%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PRO029^16 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 : Wed Feb 25 09:28:09 AM UTC 2026
% Result : Theorem 1.04s 0.97s
% Output : Refutation 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 29
% Syntax : Number of formulae : 192 ( 62 unt; 0 typ; 18 def)
% Number of atoms : 1196 ( 238 equ; 0 cnn)
% Maximal formula atoms : 17 ( 6 avg)
% Number of connectives : 1533 ( 123 ~; 165 |; 20 &;1051 @)
% ( 18 <=>; 105 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 68 ( 68 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 36 usr; 25 con; 0-3 aty)
% ( 51 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 247 ( 185 ^; 62 !; 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 > mworld ).
thf(func_def_35,type,
sK3: mworld ).
thf(f575,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f174,f179,f188,f196,f227,f231,f237,f244,f275,f292,f306,f338,f339,f347,f354,f492,f506,f529,f574]) ).
thf(f574,plain,
~ spl0_28,
inference(avatar_contradiction_clause,[status(thm)],[f573]) ).
thf(f573,plain,
( $false
| ~ spl0_28 ),
inference(trivial_inequality_removal,[status(thm)],[f567]) ).
thf(f567,plain,
( ( $true = $false )
| ~ spl0_28 ),
inference(superposition,[status(thm)],[f160,f484]) ).
thf(f484,plain,
( ( ( mrel @ '#u' @ mactual @ sK3 )
= $false )
| ~ spl0_28 ),
inference(avatar_component_clause,[status(thm)],[f482]) ).
thf(f482,definition,
( spl0_28
<=> ( ( mrel @ '#u' @ mactual @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_28])],[avatar_definition]) ).
thf(f160,plain,
( ( mrel @ '#u' @ mactual @ sK3 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f158]) ).
thf(f158,plain,
( ( ( mrel @ '#u' @ mactual @ sK3 )
=> ~ ( ( charge @ sK3 )
=> ( ~ ( paid @ sK3 )
& ( called @ sK3 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f157]) ).
thf(f157,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( ( charge @ Y0 )
=> ( ~ ( paid @ Y0 )
& ( called @ Y0 ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f150]) ).
thf(f150,plain,
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( ( charge @ Y0 )
=> ( ~ ( paid @ Y0 )
& ( called @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f149]) ).
thf(f149,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,[status(thm)],[f84]) ).
thf(f84,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,[status(thm)],[f67,f64,f76,f68,f76,f80,f68,f81,f68,f76,f80,f68]) ).
thf(f81,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
thf(f56,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f55]) ).
thf(f55,plain,
( mbox
= ( ^ [X0: mindex,X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( mbox
= ( ^ [X4: mindex,X0: mworld > $o,X2: mworld] :
! [X5: mworld] :
( ( mrel @ X4 @ X2 @ X5 )
=> ( X0 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.StopnhNuQj/DTF2THF_15568.p',mbox_def) ).
thf(f80,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f28]) ).
thf(f28,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( mand
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.StopnhNuQj/DTF2THF_15568.p',mand_def) ).
thf(f68,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
thf(f58,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f57]) ).
thf(f57,plain,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( mnot
= ( ^ [X1: mworld > $o,X2: mworld] :
~ ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.StopnhNuQj/DTF2THF_15568.p',mnot_def) ).
thf(f76,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
thf(f48,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X3 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox/tmp/tmp.StopnhNuQj/DTF2THF_15568.p',mimplies_def) ).
thf(f64,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
thf(f44,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox/tmp/tmp.StopnhNuQj/DTF2THF_15568.p',mlocal_def) ).
thf(f67,plain,
( ( mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[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,[status(thm)],[f35]) ).
thf(f35,plain,
( ( mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f34]) ).
thf(f34,plain,
~ ( mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[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,[status(cth)],[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/sandbox/tmp/tmp.StopnhNuQj/DTF2THF_15568.p',requirement_1) ).
thf(f529,plain,
( ~ spl0_14
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[status(thm)],[f528]) ).
thf(f528,plain,
( $false
| ~ spl0_14
| ~ spl0_27 ),
inference(trivial_inequality_removal,[status(thm)],[f525]) ).
thf(f525,plain,
( ( $true = $false )
| ~ spl0_14
| ~ spl0_27 ),
inference(superposition,[status(thm)],[f373,f480]) ).
thf(f480,plain,
( ( $true
= ( called @ ( sK1 @ sK3 ) ) )
| ~ spl0_27 ),
inference(avatar_component_clause,[status(thm)],[f478]) ).
thf(f478,definition,
( spl0_27
<=> ( $true
= ( called @ ( sK1 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_27])],[avatar_definition]) ).
thf(f373,plain,
( ( $false
= ( called @ ( sK1 @ sK3 ) ) )
| ~ spl0_14 ),
inference(trivial_inequality_removal,[status(thm)],[f368]) ).
thf(f368,plain,
( ( $false
= ( called @ ( sK1 @ sK3 ) ) )
| ( $true = $false )
| ~ spl0_14 ),
inference(superposition,[status(thm)],[f223,f160]) ).
thf(f223,plain,
( ! [X1: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $false
= ( called @ ( sK1 @ X1 ) ) ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[status(thm)],[f222]) ).
thf(f222,definition,
( spl0_14
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $false
= ( called @ ( sK1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition]) ).
thf(f506,plain,
( ~ spl0_2
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[status(thm)],[f505]) ).
thf(f505,plain,
( $false
| ~ spl0_2
| ~ spl0_18 ),
inference(trivial_inequality_removal,[status(thm)],[f502]) ).
thf(f502,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_18 ),
inference(superposition,[status(thm)],[f173,f290]) ).
thf(f290,plain,
( ( $false
= ( called @ sK3 ) )
| ~ spl0_18 ),
inference(avatar_component_clause,[status(thm)],[f288]) ).
thf(f288,definition,
( spl0_18
<=> ( $false
= ( called @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition]) ).
thf(f173,plain,
( ( $true
= ( called @ sK3 ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f171]) ).
thf(f171,definition,
( spl0_2
<=> ( $true
= ( called @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f492,plain,
( spl0_27
| spl0_28
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[status(thm)],[f453,f285,f229,f482,f478]) ).
thf(f229,definition,
( spl0_16
<=> ! [X1: mworld] :
( ( $true
= ( mrel @ '#c' @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition]) ).
thf(f285,definition,
( spl0_17
<=> ! [X0: mworld] :
( ( $true
= ( called @ X0 ) )
| ( $false
= ( mrel @ '#c' @ sK3 @ X0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition]) ).
thf(f453,plain,
( ( $true
= ( called @ ( sK1 @ sK3 ) ) )
| ( ( mrel @ '#u' @ mactual @ sK3 )
= $false )
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[status(thm)],[f443]) ).
thf(f443,plain,
( ( ( mrel @ '#u' @ mactual @ sK3 )
= $false )
| ( $true = $false )
| ( $true
= ( called @ ( sK1 @ sK3 ) ) )
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[status(thm)],[f230,f286]) ).
thf(f286,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ '#c' @ sK3 @ X0 ) )
| ( $true
= ( called @ X0 ) ) )
| ~ spl0_17 ),
inference(avatar_component_clause,[status(thm)],[f285]) ).
thf(f230,plain,
( ! [X1: mworld] :
( ( $true
= ( mrel @ '#c' @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X1 ) ) )
| ~ spl0_16 ),
inference(avatar_component_clause,[status(thm)],[f229]) ).
thf(f354,plain,
~ spl0_20,
inference(avatar_contradiction_clause,[status(thm)],[f353]) ).
thf(f353,plain,
( $false
| ~ spl0_20 ),
inference(trivial_inequality_removal,[status(thm)],[f349]) ).
thf(f349,plain,
( ( $true = $false )
| ~ spl0_20 ),
inference(superposition,[status(thm)],[f332,f65]) ).
thf(f65,plain,
! [X0: mworld] :
( ( mrel @ '#c' @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f46,plain,
! [X0: mworld] :
( ( mrel @ '#c' @ X0 @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f45]) ).
thf(f45,plain,
! [X0: mworld] : ( mrel @ '#c' @ X0 @ X0 ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
! [X2: mworld] : ( mrel @ '#c' @ X2 @ X2 ),
file('/export/starexec/sandbox/tmp/tmp.StopnhNuQj/DTF2THF_15568.p','mrel_#c_reflexive') ).
thf(f332,plain,
( ( $false
= ( mrel @ '#c' @ mactual @ mactual ) )
| ~ spl0_20 ),
inference(avatar_component_clause,[status(thm)],[f330]) ).
thf(f330,definition,
( spl0_20
<=> ( $false
= ( mrel @ '#c' @ mactual @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl0_20])],[avatar_definition]) ).
thf(f347,plain,
( ~ spl0_3
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[status(thm)],[f346]) ).
thf(f346,plain,
( $false
| ~ spl0_3
| ~ spl0_19 ),
inference(trivial_inequality_removal,[status(thm)],[f343]) ).
thf(f343,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_19 ),
inference(superposition,[status(thm)],[f178,f328]) ).
thf(f328,plain,
( ( $true
= ( paid @ sK3 ) )
| ~ spl0_19 ),
inference(avatar_component_clause,[status(thm)],[f326]) ).
thf(f326,definition,
( spl0_19
<=> ( $true
= ( paid @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition]) ).
thf(f178,plain,
( ( $false
= ( paid @ sK3 ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f176]) ).
thf(f176,definition,
( spl0_3
<=> ( $false
= ( paid @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f339,plain,
( spl0_19
| spl0_20
| spl0_12 ),
inference(avatar_split_clause,[status(thm)],[f322,f213,f330,f326]) ).
thf(f213,definition,
( spl0_12
<=> ( ( paid @ mactual )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f322,plain,
( ( $true
= ( paid @ sK3 ) )
| ( ( paid @ mactual )
= $false )
| ( $false
= ( mrel @ '#c' @ mactual @ mactual ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f317]) ).
thf(f317,plain,
( ( $false
= ( mrel @ '#c' @ mactual @ mactual ) )
| ( $true
= ( paid @ sK3 ) )
| ( $true = $false )
| ( ( paid @ mactual )
= $false ) ),
inference(superposition,[status(thm)],[f148,f160]) ).
thf(f148,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#u' @ X1 @ X2 )
= $false )
| ( $true
= ( paid @ X2 ) )
| ( ( mrel @ '#c' @ mactual @ X1 )
= $false )
| ( $false
= ( paid @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f147]) ).
thf(f147,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( paid @ X1 ) )
| ( $true
= ( ( mrel @ '#u' @ X1 @ X2 )
=> ( paid @ X2 ) ) )
| ( ( mrel @ '#c' @ mactual @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f146]) ).
thf(f146,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#c' @ mactual @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#u' @ X1 @ Y0 )
=> ( paid @ Y0 ) )
@ X2 ) )
| ( $false
= ( paid @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f145]) ).
thf(f145,plain,
! [X1: mworld] :
( ( $false
= ( paid @ X1 ) )
| ( ( mrel @ '#c' @ mactual @ X1 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ X1 @ Y0 )
=> ( paid @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f144]) ).
thf(f144,plain,
! [X1: mworld] :
( ( ( mrel @ '#c' @ mactual @ X1 )
= $false )
| ( $true
= ( ( paid @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ X1 @ Y0 )
=> ( paid @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f143]) ).
thf(f143,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ '#c' @ mactual @ X1 )
=> ( ( paid @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ X1 @ Y0 )
=> ( paid @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f142]) ).
thf(f142,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( ( paid @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#u' @ Y0 @ Y1 )
=> ( paid @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f141]) ).
thf(f141,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( ( paid @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#u' @ Y0 @ Y1 )
=> ( paid @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[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 ) ) )
@ '#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 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f66,f64,f81,f76,f81]) ).
thf(f66,plain,
( ( mlocal @ ( mbox @ '#c' @ ( mimplies @ paid @ ( mbox @ '#u' @ paid ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f50]) ).
thf(f50,plain,
( ( mlocal @ ( mbox @ '#c' @ ( mimplies @ paid @ ( mbox @ '#u' @ paid ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f49]) ).
thf(f49,plain,
mlocal @ ( mbox @ '#c' @ ( mimplies @ paid @ ( mbox @ '#u' @ paid ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,axiom,
mlocal @ ( mbox @ '#c' @ ( mimplies @ paid @ ( mbox @ '#u' @ paid ) ) ),
file('/export/starexec/sandbox/tmp/tmp.StopnhNuQj/DTF2THF_15568.p',axiom_2) ).
thf(f338,plain,
( spl0_13
| ~ spl0_15 ),
inference(avatar_split_clause,[status(thm)],[f310,f225,f217]) ).
thf(f217,definition,
( spl0_13
<=> ( $true
= ( called @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f225,definition,
( spl0_15
<=> ! [X2: mworld] :
( ( ( mrel @ '#c' @ mactual @ X2 )
= $false )
| ( $true
= ( called @ X2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition]) ).
thf(f310,plain,
( ( $true
= ( called @ mactual ) )
| ~ spl0_15 ),
inference(trivial_inequality_removal,[status(thm)],[f309]) ).
thf(f309,plain,
( ( $true
= ( called @ mactual ) )
| ( $true = $false )
| ~ spl0_15 ),
inference(superposition,[status(thm)],[f65,f226]) ).
thf(f226,plain,
( ! [X2: mworld] :
( ( ( mrel @ '#c' @ mactual @ X2 )
= $false )
| ( $true
= ( called @ X2 ) ) )
| ~ spl0_15 ),
inference(avatar_component_clause,[status(thm)],[f225]) ).
thf(f306,plain,
( ~ spl0_1
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f305]) ).
thf(f305,plain,
( $false
| ~ spl0_1
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f301]) ).
thf(f301,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f169,f253]) ).
thf(f253,plain,
( ( $true
= ( charge @ sK3 ) )
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f246]) ).
thf(f246,plain,
( ( $true
= ( charge @ sK3 ) )
| ( $true = $false )
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f195,f160]) ).
thf(f195,plain,
( ! [X1: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $true
= ( charge @ X1 ) ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f194]) ).
thf(f194,definition,
( spl0_7
<=> ! [X1: mworld] :
( ( $true
= ( charge @ X1 ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f169,plain,
( ( $false
= ( charge @ sK3 ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f167]) ).
thf(f167,definition,
( spl0_1
<=> ( $false
= ( charge @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f292,plain,
( spl0_18
| spl0_17 ),
inference(avatar_split_clause,[status(thm)],[f280,f285,f288]) ).
thf(f280,plain,
! [X0: mworld] :
( ( $true
= ( called @ X0 ) )
| ( $false
= ( called @ sK3 ) )
| ( $false
= ( mrel @ '#c' @ sK3 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f278]) ).
thf(f278,plain,
! [X0: mworld] :
( ( $false
= ( called @ sK3 ) )
| ( $true = $false )
| ( $true
= ( called @ X0 ) )
| ( $false
= ( mrel @ '#c' @ sK3 @ X0 ) ) ),
inference(superposition,[status(thm)],[f160,f97]) ).
thf(f97,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( ( mrel @ '#c' @ X1 @ X2 )
= $false )
| ( $false
= ( called @ X1 ) )
| ( $true
= ( called @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f96]) ).
thf(f96,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ '#c' @ X1 @ X2 )
=> ( called @ X2 ) )
= $true )
| ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $false
= ( called @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f95]) ).
thf(f95,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $false
= ( called @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
! [X1: mworld] :
( ( $false
= ( called @ X1 ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
! [X1: mworld] :
( ( $true
= ( ( called @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f92]) ).
thf(f92,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ '#u' @ mactual @ X1 )
=> ( ( called @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f91]) ).
thf(f91,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ( ( called @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#c' @ Y0 @ Y1 )
=> ( called @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ( ( called @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#c' @ Y0 @ Y1 )
=> ( called @ Y1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f87]) ).
thf(f87,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,[status(thm)],[f75,f64,f81,f76,f81]) ).
thf(f75,plain,
( ( mlocal @ ( mbox @ '#u' @ ( mimplies @ called @ ( mbox @ '#c' @ called ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
( ( mlocal @ ( mbox @ '#u' @ ( mimplies @ called @ ( mbox @ '#c' @ called ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f40]) ).
thf(f40,plain,
mlocal @ ( mbox @ '#u' @ ( mimplies @ called @ ( mbox @ '#c' @ called ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,axiom,
mlocal @ ( mbox @ '#u' @ ( mimplies @ called @ ( mbox @ '#c' @ called ) ) ),
file('/export/starexec/sandbox/tmp/tmp.StopnhNuQj/DTF2THF_15568.p',axiom_1) ).
thf(f275,plain,
( ~ spl0_5
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f274]) ).
thf(f274,plain,
( $false
| ~ spl0_5
| ~ spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f270]) ).
thf(f270,plain,
( ( $true = $false )
| ~ spl0_5
| ~ spl0_13 ),
inference(superposition,[status(thm)],[f219,f187]) ).
thf(f187,plain,
( ( $false
= ( called @ mactual ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f185]) ).
thf(f185,definition,
( spl0_5
<=> ( $false
= ( called @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f219,plain,
( ( $true
= ( called @ mactual ) )
| ~ spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f217]) ).
thf(f244,plain,
( ~ spl0_4
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f243]) ).
thf(f243,plain,
( $false
| ~ spl0_4
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f239]) ).
thf(f239,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f183,f215]) ).
thf(f215,plain,
( ( ( paid @ mactual )
= $false )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f213]) ).
thf(f183,plain,
( ( ( paid @ mactual )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f181]) ).
thf(f181,definition,
( spl0_4
<=> ( ( paid @ mactual )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f237,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[status(thm)],[f236]) ).
thf(f236,plain,
( $false
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f233]) ).
thf(f233,plain,
( ( $true = $false )
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f192,f154]) ).
thf(f154,plain,
( $true
= ( charge @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f152]) ).
thf(f152,plain,
( ( ( charge @ mactual )
=> ( ~ ( paid @ mactual )
& ( called @ mactual ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f151]) ).
thf(f151,plain,
( $true
= ( ~ ( ( charge @ mactual )
=> ( ~ ( paid @ mactual )
& ( called @ mactual ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f149]) ).
thf(f192,plain,
( ( $false
= ( charge @ mactual ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f190]) ).
thf(f190,definition,
( spl0_6
<=> ( $false
= ( charge @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f231,plain,
( spl0_16
| spl0_15 ),
inference(avatar_split_clause,[status(thm)],[f111,f225,f229]) ).
thf(f111,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( mrel @ '#c' @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( ( mrel @ '#c' @ mactual @ X2 )
= $false )
| ( $true
= ( called @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $true
= ( mrel @ '#c' @ X1 @ ( sK1 @ X1 ) ) )
| ( $true
= ( ( mrel @ '#c' @ mactual @ X2 )
=> ( called @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f109]) ).
thf(f109,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( mrel @ '#c' @ X1 @ ( sK1 @ X1 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) )
@ X2 ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f108]) ).
thf(f108,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) ) ) )
| ( $true
= ( mrel @ '#c' @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
! [X1: mworld] :
( ( ( ( mrel @ '#c' @ X1 @ ( sK1 @ X1 ) )
=> ( called @ ( sK1 @ X1 ) ) )
= $false )
| ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f105]) ).
thf(f105,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) )
@ ( sK1 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f104]) ).
thf(f104,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
! [X1: mworld] :
( ( $true
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ '#u' @ mactual @ X1 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
! [X1: mworld] :
( ( $false
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) ) ) ) )
| ( $true
= ( ( mrel @ '#u' @ mactual @ X1 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ X1 @ Y0 )
=> ( called @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f100]) ).
thf(f100,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#c' @ Y0 @ Y1 )
=> ( called @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f99]) ).
thf(f99,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,[status(thm)],[f98]) ).
thf(f98,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,[status(thm)],[f86]) ).
thf(f86,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,[status(thm)],[f72,f64,f76,f68,f81,f81,f68,f81]) ).
thf(f72,plain,
( ( mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#c' @ called ) ) @ ( mbox @ '#u' @ ( mnot @ ( mbox @ '#c' @ called ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#c' @ called ) ) @ ( mbox @ '#u' @ ( mnot @ ( mbox @ '#c' @ called ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f32]) ).
thf(f32,plain,
mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#c' @ called ) ) @ ( mbox @ '#u' @ ( mnot @ ( mbox @ '#c' @ called ) ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,axiom,
mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#c' @ called ) ) @ ( mbox @ '#u' @ ( mnot @ ( mbox @ '#c' @ called ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.StopnhNuQj/DTF2THF_15568.p',axiom_3) ).
thf(f227,plain,
( spl0_14
| spl0_15 ),
inference(avatar_split_clause,[status(thm)],[f114,f225,f222]) ).
thf(f114,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $false
= ( called @ ( sK1 @ X1 ) ) )
| ( ( mrel @ '#c' @ mactual @ X2 )
= $false )
| ( $true
= ( called @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f113,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ '#c' @ mactual @ X2 )
=> ( called @ X2 ) ) )
| ( $false
= ( called @ ( sK1 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f112]) ).
thf(f112,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $false
= ( called @ ( sK1 @ X1 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
! [X1: mworld] :
( ( $false
= ( called @ ( sK1 @ X1 ) ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( called @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f106]) ).
thf(f196,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f140,f194,f190]) ).
thf(f140,plain,
! [X1: mworld] :
( ( $true
= ( charge @ X1 ) )
| ( $false
= ( mrel @ '#u' @ mactual @ X1 ) )
| ( $false
= ( charge @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f139]) ).
thf(f139,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ '#u' @ mactual @ X1 )
=> ( charge @ X1 ) ) )
| ( $false
= ( charge @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f138]) ).
thf(f138,plain,
! [X1: mworld] :
( ( $false
= ( charge @ mactual ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ( charge @ Y0 ) )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f133]) ).
thf(f133,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ( charge @ Y0 ) ) ) )
| ( $false
= ( charge @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f132]) ).
thf(f132,plain,
( ( $false
= ( charge @ mactual ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#c' @ mactual @ Y0 )
=> ( charge @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#u' @ mactual @ Y0 )
=> ( charge @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f131]) ).
thf(f131,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,[status(thm)],[f85]) ).
thf(f85,plain,
( ( ^ [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 ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f71,f64,f76,f80,f81,f81]) ).
thf(f71,plain,
( ( mlocal @ ( mimplies @ charge @ ( mand @ ( mbox @ '#u' @ charge ) @ ( mbox @ '#c' @ charge ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f54]) ).
thf(f54,plain,
( ( mlocal @ ( mimplies @ charge @ ( mand @ ( mbox @ '#u' @ charge ) @ ( mbox @ '#c' @ charge ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f53]) ).
thf(f53,plain,
mlocal @ ( mimplies @ charge @ ( mand @ ( mbox @ '#u' @ charge ) @ ( mbox @ '#c' @ charge ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
mlocal @ ( mimplies @ charge @ ( mand @ ( mbox @ '#u' @ charge ) @ ( mbox @ '#c' @ charge ) ) ),
file('/export/starexec/sandbox/tmp/tmp.StopnhNuQj/DTF2THF_15568.p',axiom_charge_u) ).
thf(f188,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f156,f185,f181]) ).
thf(f156,plain,
( ( ( paid @ mactual )
= $true )
| ( $false
= ( called @ mactual ) ) ),
inference(not_proxy_clausification,[status(thm)],[f155]) ).
thf(f155,plain,
( ( ( ~ ( paid @ mactual ) )
= $false )
| ( $false
= ( called @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f153]) ).
thf(f153,plain,
( ( ~ ( paid @ mactual )
& ( called @ mactual ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f152]) ).
thf(f179,plain,
( spl0_1
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f165,f176,f167]) ).
thf(f165,plain,
( ( $false
= ( paid @ sK3 ) )
| ( $false
= ( charge @ sK3 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f164]) ).
thf(f164,plain,
( ( $true
= ( ~ ( paid @ sK3 ) ) )
| ( $false
= ( charge @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f162]) ).
thf(f162,plain,
( ( $false
= ( charge @ sK3 ) )
| ( $true
= ( ~ ( paid @ sK3 )
& ( called @ sK3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f161]) ).
thf(f161,plain,
( $true
= ( ( charge @ sK3 )
=> ( ~ ( paid @ sK3 )
& ( called @ sK3 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f159]) ).
thf(f159,plain,
( $false
= ( ~ ( ( charge @ sK3 )
=> ( ~ ( paid @ sK3 )
& ( called @ sK3 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f158]) ).
thf(f174,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f163,f171,f167]) ).
thf(f163,plain,
( ( $true
= ( called @ sK3 ) )
| ( $false
= ( charge @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : PRO029^16 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 11:29:45 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.32 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : PRO029^16 : TPTP v9.2.1. Released v8.1.0.
% 0.07/0.32 % Domain : Processes
% 0.07/0.32 % Problem : Phone user and company (requirement 1)
% 0.07/0.32 % Version : [BP13] axioms.
% 0.07/0.32 % English : Phone user U and phone company C have following relationship:
% 0.07/0.32 % + U does not pay a call before he has dialled it.
% 0.07/0.32 % + Both U nd C are able to prove when U is being charged.
% 0.07/0.32 % + U is able to prove that C can prove that U has made a call,
% 0.07/0.32 % + C is able to prove that U can prove that U has paid his call,
% 0.07/0.32 % + U is able to prove that C cannot prove that U has made a call,
% 0.07/0.32 % + C is able to prove that U cannot prove that he has paid his
% 0.07/0.32 % call, whenever these facts are true.
% 0.07/0.32 % Then the following requirement is true: From U's point of view,
% 0.07/0.32 % C should charge U only if he has made a call that is not yet paid.
% 0.07/0.32
% 0.07/0.32 % Refs : [HA97] Huima & Aura (1997), Using Multimodal Logic to Express
% 0.07/0.32 % : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.07/0.32 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.07/0.32 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.07/0.32 % Source : [TPTP]
% 0.07/0.32 % Names : MML011+1 [QMLTP]
% 0.07/0.32 % : MML011^1.016_s4_cumulative_rigid.p [QMLTP/5_THF]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0
% 0.07/0.32 % Syntax : Number of formulae : 36 ( 10 unt; 17 typ; 8 def)
% 0.07/0.32 % Number of atoms : 85 ( 8 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 17 ( 4 avg)
% 0.07/0.32 % Number of connectives : 118 ( 1 ~; 1 |; 4 &; 107 @)
% 0.07/0.32 % ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 9 ( 4 avg)
% 0.07/0.32 % Number of types : 3 ( 2 usr)
% 0.07/0.32 % Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 16 ( 15 usr; 3 con; 0-3 aty)
% 0.07/0.32 % Number of variables : 31 ( 21 ^; 9 !; 1 ?; 31 :)
% 0.07/0.32 % SPC : TH0_THM_EQU_NAR
% 0.07/0.32
% 0.07/0.32 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.07/0.32 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.07/0.32 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.07/0.32 % $modal == [$constants == $rigid,$quantification == $cumulative,
% 0.07/0.32 % $modalities == $modal_system_S4].
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 thf(mworld,type,
% 0.07/0.32 mworld: $tType ).
% 0.07/0.32
% 0.07/0.32 thf(mindex,type,
% 0.07/0.32 mindex: $tType ).
% 0.07/0.32
% 0.07/0.32 thf(mrel_type,type,
% 0.07/0.32 mrel: mindex > mworld > mworld > $o ).
% 0.07/0.32
% 0.07/0.32 thf('#c_type',type,
% 0.07/0.32 '#c': mindex ).
% 0.07/0.32
% 0.07/0.32 thf('#u_type',type,
% 0.07/0.32 '#u': mindex ).
% 0.07/0.32
% 0.07/0.32 thf(mactual_type,type,
% 0.07/0.32 mactual: mworld ).
% 0.07/0.32
% 0.07/0.32 thf(mlocal_type,type,
% 0.07/0.32 mlocal: ( mworld > $o ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(mlocal_def,definition,
% 0.07/0.32 ( mlocal
% 0.07/0.32 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(mnot_type,type,
% 0.07/0.32 mnot: ( mworld > $o ) > mworld > $o ).
% 0.07/0.32
% 0.07/0.32 thf(mand_type,type,
% 0.07/0.32 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.07/0.32
% 0.07/0.32 thf(mor_type,type,
% 0.07/0.32 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.07/0.32
% 0.07/0.32 thf(mimplies_type,type,
% 0.07/0.32 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.07/0.32
% 0.07/0.32 thf(mequiv_type,type,
% 0.07/0.32 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.07/0.32
% 0.07/0.32 thf(mnot_def,definition,
% 0.07/0.32 ( mnot
% 0.07/0.32 = ( ^ [A: mworld > $o,W: mworld] :
% 0.07/0.32 ~ ( A @ W ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(mand_def,definition,
% 0.07/0.32 ( mand
% 0.07/0.32 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.07/0.32 ( ( A @ W )
% 0.07/0.32 & ( B @ W ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(mor_def,definition,
% 0.07/0.32 ( mor
% 0.07/0.32 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.07/0.32 ( ( A @ W )
% 0.07/0.32 | ( B @ W ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(mimplies_def,definition,
% 0.07/0.32 ( mimplies
% 0.07/0.32 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.07/0.32 ( ( A @ W )
% 0.07/0.32 => ( B @ W ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(mequiv_def,definition,
% 0.07/0.32 ( mequiv
% 0.07/0.32 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.07/0.32 ( ( A @ W )
% 0.07/0.32 <=> ( B @ W ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(mbox_type,type,
% 0.07/0.32 mbox: mindex > ( mworld > $o ) > mworld > $o ).
% 0.07/0.32
% 0.07/0.32 thf(mbox_def,definition,
% 0.07/0.32 ( mbox
% 0.07/0.32 = ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
% 0.07/0.32 ! [V: mworld] :
% 0.07/0.32 ( ( mrel @ R @ W @ V )
% 0.07/0.32 => ( Phi @ V ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(mdia_type,type,
% 0.07/0.32 mdia: mindex > ( mworld > $o ) > mworld > $o ).
% 0.07/0.32
% 0.07/0.32 thf(mdia_def,definition,
% 0.07/0.32 ( mdia
% 0.07/0.32 = ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
% 0.07/0.32 ? [V: mworld] :
% 0.07/0.32 ( ( mrel @ R @ W @ V )
% 0.07/0.32 & ( Phi @ V ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf('mrel_#c_reflexive',axiom,
% 0.07/0.32 ! [W: mworld] : ( mrel @ '#c' @ W @ W ) ).
% 0.07/0.32
% 0.07/0.32 thf('mrel_#c_transitive',axiom,
% 0.07/0.32 ! [W: mworld,V: mworld,U: mworld] :
% 0.07/0.32 ( ( ( mrel @ '#c' @ W @ V )
% 0.07/0.32 & ( mrel @ '#c' @ V @ U ) )
% 0.07/0.32 => ( mrel @ '#c' @ W @ U ) ) ).
% 0.07/0.32
% 0.07/0.32 thf('mrel_#u_reflexive',axiom,
% 0.07/0.32 ! [W: mworld] : ( mrel @ '#u' @ W @ W ) ).
% 0.07/0.32
% 0.07/0.32 thf('mrel_#u_transitive',axiom,
% 0.07/0.32 ! [W: mworld,V: mworld,U: mworld] :
% 0.07/0.32 ( ( ( mrel @ '#u' @ W @ V )
% 0.07/0.32 & ( mrel @ '#u' @ V @ U ) )
% 0.07/0.32 => ( mrel @ '#u' @ W @ U ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(charge_decl,type,
% 0.07/0.32 charge: mworld > $o ).
% 0.07/0.32
% 0.07/0.32 thf(called_decl,type,
% 0.07/0.32 called: mworld > $o ).
% 0.07/0.32
% 0.07/0.32 thf(paid_decl,type,
% 0.07/0.32 paid: mworld > $o ).
% 0.07/0.32
% 0.07/0.32 thf(aciom_paid_charge,axiom,
% 0.07/0.32 mlocal @ ( mimplies @ paid @ called ) ).
% 0.07/0.32
% 0.07/0.32 thf(axiom_charge_u,axiom,
% 0.07/0.32 mlocal @ ( mimplies @ charge @ ( mand @ ( mbox @ '#u' @ charge ) @ ( mbox @ '#c' @ charge ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(axiom_1,axiom,
% 0.07/0.32 mlocal @ ( mbox @ '#u' @ ( mimplies @ called @ ( mbox @ '#c' @ called ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(axiom_2,axiom,
% 0.07/0.32 mlocal @ ( mbox @ '#c' @ ( mimplies @ paid @ ( mbox @ '#u' @ paid ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(axiom_3,axiom,
% 0.07/0.32 mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#c' @ called ) ) @ ( mbox @ '#u' @ ( mnot @ ( mbox @ '#c' @ called ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(axiom_4,axiom,
% 0.07/0.32 mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#u' @ paid ) ) @ ( mbox @ '#c' @ ( mnot @ ( mbox @ '#u' @ paid ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(requirement_1,conjecture,
% 0.07/0.32 mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 1.04/0.93 ---- Embedded in THF ---
% 1.04/0.93 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.04/0.93 %%% Generated on Tue Feb 24 11:29:46 EST 2026
% 1.04/0.93 %%% using '$$dhol' embedding, version 1.3.0.
% 1.04/0.93 %%% Logic specification used:
% 1.04/0.93 %%% thf(spec, logic, $$dhol).
% 1.04/0.93
% 1.04/0.93 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.StopnhNuQj/DTF2DTF15568.p
% See solution above
% 1.04/0.93 ------------------------
% 1.04/0.94 ---- Cleaned THF ---
% 1.04/0.94 thf(mworld,type,
% 1.04/0.94 mworld: $tType ).
% 1.04/0.94
% 1.04/0.94 thf(mindex,type,
% 1.04/0.94 mindex: $tType ).
% 1.04/0.94
% 1.04/0.94 thf(mrel_type,type,
% 1.04/0.94 mrel: mindex > mworld > mworld > $o ).
% 1.04/0.94
% 1.04/0.94 thf('#c_type',type,
% 1.04/0.94 '#c': mindex ).
% 1.04/0.94
% 1.04/0.94 thf('#u_type',type,
% 1.04/0.94 '#u': mindex ).
% 1.04/0.94
% 1.04/0.94 thf(mactual_type,type,
% 1.04/0.94 mactual: mworld ).
% 1.04/0.94
% 1.04/0.94 thf(mlocal_type,type,
% 1.04/0.94 mlocal: ( mworld > $o ) > $o ).
% 1.04/0.94
% 1.04/0.94 thf(mlocal_def,definition,
% 1.04/0.94 ( mlocal
% 1.04/0.94 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.04/0.94
% 1.04/0.94 thf(mnot_type,type,
% 1.04/0.94 mnot: ( mworld > $o ) > mworld > $o ).
% 1.04/0.94
% 1.04/0.94 thf(mand_type,type,
% 1.04/0.94 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.04/0.94
% 1.04/0.94 thf(mor_type,type,
% 1.04/0.94 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.04/0.94
% 1.04/0.94 thf(mimplies_type,type,
% 1.04/0.94 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.04/0.94
% 1.04/0.94 thf(mequiv_type,type,
% 1.04/0.94 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.04/0.94
% 1.04/0.94 thf(mnot_def,definition,
% 1.04/0.94 ( mnot
% 1.04/0.94 = ( ^ [A: mworld > $o,W: mworld] :
% 1.04/0.94 ~ ( A @ W ) ) ) ).
% 1.04/0.94
% 1.04/0.94 thf(mand_def,definition,
% 1.04/0.94 ( mand
% 1.04/0.94 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.04/0.94 ( ( A @ W )
% 1.04/0.94 & ( B @ W ) ) ) ) ).
% 1.04/0.94
% 1.04/0.94 thf(mor_def,definition,
% 1.04/0.94 ( mor
% 1.04/0.94 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.04/0.94 ( ( A @ W )
% 1.04/0.94 | ( B @ W ) ) ) ) ).
% 1.04/0.94
% 1.04/0.94 thf(mimplies_def,definition,
% 1.04/0.94 ( mimplies
% 1.04/0.94 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.04/0.94 ( ( A @ W )
% 1.04/0.94 => ( B @ W ) ) ) ) ).
% 1.04/0.94
% 1.04/0.94 thf(mequiv_def,definition,
% 1.04/0.94 ( mequiv
% 1.04/0.94 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.04/0.94 ( ( A @ W )
% 1.04/0.94 <=> ( B @ W ) ) ) ) ).
% 1.04/0.94
% 1.04/0.94 thf(mbox_type,type,
% 1.04/0.94 mbox: mindex > ( mworld > $o ) > mworld > $o ).
% 1.04/0.94
% 1.04/0.94 thf(mbox_def,definition,
% 1.04/0.94 ( mbox
% 1.04/0.94 = ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
% 1.04/0.94 ! [V: mworld] :
% 1.04/0.94 ( ( mrel @ R @ W @ V )
% 1.04/0.94 => ( Phi @ V ) ) ) ) ).
% 1.04/0.94
% 1.04/0.94 thf(mdia_type,type,
% 1.04/0.94 mdia: mindex > ( mworld > $o ) > mworld > $o ).
% 1.04/0.94
% 1.04/0.94 thf(mdia_def,definition,
% 1.04/0.94 ( mdia
% 1.04/0.94 = ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
% 1.04/0.94 ? [V: mworld] :
% 1.04/0.94 ( ( mrel @ R @ W @ V )
% 1.04/0.94 & ( Phi @ V ) ) ) ) ).
% 1.04/0.94
% 1.04/0.94 thf('mrel_#c_reflexive',axiom,
% 1.04/0.94 ! [W: mworld] : ( mrel @ '#c' @ W @ W ) ).
% 1.04/0.94
% 1.04/0.94 thf('mrel_#c_transitive',axiom,
% 1.04/0.94 ! [W: mworld,V: mworld,U: mworld] :
% 1.04/0.94 ( ( ( mrel @ '#c' @ W @ V )
% 1.04/0.94 & ( mrel @ '#c' @ V @ U ) )
% 1.04/0.94 => ( mrel @ '#c' @ W @ U ) ) ).
% 1.04/0.94
% 1.04/0.94 thf('mrel_#u_reflexive',axiom,
% 1.04/0.94 ! [W: mworld] : ( mrel @ '#u' @ W @ W ) ).
% 1.04/0.94
% 1.04/0.94 thf('mrel_#u_transitive',axiom,
% 1.04/0.94 ! [W: mworld,V: mworld,U: mworld] :
% 1.04/0.94 ( ( ( mrel @ '#u' @ W @ V )
% 1.04/0.94 & ( mrel @ '#u' @ V @ U ) )
% 1.04/0.94 => ( mrel @ '#u' @ W @ U ) ) ).
% 1.04/0.94
% 1.04/0.94 thf(charge_decl,type,
% 1.04/0.94 charge: mworld > $o ).
% 1.04/0.94
% 1.04/0.94 thf(called_decl,type,
% 1.04/0.94 called: mworld > $o ).
% 1.04/0.94
% 1.04/0.94 thf(paid_decl,type,
% 1.04/0.94 paid: mworld > $o ).
% 1.04/0.94
% 1.04/0.94 thf(aciom_paid_charge,axiom,
% 1.04/0.94 mlocal @ ( mimplies @ paid @ called ) ).
% 1.04/0.94
% 1.04/0.94 thf(axiom_charge_u,axiom,
% 1.04/0.94 mlocal @ ( mimplies @ charge @ ( mand @ ( mbox @ '#u' @ charge ) @ ( mbox @ '#c' @ charge ) ) ) ).
% 1.04/0.94
% 1.04/0.94 thf(axiom_1,axiom,
% 1.04/0.94 mlocal @ ( mbox @ '#u' @ ( mimplies @ called @ ( mbox @ '#c' @ called ) ) ) ).
% 1.04/0.94
% 1.04/0.94 thf(axiom_2,axiom,
% 1.04/0.94 mlocal @ ( mbox @ '#c' @ ( mimplies @ paid @ ( mbox @ '#u' @ paid ) ) ) ).
% 1.04/0.94
% 1.04/0.94 thf(axiom_3,axiom,
% 1.04/0.94 mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#c' @ called ) ) @ ( mbox @ '#u' @ ( mnot @ ( mbox @ '#c' @ called ) ) ) ) ).
% 1.04/0.94
% 1.04/0.94 thf(axiom_4,axiom,
% 1.04/0.94 mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#u' @ paid ) ) @ ( mbox @ '#c' @ ( mnot @ ( mbox @ '#u' @ paid ) ) ) ) ).
% 1.04/0.94
% 1.04/0.94 thf(requirement_1,conjecture,
% 1.04/0.94 mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ) ).
% 1.04/0.94 ------------------------
% 1.04/0.95 % (15833)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_15568 for (2999ds/2Mi)
% 1.04/0.95 % (15832)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15568 for (2999ds/2Mi)
% 1.04/0.95 % (15831)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 DTF2THF_15568 for (2999ds/27Mi)
% 1.04/0.95 % (15834)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_15568 for (2999ds/275Mi)
% 1.04/0.95 % (15829)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15568 for (2999ds/183Mi)
% 1.04/0.95 % (15830)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 DTF2THF_15568 for (2999ds/4Mi)
% 1.04/0.95 % (15835)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15568 for (2999ds/18Mi)
% 1.04/0.95 % (15832)Instruction limit reached!
% 1.04/0.95 % (15832)------------------------------
% 1.04/0.95 % (15832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.95 % (15832)Termination reason: Unknown
% 1.04/0.95 % (15832)Termination phase: shuffling
% 1.04/0.95
% 1.04/0.95 % (15832)Memory used [KB]: 1023
% 1.04/0.95 % (15832)Time elapsed: 0.002 s
% 1.04/0.95 % (15832)Instructions burned: 3 (million)
% 1.04/0.95 % (15832)------------------------------
% 1.04/0.95 % (15832)------------------------------
% 1.04/0.95 % (15833)Instruction limit reached!
% 1.04/0.95 % (15833)------------------------------
% 1.04/0.95 % (15833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.95 % (15833)Termination reason: Unknown
% 1.04/0.95 % (15833)Termination phase: Property scanning
% 1.04/0.95
% 1.04/0.95 % (15833)Memory used [KB]: 1023
% 1.04/0.95 % (15833)Time elapsed: 0.002 s
% 1.04/0.95 % (15833)Instructions burned: 3 (million)
% 1.04/0.95 % (15833)------------------------------
% 1.04/0.95 % (15833)------------------------------
% 1.04/0.95 % (15830)Instruction limit reached!
% 1.04/0.95 % (15830)------------------------------
% 1.04/0.95 % (15830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.95 % (15830)Termination reason: Unknown
% 1.04/0.95 % (15830)Termination phase: Property scanning
% 1.04/0.95
% 1.04/0.95 % (15830)Memory used [KB]: 1023
% 1.04/0.95 % (15830)Time elapsed: 0.003 s
% 1.04/0.95 % (15830)Instructions burned: 6 (million)
% 1.04/0.95 % (15830)------------------------------
% 1.04/0.95 % (15830)------------------------------
% 1.04/0.95 % (15834)Refutation not found, incomplete strategy
% 1.04/0.95 % (15834)------------------------------
% 1.04/0.95 % (15834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.95 % (15834)Termination reason: Refutation not found, incomplete strategy
% 1.04/0.95
% 1.04/0.95
% 1.04/0.95 % (15834)Memory used [KB]: 5500
% 1.04/0.95 % (15834)Time elapsed: 0.003 s
% 1.04/0.95 % (15834)Instructions burned: 5 (million)
% 1.04/0.95 % (15834)------------------------------
% 1.04/0.95 % (15834)------------------------------
% 1.04/0.96 % (15835)Instruction limit reached!
% 1.04/0.96 % (15835)------------------------------
% 1.04/0.96 % (15835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.96 % (15835)Termination reason: Unknown
% 1.04/0.96 % (15835)Termination phase: Saturation
% 1.04/0.96
% 1.04/0.96 % (15835)Memory used [KB]: 5628
% 1.04/0.96 % (15835)Time elapsed: 0.007 s
% 1.04/0.96 % (15835)Instructions burned: 19 (million)
% 1.04/0.96 % (15835)------------------------------
% 1.04/0.96 % (15835)------------------------------
% 1.04/0.96 % (15831)Instruction limit reached!
% 1.04/0.96 % (15831)------------------------------
% 1.04/0.96 % (15831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.96 % (15831)Termination reason: Unknown
% 1.04/0.96 % (15831)Termination phase: Saturation
% 1.04/0.96
% 1.04/0.96 % (15831)Memory used [KB]: 5756
% 1.04/0.96 % (15831)Time elapsed: 0.011 s
% 1.04/0.96 % (15831)Instructions burned: 29 (million)
% 1.04/0.96 % (15831)------------------------------
% 1.04/0.96 % (15831)------------------------------
% 1.04/0.96 % (15836)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15568 for (2999ds/3Mi)
% 1.04/0.96 % (15837)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 DTF2THF_15568 for (2999ds/37Mi)
% 1.04/0.96 % (15838)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 DTF2THF_15568 for (2999ds/15Mi)
% 1.04/0.96 % (15836)Instruction limit reached!
% 1.04/0.96 % (15836)------------------------------
% 1.04/0.96 % (15836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.96 % (15836)Termination reason: Unknown
% 1.04/0.96 % (15836)Termination phase: Property scanning
% 1.04/0.96
% 1.04/0.96 % (15836)Memory used [KB]: 1023
% 1.04/0.96 % (15836)Time elapsed: 0.002 s
% 1.04/0.96 % (15836)Instructions burned: 3 (million)
% 1.04/0.96 % (15836)------------------------------
% 1.04/0.96 % (15836)------------------------------
% 1.04/0.96 % (15839)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15568 for (2999ds/3Mi)
% 1.04/0.96 % (15839)Instruction limit reached!
% 1.04/0.96 % (15839)------------------------------
% 1.04/0.96 % (15839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.96 % (15839)Termination reason: Unknown
% 1.04/0.96 % (15839)Termination phase: Property scanning
% 1.04/0.96
% 1.04/0.96 % (15839)Memory used [KB]: 1023
% 1.04/0.96 % (15839)Time elapsed: 0.002 s
% 1.04/0.96 % (15839)Instructions burned: 3 (million)
% 1.04/0.96 % (15839)------------------------------
% 1.04/0.96 % (15839)------------------------------
% 1.04/0.96 % (15840)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 DTF2THF_15568 for (2999ds/1041Mi)
% 1.04/0.97 % (15838)Instruction limit reached!
% 1.04/0.97 % (15838)------------------------------
% 1.04/0.97 % (15838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.97 % (15838)Termination reason: Unknown
% 1.04/0.97 % (15838)Termination phase: Saturation
% 1.04/0.97
% 1.04/0.97 % (15838)Memory used [KB]: 5756
% 1.04/0.97 % (15838)Time elapsed: 0.006 s
% 1.04/0.97 % (15838)Instructions burned: 15 (million)
% 1.04/0.97 % (15838)------------------------------
% 1.04/0.97 % (15838)------------------------------
% 1.04/0.97 % (15829)First to succeed.
% 1.04/0.97 % (15841)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_15568 for (2999ds/7Mi)
% 1.04/0.97 % (15842)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_15568 for (2999ds/16Mi)
% 1.04/0.97 % (15829)Refutation found. Thanks to Tanya!
% 1.04/0.97 % SZS status Theorem for DTF2THF_15568
% 1.04/0.97 % SZS output start Proof for DTF2THF_15568
% 1.04/0.97 thf(type_def_5, type, mindex: $tType).
% 1.04/0.97 thf(type_def_6, type, mworld: $tType).
% 1.04/0.97 thf(func_def_0, type, mworld: $tType).
% 1.04/0.97 thf(func_def_1, type, mindex: $tType).
% 1.04/0.97 thf(func_def_2, type, mrel: mindex > mworld > mworld > $o).
% 1.04/0.97 thf(func_def_3, type, '#c': mindex).
% 1.04/0.97 thf(func_def_4, type, '#u': mindex).
% 1.04/0.97 thf(func_def_5, type, mactual: mworld).
% 1.04/0.97 thf(func_def_6, type, mlocal: (mworld > $o) > $o).
% 1.04/0.97 thf(func_def_8, type, mnot: (mworld > $o) > mworld > $o).
% 1.04/0.97 thf(func_def_9, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.04/0.97 thf(func_def_10, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.04/0.97 thf(func_def_11, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.04/0.97 thf(func_def_12, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.04/0.97 thf(func_def_13, type, mbox: mindex > (mworld > $o) > mworld > $o).
% 1.04/0.97 thf(func_def_14, type, mdia: mindex > (mworld > $o) > mworld > $o).
% 1.04/0.97 thf(func_def_15, type, charge: mworld > $o).
% 1.04/0.97 thf(func_def_16, type, called: mworld > $o).
% 1.04/0.97 thf(func_def_17, type, paid: mworld > $o).
% 1.04/0.97 thf(func_def_33, type, sK1: mworld > mworld).
% 1.04/0.97 thf(func_def_34, type, sK2: mworld > mworld).
% 1.04/0.97 thf(func_def_35, type, sK3: mworld).
% 1.04/0.97 thf(f575,plain,(
% 1.04/0.97 $false),
% 1.04/0.97 inference(avatar_sat_refutation,[status(thm)],[f174,f179,f188,f196,f227,f231,f237,f244,f275,f292,f306,f338,f339,f347,f354,f492,f506,f529,f574])).
% 1.04/0.97 thf(f574,plain,(
% 1.04/0.97 ~spl0_28),
% 1.04/0.97 inference(avatar_contradiction_clause,[status(thm)],[f573])).
% 1.04/0.97 thf(f573,plain,(
% 1.04/0.97 $false | ~spl0_28),
% 1.04/0.97 inference(trivial_inequality_removal,[status(thm)],[f567])).
% 1.04/0.97 thf(f567,plain,(
% 1.04/0.97 ($true = $false) | ~spl0_28),
% 1.04/0.97 inference(superposition,[status(thm)],[f160,f484])).
% 1.04/0.97 thf(f484,plain,(
% 1.04/0.97 ((mrel @ '#u' @ mactual @ sK3) = $false) | ~spl0_28),
% 1.04/0.97 inference(avatar_component_clause,[status(thm)],[f482])).
% 1.04/0.97 thf(f482,definition,(
% 1.04/0.97 spl0_28 <=> ((mrel @ '#u' @ mactual @ sK3) = $false)),
% 1.04/0.97 introduced(definition,[new_symbols(naming,[spl0_28])],[avatar_definition])).
% 1.04/0.97 thf(f160,plain,(
% 1.04/0.97 ((mrel @ '#u' @ mactual @ sK3) = $true)),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f158])).
% 1.04/0.97 thf(f158,plain,(
% 1.04/0.97 (((mrel @ '#u' @ mactual @ sK3) => (~ ((charge @ sK3) => ((~ (paid @ sK3)) & (called @ sK3))))) = $false)),
% 1.04/0.97 inference(beta_eta_normalization,[status(thm)],[f157])).
% 1.04/0.97 thf(f157,plain,(
% 1.04/0.97 ($false = ((^[Y0 : mworld]: ((mrel @ '#u' @ mactual @ Y0) => (~ ((charge @ Y0) => ((~ (paid @ Y0)) & (called @ Y0)))))) @ sK3))),
% 1.04/0.97 inference(sigma_clausification,[status(thm)],[f150])).
% 1.04/0.97 thf(f150,plain,(
% 1.04/0.97 ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#u' @ mactual @ Y0) => (~ ((charge @ Y0) => ((~ (paid @ Y0)) & (called @ Y0))))))))),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f149])).
% 1.04/0.97 thf(f149,plain,(
% 1.04/0.97 ($true != ((~ ((charge @ mactual) => ((~ (paid @ mactual)) & (called @ mactual)))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#u' @ mactual @ Y0) => (~ ((charge @ Y0) => ((~ (paid @ Y0)) & (called @ Y0)))))))))),
% 1.04/0.97 inference(beta_eta_normalization,[status(thm)],[f84])).
% 1.04/0.97 thf(f84,plain,(
% 1.04/0.97 (((^[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)),
% 1.04/0.97 inference(definition_unfolding,[status(thm)],[f67,f64,f76,f68,f76,f80,f68,f81,f68,f76,f80,f68])).
% 1.04/0.97 thf(f81,plain,(
% 1.04/0.97 (mbox = (^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 1.04/0.97 inference(cnf_transformation,[status(thm)],[f56])).
% 1.04/0.97 thf(f56,plain,(
% 1.04/0.97 (mbox = (^[Y0 : mindex]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 1.04/0.97 inference(fool_elimination,[status(thm)],[f55])).
% 1.04/0.97 thf(f55,plain,(
% 1.04/0.97 (mbox = (^[X0 : mindex, X1 : mworld > $o, X2 : mworld] : (! [X3 : mworld] : ((mrel @ X0 @ X2 @ X3) => (X1 @ X3)))))),
% 1.04/0.97 inference(rectify,[status(thm)],[f7])).
% 1.04/0.97 thf(f7,axiom,(
% 1.04/0.97 (mbox = (^[X4 : mindex, X0 : mworld > $o, X2 : mworld] : (! [X5 : mworld] : ((mrel @ X4 @ X2 @ X5) => (X0 @ X5)))))),
% 1.04/0.97 file('/export/starexec/sandbox/tmp/tmp.StopnhNuQj/DTF2THF_15568.p',mbox_def)).
% 1.04/0.97 thf(f80,plain,(
% 1.04/0.97 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.04/0.97 inference(cnf_transformation,[status(thm)],[f29])).
% 1.04/0.97 thf(f29,plain,(
% 1.04/0.97 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.04/0.97 inference(fool_elimination,[status(thm)],[f28])).
% 1.04/0.97 thf(f28,plain,(
% 1.04/0.97 (mand = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) & (X1 @ X2))))),
% 1.04/0.97 inference(rectify,[status(thm)],[f3])).
% 1.04/0.97 thf(f3,axiom,(
% 1.04/0.97 (mand = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X3 @ X2))))),
% 1.04/0.97 file('/export/starexec/sandbox/tmp/tmp.StopnhNuQj/DTF2THF_15568.p',mand_def)).
% 1.04/0.97 thf(f68,plain,(
% 1.04/0.97 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 1.04/0.97 inference(cnf_transformation,[status(thm)],[f58])).
% 1.04/0.97 thf(f58,plain,(
% 1.04/0.97 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 1.04/0.97 inference(fool_elimination,[status(thm)],[f57])).
% 1.04/0.97 thf(f57,plain,(
% 1.04/0.97 (mnot = (^[X0 : mworld > $o, X1 : mworld] : (~(X0 @ X1))))),
% 1.04/0.97 inference(rectify,[status(thm)],[f2])).
% 1.04/0.97 thf(f2,axiom,(
% 1.04/0.97 (mnot = (^[X1 : mworld > $o, X2 : mworld] : (~(X1 @ X2))))),
% 1.04/0.97 file('/export/starexec/sandbox/tmp/tmp.StopnhNuQj/DTF2THF_15568.p',mnot_def)).
% 1.04/0.97 thf(f76,plain,(
% 1.04/0.97 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.04/0.97 inference(cnf_transformation,[status(thm)],[f48])).
% 1.04/0.97 thf(f48,plain,(
% 1.04/0.97 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.04/0.97 inference(fool_elimination,[status(thm)],[f47])).
% 1.04/0.97 thf(f47,plain,(
% 1.04/0.97 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 1.04/0.97 inference(rectify,[status(thm)],[f5])).
% 1.04/0.97 thf(f5,axiom,(
% 1.04/0.97 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))) = mimplies)),
% 1.04/0.97 file('/export/starexec/sandbox/tmp/tmp.StopnhNuQj/DTF2THF_15568.p',mimplies_def)).
% 1.04/0.97 thf(f64,plain,(
% 1.04/0.97 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.04/0.97 inference(cnf_transformation,[status(thm)],[f44])).
% 1.04/0.97 thf(f44,plain,(
% 1.04/0.97 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.04/0.97 inference(fool_elimination,[status(thm)],[f1])).
% 1.04/0.97 thf(f1,axiom,(
% 1.04/0.97 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 1.04/0.97 file('/export/starexec/sandbox/tmp/tmp.StopnhNuQj/DTF2THF_15568.p',mlocal_def)).
% 1.04/0.97 thf(f67,plain,(
% 1.04/0.97 ((mlocal @ (mimplies @ (mnot @ (mimplies @ charge @ (mand @ called @ (mnot @ paid)))) @ (mbox @ '#u' @ (mnot @ (mimplies @ charge @ (mand @ called @ (mnot @ paid))))))) != $true)),
% 1.04/0.97 inference(cnf_transformation,[status(thm)],[f59])).
% 1.04/0.97 thf(f59,plain,(
% 1.04/0.97 ((mlocal @ (mimplies @ (mnot @ (mimplies @ charge @ (mand @ called @ (mnot @ paid)))) @ (mbox @ '#u' @ (mnot @ (mimplies @ charge @ (mand @ called @ (mnot @ paid))))))) != $true)),
% 1.04/0.97 inference(flattening,[status(thm)],[f35])).
% 1.04/0.97 thf(f35,plain,(
% 1.04/0.97 ~((mlocal @ (mimplies @ (mnot @ (mimplies @ charge @ (mand @ called @ (mnot @ paid)))) @ (mbox @ '#u' @ (mnot @ (mimplies @ charge @ (mand @ called @ (mnot @ paid))))))) = $true)),
% 1.04/0.97 inference(fool_elimination,[status(thm)],[f34])).
% 1.04/0.97 thf(f34,plain,(
% 1.04/0.97 ~(mlocal @ (mimplies @ (mnot @ (mimplies @ charge @ (mand @ called @ (mnot @ paid)))) @ (mbox @ '#u' @ (mnot @ (mimplies @ charge @ (mand @ called @ (mnot @ paid)))))))),
% 1.04/0.97 inference(rectify,[status(thm)],[f20])).
% 1.04/0.97 thf(f20,negated_conjecture,(
% 1.04/0.97 ~(mlocal @ (mimplies @ (mnot @ (mimplies @ charge @ (mand @ called @ (mnot @ paid)))) @ (mbox @ '#u' @ (mnot @ (mimplies @ charge @ (mand @ called @ (mnot @ paid)))))))),
% 1.04/0.97 inference(negated_conjecture,[status(cth)],[f19])).
% 1.04/0.97 thf(f19,conjecture,(
% 1.04/0.97 (mlocal @ (mimplies @ (mnot @ (mimplies @ charge @ (mand @ called @ (mnot @ paid)))) @ (mbox @ '#u' @ (mnot @ (mimplies @ charge @ (mand @ called @ (mnot @ paid)))))))),
% 1.04/0.97 file('/export/starexec/sandbox/tmp/tmp.StopnhNuQj/DTF2THF_15568.p',requirement_1)).
% 1.04/0.97 thf(f529,plain,(
% 1.04/0.97 ~spl0_14 | ~spl0_27),
% 1.04/0.97 inference(avatar_contradiction_clause,[status(thm)],[f528])).
% 1.04/0.97 thf(f528,plain,(
% 1.04/0.97 $false | (~spl0_14 | ~spl0_27)),
% 1.04/0.97 inference(trivial_inequality_removal,[status(thm)],[f525])).
% 1.04/0.97 thf(f525,plain,(
% 1.04/0.97 ($true = $false) | (~spl0_14 | ~spl0_27)),
% 1.04/0.97 inference(superposition,[status(thm)],[f373,f480])).
% 1.04/0.97 thf(f480,plain,(
% 1.04/0.97 ($true = (called @ (sK1 @ sK3))) | ~spl0_27),
% 1.04/0.97 inference(avatar_component_clause,[status(thm)],[f478])).
% 1.04/0.97 thf(f478,definition,(
% 1.04/0.97 spl0_27 <=> ($true = (called @ (sK1 @ sK3)))),
% 1.04/0.97 introduced(definition,[new_symbols(naming,[spl0_27])],[avatar_definition])).
% 1.04/0.97 thf(f373,plain,(
% 1.04/0.97 ($false = (called @ (sK1 @ sK3))) | ~spl0_14),
% 1.04/0.97 inference(trivial_inequality_removal,[status(thm)],[f368])).
% 1.04/0.97 thf(f368,plain,(
% 1.04/0.97 ($false = (called @ (sK1 @ sK3))) | ($true = $false) | ~spl0_14),
% 1.04/0.97 inference(superposition,[status(thm)],[f223,f160])).
% 1.04/0.97 thf(f223,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : (($false = (mrel @ '#u' @ mactual @ X1)) | ($false = (called @ (sK1 @ X1)))) ) | ~spl0_14),
% 1.04/0.97 inference(avatar_component_clause,[status(thm)],[f222])).
% 1.04/0.97 thf(f222,definition,(
% 1.04/0.97 spl0_14 <=> ! [X1 : mworld] : (($false = (mrel @ '#u' @ mactual @ X1)) | ($false = (called @ (sK1 @ X1))))),
% 1.04/0.97 introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition])).
% 1.04/0.97 thf(f506,plain,(
% 1.04/0.97 ~spl0_2 | ~spl0_18),
% 1.04/0.97 inference(avatar_contradiction_clause,[status(thm)],[f505])).
% 1.04/0.97 thf(f505,plain,(
% 1.04/0.97 $false | (~spl0_2 | ~spl0_18)),
% 1.04/0.97 inference(trivial_inequality_removal,[status(thm)],[f502])).
% 1.04/0.97 thf(f502,plain,(
% 1.04/0.97 ($true = $false) | (~spl0_2 | ~spl0_18)),
% 1.04/0.97 inference(superposition,[status(thm)],[f173,f290])).
% 1.04/0.97 thf(f290,plain,(
% 1.04/0.97 ($false = (called @ sK3)) | ~spl0_18),
% 1.04/0.97 inference(avatar_component_clause,[status(thm)],[f288])).
% 1.04/0.97 thf(f288,definition,(
% 1.04/0.97 spl0_18 <=> ($false = (called @ sK3))),
% 1.04/0.97 introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition])).
% 1.04/0.97 thf(f173,plain,(
% 1.04/0.97 ($true = (called @ sK3)) | ~spl0_2),
% 1.04/0.97 inference(avatar_component_clause,[status(thm)],[f171])).
% 1.04/0.97 thf(f171,definition,(
% 1.04/0.97 spl0_2 <=> ($true = (called @ sK3))),
% 1.04/0.97 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.04/0.97 thf(f492,plain,(
% 1.04/0.97 spl0_27 | spl0_28 | ~spl0_16 | ~spl0_17),
% 1.04/0.97 inference(avatar_split_clause,[status(thm)],[f453,f285,f229,f482,f478])).
% 1.04/0.97 thf(f229,definition,(
% 1.04/0.97 spl0_16 <=> ! [X1 : mworld] : (($true = (mrel @ '#c' @ X1 @ (sK1 @ X1))) | ($false = (mrel @ '#u' @ mactual @ X1)))),
% 1.04/0.97 introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition])).
% 1.04/0.97 thf(f285,definition,(
% 1.04/0.97 spl0_17 <=> ! [X0 : mworld] : (($true = (called @ X0)) | ($false = (mrel @ '#c' @ sK3 @ X0)))),
% 1.04/0.97 introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition])).
% 1.04/0.97 thf(f453,plain,(
% 1.04/0.97 ($true = (called @ (sK1 @ sK3))) | ((mrel @ '#u' @ mactual @ sK3) = $false) | (~spl0_16 | ~spl0_17)),
% 1.04/0.97 inference(trivial_inequality_removal,[status(thm)],[f443])).
% 1.04/0.97 thf(f443,plain,(
% 1.04/0.97 ((mrel @ '#u' @ mactual @ sK3) = $false) | ($true = $false) | ($true = (called @ (sK1 @ sK3))) | (~spl0_16 | ~spl0_17)),
% 1.04/0.97 inference(superposition,[status(thm)],[f230,f286])).
% 1.04/0.97 thf(f286,plain,(
% 1.04/0.97 ( ! [X0 : mworld] : (($false = (mrel @ '#c' @ sK3 @ X0)) | ($true = (called @ X0))) ) | ~spl0_17),
% 1.04/0.97 inference(avatar_component_clause,[status(thm)],[f285])).
% 1.04/0.97 thf(f230,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : (($true = (mrel @ '#c' @ X1 @ (sK1 @ X1))) | ($false = (mrel @ '#u' @ mactual @ X1))) ) | ~spl0_16),
% 1.04/0.97 inference(avatar_component_clause,[status(thm)],[f229])).
% 1.04/0.97 thf(f354,plain,(
% 1.04/0.97 ~spl0_20),
% 1.04/0.97 inference(avatar_contradiction_clause,[status(thm)],[f353])).
% 1.04/0.97 thf(f353,plain,(
% 1.04/0.97 $false | ~spl0_20),
% 1.04/0.97 inference(trivial_inequality_removal,[status(thm)],[f349])).
% 1.04/0.97 thf(f349,plain,(
% 1.04/0.97 ($true = $false) | ~spl0_20),
% 1.04/0.97 inference(superposition,[status(thm)],[f332,f65])).
% 1.04/0.97 thf(f65,plain,(
% 1.04/0.97 ( ! [X0 : mworld] : (((mrel @ '#c' @ X0 @ X0) = $true)) )),
% 1.04/0.97 inference(cnf_transformation,[status(thm)],[f46])).
% 1.04/0.97 thf(f46,plain,(
% 1.04/0.97 ! [X0 : mworld] : ((mrel @ '#c' @ X0 @ X0) = $true)),
% 1.04/0.97 inference(fool_elimination,[status(thm)],[f45])).
% 1.04/0.97 thf(f45,plain,(
% 1.04/0.97 ! [X0 : mworld] : (mrel @ '#c' @ X0 @ X0)),
% 1.04/0.97 inference(rectify,[status(thm)],[f9])).
% 1.04/0.97 thf(f9,axiom,(
% 1.04/0.97 ! [X2 : mworld] : (mrel @ '#c' @ X2 @ X2)),
% 1.04/0.97 file('/export/starexec/sandbox/tmp/tmp.StopnhNuQj/DTF2THF_15568.p','mrel_#c_reflexive')).
% 1.04/0.97 thf(f332,plain,(
% 1.04/0.97 ($false = (mrel @ '#c' @ mactual @ mactual)) | ~spl0_20),
% 1.04/0.97 inference(avatar_component_clause,[status(thm)],[f330])).
% 1.04/0.97 thf(f330,definition,(
% 1.04/0.97 spl0_20 <=> ($false = (mrel @ '#c' @ mactual @ mactual))),
% 1.04/0.97 introduced(definition,[new_symbols(naming,[spl0_20])],[avatar_definition])).
% 1.04/0.97 thf(f347,plain,(
% 1.04/0.97 ~spl0_3 | ~spl0_19),
% 1.04/0.97 inference(avatar_contradiction_clause,[status(thm)],[f346])).
% 1.04/0.97 thf(f346,plain,(
% 1.04/0.97 $false | (~spl0_3 | ~spl0_19)),
% 1.04/0.97 inference(trivial_inequality_removal,[status(thm)],[f343])).
% 1.04/0.97 thf(f343,plain,(
% 1.04/0.97 ($true = $false) | (~spl0_3 | ~spl0_19)),
% 1.04/0.97 inference(superposition,[status(thm)],[f178,f328])).
% 1.04/0.97 thf(f328,plain,(
% 1.04/0.97 ($true = (paid @ sK3)) | ~spl0_19),
% 1.04/0.97 inference(avatar_component_clause,[status(thm)],[f326])).
% 1.04/0.97 thf(f326,definition,(
% 1.04/0.97 spl0_19 <=> ($true = (paid @ sK3))),
% 1.04/0.97 introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition])).
% 1.04/0.97 thf(f178,plain,(
% 1.04/0.97 ($false = (paid @ sK3)) | ~spl0_3),
% 1.04/0.97 inference(avatar_component_clause,[status(thm)],[f176])).
% 1.04/0.97 thf(f176,definition,(
% 1.04/0.97 spl0_3 <=> ($false = (paid @ sK3))),
% 1.04/0.97 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.04/0.97 thf(f339,plain,(
% 1.04/0.97 spl0_19 | spl0_20 | spl0_12),
% 1.04/0.97 inference(avatar_split_clause,[status(thm)],[f322,f213,f330,f326])).
% 1.04/0.97 thf(f213,definition,(
% 1.04/0.97 spl0_12 <=> ((paid @ mactual) = $false)),
% 1.04/0.97 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.04/0.97 thf(f322,plain,(
% 1.04/0.97 ($true = (paid @ sK3)) | ((paid @ mactual) = $false) | ($false = (mrel @ '#c' @ mactual @ mactual))),
% 1.04/0.97 inference(trivial_inequality_removal,[status(thm)],[f317])).
% 1.04/0.97 thf(f317,plain,(
% 1.04/0.97 ($false = (mrel @ '#c' @ mactual @ mactual)) | ($true = (paid @ sK3)) | ($true = $false) | ((paid @ mactual) = $false)),
% 1.04/0.97 inference(superposition,[status(thm)],[f148,f160])).
% 1.04/0.97 thf(f148,plain,(
% 1.04/0.97 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ '#u' @ X1 @ X2) = $false) | ($true = (paid @ X2)) | ((mrel @ '#c' @ mactual @ X1) = $false) | ($false = (paid @ X1))) )),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f147])).
% 1.04/0.97 thf(f147,plain,(
% 1.04/0.97 ( ! [X2 : mworld,X1 : mworld] : (($false = (paid @ X1)) | ($true = ((mrel @ '#u' @ X1 @ X2) => (paid @ X2))) | ((mrel @ '#c' @ mactual @ X1) = $false)) )),
% 1.04/0.97 inference(beta_eta_normalization,[status(thm)],[f146])).
% 1.04/0.97 thf(f146,plain,(
% 1.04/0.97 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ '#c' @ mactual @ X1) = $false) | ($true = ((^[Y0 : mworld]: ((mrel @ '#u' @ X1 @ Y0) => (paid @ Y0))) @ X2)) | ($false = (paid @ X1))) )),
% 1.04/0.97 inference(pi_clausification,[status(thm)],[f145])).
% 1.04/0.97 thf(f145,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : (($false = (paid @ X1)) | ((mrel @ '#c' @ mactual @ X1) = $false) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#u' @ X1 @ Y0) => (paid @ Y0)))))) )),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f144])).
% 1.04/0.97 thf(f144,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : (((mrel @ '#c' @ mactual @ X1) = $false) | ($true = ((paid @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#u' @ X1 @ Y0) => (paid @ Y0))))))) )),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f143])).
% 1.04/0.97 thf(f143,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : (($true = ((mrel @ '#c' @ mactual @ X1) => ((paid @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#u' @ X1 @ Y0) => (paid @ Y0)))))))) )),
% 1.04/0.97 inference(beta_eta_normalization,[status(thm)],[f142])).
% 1.04/0.97 thf(f142,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ '#c' @ mactual @ Y0) => ((paid @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ '#u' @ Y0 @ Y1) => (paid @ Y1))))))) @ X1))) )),
% 1.04/0.97 inference(pi_clausification,[status(thm)],[f141])).
% 1.04/0.97 thf(f141,plain,(
% 1.04/0.97 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#c' @ mactual @ Y0) => ((paid @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ '#u' @ Y0 @ Y1) => (paid @ Y1)))))))))),
% 1.04/0.97 inference(beta_eta_normalization,[status(thm)],[f83])).
% 1.04/0.97 thf(f83,plain,(
% 1.04/0.97 ($true = ((^[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)))))),
% 1.04/0.97 inference(definition_unfolding,[status(thm)],[f66,f64,f81,f76,f81])).
% 1.04/0.97 thf(f66,plain,(
% 1.04/0.97 ((mlocal @ (mbox @ '#c' @ (mimplies @ paid @ (mbox @ '#u' @ paid)))) = $true)),
% 1.04/0.97 inference(cnf_transformation,[status(thm)],[f50])).
% 1.04/0.97 thf(f50,plain,(
% 1.04/0.97 ((mlocal @ (mbox @ '#c' @ (mimplies @ paid @ (mbox @ '#u' @ paid)))) = $true)),
% 1.04/0.97 inference(fool_elimination,[status(thm)],[f49])).
% 1.04/0.97 thf(f49,plain,(
% 1.04/0.97 (mlocal @ (mbox @ '#c' @ (mimplies @ paid @ (mbox @ '#u' @ paid))))),
% 1.04/0.97 inference(rectify,[status(thm)],[f16])).
% 1.04/0.97 thf(f16,axiom,(
% 1.04/0.97 (mlocal @ (mbox @ '#c' @ (mimplies @ paid @ (mbox @ '#u' @ paid))))),
% 1.04/0.97 file('/export/starexec/sandbox/tmp/tmp.StopnhNuQj/DTF2THF_15568.p',axiom_2)).
% 1.04/0.97 thf(f338,plain,(
% 1.04/0.97 spl0_13 | ~spl0_15),
% 1.04/0.97 inference(avatar_split_clause,[status(thm)],[f310,f225,f217])).
% 1.04/0.97 thf(f217,definition,(
% 1.04/0.97 spl0_13 <=> ($true = (called @ mactual))),
% 1.04/0.97 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 1.04/0.97 thf(f225,definition,(
% 1.04/0.97 spl0_15 <=> ! [X2 : mworld] : (((mrel @ '#c' @ mactual @ X2) = $false) | ($true = (called @ X2)))),
% 1.04/0.97 introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition])).
% 1.04/0.97 thf(f310,plain,(
% 1.04/0.97 ($true = (called @ mactual)) | ~spl0_15),
% 1.04/0.97 inference(trivial_inequality_removal,[status(thm)],[f309])).
% 1.04/0.97 thf(f309,plain,(
% 1.04/0.97 ($true = (called @ mactual)) | ($true = $false) | ~spl0_15),
% 1.04/0.97 inference(superposition,[status(thm)],[f65,f226])).
% 1.04/0.97 thf(f226,plain,(
% 1.04/0.97 ( ! [X2 : mworld] : (((mrel @ '#c' @ mactual @ X2) = $false) | ($true = (called @ X2))) ) | ~spl0_15),
% 1.04/0.97 inference(avatar_component_clause,[status(thm)],[f225])).
% 1.04/0.97 thf(f306,plain,(
% 1.04/0.97 ~spl0_1 | ~spl0_7),
% 1.04/0.97 inference(avatar_contradiction_clause,[status(thm)],[f305])).
% 1.04/0.97 thf(f305,plain,(
% 1.04/0.97 $false | (~spl0_1 | ~spl0_7)),
% 1.04/0.97 inference(trivial_inequality_removal,[status(thm)],[f301])).
% 1.04/0.97 thf(f301,plain,(
% 1.04/0.97 ($true = $false) | (~spl0_1 | ~spl0_7)),
% 1.04/0.97 inference(superposition,[status(thm)],[f169,f253])).
% 1.04/0.97 thf(f253,plain,(
% 1.04/0.97 ($true = (charge @ sK3)) | ~spl0_7),
% 1.04/0.97 inference(trivial_inequality_removal,[status(thm)],[f246])).
% 1.04/0.97 thf(f246,plain,(
% 1.04/0.97 ($true = (charge @ sK3)) | ($true = $false) | ~spl0_7),
% 1.04/0.97 inference(superposition,[status(thm)],[f195,f160])).
% 1.04/0.97 thf(f195,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : (($false = (mrel @ '#u' @ mactual @ X1)) | ($true = (charge @ X1))) ) | ~spl0_7),
% 1.04/0.97 inference(avatar_component_clause,[status(thm)],[f194])).
% 1.04/0.97 thf(f194,definition,(
% 1.04/0.97 spl0_7 <=> ! [X1 : mworld] : (($true = (charge @ X1)) | ($false = (mrel @ '#u' @ mactual @ X1)))),
% 1.04/0.97 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.04/0.97 thf(f169,plain,(
% 1.04/0.97 ($false = (charge @ sK3)) | ~spl0_1),
% 1.04/0.97 inference(avatar_component_clause,[status(thm)],[f167])).
% 1.04/0.97 thf(f167,definition,(
% 1.04/0.97 spl0_1 <=> ($false = (charge @ sK3))),
% 1.04/0.97 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.04/0.97 thf(f292,plain,(
% 1.04/0.97 spl0_18 | spl0_17),
% 1.04/0.97 inference(avatar_split_clause,[status(thm)],[f280,f285,f288])).
% 1.04/0.97 thf(f280,plain,(
% 1.04/0.97 ( ! [X0 : mworld] : (($true = (called @ X0)) | ($false = (called @ sK3)) | ($false = (mrel @ '#c' @ sK3 @ X0))) )),
% 1.04/0.97 inference(trivial_inequality_removal,[status(thm)],[f278])).
% 1.04/0.97 thf(f278,plain,(
% 1.04/0.97 ( ! [X0 : mworld] : (($false = (called @ sK3)) | ($true = $false) | ($true = (called @ X0)) | ($false = (mrel @ '#c' @ sK3 @ X0))) )),
% 1.04/0.97 inference(superposition,[status(thm)],[f160,f97])).
% 1.04/0.97 thf(f97,plain,(
% 1.04/0.97 ( ! [X2 : mworld,X1 : mworld] : (($false = (mrel @ '#u' @ mactual @ X1)) | ((mrel @ '#c' @ X1 @ X2) = $false) | ($false = (called @ X1)) | ($true = (called @ X2))) )),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f96])).
% 1.04/0.97 thf(f96,plain,(
% 1.04/0.97 ( ! [X2 : mworld,X1 : mworld] : ((((mrel @ '#c' @ X1 @ X2) => (called @ X2)) = $true) | ($false = (mrel @ '#u' @ mactual @ X1)) | ($false = (called @ X1))) )),
% 1.04/0.97 inference(beta_eta_normalization,[status(thm)],[f95])).
% 1.04/0.97 thf(f95,plain,(
% 1.04/0.97 ( ! [X2 : mworld,X1 : mworld] : (($false = (mrel @ '#u' @ mactual @ X1)) | ($false = (called @ X1)) | ($true = ((^[Y0 : mworld]: ((mrel @ '#c' @ X1 @ Y0) => (called @ Y0))) @ X2))) )),
% 1.04/0.97 inference(pi_clausification,[status(thm)],[f94])).
% 1.04/0.97 thf(f94,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : (($false = (called @ X1)) | ($false = (mrel @ '#u' @ mactual @ X1)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#c' @ X1 @ Y0) => (called @ Y0)))))) )),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f93])).
% 1.04/0.97 thf(f93,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : (($true = ((called @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#c' @ X1 @ Y0) => (called @ Y0)))))) | ($false = (mrel @ '#u' @ mactual @ X1))) )),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f92])).
% 1.04/0.97 thf(f92,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : (($true = ((mrel @ '#u' @ mactual @ X1) => ((called @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#c' @ X1 @ Y0) => (called @ Y0)))))))) )),
% 1.04/0.97 inference(beta_eta_normalization,[status(thm)],[f91])).
% 1.04/0.97 thf(f91,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ '#u' @ mactual @ Y0) => ((called @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ '#c' @ Y0 @ Y1) => (called @ Y1))))))) @ X1))) )),
% 1.04/0.97 inference(pi_clausification,[status(thm)],[f90])).
% 1.04/0.97 thf(f90,plain,(
% 1.04/0.97 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#u' @ mactual @ Y0) => ((called @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ '#c' @ Y0 @ Y1) => (called @ Y1)))))))) = $true)),
% 1.04/0.97 inference(beta_eta_normalization,[status(thm)],[f87])).
% 1.04/0.97 thf(f87,plain,(
% 1.04/0.97 ($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)))))),
% 1.04/0.97 inference(definition_unfolding,[status(thm)],[f75,f64,f81,f76,f81])).
% 1.04/0.97 thf(f75,plain,(
% 1.04/0.97 ((mlocal @ (mbox @ '#u' @ (mimplies @ called @ (mbox @ '#c' @ called)))) = $true)),
% 1.04/0.97 inference(cnf_transformation,[status(thm)],[f41])).
% 1.04/0.97 thf(f41,plain,(
% 1.04/0.97 ((mlocal @ (mbox @ '#u' @ (mimplies @ called @ (mbox @ '#c' @ called)))) = $true)),
% 1.04/0.97 inference(fool_elimination,[status(thm)],[f40])).
% 1.04/0.97 thf(f40,plain,(
% 1.04/0.97 (mlocal @ (mbox @ '#u' @ (mimplies @ called @ (mbox @ '#c' @ called))))),
% 1.04/0.97 inference(rectify,[status(thm)],[f15])).
% 1.04/0.97 thf(f15,axiom,(
% 1.04/0.97 (mlocal @ (mbox @ '#u' @ (mimplies @ called @ (mbox @ '#c' @ called))))),
% 1.04/0.97 file('/export/starexec/sandbox/tmp/tmp.StopnhNuQj/DTF2THF_15568.p',axiom_1)).
% 1.04/0.97 thf(f275,plain,(
% 1.04/0.97 ~spl0_5 | ~spl0_13),
% 1.04/0.97 inference(avatar_contradiction_clause,[status(thm)],[f274])).
% 1.04/0.97 thf(f274,plain,(
% 1.04/0.97 $false | (~spl0_5 | ~spl0_13)),
% 1.04/0.97 inference(trivial_inequality_removal,[status(thm)],[f270])).
% 1.04/0.97 thf(f270,plain,(
% 1.04/0.97 ($true = $false) | (~spl0_5 | ~spl0_13)),
% 1.04/0.97 inference(superposition,[status(thm)],[f219,f187])).
% 1.04/0.97 thf(f187,plain,(
% 1.04/0.97 ($false = (called @ mactual)) | ~spl0_5),
% 1.04/0.97 inference(avatar_component_clause,[status(thm)],[f185])).
% 1.04/0.97 thf(f185,definition,(
% 1.04/0.97 spl0_5 <=> ($false = (called @ mactual))),
% 1.04/0.97 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.04/0.97 thf(f219,plain,(
% 1.04/0.97 ($true = (called @ mactual)) | ~spl0_13),
% 1.04/0.97 inference(avatar_component_clause,[status(thm)],[f217])).
% 1.04/0.97 thf(f244,plain,(
% 1.04/0.97 ~spl0_4 | ~spl0_12),
% 1.04/0.97 inference(avatar_contradiction_clause,[status(thm)],[f243])).
% 1.04/0.97 thf(f243,plain,(
% 1.04/0.97 $false | (~spl0_4 | ~spl0_12)),
% 1.04/0.97 inference(trivial_inequality_removal,[status(thm)],[f239])).
% 1.04/0.97 thf(f239,plain,(
% 1.04/0.97 ($true = $false) | (~spl0_4 | ~spl0_12)),
% 1.04/0.97 inference(superposition,[status(thm)],[f183,f215])).
% 1.04/0.97 thf(f215,plain,(
% 1.04/0.97 ((paid @ mactual) = $false) | ~spl0_12),
% 1.04/0.97 inference(avatar_component_clause,[status(thm)],[f213])).
% 1.04/0.97 thf(f183,plain,(
% 1.04/0.97 ((paid @ mactual) = $true) | ~spl0_4),
% 1.04/0.97 inference(avatar_component_clause,[status(thm)],[f181])).
% 1.04/0.97 thf(f181,definition,(
% 1.04/0.97 spl0_4 <=> ((paid @ mactual) = $true)),
% 1.04/0.97 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.04/0.97 thf(f237,plain,(
% 1.04/0.97 ~spl0_6),
% 1.04/0.97 inference(avatar_contradiction_clause,[status(thm)],[f236])).
% 1.04/0.97 thf(f236,plain,(
% 1.04/0.97 $false | ~spl0_6),
% 1.04/0.97 inference(trivial_inequality_removal,[status(thm)],[f233])).
% 1.04/0.97 thf(f233,plain,(
% 1.04/0.97 ($true = $false) | ~spl0_6),
% 1.04/0.97 inference(superposition,[status(thm)],[f192,f154])).
% 1.04/0.97 thf(f154,plain,(
% 1.04/0.97 ($true = (charge @ mactual))),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f152])).
% 1.04/0.97 thf(f152,plain,(
% 1.04/0.97 (((charge @ mactual) => ((~ (paid @ mactual)) & (called @ mactual))) = $false)),
% 1.04/0.97 inference(not_proxy_clausification,[status(thm)],[f151])).
% 1.04/0.97 thf(f151,plain,(
% 1.04/0.97 ($true = (~ ((charge @ mactual) => ((~ (paid @ mactual)) & (called @ mactual)))))),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f149])).
% 1.04/0.97 thf(f192,plain,(
% 1.04/0.97 ($false = (charge @ mactual)) | ~spl0_6),
% 1.04/0.97 inference(avatar_component_clause,[status(thm)],[f190])).
% 1.04/0.97 thf(f190,definition,(
% 1.04/0.97 spl0_6 <=> ($false = (charge @ mactual))),
% 1.04/0.97 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.04/0.97 thf(f231,plain,(
% 1.04/0.97 spl0_16 | spl0_15),
% 1.04/0.97 inference(avatar_split_clause,[status(thm)],[f111,f225,f229])).
% 1.04/0.97 thf(f111,plain,(
% 1.04/0.97 ( ! [X2 : mworld,X1 : mworld] : (($true = (mrel @ '#c' @ X1 @ (sK1 @ X1))) | ($false = (mrel @ '#u' @ mactual @ X1)) | ((mrel @ '#c' @ mactual @ X2) = $false) | ($true = (called @ X2))) )),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f110])).
% 1.04/0.97 thf(f110,plain,(
% 1.04/0.97 ( ! [X2 : mworld,X1 : mworld] : (($false = (mrel @ '#u' @ mactual @ X1)) | ($true = (mrel @ '#c' @ X1 @ (sK1 @ X1))) | ($true = ((mrel @ '#c' @ mactual @ X2) => (called @ X2)))) )),
% 1.04/0.97 inference(beta_eta_normalization,[status(thm)],[f109])).
% 1.04/0.97 thf(f109,plain,(
% 1.04/0.97 ( ! [X2 : mworld,X1 : mworld] : (($true = (mrel @ '#c' @ X1 @ (sK1 @ X1))) | ($true = ((^[Y0 : mworld]: ((mrel @ '#c' @ mactual @ Y0) => (called @ Y0))) @ X2)) | ($false = (mrel @ '#u' @ mactual @ X1))) )),
% 1.04/0.97 inference(pi_clausification,[status(thm)],[f108])).
% 1.04/0.97 thf(f108,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#c' @ mactual @ Y0) => (called @ Y0))))) | ($true = (mrel @ '#c' @ X1 @ (sK1 @ X1))) | ($false = (mrel @ '#u' @ mactual @ X1))) )),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f106])).
% 1.04/0.97 thf(f106,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : ((((mrel @ '#c' @ X1 @ (sK1 @ X1)) => (called @ (sK1 @ X1))) = $false) | ($false = (mrel @ '#u' @ mactual @ X1)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#c' @ mactual @ Y0) => (called @ Y0)))))) )),
% 1.04/0.97 inference(beta_eta_normalization,[status(thm)],[f105])).
% 1.04/0.97 thf(f105,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : (($false = (mrel @ '#u' @ mactual @ X1)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#c' @ mactual @ Y0) => (called @ Y0))))) | ($false = ((^[Y0 : mworld]: ((mrel @ '#c' @ X1 @ Y0) => (called @ Y0))) @ (sK1 @ X1)))) )),
% 1.04/0.97 inference(sigma_clausification,[status(thm)],[f104])).
% 1.04/0.97 thf(f104,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : (($false = (mrel @ '#u' @ mactual @ X1)) | ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#c' @ X1 @ Y0) => (called @ Y0))))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#c' @ mactual @ Y0) => (called @ Y0)))))) )),
% 1.04/0.97 inference(not_proxy_clausification,[status(thm)],[f103])).
% 1.04/0.97 thf(f103,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : (($true = (~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#c' @ X1 @ Y0) => (called @ Y0)))))) | ($false = (mrel @ '#u' @ mactual @ X1)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#c' @ mactual @ Y0) => (called @ Y0)))))) )),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f102])).
% 1.04/0.97 thf(f102,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : (($true = ((mrel @ '#u' @ mactual @ X1) => (~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#c' @ X1 @ Y0) => (called @ Y0))))))) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#c' @ mactual @ Y0) => (called @ Y0)))))) )),
% 1.04/0.97 inference(not_proxy_clausification,[status(thm)],[f101])).
% 1.04/0.97 thf(f101,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : (($false = (~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#c' @ mactual @ Y0) => (called @ Y0)))))) | ($true = ((mrel @ '#u' @ mactual @ X1) => (~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#c' @ X1 @ Y0) => (called @ Y0)))))))) )),
% 1.04/0.97 inference(beta_eta_normalization,[status(thm)],[f100])).
% 1.04/0.97 thf(f100,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ '#u' @ mactual @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ '#c' @ Y0 @ Y1) => (called @ Y1))))))) @ X1)) | ($false = (~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#c' @ mactual @ Y0) => (called @ Y0))))))) )),
% 1.04/0.97 inference(pi_clausification,[status(thm)],[f99])).
% 1.04/0.97 thf(f99,plain,(
% 1.04/0.97 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#u' @ mactual @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ '#c' @ Y0 @ Y1) => (called @ Y1))))))))) | ($false = (~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#c' @ mactual @ Y0) => (called @ Y0))))))),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f98])).
% 1.04/0.97 thf(f98,plain,(
% 1.04/0.97 ($true = ((~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#c' @ mactual @ Y0) => (called @ Y0))))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#u' @ mactual @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ '#c' @ Y0 @ Y1) => (called @ Y1))))))))))),
% 1.04/0.97 inference(beta_eta_normalization,[status(thm)],[f86])).
% 1.04/0.97 thf(f86,plain,(
% 1.04/0.97 ($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))))))),
% 1.04/0.97 inference(definition_unfolding,[status(thm)],[f72,f64,f76,f68,f81,f81,f68,f81])).
% 1.04/0.97 thf(f72,plain,(
% 1.04/0.97 ((mlocal @ (mimplies @ (mnot @ (mbox @ '#c' @ called)) @ (mbox @ '#u' @ (mnot @ (mbox @ '#c' @ called))))) = $true)),
% 1.04/0.97 inference(cnf_transformation,[status(thm)],[f33])).
% 1.04/0.97 thf(f33,plain,(
% 1.04/0.97 ((mlocal @ (mimplies @ (mnot @ (mbox @ '#c' @ called)) @ (mbox @ '#u' @ (mnot @ (mbox @ '#c' @ called))))) = $true)),
% 1.04/0.97 inference(fool_elimination,[status(thm)],[f32])).
% 1.04/0.97 thf(f32,plain,(
% 1.04/0.97 (mlocal @ (mimplies @ (mnot @ (mbox @ '#c' @ called)) @ (mbox @ '#u' @ (mnot @ (mbox @ '#c' @ called)))))),
% 1.04/0.97 inference(rectify,[status(thm)],[f17])).
% 1.04/0.97 thf(f17,axiom,(
% 1.04/0.97 (mlocal @ (mimplies @ (mnot @ (mbox @ '#c' @ called)) @ (mbox @ '#u' @ (mnot @ (mbox @ '#c' @ called)))))),
% 1.04/0.97 file('/export/starexec/sandbox/tmp/tmp.StopnhNuQj/DTF2THF_15568.p',axiom_3)).
% 1.04/0.97 thf(f227,plain,(
% 1.04/0.97 spl0_14 | spl0_15),
% 1.04/0.97 inference(avatar_split_clause,[status(thm)],[f114,f225,f222])).
% 1.04/0.97 thf(f114,plain,(
% 1.04/0.97 ( ! [X2 : mworld,X1 : mworld] : (($false = (mrel @ '#u' @ mactual @ X1)) | ($false = (called @ (sK1 @ X1))) | ((mrel @ '#c' @ mactual @ X2) = $false) | ($true = (called @ X2))) )),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 1.04/0.97 thf(f113,plain,(
% 1.04/0.97 ( ! [X2 : mworld,X1 : mworld] : (($false = (mrel @ '#u' @ mactual @ X1)) | ($true = ((mrel @ '#c' @ mactual @ X2) => (called @ X2))) | ($false = (called @ (sK1 @ X1)))) )),
% 1.04/0.97 inference(beta_eta_normalization,[status(thm)],[f112])).
% 1.04/0.97 thf(f112,plain,(
% 1.04/0.97 ( ! [X2 : mworld,X1 : mworld] : (($false = (mrel @ '#u' @ mactual @ X1)) | ($false = (called @ (sK1 @ X1))) | ($true = ((^[Y0 : mworld]: ((mrel @ '#c' @ mactual @ Y0) => (called @ Y0))) @ X2))) )),
% 1.04/0.97 inference(pi_clausification,[status(thm)],[f107])).
% 1.04/0.97 thf(f107,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : (($false = (called @ (sK1 @ X1))) | ($false = (mrel @ '#u' @ mactual @ X1)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#c' @ mactual @ Y0) => (called @ Y0)))))) )),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f106])).
% 1.04/0.97 thf(f196,plain,(
% 1.04/0.97 spl0_6 | spl0_7),
% 1.04/0.97 inference(avatar_split_clause,[status(thm)],[f140,f194,f190])).
% 1.04/0.97 thf(f140,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : (($true = (charge @ X1)) | ($false = (mrel @ '#u' @ mactual @ X1)) | ($false = (charge @ mactual))) )),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f139])).
% 1.04/0.97 thf(f139,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : (($true = ((mrel @ '#u' @ mactual @ X1) => (charge @ X1))) | ($false = (charge @ mactual))) )),
% 1.04/0.97 inference(beta_eta_normalization,[status(thm)],[f138])).
% 1.04/0.97 thf(f138,plain,(
% 1.04/0.97 ( ! [X1 : mworld] : (($false = (charge @ mactual)) | ($true = ((^[Y0 : mworld]: ((mrel @ '#u' @ mactual @ Y0) => (charge @ Y0))) @ X1))) )),
% 1.04/0.97 inference(pi_clausification,[status(thm)],[f133])).
% 1.04/0.97 thf(f133,plain,(
% 1.04/0.97 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#u' @ mactual @ Y0) => (charge @ Y0))))) | ($false = (charge @ mactual))),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f132])).
% 1.04/0.97 thf(f132,plain,(
% 1.04/0.97 ($false = (charge @ mactual)) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#c' @ mactual @ Y0) => (charge @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#u' @ mactual @ Y0) => (charge @ Y0))))))),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f131])).
% 1.04/0.97 thf(f131,plain,(
% 1.04/0.97 ($true = ((charge @ mactual) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#c' @ mactual @ Y0) => (charge @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ '#u' @ mactual @ Y0) => (charge @ Y0)))))))),
% 1.04/0.97 inference(beta_eta_normalization,[status(thm)],[f85])).
% 1.04/0.97 thf(f85,plain,(
% 1.04/0.97 (((^[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)))) = $true)),
% 1.04/0.97 inference(definition_unfolding,[status(thm)],[f71,f64,f76,f80,f81,f81])).
% 1.04/0.97 thf(f71,plain,(
% 1.04/0.97 ((mlocal @ (mimplies @ charge @ (mand @ (mbox @ '#u' @ charge) @ (mbox @ '#c' @ charge)))) = $true)),
% 1.04/0.97 inference(cnf_transformation,[status(thm)],[f54])).
% 1.04/0.97 thf(f54,plain,(
% 1.04/0.97 ((mlocal @ (mimplies @ charge @ (mand @ (mbox @ '#u' @ charge) @ (mbox @ '#c' @ charge)))) = $true)),
% 1.04/0.97 inference(fool_elimination,[status(thm)],[f53])).
% 1.04/0.97 thf(f53,plain,(
% 1.04/0.97 (mlocal @ (mimplies @ charge @ (mand @ (mbox @ '#u' @ charge) @ (mbox @ '#c' @ charge))))),
% 1.04/0.97 inference(rectify,[status(thm)],[f14])).
% 1.04/0.97 thf(f14,axiom,(
% 1.04/0.97 (mlocal @ (mimplies @ charge @ (mand @ (mbox @ '#u' @ charge) @ (mbox @ '#c' @ charge))))),
% 1.04/0.97 file('/export/starexec/sandbox/tmp/tmp.StopnhNuQj/DTF2THF_15568.p',axiom_charge_u)).
% 1.04/0.97 thf(f188,plain,(
% 1.04/0.97 spl0_4 | spl0_5),
% 1.04/0.97 inference(avatar_split_clause,[status(thm)],[f156,f185,f181])).
% 1.04/0.97 thf(f156,plain,(
% 1.04/0.97 ((paid @ mactual) = $true) | ($false = (called @ mactual))),
% 1.04/0.97 inference(not_proxy_clausification,[status(thm)],[f155])).
% 1.04/0.97 thf(f155,plain,(
% 1.04/0.97 ((~ (paid @ mactual)) = $false) | ($false = (called @ mactual))),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f153])).
% 1.04/0.97 thf(f153,plain,(
% 1.04/0.97 (((~ (paid @ mactual)) & (called @ mactual)) = $false)),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f152])).
% 1.04/0.97 thf(f179,plain,(
% 1.04/0.97 spl0_1 | spl0_3),
% 1.04/0.97 inference(avatar_split_clause,[status(thm)],[f165,f176,f167])).
% 1.04/0.97 thf(f165,plain,(
% 1.04/0.97 ($false = (paid @ sK3)) | ($false = (charge @ sK3))),
% 1.04/0.97 inference(not_proxy_clausification,[status(thm)],[f164])).
% 1.04/0.97 thf(f164,plain,(
% 1.04/0.97 ($true = (~ (paid @ sK3))) | ($false = (charge @ sK3))),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f162])).
% 1.04/0.97 thf(f162,plain,(
% 1.04/0.97 ($false = (charge @ sK3)) | ($true = ((~ (paid @ sK3)) & (called @ sK3)))),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f161])).
% 1.04/0.97 thf(f161,plain,(
% 1.04/0.97 ($true = ((charge @ sK3) => ((~ (paid @ sK3)) & (called @ sK3))))),
% 1.04/0.97 inference(not_proxy_clausification,[status(thm)],[f159])).
% 1.04/0.97 thf(f159,plain,(
% 1.04/0.97 ($false = (~ ((charge @ sK3) => ((~ (paid @ sK3)) & (called @ sK3)))))),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f158])).
% 1.04/0.97 thf(f174,plain,(
% 1.04/0.97 spl0_1 | spl0_2),
% 1.04/0.97 inference(avatar_split_clause,[status(thm)],[f163,f171,f167])).
% 1.04/0.97 thf(f163,plain,(
% 1.04/0.97 ($true = (called @ sK3)) | ($false = (charge @ sK3))),
% 1.04/0.97 inference(binary_proxy_clausification,[status(thm)],[f162])).
% 1.04/0.97 % SZS output end Proof for DTF2THF_15568
% 1.04/0.97 % (15829)------------------------------
% 1.04/0.97 % (15829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.04/0.97 % (15829)Termination reason: Refutation
% 1.04/0.97
% 1.04/0.97 % (15829)Memory used [KB]: 6012
% 1.04/0.97 % (15829)Time elapsed: 0.021 s
% 1.04/0.97 % (15829)Instructions burned: 51 (million)
% 1.04/0.97 % (15829)------------------------------
% 1.04/0.97 % (15829)------------------------------
% 1.04/0.97 % (15828)Success in time 0.026 s
%------------------------------------------------------------------------------