( sK3 @ X1 @ X2 ) ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(and_proxy_clausification,[],[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,[],[f93]) ).
thf(f96,plain,
! [X1: mworld] :
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
& ( a @ Y1 @ Y2 )
& ( b @ Y1 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f71]) ).
thf(f97,plain,
! [X1: mworld] :
( $false
= ( ( mrel @ mactual @ X1 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
& ( a @ Y0 @ Y1 )
& ( b @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f96]) ).
thf(f98,plain,
! [X1: mworld] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
& ( a @ Y0 @ Y1 )
& ( b @ Y0 @ Y1 ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(and_proxy_clausification,[],[f97]) ).
thf(f99,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
& ( a @ Y0 @ Y1 )
& ( b @ Y0 @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f98]) ).
thf(f100,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( ( eiw_di @ X2 @ X1 )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( a @ X2 @ Y0 )
& ( b @ X2 @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f99]) ).
thf(f101,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( a @ X2 @ Y0 )
& ( b @ X2 @ Y0 ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f100]) ).
thf(f102,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( a @ X2 @ Y0 )
& ( b @ X2 @ Y0 ) )
@ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( ( mrel @ X1 @ X3 )
& ( a @ X2 @ X3 )
& ( b @ X2 @ X3 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f104,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( ( a @ X2 @ X3 )
& ( b @ X2 @ X3 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f103]) ).
thf(f105,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,[],[f104]) ).
thf(f122,plain,
! [X2: $i,X0: mworld,X1: $i] :
( ( $true = $false )
| ( ( eiw_di @ X1 @ X0 )
= $false )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( b @ X2 @ ( sK3 @ X0 @ X1 ) ) )
| ( ( eiw_di @ X2 @ X0 )
= $false )
| ( $false
= ( a @ X2 @ ( sK3 @ X0 @ X1 ) ) ) ),
inference(constrained_superposition,[],[f95,f105]) ).
thf(f131,plain,
! [X2: $i,X0: mworld,X1: $i] :
( ( $true = $false )
| ( ( eiw_di @ X1 @ X0 )
= $false )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( b @ X2 @ ( sK3 @ X0 @ X1 ) ) )
| ( ( eiw_di @ X2 @ X0 )
= $false )
| ( $false
= ( a @ X2 @ ( sK3 @ X0 @ X1 ) ) ) ),
inference(duplicate_literal_removal,[],[f122]) ).
thf(f132,plain,
! [X2: $i,X0: mworld,X1: $i] :
( ( ( eiw_di @ X1 @ X0 )
= $false )
| ( $false
= ( b @ X2 @ ( sK3 @ X0 @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( ( eiw_di @ X2 @ X0 )
= $false )
| ( $false
= ( a @ X2 @ ( sK3 @ X0 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f131]) ).
thf(f160,plain,
! [X0: $i,X1: mworld] :
( ( $true = $false )
| ( $false
= ( eiw_di @ X0 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X0 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X0 @ X1 ) )
| ( $false
= ( a @ X0 @ ( sK3 @ X1 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f94,f132]) ).
thf(f161,plain,
! [X0: $i,X1: mworld] :
( ( $true = $false )
| ( $false
= ( eiw_di @ X0 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( a @ X0 @ ( sK3 @ X1 @ X0 ) ) ) ),
inference(duplicate_literal_removal,[],[f160]) ).
thf(f162,plain,
! [X0: $i,X1: mworld] :
( ( $false
= ( a @ X0 @ ( sK3 @ X1 @ X0 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f161]) ).
thf(f169,plain,
! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ sK1 @ ( sK3 @ X0 @ sK2 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( eiw_di @ sK2 @ X0 ) ) ),
inference(constrained_superposition,[],[f85,f162]) ).
thf(f170,plain,
! [X0: mworld] :
( ( $false
= ( mrel @ sK1 @ ( sK3 @ X0 @ sK2 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( eiw_di @ sK2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f169]) ).
thf(f173,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK1 ) )
| ( $false
= ( eiw_di @ sK2 @ sK1 ) )
| ( $false
= ( eiw_di @ sK2 @ sK1 ) )
| ( $false
= ( mrel @ mactual @ sK1 ) ) ),
inference(constrained_superposition,[],[f170,f95]) ).
thf(f179,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK1 ) )
| ( $false
= ( eiw_di @ sK2 @ sK1 ) ) ),
inference(duplicate_literal_removal,[],[f173]) ).
thf(f180,plain,
( ( $false
= ( mrel @ mactual @ sK1 ) )
| ( $false
= ( eiw_di @ sK2 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f179]) ).
thf(f182,definition,
( spl4_4
<=> ( $false
= ( mrel @ mactual @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f184,plain,
( ( $false
= ( mrel @ mactual @ sK1 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f182]) ).
thf(f186,definition,
( spl4_5
<=> ( $false
= ( eiw_di @ sK2 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f188,plain,
( ( $false
= ( eiw_di @ sK2 @ sK1 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f186]) ).
thf(f190,plain,
( spl4_5
| spl4_4 ),
inference(avatar_split_clause,[],[f180,f182,f186]) ).
thf(f191,plain,
( ( $true = $false )
| ~ spl4_4 ),
inference(constrained_superposition,[],[f184,f78]) ).
thf(f197,plain,
( $false
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f191]) ).
thf(f198,plain,
~ spl4_4,
inference(avatar_contradiction_clause,[],[f197]) ).
thf(f203,plain,
( ( $true = $false )
| ~ spl4_5 ),
inference(constrained_superposition,[],[f188,f82]) ).
thf(f209,plain,
( $false
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f203]) ).
thf(f210,plain,
~ spl4_5,
inference(avatar_contradiction_clause,[],[f209]) ).
cnf(s6,plain,
( spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f190]) ).
cnf(s8,plain,
~ spl4_4,
inference(sat_conversion,[],[f198]) ).
cnf(s10,plain,
~ spl4_5,
inference(sat_conversion,[],[f210]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s6,s10,s8]) ).
thf(f211,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO889^16 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n019.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 17:25:48 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.20/0.29 % (1111620)Will run a generic schedule for satisfiability detection.
% 0.20/0.29 % (1111629)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1801664596:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.29 % (1111629)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % (1111626)% WARNING: option uhcvi not known.
% 0.20/0.29 % (1111626)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2870183084:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.29 % (1111628)dis+10_1_sil=32000:sp=arity:random_seed=3649775173:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.29 % (1111627)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1750962760:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.29 % (1111625)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1396472407_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.29 % (1111626)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % (1111626)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.29 % Exception at run slice level
% 0.20/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.29 % (1111630)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=181490637:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.29 % (1111631)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=431451082:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.29 % (1111631) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1111620-1111631"...
% 0.20/0.29 % (1111631)...printing done.
% 0.20/0.29 % (1111631)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (1111631)------------------------------
% 0.20/0.29 % (1111631)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1111631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1111631)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1111631)Termination reason: Refutation
% 0.20/0.29 % (1111631)Time elapsed: 0.012 s
% 0.20/0.29 % (1111631)Peak memory usage: 13 MB
% 0.20/0.29 % (1111631)Instructions burned: 21 (million)
% 0.20/0.29 % (1111620)Success in time 0.06 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------