%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO888^10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 08:50:32 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 7
% Syntax : Number of formulae : 73 ( 50 unt; 0 typ; 0 def)
% Number of atoms : 551 ( 105 equ; 0 cnn)
% Maximal formula atoms : 18 ( 7 avg)
% Number of connectives : 766 ( 7 ~; 38 |; 7 &; 596 @)
% ( 0 <=>; 80 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 31 usr; 6 con; 0-4 aty)
% ( 38 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 164 ( 136 ^; 28 !; 0 ?; 164 :)
% 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,
f: $i > mworld > $o ).
thf(func_def_15,type,
g: $i > mworld > $o ).
thf(func_def_16,type,
h: $i > mworld > $o ).
thf(func_def_17,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_19,type,
vNOT: $o > $o ).
thf(func_def_20,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
vAND: $o > $o > $o ).
thf(func_def_22,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
vOR: $o > $o > $o ).
thf(func_def_24,type,
vIMP: $o > $o > $o ).
thf(func_def_25,type,
vIFF: $o > $o > $o ).
thf(func_def_26,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_30,type,
sK0: mworld > $i ).
thf(func_def_32,type,
sK2: mworld ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f3,axiom,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
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,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f9,axiom,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(f12,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,conjecture,
( mlocal
@ ( mimplies
@ ( mand
@ ( mforall_di
@ ^ [X0: $i] : ( mimplies @ ( f @ X0 ) @ ( mbox @ ( g @ X0 ) ) ) )
@ ( mforall_di
@ ^ [X0: $i] : ( mimplies @ ( g @ X0 ) @ ( mbox @ ( h @ X0 ) ) ) ) )
@ ( mforall_di
@ ^ [X0: $i] : ( mimplies @ ( f @ X0 ) @ ( mbox @ ( h @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f15,negated_conjecture,
~ ( mlocal
@ ( mimplies
@ ( mand
@ ( mforall_di
@ ^ [X0: $i] : ( mimplies @ ( f @ X0 ) @ ( mbox @ ( g @ X0 ) ) ) )
@ ( mforall_di
@ ^ [X0: $i] : ( mimplies @ ( g @ X0 ) @ ( mbox @ ( h @ X0 ) ) ) ) )
@ ( mforall_di
@ ^ [X0: $i] : ( mimplies @ ( f @ X0 ) @ ( mbox @ ( h @ X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
thf(f16,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f19,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f20,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
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,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f28,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f31,plain,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
inference(rectify,[],[f9]) ).
thf(f32,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f31]) ).
thf(f37,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f38,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f41,plain,
~ ( mlocal
@ ( mimplies
@ ( mand
@ ( mforall_di
@ ^ [X0: $i] : ( mimplies @ ( f @ X0 ) @ ( mbox @ ( g @ X0 ) ) ) )
@ ( mforall_di
@ ^ [X1: $i] : ( mimplies @ ( g @ X1 ) @ ( mbox @ ( h @ X1 ) ) ) ) )
@ ( mforall_di
@ ^ [X2: $i] : ( mimplies @ ( f @ X2 ) @ ( mbox @ ( h @ X2 ) ) ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f42,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mand
@ ( mforall_di
@ ^ [Y0: $i] : ( mimplies @ ( f @ Y0 ) @ ( mbox @ ( g @ Y0 ) ) ) )
@ ( mforall_di
@ ^ [Y0: $i] : ( mimplies @ ( g @ Y0 ) @ ( mbox @ ( h @ Y0 ) ) ) ) )
@ ( mforall_di
@ ^ [Y0: $i] : ( mimplies @ ( f @ Y0 ) @ ( mbox @ ( h @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f43,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mand
@ ( mforall_di
@ ^ [Y0: $i] : ( mimplies @ ( f @ Y0 ) @ ( mbox @ ( g @ Y0 ) ) ) )
@ ( mforall_di
@ ^ [Y0: $i] : ( mimplies @ ( g @ Y0 ) @ ( mbox @ ( h @ Y0 ) ) ) ) )
@ ( mforall_di
@ ^ [Y0: $i] : ( mimplies @ ( f @ Y0 ) @ ( mbox @ ( h @ Y0 ) ) ) ) ) ) ),
inference(flattening,[],[f42]) ).
thf(f47,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f49,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f51,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f53,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f55,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f32]) ).
thf(f58,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f60,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mand
@ ( mforall_di
@ ^ [Y0: $i] : ( mimplies @ ( f @ Y0 ) @ ( mbox @ ( g @ Y0 ) ) ) )
@ ( mforall_di
@ ^ [Y0: $i] : ( mimplies @ ( g @ Y0 ) @ ( mbox @ ( h @ Y0 ) ) ) ) )
@ ( mforall_di
@ ^ [Y0: $i] : ( mimplies @ ( f @ Y0 ) @ ( mbox @ ( h @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f63,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: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld > $o,Y3: mworld] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) )
@ ( f @ Y0 )
@ ( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( g @ Y0 ) ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld > $o,Y3: mworld] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) )
@ ( g @ Y0 )
@ ( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( h @ Y0 ) ) ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld > $o,Y3: mworld] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) )
@ ( f @ Y0 )
@ ( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( h @ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f60,f47,f51,f49,f58,f51,f53,f58,f51,f53,f58,f51,f53]) ).
thf(f64,plain,
( $true
!= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( f @ Y0 @ mactual )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( g @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( g @ Y0 @ mactual )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( h @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( f @ Y0 @ mactual )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( h @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f63]) ).
thf(f65,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( f @ Y0 @ mactual )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( h @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f64]) ).
thf(f66,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( f @ Y0 @ mactual )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( g @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( g @ Y0 @ mactual )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( h @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f64]) ).
thf(f67,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( g @ Y0 @ mactual )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( h @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f66]) ).
thf(f68,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( f @ Y0 @ mactual )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( g @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f66]) ).
thf(f69,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( f @ Y0 @ mactual )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( g @ Y0 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f68]) ).
thf(f70,plain,
! [X1: $i] :
( $true
= ( ( eiw_di @ X1 @ mactual )
=> ( ( f @ X1 @ mactual )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( g @ X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f71,plain,
! [X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( ( f @ X1 @ mactual )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( g @ X1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f70]) ).
thf(f72,plain,
! [X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( f @ X1 @ mactual ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( g @ X1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f71]) ).
thf(f73,plain,
! [X2: mworld,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( f @ X1 @ mactual ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( g @ X1 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f72]) ).
thf(f74,plain,
! [X2: mworld,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( f @ X1 @ mactual ) )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( g @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f73]) ).
thf(f75,plain,
! [X2: mworld,X1: $i] :
( ( $true
= ( g @ X1 @ X2 ) )
| ( $false
= ( f @ X1 @ mactual ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f74]) ).
thf(f76,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( g @ Y0 @ mactual )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( h @ Y0 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f67]) ).
thf(f77,plain,
! [X1: $i] :
( $true
= ( ( eiw_di @ X1 @ mactual )
=> ( ( g @ X1 @ mactual )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( h @ X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f76]) ).
thf(f78,plain,
! [X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( ( g @ X1 @ mactual )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( h @ X1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( g @ X1 @ mactual ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( h @ X1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f78]) ).
thf(f80,plain,
! [X2: mworld,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( g @ X1 @ mactual ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( h @ X1 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X2: mworld,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( g @ X1 @ mactual ) )
| ( $true
= ( ( mrel @ mactual @ X2 )
=> ( h @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f80]) ).
thf(f82,plain,
! [X2: mworld,X1: $i] :
( ( $true
= ( h @ X1 @ X2 ) )
| ( $false
= ( g @ X1 @ mactual ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f81]) ).
thf(f83,plain,
( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( f @ Y0 @ mactual )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( h @ Y0 @ Y1 ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f65]) ).
thf(f84,plain,
( $false
= ( ( eiw_di @ sK1 @ mactual )
=> ( ( f @ sK1 @ mactual )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( h @ sK1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f83]) ).
thf(f85,plain,
( $false
= ( ( f @ sK1 @ mactual )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( h @ sK1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f84]) ).
thf(f86,plain,
( $true
= ( eiw_di @ sK1 @ mactual ) ),
inference(imp_proxy_clausification,[],[f84]) ).
thf(f87,plain,
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( h @ sK1 @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f85]) ).
thf(f88,plain,
( $true
= ( f @ sK1 @ mactual ) ),
inference(imp_proxy_clausification,[],[f85]) ).
thf(f89,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( h @ sK1 @ Y0 ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f87]) ).
thf(f90,plain,
( $false
= ( ( mrel @ mactual @ sK2 )
=> ( h @ sK1 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f89]) ).
thf(f91,plain,
( $false
= ( h @ sK1 @ sK2 ) ),
inference(imp_proxy_clausification,[],[f90]) ).
thf(f92,plain,
( $true
= ( mrel @ mactual @ sK2 ) ),
inference(imp_proxy_clausification,[],[f90]) ).
thf(f127,plain,
( ( $true = $false )
| ( $false
= ( g @ sK1 @ mactual ) )
| ( $false
= ( mrel @ mactual @ sK2 ) )
| ( $false
= ( eiw_di @ sK1 @ mactual ) ) ),
inference(constrained_superposition,[],[f91,f82]) ).
thf(f128,plain,
( ( $false
= ( g @ sK1 @ mactual ) )
| ( $false
= ( mrel @ mactual @ sK2 ) )
| ( $false
= ( eiw_di @ sK1 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f127]) ).
thf(f130,plain,
( ( $true = $false )
| ( $false
= ( g @ sK1 @ mactual ) )
| ( $false
= ( eiw_di @ sK1 @ mactual ) ) ),
inference(forward_demodulation,[],[f128,f92]) ).
thf(f131,plain,
( ( $false
= ( g @ sK1 @ mactual ) )
| ( $false
= ( eiw_di @ sK1 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f130]) ).
thf(f134,plain,
( ( $true = $false )
| ( $false
= ( g @ sK1 @ mactual ) ) ),
inference(forward_demodulation,[],[f131,f86]) ).
thf(f135,plain,
( $false
= ( g @ sK1 @ mactual ) ),
inference(trivial_inequality_removal,[],[f134]) ).
thf(f140,plain,
( ( $true = $false )
| ( $false
= ( f @ sK1 @ mactual ) )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ( $false
= ( eiw_di @ sK1 @ mactual ) ) ),
inference(constrained_superposition,[],[f75,f135]) ).
thf(f141,plain,
( ( $false
= ( f @ sK1 @ mactual ) )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ( $false
= ( eiw_di @ sK1 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f140]) ).
thf(f144,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ( $false
= ( eiw_di @ sK1 @ mactual ) ) ),
inference(forward_demodulation,[],[f141,f88]) ).
thf(f145,plain,
( ( $false
= ( mrel @ mactual @ mactual ) )
| ( $false
= ( eiw_di @ sK1 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f144]) ).
thf(f148,plain,
( ( $true = $false )
| ( $false
= ( eiw_di @ sK1 @ mactual ) ) ),
inference(forward_demodulation,[],[f145,f55]) ).
thf(f149,plain,
( $false
= ( eiw_di @ sK1 @ mactual ) ),
inference(trivial_inequality_removal,[],[f148]) ).
thf(f196,plain,
$true = $false,
inference(constrained_superposition,[],[f86,f149]) ).
thf(f197,plain,
$false,
inference(trivial_inequality_removal,[],[f196]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO888^10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 17:26:34 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.26 % (1354564)Will run a generic schedule for satisfiability detection.
% 0.08/0.26 % (1354574)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1547878269:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.26 % (1354570)% WARNING: option uhcvi not known.
% 0.08/0.26 % (1354574) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1354564-1354574"...
% 0.08/0.26 % (1354574)...printing done.
% 0.08/0.26 % (1354569)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1802535819_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.26 % (1354574)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
% 0.19/0.26 % (1354574)------------------------------
% 0.19/0.26 % (1354574)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.26 % (1354574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.26 % (1354574)CaDiCaL version: 2.1.3
% 0.19/0.26 % (1354574)Termination reason: Refutation
% 0.19/0.26 % (1354574)Time elapsed: 0.005 s
% 0.19/0.26 % (1354574)Peak memory usage: 12 MB
% 0.19/0.26 % (1354574)Instructions burned: 17 (million)
% 0.19/0.26 % (1354564)Success in time 0.032 s
% 0.19/0.26 % Vampire exiting
%------------------------------------------------------------------------------