TSTP Solution File: PRO029^16 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : PRO029^16 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n009.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 : Tue May 21 02:23:14 EDT 2024
% Result : Theorem 0.20s 0.41s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 50
% Syntax : Number of formulae : 210 ( 61 unt; 22 typ; 0 def)
% Number of atoms : 1183 ( 236 equ; 0 cnn)
% Maximal formula atoms : 17 ( 6 avg)
% Number of connectives : 1502 ( 126 ~; 167 |; 20 &;1022 @)
% ( 17 <=>; 101 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 109 ( 109 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 35 usr; 24 con; 0-3 aty)
% ( 49 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 247 ( 182 ^ 65 !; 0 ?; 247 :)
% 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,
'#c': mindex ).
thf(func_def_4,type,
'#u': 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,
charge: mworld > $o ).
thf(func_def_16,type,
called: mworld > $o ).
thf(func_def_17,type,
paid: mworld > $o ).
thf(func_def_33,type,
sK1: mworld > mworld ).
thf(func_def_34,type,
sK2: mworld ).
thf(func_def_35,type,
sK3: mworld > mworld ).
thf(f541,plain,
$false,
inference(avatar_sat_refutation,[],[f181,f203,f208,f217,f224,f228,f234,f241,f258,f285,f291,f298,f323,f327,f446,f491,f534,f540]) ).
thf(f540,plain,
( ~ spl0_10
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f539]) ).
thf(f539,plain,
( $false
| ~ spl0_10
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f535]) ).
thf(f535,plain,
( ( $true = $false )
| ~ spl0_10
| ~ spl0_18 ),
inference(superposition,[],[f283,f202]) ).
thf(f202,plain,
( ( $true
= ( called @ sK2 ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f200]) ).
thf(f200,plain,
( spl0_10
<=> ( $true
= ( called @ sK2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
thf(f283,plain,
( ( $false
= ( called @ sK2 ) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f281]) ).
thf(f281,plain,
( spl0_18
<=> ( $false
= ( called @ sK2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
thf(f534,plain,
~ spl0_25,
inference(avatar_contradiction_clause,[],[f533]) ).
thf(f533,plain,
( $false
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f525]) ).
thf(f525,plain,
( ( $true = $false )
| ~ spl0_25 ),
inference(superposition,[],[f431,f115]) ).
thf(f115,plain,
( $true
= ( mrel @ '#u' @ mactual @ sK2 ) ),
inference(binary_proxy_clausification,[],[f113]) ).
thf(f113,plain,
( ( ( mrel @ '#u' @ mactual @ sK2 )
=> ~ ( ( charge @ sK2 )
=> ( ~ ( paid @ sK2 )
& ( called @ sK2 ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f112]) ).
thf(f112,plain,
( ( ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( ( charge @ Y0 )
=> ( ~ ( paid @ Y0 )
& ( called @ Y0 ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[],[f105]) ).
thf(f105,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( ( charge @ Y0 )
=> ( ~ ( paid @ Y0 )
& ( called @ Y0 ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f104]) ).
thf(f104,plain,
( $true
!= ( ~ ( ( charge @ mactual )
=> ( ~ ( paid @ mactual )
& ( called @ mactual ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( ( charge @ Y0 )
=> ( ~ ( paid @ Y0 )
& ( called @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f86]) ).
thf(f86,plain,
( ( ^ [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: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ charge
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ called
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ paid ) ) ) )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#u'
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ charge
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ called
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ paid ) ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f72,f82,f79,f65,f79,f66,f65,f71,f65,f79,f66,f65]) ).
thf(f71,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f47,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f46,plain,
( mbox
= ( ^ [X0: mindex,X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
( mbox
= ( ^ [X4: mindex,X0: mworld > $o,X2: mworld] :
! [X5: mworld] :
( ( mrel @ X4 @ X2 @ X5 )
=> ( X0 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f66,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f33,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f32,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
( mand
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(f65,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f31,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f30,plain,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
( mnot
= ( ^ [X1: mworld > $o,X2: mworld] :
~ ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_def) ).
thf(f79,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f45,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f44,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(f82,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f54,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(f72,plain,
( ( mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f59]) ).
thf(f59,plain,
( ( mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f53]) ).
thf(f53,plain,
( ( mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f52]) ).
thf(f52,plain,
~ ( mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f20,negated_conjecture,
~ ( mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f19]) ).
thf(f19,conjecture,
mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',requirement_1) ).
thf(f431,plain,
( ( ( mrel @ '#u' @ mactual @ sK2 )
= $false )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f429]) ).
thf(f429,plain,
( spl0_25
<=> ( ( mrel @ '#u' @ mactual @ sK2 )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
thf(f491,plain,
( ~ spl0_15
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f490]) ).
thf(f490,plain,
( $false
| ~ spl0_15
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f487]) ).
thf(f487,plain,
( ( $true = $false )
| ~ spl0_15
| ~ spl0_24 ),
inference(superposition,[],[f337,f427]) ).
thf(f427,plain,
( ( ( called @ ( sK1 @ sK2 ) )
= $true )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f425]) ).
thf(f425,plain,
( spl0_24
<=> ( ( called @ ( sK1 @ sK2 ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
thf(f337,plain,
( ( ( called @ ( sK1 @ sK2 ) )
= $false )
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f333]) ).
thf(f333,plain,
( ( ( called @ ( sK1 @ sK2 ) )
= $false )
| ( $true = $false )
| ~ spl0_15 ),
inference(superposition,[],[f115,f223]) ).
thf(f223,plain,
( ! [X1: mworld] :
( ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( ( called @ ( sK1 @ X1 ) )
= $false ) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f222]) ).
thf(f222,plain,
( spl0_15
<=> ! [X1: mworld] :
( ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( ( called @ ( sK1 @ X1 ) )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
thf(f446,plain,
( spl0_24
| spl0_25
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f420,f278,f226,f429,f425]) ).
thf(f226,plain,
( spl0_16
<=> ! [X1: mworld] :
( ( ( mrel @ '#c' @ X1 @ ( sK1 @ X1 ) )
= $true )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
thf(f278,plain,
( spl0_17
<=> ! [X0: mworld] :
( ( $false
= ( mrel @ '#c' @ sK2 @ X0 ) )
| ( ( called @ X0 )
= $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
thf(f420,plain,
( ( ( mrel @ '#u' @ mactual @ sK2 )
= $false )
| ( ( called @ ( sK1 @ sK2 ) )
= $true )
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f413]) ).
thf(f413,plain,
( ( ( called @ ( sK1 @ sK2 ) )
= $true )
| ( ( mrel @ '#u' @ mactual @ sK2 )
= $false )
| ( $true = $false )
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f279,f227]) ).
thf(f227,plain,
( ! [X1: mworld] :
( ( ( mrel @ '#c' @ X1 @ ( sK1 @ X1 ) )
= $true )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false ) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f226]) ).
thf(f279,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ '#c' @ sK2 @ X0 ) )
| ( ( called @ X0 )
= $true ) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f278]) ).
thf(f327,plain,
( spl0_7
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f326]) ).
thf(f326,plain,
( $false
| spl0_7
| ~ spl0_14 ),
inference(subsumption_resolution,[],[f305,f188]) ).
thf(f188,plain,
( ( $true
!= ( called @ mactual ) )
| spl0_7 ),
inference(avatar_component_clause,[],[f187]) ).
thf(f187,plain,
( spl0_7
<=> ( $true
= ( called @ mactual ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f305,plain,
( ( $true
= ( called @ mactual ) )
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f304]) ).
thf(f304,plain,
( ( $true = $false )
| ( $true
= ( called @ mactual ) )
| ~ spl0_14 ),
inference(superposition,[],[f76,f220]) ).
thf(f220,plain,
( ! [X2: mworld] :
( ( ( mrel @ '#c' @ mactual @ X2 )
= $false )
| ( ( called @ X2 )
= $true ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f219]) ).
thf(f219,plain,
( spl0_14
<=> ! [X2: mworld] :
( ( ( called @ X2 )
= $true )
| ( ( mrel @ '#c' @ mactual @ X2 )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f76,plain,
! [X0: mworld] :
( ( mrel @ '#c' @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f35]) ).
thf(f35,plain,
! [X0: mworld] :
( ( mrel @ '#c' @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f34]) ).
thf(f34,plain,
! [X0: mworld] : ( mrel @ '#c' @ X0 @ X0 ),
inference(rectify,[],[f9]) ).
thf(f9,axiom,
! [X2: mworld] : ( mrel @ '#c' @ X2 @ X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_#c_reflexive') ).
thf(f323,plain,
( spl0_2
| spl0_8 ),
inference(avatar_split_clause,[],[f317,f191,f167]) ).
thf(f167,plain,
( spl0_2
<=> ! [X2: mworld] :
( ( $true
= ( paid @ X2 ) )
| ( ( mrel @ '#u' @ mactual @ X2 )
= $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f191,plain,
( spl0_8
<=> ( $false
= ( paid @ mactual ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f317,plain,
! [X0: mworld] :
( ( ( mrel @ '#u' @ mactual @ X0 )
= $false )
| ( $false
= ( paid @ mactual ) )
| ( ( paid @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f315]) ).
thf(f315,plain,
! [X0: mworld] :
( ( ( paid @ X0 )
= $true )
| ( $true = $false )
| ( $false
= ( paid @ mactual ) )
| ( ( mrel @ '#u' @ mactual @ X0 )
= $false ) ),
inference(superposition,[],[f136,f76]) ).
thf(f136,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#c' @ mactual @ X1 ) )
| ( ( paid @ X1 )
= $false )
| ( ( mrel @ '#u' @ X1 @ X2 )
= $false )
| ( $true
= ( paid @ X2 ) ) ),
inference(binary_proxy_clausification,[],[f135]) ).
thf(f135,plain,
! [X2: mworld,X1: mworld] :
( ( ( paid @ X1 )
= $false )
| ( $true
= ( ( mrel @ '#u' @ X1 @ X2 )
=> ( paid @ X2 ) ) )
| ( $false
= ( mrel @ '#c' @ mactual @ X1 ) ) ),
inference(beta_eta_normalization,[],[f134]) ).
thf(f134,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#c' @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ '#u' @ X1 @ Y0 )
=> ( paid @ Y0 ) )
@ X2 )
= $true )
| ( ( paid @ X1 )
= $false ) ),
inference(pi_clausification,[],[f133]) ).
thf(f133,plain,
! [X1: mworld] :
( ( ( paid @ X1 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ X1 @ Y0 )
=> ( paid @ Y0 ) ) ) )
| ( $false
= ( mrel @ '#c' @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[],[f132]) ).
thf(f132,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#c' @ mactual @ X1 ) )
| ( ( ( paid @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ X1 @ Y0 )
=> ( paid @ Y0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f131]) ).
thf(f131,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ '#c' @ mactual @ X1 )
=> ( ( paid @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ X1 @ Y0 )
=> ( paid @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f130]) ).
thf(f130,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( ( paid @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#u' @ Y0 @ Y1 )
=> ( paid @ Y1 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f129]) ).
thf(f129,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( ( paid @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#u' @ Y0 @ Y1 )
=> ( paid @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f88]) ).
thf(f88,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#c'
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ paid
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#u'
@ paid ) ) ) )
= $true ),
inference(definition_unfolding,[],[f78,f82,f71,f79,f71]) ).
thf(f78,plain,
( ( mlocal @ ( mbox @ '#c' @ ( mimplies @ paid @ ( mbox @ '#u' @ paid ) ) ) )
= $true ),
inference(cnf_transformation,[],[f49]) ).
thf(f49,plain,
( ( mlocal @ ( mbox @ '#c' @ ( mimplies @ paid @ ( mbox @ '#u' @ paid ) ) ) )
= $true ),
inference(fool_elimination,[],[f48]) ).
thf(f48,plain,
mlocal @ ( mbox @ '#c' @ ( mimplies @ paid @ ( mbox @ '#u' @ paid ) ) ),
inference(rectify,[],[f16]) ).
thf(f16,axiom,
mlocal @ ( mbox @ '#c' @ ( mimplies @ paid @ ( mbox @ '#u' @ paid ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(f298,plain,
( ~ spl0_2
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f297]) ).
thf(f297,plain,
( $false
| ~ spl0_2
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f293]) ).
thf(f293,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f207,f248]) ).
thf(f248,plain,
( ( $true
= ( paid @ sK2 ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f243]) ).
thf(f243,plain,
( ( $true
= ( paid @ sK2 ) )
| ( $true = $false )
| ~ spl0_2 ),
inference(superposition,[],[f168,f115]) ).
thf(f168,plain,
( ! [X2: mworld] :
( ( ( mrel @ '#u' @ mactual @ X2 )
= $false )
| ( $true
= ( paid @ X2 ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f167]) ).
thf(f207,plain,
( ( $false
= ( paid @ sK2 ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f205]) ).
thf(f205,plain,
( spl0_11
<=> ( $false
= ( paid @ sK2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
thf(f291,plain,
( ~ spl0_5
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f290]) ).
thf(f290,plain,
( $false
| ~ spl0_5
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f286]) ).
thf(f286,plain,
( ( $true = $false )
| ~ spl0_5
| ~ spl0_9 ),
inference(superposition,[],[f267,f198]) ).
thf(f198,plain,
( ( ( charge @ sK2 )
= $false )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f196]) ).
thf(f196,plain,
( spl0_9
<=> ( ( charge @ sK2 )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
thf(f267,plain,
( ( ( charge @ sK2 )
= $true )
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f261]) ).
thf(f261,plain,
( ( $true = $false )
| ( ( charge @ sK2 )
= $true )
| ~ spl0_5 ),
inference(superposition,[],[f180,f115]) ).
thf(f180,plain,
( ! [X1: mworld] :
( ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( $true
= ( charge @ X1 ) ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f179]) ).
thf(f179,plain,
( spl0_5
<=> ! [X1: mworld] :
( ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( $true
= ( charge @ X1 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f285,plain,
( spl0_17
| spl0_18 ),
inference(avatar_split_clause,[],[f273,f281,f278]) ).
thf(f273,plain,
! [X0: mworld] :
( ( $false
= ( called @ sK2 ) )
| ( ( called @ X0 )
= $true )
| ( $false
= ( mrel @ '#c' @ sK2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f271]) ).
thf(f271,plain,
! [X0: mworld] :
( ( $false
= ( called @ sK2 ) )
| ( $true = $false )
| ( ( called @ X0 )
= $true )
| ( $false
= ( mrel @ '#c' @ sK2 @ X0 ) ) ),
inference(superposition,[],[f115,f128]) ).
thf(f128,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( ( called @ X1 )
= $false )
| ( ( mrel @ '#c' @ X1 @ X2 )
= $false )
| ( ( called @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[],[f127]) ).
thf(f127,plain,
! [X2: mworld,X1: mworld] :
( ( ( called @ X1 )
= $false )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( $true
= ( ( mrel @ '#c' @ X1 @ X2 )
=> ( called @ X2 ) ) ) ),
inference(beta_eta_normalization,[],[f126]) ).
thf(f126,plain,
! [X2: mworld,X1: mworld] :
( ( ( called @ X1 )
= $false )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) )
@ X2 ) ) ),
inference(pi_clausification,[],[f125]) ).
thf(f125,plain,
! [X1: mworld] :
( ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( ( called @ X1 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f124]) ).
thf(f124,plain,
! [X1: mworld] :
( ( ( ( called @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) )
= $true )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[],[f123]) ).
thf(f123,plain,
! [X1: mworld] :
( ( ( mrel @ '#u' @ mactual @ X1 )
=> ( ( called @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f122]) ).
thf(f122,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ( ( called @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#c' @ Y0 @ Y1 )
=> ( called @ Y1 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f121]) ).
thf(f121,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ( ( called @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#c' @ Y0 @ Y1 )
=> ( called @ Y1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f83]) ).
thf(f83,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#u'
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ called
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#c'
@ called ) ) ) ) ),
inference(definition_unfolding,[],[f64,f82,f71,f79,f71]) ).
thf(f64,plain,
( ( mlocal @ ( mbox @ '#u' @ ( mimplies @ called @ ( mbox @ '#c' @ called ) ) ) )
= $true ),
inference(cnf_transformation,[],[f58]) ).
thf(f58,plain,
( ( mlocal @ ( mbox @ '#u' @ ( mimplies @ called @ ( mbox @ '#c' @ called ) ) ) )
= $true ),
inference(fool_elimination,[],[f57]) ).
thf(f57,plain,
mlocal @ ( mbox @ '#u' @ ( mimplies @ called @ ( mbox @ '#c' @ called ) ) ),
inference(rectify,[],[f15]) ).
thf(f15,axiom,
mlocal @ ( mbox @ '#u' @ ( mimplies @ called @ ( mbox @ '#c' @ called ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(f258,plain,
( ~ spl0_8
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f257]) ).
thf(f257,plain,
( $false
| ~ spl0_8
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f253]) ).
thf(f253,plain,
( ( $true = $false )
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f216,f193]) ).
thf(f193,plain,
( ( $false
= ( paid @ mactual ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f191]) ).
thf(f216,plain,
( ( $true
= ( paid @ mactual ) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f214]) ).
thf(f214,plain,
( spl0_13
<=> ( $true
= ( paid @ mactual ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
thf(f241,plain,
( ~ spl0_7
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f240]) ).
thf(f240,plain,
( $false
| ~ spl0_7
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f237]) ).
thf(f237,plain,
( ( $true = $false )
| ~ spl0_7
| ~ spl0_12 ),
inference(superposition,[],[f189,f212]) ).
thf(f212,plain,
( ( $false
= ( called @ mactual ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f210]) ).
thf(f210,plain,
( spl0_12
<=> ( $false
= ( called @ mactual ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
thf(f189,plain,
( ( $true
= ( called @ mactual ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f187]) ).
thf(f234,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f233]) ).
thf(f233,plain,
( $false
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f230]) ).
thf(f230,plain,
( ( $true = $false )
| ~ spl0_4 ),
inference(superposition,[],[f177,f109]) ).
thf(f109,plain,
( ( charge @ mactual )
= $true ),
inference(binary_proxy_clausification,[],[f107]) ).
thf(f107,plain,
( ( ( charge @ mactual )
=> ( ~ ( paid @ mactual )
& ( called @ mactual ) ) )
= $false ),
inference(not_proxy_clausification,[],[f106]) ).
thf(f106,plain,
( $true
= ( ~ ( ( charge @ mactual )
=> ( ~ ( paid @ mactual )
& ( called @ mactual ) ) ) ) ),
inference(binary_proxy_clausification,[],[f104]) ).
thf(f177,plain,
( ( ( charge @ mactual )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f175]) ).
thf(f175,plain,
( spl0_4
<=> ( ( charge @ mactual )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f228,plain,
( spl0_16
| spl0_14 ),
inference(avatar_split_clause,[],[f103,f219,f226]) ).
thf(f103,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#c' @ X1 @ ( sK1 @ X1 ) )
= $true )
| ( ( called @ X2 )
= $true )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( ( mrel @ '#c' @ mactual @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[],[f101]) ).
thf(f101,plain,
! [X2: mworld,X1: mworld] :
( ( ( called @ X2 )
= $true )
| ( ( mrel @ '#c' @ mactual @ X2 )
= $false )
| ( ( ( mrel @ '#c' @ X1 @ ( sK1 @ X1 ) )
=> ( called @ ( sK1 @ X1 ) ) )
= $false )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false ) ),
inference(beta_eta_normalization,[],[f100]) ).
thf(f100,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( ( mrel @ '#c' @ mactual @ X2 )
= $false )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) )
@ ( sK1 @ X1 ) ) )
| ( ( called @ X2 )
= $true ) ),
inference(sigma_clausification,[],[f99]) ).
thf(f99,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#c' @ mactual @ X2 )
= $false )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( ( called @ X2 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f98]) ).
thf(f98,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) ) )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( ( called @ X2 )
= $true )
| ( ( mrel @ '#c' @ mactual @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[],[f97]) ).
thf(f97,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ '#c' @ mactual @ X2 )
=> ( called @ X2 ) ) )
| ( $true
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) ) )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false ) ),
inference(beta_eta_normalization,[],[f96]) ).
thf(f96,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) )
@ X2 ) )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) ) ) ),
inference(pi_clausification,[],[f95]) ).
thf(f95,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) ) )
= $true )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f94]) ).
thf(f94,plain,
! [X1: mworld] :
( ( ( ( mrel @ '#u' @ mactual @ X1 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f93]) ).
thf(f93,plain,
! [X1: mworld] :
( ( $false
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) ) ) ) )
| ( ( ( mrel @ '#u' @ mactual @ X1 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[],[f92]) ).
thf(f92,plain,
! [X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#c' @ Y0 @ Y1 )
=> ( called @ Y1 ) ) ) )
@ X1 )
= $true )
| ( $false
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) ) ) ) ) ),
inference(pi_clausification,[],[f91]) ).
thf(f91,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#c' @ Y0 @ Y1 )
=> ( called @ Y1 ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f90]) ).
thf(f90,plain,
( $true
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#c' @ Y0 @ Y1 )
=> ( called @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f84]) ).
thf(f84,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 ) ) )
@ '#c'
@ called ) )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#u'
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#c'
@ called ) ) ) ) ) ),
inference(definition_unfolding,[],[f67,f82,f79,f65,f71,f71,f65,f71]) ).
thf(f67,plain,
( ( mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#c' @ called ) ) @ ( mbox @ '#u' @ ( mnot @ ( mbox @ '#c' @ called ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f27]) ).
thf(f27,plain,
( ( mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#c' @ called ) ) @ ( mbox @ '#u' @ ( mnot @ ( mbox @ '#c' @ called ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f26]) ).
thf(f26,plain,
mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#c' @ called ) ) @ ( mbox @ '#u' @ ( mnot @ ( mbox @ '#c' @ called ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f17,axiom,
mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#c' @ called ) ) @ ( mbox @ '#u' @ ( mnot @ ( mbox @ '#c' @ called ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(f224,plain,
( spl0_14
| spl0_15 ),
inference(avatar_split_clause,[],[f102,f222,f219]) ).
thf(f102,plain,
! [X2: mworld,X1: mworld] :
( ( ( called @ X2 )
= $true )
| ( ( mrel @ '#c' @ mactual @ X2 )
= $false )
| ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( ( called @ ( sK1 @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f101]) ).
thf(f217,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f111,f214,f210]) ).
thf(f111,plain,
( ( $false
= ( called @ mactual ) )
| ( $true
= ( paid @ mactual ) ) ),
inference(not_proxy_clausification,[],[f110]) ).
thf(f110,plain,
( ( $false
= ( called @ mactual ) )
| ( $false
= ( ~ ( paid @ mactual ) ) ) ),
inference(binary_proxy_clausification,[],[f108]) ).
thf(f108,plain,
( ( ~ ( paid @ mactual )
& ( called @ mactual ) )
= $false ),
inference(binary_proxy_clausification,[],[f107]) ).
thf(f208,plain,
( spl0_11
| spl0_9 ),
inference(avatar_split_clause,[],[f120,f196,f205]) ).
thf(f120,plain,
( ( ( charge @ sK2 )
= $false )
| ( $false
= ( paid @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f119]) ).
thf(f119,plain,
( ( ( charge @ sK2 )
= $false )
| ( $true
= ( ~ ( paid @ sK2 ) ) ) ),
inference(binary_proxy_clausification,[],[f117]) ).
thf(f117,plain,
( ( $true
= ( ~ ( paid @ sK2 )
& ( called @ sK2 ) ) )
| ( ( charge @ sK2 )
= $false ) ),
inference(binary_proxy_clausification,[],[f116]) ).
thf(f116,plain,
( $true
= ( ( charge @ sK2 )
=> ( ~ ( paid @ sK2 )
& ( called @ sK2 ) ) ) ),
inference(not_proxy_clausification,[],[f114]) ).
thf(f114,plain,
( $false
= ( ~ ( ( charge @ sK2 )
=> ( ~ ( paid @ sK2 )
& ( called @ sK2 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f113]) ).
thf(f203,plain,
( spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f118,f200,f196]) ).
thf(f118,plain,
( ( ( charge @ sK2 )
= $false )
| ( $true
= ( called @ sK2 ) ) ),
inference(binary_proxy_clausification,[],[f117]) ).
thf(f181,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f148,f179,f175]) ).
thf(f148,plain,
! [X1: mworld] :
( ( ( mrel @ '#u' @ mactual @ X1 )
= $false )
| ( $true
= ( charge @ X1 ) )
| ( ( charge @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[],[f147]) ).
thf(f147,plain,
! [X1: mworld] :
( ( ( charge @ mactual )
= $false )
| ( $true
= ( ( mrel @ '#u' @ mactual @ X1 )
=> ( charge @ X1 ) ) ) ),
inference(beta_eta_normalization,[],[f146]) ).
thf(f146,plain,
! [X1: mworld] :
( ( ( charge @ mactual )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ( charge @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_clausification,[],[f141]) ).
thf(f141,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ( charge @ Y0 ) ) ) )
| ( ( charge @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[],[f140]) ).
thf(f140,plain,
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( charge @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ( charge @ Y0 ) ) ) )
= $true )
| ( ( charge @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[],[f139]) ).
thf(f139,plain,
( $true
= ( ( charge @ mactual )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( charge @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ( charge @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f85]) ).
thf(f85,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ charge
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#u'
@ charge )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#c'
@ charge ) ) ) ) ),
inference(definition_unfolding,[],[f68,f82,f79,f66,f71,f71]) ).
thf(f68,plain,
( ( mlocal @ ( mimplies @ charge @ ( mand @ ( mbox @ '#u' @ charge ) @ ( mbox @ '#c' @ charge ) ) ) )
= $true ),
inference(cnf_transformation,[],[f43]) ).
thf(f43,plain,
( ( mlocal @ ( mimplies @ charge @ ( mand @ ( mbox @ '#u' @ charge ) @ ( mbox @ '#c' @ charge ) ) ) )
= $true ),
inference(fool_elimination,[],[f42]) ).
thf(f42,plain,
mlocal @ ( mimplies @ charge @ ( mand @ ( mbox @ '#u' @ charge ) @ ( mbox @ '#c' @ charge ) ) ),
inference(rectify,[],[f14]) ).
thf(f14,axiom,
mlocal @ ( mimplies @ charge @ ( mand @ ( mbox @ '#u' @ charge ) @ ( mbox @ '#c' @ charge ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_charge_u) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PRO029^16 : TPTP v8.2.0. Released v8.1.0.
% 0.13/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 03:57:37 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 This is a TH0_THM_EQU_NAR problem
% 0.13/0.34 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.36 % (5529)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)
% 0.20/0.36 % (5534)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)
% 0.20/0.37 % (5534)Instruction limit reached!
% 0.20/0.37 % (5534)------------------------------
% 0.20/0.37 % (5534)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.37 % (5534)Termination reason: Unknown
% 0.20/0.37 % (5534)Termination phase: Property scanning
% 0.20/0.37
% 0.20/0.37 % (5534)Memory used [KB]: 1023
% 0.20/0.37 % (5534)Time elapsed: 0.004 s
% 0.20/0.37 % (5534)Instructions burned: 3 (million)
% 0.20/0.37 % (5534)------------------------------
% 0.20/0.37 % (5534)------------------------------
% 0.20/0.37 % (5533)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.37 % (5532)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)
% 0.20/0.38 % (5531)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)
% 0.20/0.38 % (5527)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.20/0.38 % (5531)Instruction limit reached!
% 0.20/0.38 % (5531)------------------------------
% 0.20/0.38 % (5531)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (5531)Termination reason: Unknown
% 0.20/0.38 % (5531)Termination phase: Property scanning
% 0.20/0.38
% 0.20/0.38 % (5531)Memory used [KB]: 1023
% 0.20/0.38 % (5531)Time elapsed: 0.003 s
% 0.20/0.38 % (5531)Instructions burned: 3 (million)
% 0.20/0.38 % (5531)------------------------------
% 0.20/0.38 % (5531)------------------------------
% 0.20/0.38 % (5532)Refutation not found, incomplete strategy
% 0.20/0.38 % (5532)------------------------------
% 0.20/0.38 % (5532)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (5532)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.38
% 0.20/0.38
% 0.20/0.38 % (5532)Memory used [KB]: 5500
% 0.20/0.38 % (5532)Time elapsed: 0.005 s
% 0.20/0.38 % (5532)Instructions burned: 5 (million)
% 0.20/0.38 % (5532)------------------------------
% 0.20/0.38 % (5532)------------------------------
% 0.20/0.38 % (5528)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)
% 0.20/0.38 % (5530)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.38 % (5528)Instruction limit reached!
% 0.20/0.38 % (5528)------------------------------
% 0.20/0.38 % (5528)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (5535)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)
% 0.20/0.38 % (5528)Termination reason: Unknown
% 0.20/0.38 % (5528)Termination phase: Property scanning
% 0.20/0.38
% 0.20/0.38 % (5528)Memory used [KB]: 1023
% 0.20/0.38 % (5528)Time elapsed: 0.005 s
% 0.20/0.38 % (5528)Instructions burned: 4 (million)
% 0.20/0.38 % (5528)------------------------------
% 0.20/0.38 % (5528)------------------------------
% 0.20/0.38 % (5530)Instruction limit reached!
% 0.20/0.38 % (5530)------------------------------
% 0.20/0.38 % (5530)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (5530)Termination reason: Unknown
% 0.20/0.38 % (5530)Termination phase: Property scanning
% 0.20/0.38
% 0.20/0.38 % (5530)Memory used [KB]: 1023
% 0.20/0.38 % (5530)Time elapsed: 0.003 s
% 0.20/0.38 % (5530)Instructions burned: 3 (million)
% 0.20/0.38 % (5530)------------------------------
% 0.20/0.38 % (5530)------------------------------
% 0.20/0.38 % (5529)Instruction limit reached!
% 0.20/0.38 % (5529)------------------------------
% 0.20/0.38 % (5529)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (5529)Termination reason: Unknown
% 0.20/0.38 % (5529)Termination phase: Saturation
% 0.20/0.38
% 0.20/0.38 % (5529)Memory used [KB]: 5756
% 0.20/0.38 % (5529)Time elapsed: 0.020 s
% 0.20/0.38 % (5529)Instructions burned: 27 (million)
% 0.20/0.38 % (5529)------------------------------
% 0.20/0.38 % (5529)------------------------------
% 0.20/0.38 % (5533)Instruction limit reached!
% 0.20/0.38 % (5533)------------------------------
% 0.20/0.38 % (5533)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (5533)Termination reason: Unknown
% 0.20/0.38 % (5533)Termination phase: Saturation
% 0.20/0.38
% 0.20/0.38 % (5533)Memory used [KB]: 5628
% 0.20/0.38 % (5533)Time elapsed: 0.018 s
% 0.20/0.38 % (5533)Instructions burned: 19 (million)
% 0.20/0.38 % (5533)------------------------------
% 0.20/0.38 % (5533)------------------------------
% 0.20/0.39 % (5536)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)
% 0.20/0.39 % (5537)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.39 % (5537)Instruction limit reached!
% 0.20/0.39 % (5537)------------------------------
% 0.20/0.39 % (5537)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (5537)Termination reason: Unknown
% 0.20/0.39 % (5537)Termination phase: Property scanning
% 0.20/0.39
% 0.20/0.39 % (5537)Memory used [KB]: 1023
% 0.20/0.39 % (5537)Time elapsed: 0.003 s
% 0.20/0.39 % (5537)Instructions burned: 3 (million)
% 0.20/0.39 % (5537)------------------------------
% 0.20/0.39 % (5537)------------------------------
% 0.20/0.39 % (5538)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.20/0.39 % (5539)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.40 % (5540)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.40 % (5535)Instruction limit reached!
% 0.20/0.40 % (5535)------------------------------
% 0.20/0.40 % (5535)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (5535)Termination reason: Unknown
% 0.20/0.40 % (5535)Termination phase: Saturation
% 0.20/0.40
% 0.20/0.40 % (5535)Memory used [KB]: 5756
% 0.20/0.40 % (5535)Time elapsed: 0.020 s
% 0.20/0.40 % (5535)Instructions burned: 37 (million)
% 0.20/0.40 % (5535)------------------------------
% 0.20/0.40 % (5535)------------------------------
% 0.20/0.40 % (5536)Instruction limit reached!
% 0.20/0.40 % (5536)------------------------------
% 0.20/0.40 % (5536)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (5536)Termination reason: Unknown
% 0.20/0.40 % (5536)Termination phase: Saturation
% 0.20/0.40
% 0.20/0.40 % (5536)Memory used [KB]: 5628
% 0.20/0.40 % (5536)Time elapsed: 0.010 s
% 0.20/0.40 % (5536)Instructions burned: 16 (million)
% 0.20/0.40 % (5536)------------------------------
% 0.20/0.40 % (5536)------------------------------
% 0.20/0.40 % (5539)Instruction limit reached!
% 0.20/0.40 % (5539)------------------------------
% 0.20/0.40 % (5539)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (5539)Termination reason: Unknown
% 0.20/0.40 % (5539)Termination phase: Saturation
% 0.20/0.40
% 0.20/0.40 % (5539)Memory used [KB]: 1023
% 0.20/0.40 % (5539)Time elapsed: 0.006 s
% 0.20/0.40 % (5539)Instructions burned: 7 (million)
% 0.20/0.40 % (5539)------------------------------
% 0.20/0.40 % (5539)------------------------------
% 0.20/0.40 % (5541)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.40 % (5541)Instruction limit reached!
% 0.20/0.40 % (5541)------------------------------
% 0.20/0.40 % (5541)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (5541)Termination reason: Unknown
% 0.20/0.40 % (5541)Termination phase: shuffling
% 0.20/0.40
% 0.20/0.40 % (5541)Memory used [KB]: 1023
% 0.20/0.40 % (5541)Time elapsed: 0.004 s
% 0.20/0.40 % (5541)Instructions burned: 3 (million)
% 0.20/0.40 % (5541)------------------------------
% 0.20/0.40 % (5541)------------------------------
% 0.20/0.40 % (5527)First to succeed.
% 0.20/0.40 % (5540)Instruction limit reached!
% 0.20/0.40 % (5540)------------------------------
% 0.20/0.40 % (5540)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (5540)Termination reason: Unknown
% 0.20/0.41 % (5540)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (5540)Memory used [KB]: 5628
% 0.20/0.41 % (5540)Time elapsed: 0.011 s
% 0.20/0.41 % (5540)Instructions burned: 16 (million)
% 0.20/0.41 % (5540)------------------------------
% 0.20/0.41 % (5540)------------------------------
% 0.20/0.41 % (5542)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.41 % (5542)Instruction limit reached!
% 0.20/0.41 % (5542)------------------------------
% 0.20/0.41 % (5542)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (5542)Termination reason: Unknown
% 0.20/0.41 % (5542)Termination phase: Property scanning
% 0.20/0.41
% 0.20/0.41 % (5542)Memory used [KB]: 1023
% 0.20/0.41 % (5542)Time elapsed: 0.003 s
% 0.20/0.41 % (5542)Instructions burned: 3 (million)
% 0.20/0.41 % (5542)------------------------------
% 0.20/0.41 % (5542)------------------------------
% 0.20/0.41 % (5527)Refutation found. Thanks to Tanya!
% 0.20/0.41 % SZS status Theorem for theBenchmark
% 0.20/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.41 % (5527)------------------------------
% 0.20/0.41 % (5527)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (5527)Termination reason: Refutation
% 0.20/0.41
% 0.20/0.41 % (5527)Memory used [KB]: 5884
% 0.20/0.41 % (5527)Time elapsed: 0.036 s
% 0.20/0.41 % (5527)Instructions burned: 43 (million)
% 0.20/0.41 % (5527)------------------------------
% 0.20/0.41 % (5527)------------------------------
% 0.20/0.41 % (5526)Success in time 0.053 s
% 0.20/0.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------