%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO901^11 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 0.22s 0.31s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 13
% Syntax : Number of formulae : 138 ( 40 unt; 0 typ; 6 def)
% Number of atoms : 791 ( 180 equ; 0 cnn)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 856 ( 122 ~; 155 |; 3 &; 484 @)
% ( 8 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 33 usr; 13 con; 0-4 aty)
% ( 28 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 143 ( 0 sgn 54 !; 0 ?; 143 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_14,type,
vAND: $o > $o > $o ).
thf(func_def_15,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_19,type,
vIFF: $o > $o > $o ).
thf(func_def_20,type,
vIMP: $o > $o > $o ).
thf(func_def_21,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_24,type,
vOR: $o > $o > $o ).
thf(func_def_25,type,
vNOT: $o > $o ).
thf(func_def_26,type,
sK0: mworld ).
thf(func_def_27,type,
sK1: mworld ).
thf(func_def_28,type,
sK2: mworld ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f5,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(f6,axiom,
( mequiv
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
<=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv_def) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f9,axiom,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(f10,axiom,
! [X0: mworld,X2: mworld,X1: mworld] :
( ( ( mrel @ X0 @ X2 )
& ( mrel @ X0 @ X1 ) )
=> ( mrel @ X2 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_euclidean) ).
thf(f11,conjecture,
mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f12,negated_conjecture,
~ ( mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
thf(f15,plain,
( mequiv
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
<=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f16,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[],[f5]) ).
thf(f18,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[],[f7]) ).
thf(f20,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
~ ( mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f22,plain,
( ( mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
inference(rectify,[],[f9]) ).
thf(f24,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f23]) ).
thf(f27,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f28,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X0 @ X1 )
& ( mrel @ X0 @ X2 ) )
=> ( mrel @ X1 @ X2 ) ),
inference(rectify,[],[f10]) ).
thf(f29,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( ( ( mrel @ X0 @ X2 )
= $true )
& ( ( mrel @ X0 @ X1 )
= $true ) )
=> ( ( mrel @ X1 @ X2 )
= $true ) ),
inference(fool_elimination,[],[f28]) ).
thf(f34,plain,
( ( mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ) )
!= $true ),
inference(flattening,[],[f22]) ).
thf(f35,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
= $true )
| ( ( mrel @ X0 @ X2 )
!= $true )
| ( ( mrel @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f29]) ).
thf(f36,plain,
! [X2: mworld,X1: mworld,X0: mworld] :
( ( ( mrel @ X1 @ X2 )
= $true )
| ( ( mrel @ X0 @ X2 )
!= $true )
| ( ( mrel @ X0 @ X1 )
!= $true ) ),
inference(flattening,[],[f35]) ).
thf(f37,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( $true
= ( mrel @ X1 @ X0 ) )
| ( $true
!= ( mrel @ X2 @ X0 ) )
| ( ( mrel @ X2 @ X1 )
!= $true ) ),
inference(rectify,[],[f36]) ).
thf(f38,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f39,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( $true
!= ( mrel @ X2 @ X0 ) )
| ( ( mrel @ X2 @ X1 )
!= $true )
| ( $true
= ( mrel @ X1 @ X0 ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f40,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f42,plain,
( ( mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f34]) ).
thf(f43,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f24]) ).
thf(f44,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f48,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
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] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) )
@ p
@ q ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
= ( Y0 @ 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 ) ) ) ) ) ),
inference(definition_unfolding,[],[f42,f38,f44,f48,f40,f48,f40,f48,f48]) ).
thf(f52,plain,
( $true
!= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( q @ Y0 )
= ( p @ Y0 ) ) ) )
=> ( !! @ 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,[],[f51]) ).
thf(f53,plain,
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
= ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f52]) ).
thf(f54,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( q @ Y0 )
= ( p @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f52]) ).
thf(f55,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( q @ Y0 )
= ( p @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ( q @ X1 )
= ( p @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( q @ X1 )
= ( p @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X1: mworld] :
( ( ( q @ X1 )
= ( p @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( q @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f58]) ).
thf(f60,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( q @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f58]) ).
thf(f61,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
= ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f53]) ).
thf(f62,plain,
( $false
= ( ( mrel @ mactual @ sK0 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( q @ Y0 ) ) )
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f63,plain,
( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( q @ Y0 ) ) )
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f62]) ).
thf(f64,plain,
( $true
= ( mrel @ mactual @ sK0 ) ),
inference(imp_proxy_clausification,[],[f62]) ).
thf(f65,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) )
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( q @ Y0 ) ) ) ),
inference(iff_proxy_clausification,[],[f63]) ).
thf(f66,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( q @ Y0 ) ) ) ) ),
inference(xor_proxy_clausification,[],[f65]) ).
thf(f67,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( q @ Y0 ) ) ) ) ),
inference(xor_proxy_clausification,[],[f65]) ).
thf(f68,plain,
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( p @ Y0 ) )
@ sK1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( q @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f67]) ).
thf(f69,plain,
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( q @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( p @ Y0 ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f68]) ).
thf(f70,plain,
( ( $false
= ( ( mrel @ sK0 @ sK2 )
=> ( q @ sK2 ) ) )
| ( $false
= ( ( mrel @ sK0 @ sK1 )
=> ( p @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f71,plain,
( ( $false
= ( ( mrel @ sK0 @ sK1 )
=> ( p @ sK1 ) ) )
| ( ( q @ sK2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f70]) ).
thf(f72,plain,
( ( $true
= ( mrel @ sK0 @ sK2 ) )
| ( $false
= ( ( mrel @ sK0 @ sK1 )
=> ( p @ sK1 ) ) ) ),
inference(imp_proxy_clausification,[],[f70]) ).
thf(f73,plain,
( ( $false
= ( p @ sK1 ) )
| ( $true
= ( mrel @ sK0 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f72]) ).
thf(f74,plain,
( ( $true
= ( mrel @ sK0 @ sK2 ) )
| ( ( mrel @ sK0 @ sK1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f72]) ).
thf(f75,plain,
( ( ( q @ sK2 )
= $false )
| ( $false
= ( p @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f71]) ).
thf(f76,plain,
( ( ( mrel @ sK0 @ sK1 )
= $true )
| ( ( q @ sK2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f71]) ).
thf(f77,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( p @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( q @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f66]) ).
thf(f78,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( p @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK0 @ X1 )
=> ( p @ X1 ) ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( q @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( ( mrel @ sK0 @ X2 )
=> ( q @ X2 ) ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X2: mworld,X1: mworld] :
( ( ( q @ X2 )
= $true )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X2 ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f80]) ).
thf(f83,definition,
( spl3_1
<=> ( $true
= ( mrel @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f85,plain,
( ( $true
= ( mrel @ sK0 @ sK2 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f83]) ).
thf(f87,definition,
( spl3_2
<=> ( ( mrel @ sK0 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f89,plain,
( ( ( mrel @ sK0 @ sK1 )
= $true )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f87]) ).
thf(f90,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f74,f87,f83]) ).
thf(f92,definition,
( spl3_3
<=> ( $false
= ( p @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f94,plain,
( ( $false
= ( p @ sK1 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f92]) ).
thf(f95,plain,
( spl3_1
| spl3_3 ),
inference(avatar_split_clause,[],[f73,f92,f83]) ).
thf(f97,definition,
( spl3_4
<=> ( ( q @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f99,plain,
( ( ( q @ sK2 )
= $false )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f97]) ).
thf(f100,plain,
( spl3_4
| spl3_2 ),
inference(avatar_split_clause,[],[f76,f87,f97]) ).
thf(f101,plain,
( spl3_4
| spl3_3 ),
inference(avatar_split_clause,[],[f75,f92,f97]) ).
thf(f103,definition,
( spl3_5
<=> ! [X2: mworld] :
( ( ( q @ X2 )
= $true )
| ( $false
= ( mrel @ sK0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
thf(f104,plain,
( ! [X2: mworld] :
( ( $false
= ( mrel @ sK0 @ X2 ) )
| ( ( q @ X2 )
= $true ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f103]) ).
thf(f106,definition,
( spl3_6
<=> ! [X1: mworld] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
thf(f107,plain,
( ! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) )
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f106]) ).
thf(f108,plain,
( spl3_5
| spl3_6 ),
inference(avatar_split_clause,[],[f81,f106,f103]) ).
thf(f110,plain,
( ( $true
= ( q @ sK1 ) )
| ( $false = $true )
| ~ spl3_2
| ~ spl3_5 ),
inference(constrained_superposition,[],[f104,f89]) ).
thf(f113,plain,
( ( $true
= ( q @ sK1 ) )
| ~ spl3_2
| ~ spl3_5 ),
inference(trivial_inequality_removal,[],[f110]) ).
thf(f151,plain,
! [X0: mworld,X1: mworld] :
( ( $true != $true )
| ( ( mrel @ X0 @ X1 )
!= $true )
| ( $true
= ( mrel @ X1 @ X0 ) ) ),
inference(constrained_superposition,[],[f39,f43]) ).
thf(f156,plain,
( ! [X0: mworld] :
( ( $true
= ( mrel @ X0 @ sK1 ) )
| ( $true != $true )
| ( $true
!= ( mrel @ sK0 @ X0 ) ) )
| ~ spl3_2 ),
inference(constrained_superposition,[],[f39,f89]) ).
thf(f157,plain,
! [X0: mworld,X1: mworld] :
( ( ( mrel @ X0 @ X1 )
!= $true )
| ( $true
= ( mrel @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f151]) ).
thf(f159,plain,
( ! [X0: mworld] :
( ( $true
!= ( mrel @ sK0 @ X0 ) )
| ( $true
= ( mrel @ X0 @ sK1 ) ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f156]) ).
thf(f174,plain,
( ( $true != $true )
| ( $true
= ( mrel @ sK0 @ mactual ) ) ),
inference(constrained_superposition,[],[f157,f64]) ).
thf(f176,plain,
( $true
= ( mrel @ sK0 @ mactual ) ),
inference(trivial_inequality_removal,[],[f174]) ).
thf(f179,plain,
( ( $true
= ( mrel @ mactual @ sK1 ) )
| ( $true != $true )
| ~ spl3_2 ),
inference(constrained_superposition,[],[f159,f176]) ).
thf(f182,plain,
! [X0: mworld] :
( ( $true != $true )
| ( ( mrel @ X0 @ mactual )
= $true )
| ( $true
!= ( mrel @ sK0 @ X0 ) ) ),
inference(constrained_superposition,[],[f39,f176]) ).
thf(f185,plain,
( ( $true
= ( mrel @ mactual @ sK1 ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f179]) ).
thf(f186,plain,
! [X0: mworld] :
( ( $true
!= ( mrel @ sK0 @ X0 ) )
| ( ( mrel @ X0 @ mactual )
= $true ) ),
inference(trivial_inequality_removal,[],[f182]) ).
thf(f195,plain,
( ( $false
= ( q @ sK1 ) )
| ( $false = $true )
| ( $true
= ( p @ sK1 ) )
| ~ spl3_2 ),
inference(constrained_superposition,[],[f60,f185]) ).
thf(f202,plain,
( ( $true
= ( p @ sK1 ) )
| ( $false
= ( q @ sK1 ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f195]) ).
thf(f208,plain,
( ( $false = $true )
| ( $false
= ( q @ sK1 ) )
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f202,f94]) ).
thf(f209,plain,
( ( $false
= ( q @ sK1 ) )
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f208]) ).
thf(f213,plain,
( ( $false = $true )
| ~ spl3_2
| ~ spl3_3
| ~ spl3_5 ),
inference(forward_demodulation,[],[f209,f113]) ).
thf(f214,plain,
( $false
| ~ spl3_2
| ~ spl3_3
| ~ spl3_5 ),
inference(trivial_inequality_removal,[],[f213]) ).
thf(f215,plain,
( ~ spl3_2
| ~ spl3_3
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[],[f214]) ).
thf(f217,plain,
( ( ( q @ sK2 )
= $true )
| ( $false = $true )
| ~ spl3_1
| ~ spl3_5 ),
inference(constrained_superposition,[],[f104,f85]) ).
thf(f222,plain,
( ( ( q @ sK2 )
= $true )
| ~ spl3_1
| ~ spl3_5 ),
inference(trivial_inequality_removal,[],[f217]) ).
thf(f227,plain,
( ( $false = $true )
| ~ spl3_1
| ~ spl3_4
| ~ spl3_5 ),
inference(forward_demodulation,[],[f222,f99]) ).
thf(f228,plain,
( $false
| ~ spl3_1
| ~ spl3_4
| ~ spl3_5 ),
inference(trivial_inequality_removal,[],[f227]) ).
thf(f229,plain,
( ~ spl3_1
| ~ spl3_4
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[],[f228]) ).
thf(f262,plain,
( ( ( p @ sK2 )
= $true )
| ( $false = $true )
| ~ spl3_1
| ~ spl3_6 ),
inference(constrained_superposition,[],[f85,f107]) ).
thf(f265,plain,
( ( ( p @ sK2 )
= $true )
| ~ spl3_1
| ~ spl3_6 ),
inference(trivial_inequality_removal,[],[f262]) ).
thf(f272,plain,
( ( $true
= ( mrel @ sK2 @ mactual ) )
| ( $true != $true )
| ~ spl3_1 ),
inference(constrained_superposition,[],[f186,f85]) ).
thf(f274,plain,
( ( $true
= ( mrel @ sK2 @ mactual ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f272]) ).
thf(f276,plain,
( ( $true
= ( mrel @ mactual @ sK2 ) )
| ( $true != $true )
| ~ spl3_1 ),
inference(constrained_superposition,[],[f157,f274]) ).
thf(f279,plain,
( ( $true
= ( mrel @ mactual @ sK2 ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f276]) ).
thf(f284,plain,
( ( $false
= ( p @ sK2 ) )
| ( ( q @ sK2 )
= $true )
| ( $false = $true )
| ~ spl3_1 ),
inference(constrained_superposition,[],[f59,f279]) ).
thf(f292,plain,
( ( $false
= ( p @ sK2 ) )
| ( ( q @ sK2 )
= $true )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f284]) ).
thf(f296,plain,
( ( ( q @ sK2 )
= $true )
| ( $false = $true )
| ~ spl3_1
| ~ spl3_6 ),
inference(forward_demodulation,[],[f292,f265]) ).
thf(f297,plain,
( ( ( q @ sK2 )
= $true )
| ~ spl3_1
| ~ spl3_6 ),
inference(trivial_inequality_removal,[],[f296]) ).
thf(f301,plain,
( ( $false = $true )
| ~ spl3_1
| ~ spl3_4
| ~ spl3_6 ),
inference(forward_demodulation,[],[f297,f99]) ).
thf(f302,plain,
( $false
| ~ spl3_1
| ~ spl3_4
| ~ spl3_6 ),
inference(trivial_inequality_removal,[],[f301]) ).
thf(f303,plain,
( ~ spl3_1
| ~ spl3_4
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[],[f302]) ).
thf(f309,plain,
( ( $true
= ( p @ sK1 ) )
| ( $false = $true )
| ~ spl3_2
| ~ spl3_6 ),
inference(constrained_superposition,[],[f107,f89]) ).
thf(f314,plain,
( ( $true
= ( p @ sK1 ) )
| ~ spl3_2
| ~ spl3_6 ),
inference(trivial_inequality_removal,[],[f309]) ).
thf(f320,plain,
( ( $false = $true )
| ~ spl3_2
| ~ spl3_3
| ~ spl3_6 ),
inference(forward_demodulation,[],[f314,f94]) ).
thf(f321,plain,
( $false
| ~ spl3_2
| ~ spl3_3
| ~ spl3_6 ),
inference(trivial_inequality_removal,[],[f320]) ).
thf(f322,plain,
( ~ spl3_2
| ~ spl3_3
| ~ spl3_6 ),
inference(avatar_contradiction_clause,[],[f321]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f90]) ).
cnf(s2,plain,
( spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f95]) ).
cnf(s3,plain,
( spl3_2
| spl3_4 ),
inference(sat_conversion,[],[f100]) ).
cnf(s4,plain,
( spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f101]) ).
cnf(s5,plain,
( spl3_5
| spl3_6 ),
inference(sat_conversion,[],[f108]) ).
cnf(s9,plain,
( ~ spl3_2
| ~ spl3_3
| ~ spl3_5 ),
inference(sat_conversion,[],[f215]) ).
cnf(s11,plain,
( ~ spl3_1
| ~ spl3_4
| ~ spl3_5 ),
inference(sat_conversion,[],[f229]) ).
cnf(s17,plain,
( ~ spl3_1
| ~ spl3_4
| ~ spl3_6 ),
inference(sat_conversion,[],[f303]) ).
cnf(s19,plain,
( ~ spl3_2
| ~ spl3_3
| ~ spl3_6 ),
inference(sat_conversion,[],[f322]) ).
cnf(s20,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(rat,[],[s5,s19,s9]) ).
cnf(s21,plain,
spl3_1,
inference(rat,[],[s20,s1,s2]) ).
cnf(s22,plain,
~ spl3_4,
inference(rat,[],[s5,s17,s11,s21]) ).
cnf(s23,plain,
spl3_3,
inference(rat,[],[s4,s22]) ).
cnf(s24,plain,
spl3_2,
inference(rat,[],[s3,s22]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s20,s23,s24]) ).
thf(f323,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO901^11 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n008.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 17:27:09 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.31 % (3466744)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.31 % (3466751)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1626374580:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.31 % (3466751)Refutation not found, incomplete strategy
% 0.22/0.31 % (3466751)------------------------------
% 0.22/0.31 % (3466751)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (3466751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (3466751)CaDiCaL version: 2.1.3
% 0.22/0.31 % (3466751)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.31 % (3466751)Time elapsed: 0.001 s
% 0.22/0.31 % (3466751)Peak memory usage: 12 MB
% 0.22/0.31 % (3466751)Instructions burned: 3 (million)
% 0.22/0.31 % (3466751)------------------------------
% 0.22/0.31 % (3466751)------------------------------
% 0.22/0.31 % (3466755)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.31 % (3466755)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
% 0.22/0.31 % (3466750)lrs+10_16_si=on:nwc=1.5:random_seed=3786847625:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.31 % (3466749)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=221948343:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.31 % (3466752)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=220260795:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.31 % (3466753)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=476895656:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.31 % (3466754)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1958319392:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.31 % (3466755)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=2783813711:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.31 % (3466757)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3982063281:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.31 % (3466757)Instruction limit reached!
% 0.22/0.31 % (3466757)------------------------------
% 0.22/0.31 % (3466757)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (3466757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (3466757)CaDiCaL version: 2.1.3
% 0.22/0.31 % (3466757)Termination reason: Instruction limit
% 0.22/0.31 % (3466757)Termination phase: Saturation
% 0.22/0.31 % (3466757)Time elapsed: 0.001 s
% 0.22/0.31 % (3466757)Peak memory usage: 11 MB
% 0.22/0.31 % (3466757)Instructions burned: 3 (million)
% 0.22/0.31 % (3466749) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3466744-3466749"...
% 0.22/0.31 % (3466754) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3466744-3466754"...
% 0.22/0.31 % (3466750) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3466744-3466750"...
% 0.22/0.31 % (3466749)...printing done.
% 0.22/0.31 % (3466749)Refutation found. Thanks to Tanya!
% 0.22/0.31 % SZS status Theorem for theBenchmark
% 0.22/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.31 % (3466749)------------------------------
% 0.22/0.31 % (3466749)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (3466749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (3466749)CaDiCaL version: 2.1.3
% 0.22/0.31 % (3466749)Termination reason: Refutation
% 0.22/0.31 % (3466749)Time elapsed: 0.011 s
% 0.22/0.31 % (3466749)Peak memory usage: 13 MB
% 0.22/0.31 % (3466749)Instructions burned: 17 (million)
% 0.22/0.31 % (3466744)Success in time 0.058 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------