TSTP Solution File: LCL962^16 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : LCL962^16 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n001.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 11:34:53 EDT 2024
% Result : Theorem 0.12s 0.39s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 16
% Syntax : Number of formulae : 114 ( 48 unt; 0 typ; 0 def)
% Number of atoms : 672 ( 151 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 900 ( 67 ~; 93 |; 0 &; 636 @)
% ( 7 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 22 usr; 14 con; 0-3 aty)
% ( 35 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 161 ( 113 ^ 48 !; 0 ?; 161 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mindex: $tType ).
thf(type_def_6,type,
mworld: $tType ).
thf(func_def_0,type,
mworld: $tType ).
thf(func_def_1,type,
mindex: $tType ).
thf(func_def_2,type,
mrel: mindex > mworld > mworld > $o ).
thf(func_def_3,type,
'#b': mindex ).
thf(func_def_4,type,
'#a': mindex ).
thf(func_def_5,type,
mactual: mworld ).
thf(func_def_6,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_8,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
mbox: mindex > ( mworld > $o ) > mworld > $o ).
thf(func_def_14,type,
mdia: mindex > ( mworld > $o ) > mworld > $o ).
thf(func_def_15,type,
p: mworld > $o ).
thf(func_def_31,type,
sK1: mworld > mworld ).
thf(func_def_32,type,
sK2: mworld ).
thf(f192,plain,
$false,
inference(avatar_sat_refutation,[],[f115,f119,f129,f154,f172,f178,f185,f191]) ).
thf(f191,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f190]) ).
thf(f190,plain,
( $false
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f186]) ).
thf(f186,plain,
( ( $true = $false )
| ~ spl0_4 ),
inference(superposition,[],[f149,f100]) ).
thf(f100,plain,
( $true
= ( p @ sK2 ) ),
inference(not_proxy_clausification,[],[f98]) ).
thf(f98,plain,
( $false
= ( ~ ( p @ sK2 ) ) ),
inference(binary_proxy_clausification,[],[f97]) ).
thf(f97,plain,
( ( ( mrel @ '#a' @ mactual @ sK2 )
=> ~ ( p @ sK2 ) )
= $false ),
inference(beta_eta_normalization,[],[f96]) ).
thf(f96,plain,
( ( ^ [Y0: mworld] :
( ( mrel @ '#a' @ mactual @ Y0 )
=> ~ ( p @ Y0 ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[],[f95]) ).
thf(f95,plain,
( $true
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#a' @ mactual @ Y0 )
=> ~ ( p @ Y0 ) ) ) ),
inference(beta_eta_normalization,[],[f71]) ).
thf(f71,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#a'
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ p ) ) )
!= $true ),
inference(definition_unfolding,[],[f55,f67,f70,f68]) ).
thf(f68,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f39,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f38,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
( ( ^ [X1: mworld > $o,X2: mworld] :
~ ( X1 @ X2 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_def) ).
thf(f70,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f24,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f23,plain,
( ( ^ [X0: mindex,X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
( ( ^ [X4: mindex,X0: mworld > $o,X2: mworld] :
! [X5: mworld] :
( ( mrel @ X4 @ X2 @ X5 )
=> ( X0 @ X5 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f67,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f29,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(f55,plain,
( ( mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ) )
!= $true ),
inference(cnf_transformation,[],[f50]) ).
thf(f50,plain,
( ( mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ) )
!= $true ),
inference(flattening,[],[f20]) ).
thf(f20,plain,
( ( mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ) )
!= $true ),
inference(fool_elimination,[],[f19]) ).
thf(f19,plain,
~ ( mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ) ),
inference(rectify,[],[f17]) ).
thf(f17,negated_conjecture,
~ ( mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ) ),
inference(negated_conjecture,[],[f16]) ).
thf(f16,conjecture,
mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f149,plain,
( ( ( p @ sK2 )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f147]) ).
thf(f147,plain,
( spl0_4
<=> ( ( p @ sK2 )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f185,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f184]) ).
thf(f184,plain,
( $false
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f181]) ).
thf(f181,plain,
( ( $true = $false )
| ~ spl0_7 ),
inference(superposition,[],[f99,f170]) ).
thf(f170,plain,
( ( ( mrel @ '#a' @ mactual @ sK2 )
= $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f168]) ).
thf(f168,plain,
( spl0_7
<=> ( ( mrel @ '#a' @ mactual @ sK2 )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f99,plain,
( ( mrel @ '#a' @ mactual @ sK2 )
= $true ),
inference(binary_proxy_clausification,[],[f97]) ).
thf(f178,plain,
( ~ spl0_1
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f177]) ).
thf(f177,plain,
( $false
| ~ spl0_1
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f174]) ).
thf(f174,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f137,f166]) ).
thf(f166,plain,
( ( ( p @ ( sK1 @ sK2 ) )
= $true )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f164]) ).
thf(f164,plain,
( spl0_6
<=> ( ( p @ ( sK1 @ sK2 ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f137,plain,
( ( ( p @ ( sK1 @ sK2 ) )
= $false )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f131]) ).
thf(f131,plain,
( ( $true = $false )
| ( ( p @ ( sK1 @ sK2 ) )
= $false )
| ~ spl0_1 ),
inference(superposition,[],[f111,f99]) ).
thf(f111,plain,
( ! [X1: mworld] :
( ( ( mrel @ '#a' @ mactual @ X1 )
= $false )
| ( ( p @ ( sK1 @ X1 ) )
= $false ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f110]) ).
thf(f110,plain,
( spl0_1
<=> ! [X1: mworld] :
( ( ( mrel @ '#a' @ mactual @ X1 )
= $false )
| ( ( p @ ( sK1 @ X1 ) )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f172,plain,
( spl0_7
| spl0_6
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f161,f151,f117,f164,f168]) ).
thf(f117,plain,
( spl0_3
<=> ! [X1: mworld] :
( ( ( mrel @ '#b' @ X1 @ ( sK1 @ X1 ) )
= $true )
| ( ( mrel @ '#a' @ mactual @ X1 )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f151,plain,
( spl0_5
<=> ! [X0: mworld] :
( ( ( p @ X0 )
= $true )
| ( ( mrel @ '#b' @ sK2 @ X0 )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f161,plain,
( ( ( mrel @ '#a' @ mactual @ sK2 )
= $false )
| ( ( p @ ( sK1 @ sK2 ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f159]) ).
thf(f159,plain,
( ( ( mrel @ '#a' @ mactual @ sK2 )
= $false )
| ( ( p @ ( sK1 @ sK2 ) )
= $true )
| ( $true = $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f118,f152]) ).
thf(f152,plain,
( ! [X0: mworld] :
( ( ( mrel @ '#b' @ sK2 @ X0 )
= $false )
| ( ( p @ X0 )
= $true ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f151]) ).
thf(f118,plain,
( ! [X1: mworld] :
( ( ( mrel @ '#b' @ X1 @ ( sK1 @ X1 ) )
= $true )
| ( ( mrel @ '#a' @ mactual @ X1 )
= $false ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f117]) ).
thf(f154,plain,
( spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f142,f147,f151]) ).
thf(f142,plain,
! [X0: mworld] :
( ( ( mrel @ '#b' @ sK2 @ X0 )
= $false )
| ( ( p @ X0 )
= $true )
| ( ( p @ sK2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f139]) ).
thf(f139,plain,
! [X0: mworld] :
( ( $true = $false )
| ( ( p @ sK2 )
= $false )
| ( ( mrel @ '#b' @ sK2 @ X0 )
= $false )
| ( ( p @ X0 )
= $true ) ),
inference(superposition,[],[f108,f99]) ).
thf(f108,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#a' @ mactual @ X1 )
= $false )
| ( ( p @ X1 )
= $false )
| ( ( p @ X2 )
= $true )
| ( ( mrel @ '#b' @ X1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[],[f107]) ).
thf(f107,plain,
! [X2: mworld,X1: mworld] :
( ( ( p @ X1 )
= $false )
| ( ( ( mrel @ '#b' @ X1 @ X2 )
=> ( p @ X2 ) )
= $true )
| ( ( mrel @ '#a' @ mactual @ X1 )
= $false ) ),
inference(beta_eta_normalization,[],[f106]) ).
thf(f106,plain,
! [X2: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ '#b' @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ X2 )
= $true )
| ( ( mrel @ '#a' @ mactual @ X1 )
= $false )
| ( ( p @ X1 )
= $false ) ),
inference(pi_clausification,[],[f105]) ).
thf(f105,plain,
! [X1: mworld] :
( ( ( mrel @ '#a' @ mactual @ X1 )
= $false )
| ( ( p @ X1 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f104]) ).
thf(f104,plain,
! [X1: mworld] :
( ( ( mrel @ '#a' @ mactual @ X1 )
= $false )
| ( ( ( p @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ X1 @ Y0 )
=> ( p @ Y0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f103]) ).
thf(f103,plain,
! [X1: mworld] :
( ( ( mrel @ '#a' @ mactual @ X1 )
=> ( ( p @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ X1 @ Y0 )
=> ( p @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f102]) ).
thf(f102,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#a' @ mactual @ Y0 )
=> ( ( p @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#b' @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f101]) ).
thf(f101,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#a' @ mactual @ Y0 )
=> ( ( p @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#b' @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f73]) ).
thf(f73,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#a'
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ p
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#b'
@ p ) ) ) ) ),
inference(definition_unfolding,[],[f63,f67,f70,f59,f70]) ).
thf(f59,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f43,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f42,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
( mimplies
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(f63,plain,
( ( mlocal @ ( mbox @ '#a' @ ( mimplies @ p @ ( mbox @ '#b' @ p ) ) ) )
= $true ),
inference(cnf_transformation,[],[f22]) ).
thf(f22,plain,
( ( mlocal @ ( mbox @ '#a' @ ( mimplies @ p @ ( mbox @ '#b' @ p ) ) ) )
= $true ),
inference(fool_elimination,[],[f21]) ).
thf(f21,plain,
mlocal @ ( mbox @ '#a' @ ( mimplies @ p @ ( mbox @ '#b' @ p ) ) ),
inference(rectify,[],[f13]) ).
thf(f13,axiom,
mlocal @ ( mbox @ '#a' @ ( mimplies @ p @ ( mbox @ '#b' @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_axiom_1) ).
thf(f129,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f128]) ).
thf(f128,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f124]) ).
thf(f124,plain,
( ( $true = $false )
| ~ spl0_2 ),
inference(superposition,[],[f123,f94]) ).
thf(f94,plain,
( ( p @ mactual )
= $false ),
inference(not_proxy_clausification,[],[f93]) ).
thf(f93,plain,
( $true
= ( ~ ( p @ mactual ) ) ),
inference(beta_eta_normalization,[],[f74]) ).
thf(f74,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ p ) ) ),
inference(definition_unfolding,[],[f69,f67,f68]) ).
thf(f69,plain,
( ( mlocal @ ( mnot @ p ) )
= $true ),
inference(cnf_transformation,[],[f35]) ).
thf(f35,plain,
( ( mlocal @ ( mnot @ p ) )
= $true ),
inference(fool_elimination,[],[f34]) ).
thf(f34,plain,
mlocal @ ( mnot @ p ),
inference(rectify,[],[f15]) ).
thf(f15,axiom,
mlocal @ ( mnot @ p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_a_axiom_1) ).
thf(f123,plain,
( ( $true
= ( p @ mactual ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f121]) ).
thf(f121,plain,
( ( $true = $false )
| ( $true
= ( p @ mactual ) )
| ~ spl0_2 ),
inference(superposition,[],[f61,f114]) ).
thf(f114,plain,
( ! [X2: mworld] :
( ( ( mrel @ '#b' @ mactual @ X2 )
= $false )
| ( ( p @ X2 )
= $true ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f113]) ).
thf(f113,plain,
( spl0_2
<=> ! [X2: mworld] :
( ( ( mrel @ '#b' @ mactual @ X2 )
= $false )
| ( ( p @ X2 )
= $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f61,plain,
! [X0: mworld] :
( $true
= ( mrel @ '#b' @ X0 @ X0 ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f41,plain,
! [X0: mworld] :
( $true
= ( mrel @ '#b' @ X0 @ X0 ) ),
inference(fool_elimination,[],[f40]) ).
thf(f40,plain,
! [X0: mworld] : ( mrel @ '#b' @ X0 @ X0 ),
inference(rectify,[],[f9]) ).
thf(f9,axiom,
! [X2: mworld] : ( mrel @ '#b' @ X2 @ X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_#b_reflexive') ).
thf(f119,plain,
( spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f88,f117,f113]) ).
thf(f88,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#b' @ mactual @ X2 )
= $false )
| ( ( mrel @ '#b' @ X1 @ ( sK1 @ X1 ) )
= $true )
| ( ( mrel @ '#a' @ mactual @ X1 )
= $false )
| ( ( p @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[],[f87]) ).
thf(f87,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ '#b' @ mactual @ X2 )
=> ( p @ X2 ) )
= $true )
| ( ( mrel @ '#b' @ X1 @ ( sK1 @ X1 ) )
= $true )
| ( ( mrel @ '#a' @ mactual @ X1 )
= $false ) ),
inference(beta_eta_normalization,[],[f86]) ).
thf(f86,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#b' @ X1 @ ( sK1 @ X1 ) )
= $true )
| ( ( mrel @ '#a' @ mactual @ X1 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ '#b' @ mactual @ Y0 )
=> ( p @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[],[f85]) ).
thf(f85,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ mactual @ Y0 )
=> ( p @ Y0 ) ) )
= $true )
| ( ( mrel @ '#b' @ X1 @ ( sK1 @ X1 ) )
= $true )
| ( ( mrel @ '#a' @ mactual @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f84]) ).
thf(f84,plain,
! [X1: mworld] :
( ( ( mrel @ '#b' @ X1 @ ( sK1 @ X1 ) )
= $true )
| ( ( mrel @ '#a' @ mactual @ X1 )
= $false )
| ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ mactual @ Y0 )
=> ( p @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f82]) ).
thf(f82,plain,
! [X1: mworld] :
( ( ( mrel @ '#a' @ mactual @ X1 )
= $false )
| ( ( ( mrel @ '#b' @ X1 @ ( sK1 @ X1 ) )
=> ( p @ ( sK1 @ X1 ) ) )
= $false )
| ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ mactual @ Y0 )
=> ( p @ Y0 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[],[f81]) ).
thf(f81,plain,
! [X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ '#b' @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ ( sK1 @ X1 ) )
= $false )
| ( ( mrel @ '#a' @ mactual @ X1 )
= $false )
| ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ mactual @ Y0 )
=> ( p @ Y0 ) ) ) )
= $false ) ),
inference(sigma_clausification,[],[f80]) ).
thf(f80,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
= $false )
| ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ mactual @ Y0 )
=> ( p @ Y0 ) ) ) )
= $false )
| ( ( mrel @ '#a' @ mactual @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f79]) ).
thf(f79,plain,
! [X1: mworld] :
( ( $true
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ X1 @ Y0 )
=> ( p @ Y0 ) ) ) ) )
| ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ mactual @ Y0 )
=> ( p @ Y0 ) ) ) )
= $false )
| ( ( mrel @ '#a' @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[],[f78]) ).
thf(f78,plain,
! [X1: mworld] :
( ( ( ( mrel @ '#a' @ mactual @ X1 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ X1 @ Y0 )
=> ( p @ Y0 ) ) ) )
= $true )
| ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ mactual @ Y0 )
=> ( p @ Y0 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[],[f77]) ).
thf(f77,plain,
! [X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ '#a' @ mactual @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#b' @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
@ X1 )
= $true )
| ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ mactual @ Y0 )
=> ( p @ Y0 ) ) ) )
= $false ) ),
inference(pi_clausification,[],[f76]) ).
thf(f76,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#a' @ mactual @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#b' @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) )
= $true )
| ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ mactual @ Y0 )
=> ( p @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f75]) ).
thf(f75,plain,
( $true
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ mactual @ Y0 )
=> ( p @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#a' @ mactual @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#b' @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f72]) ).
thf(f72,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#b'
@ p ) )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#a'
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#b'
@ p ) ) ) ) ) ),
inference(definition_unfolding,[],[f60,f67,f59,f68,f70,f70,f68,f70]) ).
thf(f60,plain,
( ( mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#b' @ p ) ) @ ( mbox @ '#a' @ ( mnot @ ( mbox @ '#b' @ p ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f37]) ).
thf(f37,plain,
( ( mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#b' @ p ) ) @ ( mbox @ '#a' @ ( mnot @ ( mbox @ '#b' @ p ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f36]) ).
thf(f36,plain,
mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#b' @ p ) ) @ ( mbox @ '#a' @ ( mnot @ ( mbox @ '#b' @ p ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f14,axiom,
mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#b' @ p ) ) @ ( mbox @ '#a' @ ( mnot @ ( mbox @ '#b' @ p ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_axiom_2) ).
thf(f115,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f92,f113,f110]) ).
thf(f92,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#b' @ mactual @ X2 )
= $false )
| ( ( mrel @ '#a' @ mactual @ X1 )
= $false )
| ( ( p @ X2 )
= $true )
| ( ( p @ ( sK1 @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f91]) ).
thf(f91,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#a' @ mactual @ X1 )
= $false )
| ( ( ( mrel @ '#b' @ mactual @ X2 )
=> ( p @ X2 ) )
= $true )
| ( ( p @ ( sK1 @ X1 ) )
= $false ) ),
inference(beta_eta_normalization,[],[f90]) ).
thf(f90,plain,
! [X2: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ '#b' @ mactual @ Y0 )
=> ( p @ Y0 ) )
@ X2 )
= $true )
| ( ( p @ ( sK1 @ X1 ) )
= $false )
| ( ( mrel @ '#a' @ mactual @ X1 )
= $false ) ),
inference(pi_clausification,[],[f89]) ).
thf(f89,plain,
! [X1: mworld] :
( ( ( mrel @ '#a' @ mactual @ X1 )
= $false )
| ( ( p @ ( sK1 @ X1 ) )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ mactual @ Y0 )
=> ( p @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f83]) ).
thf(f83,plain,
! [X1: mworld] :
( ( ( mrel @ '#a' @ mactual @ X1 )
= $false )
| ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b' @ mactual @ Y0 )
=> ( p @ Y0 ) ) ) )
= $false )
| ( ( p @ ( sK1 @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL962^16 : TPTP v8.2.0. Released v8.1.0.
% 0.07/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Jun 22 15:55:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.35 This is a TH0_THM_EQU_NAR problem
% 0.12/0.35 Running higher-order theorem proving
% 0.12/0.35 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
% 0.12/0.37 % (1085)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.37 % (1088)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.37 % (1089)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)
% 0.12/0.37 % (1087)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)
% 0.12/0.38 % (1090)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)
% 0.12/0.38 % (1091)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.38 % (1086)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)
% 0.12/0.38 % (1089)Instruction limit reached!
% 0.12/0.38 % (1089)------------------------------
% 0.12/0.38 % (1089)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (1089)Termination reason: Unknown
% 0.12/0.38 % (1089)Termination phase: shuffling
% 0.12/0.38
% 0.12/0.38 % (1089)Memory used [KB]: 1023
% 0.12/0.38 % (1089)Time elapsed: 0.003 s
% 0.12/0.38 % (1089)Instructions burned: 2 (million)
% 0.12/0.38 % (1089)------------------------------
% 0.12/0.38 % (1089)------------------------------
% 0.12/0.38 % (1088)Instruction limit reached!
% 0.12/0.38 % (1088)------------------------------
% 0.12/0.38 % (1088)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (1088)Termination reason: Unknown
% 0.12/0.38 % (1088)Termination phase: Function definition elimination
% 0.12/0.38
% 0.12/0.38 % (1088)Memory used [KB]: 1023
% 0.12/0.38 % (1088)Time elapsed: 0.004 s
% 0.12/0.38 % (1088)Instructions burned: 3 (million)
% 0.12/0.38 % (1088)------------------------------
% 0.12/0.38 % (1088)------------------------------
% 0.12/0.38 % (1086)Instruction limit reached!
% 0.12/0.38 % (1086)------------------------------
% 0.12/0.38 % (1086)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (1086)Termination reason: Unknown
% 0.12/0.38 % (1086)Termination phase: Property scanning
% 0.12/0.38
% 0.12/0.38 % (1086)Memory used [KB]: 1023
% 0.12/0.38 % (1086)Time elapsed: 0.004 s
% 0.12/0.38 % (1086)Instructions burned: 4 (million)
% 0.12/0.38 % (1086)------------------------------
% 0.12/0.38 % (1086)------------------------------
% 0.12/0.38 % (1090)Refutation not found, incomplete strategy
% 0.12/0.38 % (1090)------------------------------
% 0.12/0.38 % (1090)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (1090)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.38
% 0.12/0.38
% 0.12/0.38 % (1090)Memory used [KB]: 5500
% 0.12/0.38 % (1090)Time elapsed: 0.004 s
% 0.12/0.38 % (1090)Instructions burned: 3 (million)
% 0.12/0.38 % (1090)------------------------------
% 0.12/0.38 % (1090)------------------------------
% 0.12/0.38 % (1085)First to succeed.
% 0.12/0.39 % (1087)Also succeeded, but the first one will report.
% 0.12/0.39 % (1091)Also succeeded, but the first one will report.
% 0.12/0.39 % (1085)Refutation found. Thanks to Tanya!
% 0.12/0.39 % SZS status Theorem for theBenchmark
% 0.12/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.39 % (1085)------------------------------
% 0.12/0.39 % (1085)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39 % (1085)Termination reason: Refutation
% 0.12/0.39
% 0.12/0.39 % (1085)Memory used [KB]: 5628
% 0.12/0.39 % (1085)Time elapsed: 0.014 s
% 0.12/0.39 % (1085)Instructions burned: 11 (million)
% 0.12/0.39 % (1085)------------------------------
% 0.12/0.39 % (1085)------------------------------
% 0.12/0.39 % (1084)Success in time 0.039 s
%------------------------------------------------------------------------------