TSTP Solution File: SYO901^11 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SYO901^11 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 21:07:36 EDT 2024
% Result : Theorem 0.23s 0.42s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 13
% Syntax : Number of formulae : 124 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 770 ( 181 equ; 0 cnn)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 834 ( 103 ~; 141 |; 3 &; 490 @)
% ( 8 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 22 usr; 13 con; 0-3 aty)
% ( 31 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 139 ( 90 ^ 49 !; 0 ?; 139 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(func_def_0,type,
mworld: $tType ).
thf(func_def_1,type,
mrel: mworld > mworld > $o ).
thf(func_def_2,type,
mactual: mworld ).
thf(func_def_3,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_5,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
p: mworld > $o ).
thf(func_def_13,type,
q: mworld > $o ).
thf(func_def_14,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_29,type,
sK1: mworld ).
thf(func_def_30,type,
sK2: mworld ).
thf(func_def_31,type,
sK3: mworld ).
thf(f427,plain,
$false,
inference(avatar_sat_refutation,[],[f88,f97,f102,f107,f108,f253,f318,f352,f426]) ).
thf(f426,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f425]) ).
thf(f425,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f424]) ).
thf(f424,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(backward_demodulation,[],[f372,f417]) ).
thf(f417,plain,
( ( ( p @ sK3 )
= $false )
| ~ spl0_4
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f416]) ).
thf(f416,plain,
( ( ( p @ sK3 )
= $false )
| ( $true = $false )
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f410,f96]) ).
thf(f96,plain,
( ( ( q @ sK3 )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f94]) ).
thf(f94,plain,
( spl0_4
<=> ( ( q @ sK3 )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f410,plain,
( ( $true
= ( q @ sK3 ) )
| ( ( p @ sK3 )
= $false )
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f403]) ).
thf(f403,plain,
( ( ( p @ sK3 )
= $false )
| ( $true
= ( q @ sK3 ) )
| ( $true = $false )
| ~ spl0_6 ),
inference(superposition,[],[f382,f57]) ).
thf(f57,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( q @ X1 ) )
| ( ( p @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[],[f56]) ).
thf(f56,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( q @ X1 )
= ( p @ X1 ) ) ),
inference(binary_proxy_clausification,[],[f55]) ).
thf(f55,plain,
! [X1: mworld] :
( ( $true
= ( ( p @ X1 )
= ( q @ X1 ) ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[],[f54]) ).
thf(f54,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ( p @ X1 )
= ( q @ X1 ) ) ) ),
inference(beta_eta_normalization,[],[f53]) ).
thf(f53,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
= ( q @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f52]) ).
thf(f52,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
= ( q @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f50]) ).
thf(f50,plain,
( $true
!= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
= ( q @ Y0 ) ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
= ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f49]) ).
thf(f49,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) )
@ p
@ q ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q ) ) ) ) ) ),
inference(definition_unfolding,[],[f42,f47,f39,f45,f44,f45,f44,f45,f45]) ).
thf(f44,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f21,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f20,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) )
= mequiv ),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
<=> ( X3 @ X2 ) ) )
= mequiv ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv_def) ).
thf(f45,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f33,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f32,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X2: mworld] :
! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f39,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f19,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f18,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X3 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(f47,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f34,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f42,plain,
( ( mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f35]) ).
thf(f35,plain,
( ( mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ) )
!= $true ),
inference(flattening,[],[f15]) ).
thf(f15,plain,
( ( mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f14]) ).
thf(f14,plain,
~ ( mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f12,negated_conjecture,
~ ( mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ) ),
inference(negated_conjecture,[],[f11]) ).
thf(f11,conjecture,
mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f382,plain,
( ( $true
= ( mrel @ mactual @ sK3 ) )
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f379]) ).
thf(f379,plain,
( ( $true != $true )
| ( $true
= ( mrel @ mactual @ sK3 ) )
| ~ spl0_6 ),
inference(superposition,[],[f110,f341]) ).
thf(f341,plain,
( ( $true
= ( mrel @ sK3 @ mactual ) )
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f337]) ).
thf(f337,plain,
( ( $true
= ( mrel @ sK3 @ mactual ) )
| ( $true != $true )
| ~ spl0_6 ),
inference(superposition,[],[f119,f106]) ).
thf(f106,plain,
( ( $true
= ( mrel @ sK1 @ sK3 ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f104]) ).
thf(f104,plain,
( spl0_6
<=> ( $true
= ( mrel @ sK1 @ sK3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f119,plain,
! [X0: mworld] :
( ( $true
!= ( mrel @ sK1 @ X0 ) )
| ( $true
= ( mrel @ X0 @ mactual ) ) ),
inference(trivial_inequality_removal,[],[f117]) ).
thf(f117,plain,
! [X0: mworld] :
( ( $true
!= ( mrel @ sK1 @ X0 ) )
| ( $true
= ( mrel @ X0 @ mactual ) )
| ( $true != $true ) ),
inference(superposition,[],[f41,f114]) ).
thf(f114,plain,
( $true
= ( mrel @ sK1 @ mactual ) ),
inference(trivial_inequality_removal,[],[f112]) ).
thf(f112,plain,
( ( $true != $true )
| ( $true
= ( mrel @ sK1 @ mactual ) ) ),
inference(superposition,[],[f110,f62]) ).
thf(f62,plain,
( $true
= ( mrel @ mactual @ sK1 ) ),
inference(binary_proxy_clausification,[],[f60]) ).
thf(f60,plain,
( $false
= ( ( mrel @ mactual @ sK1 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f59]) ).
thf(f59,plain,
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
= ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_clausification,[],[f51]) ).
thf(f51,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
= ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f50]) ).
thf(f41,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( $true
!= ( mrel @ X0 @ X2 ) )
| ( $true
!= ( mrel @ X0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ X2 ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f37,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( $true
!= ( mrel @ X0 @ X2 ) )
| ( $true
!= ( mrel @ X0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ X2 ) ) ),
inference(flattening,[],[f36]) ).
thf(f36,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( $true
= ( mrel @ X1 @ X2 ) )
| ( $true
!= ( mrel @ X0 @ X2 ) )
| ( $true
!= ( mrel @ X0 @ X1 ) ) ),
inference(ennf_transformation,[],[f31]) ).
thf(f31,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( $true
= ( mrel @ X0 @ X2 ) )
& ( $true
= ( mrel @ X0 @ X1 ) ) )
=> ( $true
= ( mrel @ X1 @ X2 ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f30,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X0 @ X2 )
& ( mrel @ X0 @ X1 ) )
=> ( mrel @ X1 @ X2 ) ),
inference(rectify,[],[f10]) ).
thf(f10,axiom,
! [X2: mworld,X5: mworld,X4: mworld] :
( ( ( mrel @ X2 @ X4 )
& ( mrel @ X2 @ X5 ) )
=> ( mrel @ X5 @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_euclidean) ).
thf(f110,plain,
! [X0: mworld,X1: mworld] :
( ( $true
!= ( mrel @ X0 @ X1 ) )
| ( $true
= ( mrel @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f109]) ).
thf(f109,plain,
! [X0: mworld,X1: mworld] :
( ( $true
= ( mrel @ X1 @ X0 ) )
| ( $true
!= ( mrel @ X0 @ X1 ) )
| ( $true != $true ) ),
inference(superposition,[],[f41,f43]) ).
thf(f43,plain,
! [X0: mworld] :
( $true
= ( mrel @ X0 @ X0 ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f29,plain,
! [X0: mworld] :
( $true
= ( mrel @ X0 @ X0 ) ),
inference(fool_elimination,[],[f28]) ).
thf(f28,plain,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
inference(rectify,[],[f9]) ).
thf(f9,axiom,
! [X2: mworld] : ( mrel @ X2 @ X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(f372,plain,
( ( $true
= ( p @ sK3 ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f360]) ).
thf(f360,plain,
( ( $true = $false )
| ( $true
= ( p @ sK3 ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f84,f106]) ).
thf(f84,plain,
( ! [X1: mworld] :
( ( ( mrel @ sK1 @ X1 )
= $false )
| ( $true
= ( p @ X1 ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f83]) ).
thf(f83,plain,
( spl0_1
<=> ! [X1: mworld] :
( ( $true
= ( p @ X1 ) )
| ( ( mrel @ sK1 @ X1 )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f352,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f351]) ).
thf(f351,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f350]) ).
thf(f350,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f343,f96]) ).
thf(f343,plain,
( ( $true
= ( q @ sK3 ) )
| ~ spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f335]) ).
thf(f335,plain,
( ( $true = $false )
| ( $true
= ( q @ sK3 ) )
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[],[f106,f87]) ).
thf(f87,plain,
( ! [X2: mworld] :
( ( ( mrel @ sK1 @ X2 )
= $false )
| ( $true
= ( q @ X2 ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f86]) ).
thf(f86,plain,
( spl0_2
<=> ! [X2: mworld] :
( ( ( mrel @ sK1 @ X2 )
= $false )
| ( $true
= ( q @ X2 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f318,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f317]) ).
thf(f317,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f316]) ).
thf(f316,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[],[f267,f313]) ).
thf(f313,plain,
( ( ( q @ sK2 )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f312]) ).
thf(f312,plain,
( ( ( q @ sK2 )
= $false )
| ( $true = $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f308,f92]) ).
thf(f92,plain,
( ( ( p @ sK2 )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f90]) ).
thf(f90,plain,
( spl0_3
<=> ( ( p @ sK2 )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f308,plain,
( ( $true
= ( p @ sK2 ) )
| ( ( q @ sK2 )
= $false )
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f301]) ).
thf(f301,plain,
( ( ( q @ sK2 )
= $false )
| ( $true
= ( p @ sK2 ) )
| ( $true = $false )
| ~ spl0_5 ),
inference(superposition,[],[f58,f290]) ).
thf(f290,plain,
( ( $true
= ( mrel @ mactual @ sK2 ) )
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f287]) ).
thf(f287,plain,
( ( $true
= ( mrel @ mactual @ sK2 ) )
| ( $true != $true )
| ~ spl0_5 ),
inference(superposition,[],[f110,f281]) ).
thf(f281,plain,
( ( $true
= ( mrel @ sK2 @ mactual ) )
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f279]) ).
thf(f279,plain,
( ( $true != $true )
| ( $true
= ( mrel @ sK2 @ mactual ) )
| ~ spl0_5 ),
inference(superposition,[],[f119,f101]) ).
thf(f101,plain,
( ( $true
= ( mrel @ sK1 @ sK2 ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f99]) ).
thf(f99,plain,
( spl0_5
<=> ( $true
= ( mrel @ sK1 @ sK2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f58,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( p @ X1 ) )
| ( ( q @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[],[f56]) ).
thf(f267,plain,
( ( $true
= ( q @ sK2 ) )
| ~ spl0_2
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f260]) ).
thf(f260,plain,
( ( $true = $false )
| ( $true
= ( q @ sK2 ) )
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[],[f101,f87]) ).
thf(f253,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f252]) ).
thf(f252,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f251]) ).
thf(f251,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f237,f92]) ).
thf(f237,plain,
( ( $true
= ( p @ sK2 ) )
| ~ spl0_1
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f232]) ).
thf(f232,plain,
( ( $true = $false )
| ( $true
= ( p @ sK2 ) )
| ~ spl0_1
| ~ spl0_5 ),
inference(superposition,[],[f101,f84]) ).
thf(f108,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f73,f104,f99]) ).
thf(f73,plain,
( ( $true
= ( mrel @ sK1 @ sK2 ) )
| ( $true
= ( mrel @ sK1 @ sK3 ) ) ),
inference(binary_proxy_clausification,[],[f71]) ).
thf(f71,plain,
( ( $true
= ( mrel @ sK1 @ sK3 ) )
| ( ( ( mrel @ sK1 @ sK2 )
=> ( p @ sK2 ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f69]) ).
thf(f69,plain,
( ( ( ( mrel @ sK1 @ sK3 )
=> ( q @ sK3 ) )
= $false )
| ( ( ( mrel @ sK1 @ sK2 )
=> ( p @ sK2 ) )
= $false ) ),
inference(beta_eta_normalization,[],[f68]) ).
thf(f68,plain,
( ( ( ( mrel @ sK1 @ sK2 )
=> ( p @ sK2 ) )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) )
@ sK3 )
= $false ) ),
inference(sigma_clausification,[],[f67]) ).
thf(f67,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) ) )
| ( ( ( mrel @ sK1 @ sK2 )
=> ( p @ sK2 ) )
= $false ) ),
inference(beta_eta_normalization,[],[f66]) ).
thf(f66,plain,
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) )
@ sK2 )
= $false )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) ) ) ),
inference(sigma_clausification,[],[f65]) ).
thf(f65,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
= $false )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f63]) ).
thf(f63,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[],[f61]) ).
thf(f61,plain,
( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f60]) ).
thf(f107,plain,
( spl0_6
| spl0_3 ),
inference(avatar_split_clause,[],[f72,f90,f104]) ).
thf(f72,plain,
( ( $true
= ( mrel @ sK1 @ sK3 ) )
| ( ( p @ sK2 )
= $false ) ),
inference(binary_proxy_clausification,[],[f71]) ).
thf(f102,plain,
( spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f75,f94,f99]) ).
thf(f75,plain,
( ( $true
= ( mrel @ sK1 @ sK2 ) )
| ( ( q @ sK3 )
= $false ) ),
inference(binary_proxy_clausification,[],[f70]) ).
thf(f70,plain,
( ( ( q @ sK3 )
= $false )
| ( ( ( mrel @ sK1 @ sK2 )
=> ( p @ sK2 ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f69]) ).
thf(f97,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f74,f94,f90]) ).
thf(f74,plain,
( ( ( q @ sK3 )
= $false )
| ( ( p @ sK2 )
= $false ) ),
inference(binary_proxy_clausification,[],[f70]) ).
thf(f88,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f81,f86,f83]) ).
thf(f81,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( p @ X1 ) )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( mrel @ sK1 @ X2 )
= $false )
| ( $true
= ( q @ X2 ) ) ),
inference(binary_proxy_clausification,[],[f80]) ).
thf(f80,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( p @ X1 ) )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( $true
= ( ( mrel @ sK1 @ X2 )
=> ( q @ X2 ) ) ) ),
inference(beta_eta_normalization,[],[f79]) ).
thf(f79,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( p @ X1 ) )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) )
@ X2 ) ) ),
inference(pi_clausification,[],[f78]) ).
thf(f78,plain,
! [X1: mworld] :
( ( $true
= ( p @ X1 ) )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f77]) ).
thf(f77,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ sK1 @ X1 )
=> ( p @ X1 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f76]) ).
thf(f76,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) ) ) ),
inference(pi_clausification,[],[f64]) ).
thf(f64,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SYO901^11 : TPTP v8.2.0. Released v8.1.0.
% 0.08/0.14 % Command : run_vampire %s %d THM
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Jun 23 09:17:09 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.37 This is a TH0_THM_EQU_NAR problem
% 0.14/0.38 Running higher-order theorem proving
% 0.14/0.38 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.23/0.40 % (17001)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.23/0.40 % (17002)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.23/0.40 % (17000)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.23/0.40 % (16999)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.23/0.40 % (17004)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.23/0.40 % (17002)Instruction limit reached!
% 0.23/0.40 % (17002)------------------------------
% 0.23/0.40 % (17002)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.23/0.40 % (17002)Termination reason: Unknown
% 0.23/0.40 % (17002)Termination phase: shuffling
% 0.23/0.40
% 0.23/0.40 % (17002)Memory used [KB]: 1023
% 0.23/0.40 % (17002)Time elapsed: 0.004 s
% 0.23/0.40 % (17002)Instructions burned: 2 (million)
% 0.23/0.40 % (17002)------------------------------
% 0.23/0.40 % (17002)------------------------------
% 0.23/0.40 % (17000)Instruction limit reached!
% 0.23/0.40 % (17000)------------------------------
% 0.23/0.40 % (17000)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.23/0.40 % (17000)Termination reason: Unknown
% 0.23/0.40 % (17000)Termination phase: Saturation
% 0.23/0.40
% 0.23/0.40 % (17000)Memory used [KB]: 5500
% 0.23/0.40 % (17000)Time elapsed: 0.004 s
% 0.23/0.40 % (17000)Instructions burned: 4 (million)
% 0.23/0.40 % (17000)------------------------------
% 0.23/0.40 % (17000)------------------------------
% 0.23/0.40 % (17004)Refutation not found, incomplete strategy
% 0.23/0.40 % (17004)------------------------------
% 0.23/0.40 % (17004)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.23/0.40 % (17004)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.40
% 0.23/0.40
% 0.23/0.40 % (17004)Memory used [KB]: 5500
% 0.23/0.40 % (17004)Time elapsed: 0.004 s
% 0.23/0.40 % (17004)Instructions burned: 2 (million)
% 0.23/0.40 % (17004)------------------------------
% 0.23/0.40 % (17004)------------------------------
% 0.23/0.41 % (17003)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.23/0.41 % (17003)Instruction limit reached!
% 0.23/0.41 % (17003)------------------------------
% 0.23/0.41 % (17003)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.23/0.41 % (17003)Termination reason: Unknown
% 0.23/0.41 % (17003)Termination phase: Property scanning
% 0.23/0.41
% 0.23/0.41 % (17003)Memory used [KB]: 1023
% 0.23/0.41 % (17003)Time elapsed: 0.003 s
% 0.23/0.41 % (17003)Instructions burned: 2 (million)
% 0.23/0.41 % (17003)------------------------------
% 0.23/0.41 % (17003)------------------------------
% 0.23/0.41 % (17005)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.23/0.41 % (17007)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.23/0.41 % (17006)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.23/0.42 % (17001)First to succeed.
% 0.23/0.42 % (17008)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.23/0.42 % (17006)Instruction limit reached!
% 0.23/0.42 % (17006)------------------------------
% 0.23/0.42 % (17006)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.23/0.42 % (17006)Termination reason: Unknown
% 0.23/0.42 % (17006)Termination phase: Saturation
% 0.23/0.42
% 0.23/0.42 % (17006)Memory used [KB]: 5500
% 0.23/0.42 % (17006)Time elapsed: 0.004 s
% 0.23/0.42 % (17006)Instructions burned: 3 (million)
% 0.23/0.42 % (17006)------------------------------
% 0.23/0.42 % (17006)------------------------------
% 0.23/0.42 % (16999)Also succeeded, but the first one will report.
% 0.23/0.42 % (17001)Refutation found. Thanks to Tanya!
% 0.23/0.42 % SZS status Theorem for theBenchmark
% 0.23/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.42 % (17001)------------------------------
% 0.23/0.42 % (17001)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.23/0.42 % (17001)Termination reason: Refutation
% 0.23/0.42
% 0.23/0.42 % (17001)Memory used [KB]: 5756
% 0.23/0.42 % (17001)Time elapsed: 0.023 s
% 0.23/0.42 % (17001)Instructions burned: 24 (million)
% 0.23/0.42 % (17001)------------------------------
% 0.23/0.42 % (17001)------------------------------
% 0.23/0.42 % (16998)Success in time 0.023 s
%------------------------------------------------------------------------------