%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO894^8 : 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 : n006.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 09:55:08 AM UTC 2026
% Result : Theorem 1.71s 1.35s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 93 ( 31 unt; 0 typ; 7 def)
% Number of atoms : 524 ( 120 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 610 ( 89 ~; 85 |; 20 &; 353 @)
% ( 9 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 21 usr; 15 con; 0-3 aty)
% ( 13 !!; 14 ??; 0 @@+; 0 @@-)
% Number of variables : 115 ( 98 ^; 15 !; 2 ?; 115 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(func_def_0,type,
mworld: $tType ).
thf(func_def_1,type,
mrel: mworld > mworld > $o ).
thf(func_def_2,type,
mactual: mworld ).
thf(func_def_3,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_5,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
p: mworld > $o ).
thf(func_def_27,type,
sK1: mworld ).
thf(func_def_28,type,
sK2: mworld ).
thf(func_def_29,type,
sK3: mworld ).
thf(f140,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f75,f84,f89,f98,f103,f117,f127,f139]) ).
thf(f139,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f138]) ).
thf(f138,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f135]) ).
thf(f135,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f93,f133]) ).
thf(f133,plain,
( ( $false
= ( p @ sK2 ) )
| ~ spl0_1
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f131]) ).
thf(f131,plain,
( ( $false = $true )
| ( $false
= ( p @ sK2 ) )
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f74,f102]) ).
thf(f102,plain,
( ( $true
= ( mrel @ mactual @ sK2 ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f100]) ).
thf(f100,definition,
( spl0_7
<=> ( $true
= ( mrel @ mactual @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f74,plain,
( ! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( p @ X1 ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f73]) ).
thf(f73,definition,
( spl0_1
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( p @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f93,plain,
( ( $true
= ( p @ sK2 ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f91]) ).
thf(f91,definition,
( spl0_5
<=> ( $true
= ( p @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f127,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f126]) ).
thf(f126,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f123]) ).
thf(f123,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f97,f121]) ).
thf(f121,plain,
( ( $false
= ( p @ sK1 ) )
| ~ spl0_1
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f119]) ).
thf(f119,plain,
( ( $false = $true )
| ( $false
= ( p @ sK1 ) )
| ~ spl0_1
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f74,f79]) ).
thf(f79,plain,
( ( $true
= ( mrel @ mactual @ sK1 ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f77]) ).
thf(f77,definition,
( spl0_2
<=> ( $true
= ( mrel @ mactual @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f97,plain,
( ( $true
= ( p @ sK1 ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f95]) ).
thf(f95,definition,
( spl0_6
<=> ( $true
= ( p @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f117,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f116]) ).
thf(f116,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f113]) ).
thf(f113,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f83,f109]) ).
thf(f109,plain,
( ( $false
= ( p @ sK3 ) )
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f105]) ).
thf(f105,plain,
( ( $false
= ( p @ sK3 ) )
| ( $false = $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f74,f88]) ).
thf(f88,plain,
( ( $true
= ( mrel @ mactual @ sK3 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f86]) ).
thf(f86,definition,
( spl0_4
<=> ( $true
= ( mrel @ mactual @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f83,plain,
( ( $true
= ( p @ sK3 ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f81]) ).
thf(f81,definition,
( spl0_3
<=> ( $true
= ( p @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f103,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f57,f95,f100]) ).
thf(f57,plain,
( ( $true
= ( p @ sK1 ) )
| ( $true
= ( mrel @ mactual @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( $true
= ( p @ sK1 ) )
| ( $false
= ( ( mrel @ mactual @ sK2 )
=> ~ ( p @ sK2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( p @ Y0 ) )
@ sK2 ) )
| ( $true
= ( p @ sK1 ) ) ),
inference(sigma_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ( $true
= ( p @ sK1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( p @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( ( $true
= ( ( p @ sK1 )
& ( mrel @ mactual @ sK1 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( p @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( p @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) )
@ sK1 ) ) ),
inference(sigma_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) ) )
= $true )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $false
= ( ~ ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( p @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ~ ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) )
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( p @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( $true
!= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( p @ Y0 ) ) )
= ( ~ ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f44]) ).
thf(f44,plain,
( $true
!= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
=> ~ ( p @ Y0 ) ) ) )
= ( ~ ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ p
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ p ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ p ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f39,f35,f38,f37,f33,f36,f36,f40]) ).
thf(f40,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( mrel @ X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
( mdia
= ( ^ [X0: mworld > $o,X2: mworld] :
? [X4: mworld] :
( ( mrel @ X2 @ X4 )
& ( X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1yFxI6HofA/DTF2THF_5598.p',mdia_def) ).
thf(f36,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,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.1yFxI6HofA/DTF2THF_5598.p',mnot_def) ).
thf(f33,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f28]) ).
thf(f28,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.1yFxI6HofA/DTF2THF_5598.p',mimplies_def) ).
thf(f37,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f30]) ).
thf(f30,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X2: mworld] :
! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1yFxI6HofA/DTF2THF_5598.p',mbox_def) ).
thf(f38,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f26]) ).
thf(f26,plain,
( mequiv
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( mequiv
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
<=> ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1yFxI6HofA/DTF2THF_5598.p',mequiv_def) ).
thf(f35,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox/tmp/tmp.1yFxI6HofA/DTF2THF_5598.p',mlocal_def) ).
thf(f39,plain,
( ( mlocal @ ( mequiv @ ( mbox @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia @ p ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( ( mlocal @ ( mequiv @ ( mbox @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia @ p ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ( mlocal @ ( mequiv @ ( mbox @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia @ p ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( mlocal @ ( mequiv @ ( mbox @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia @ p ) ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,negated_conjecture,
~ ( mlocal @ ( mequiv @ ( mbox @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia @ p ) ) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
thf(f10,conjecture,
mlocal @ ( mequiv @ ( mbox @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia @ p ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1yFxI6HofA/DTF2THF_5598.p',con) ).
thf(f98,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f58,f95,f91]) ).
thf(f58,plain,
( ( $true
= ( p @ sK1 ) )
| ( $true
= ( p @ sK2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $false
= ( ~ ( p @ sK2 ) ) )
| ( $true
= ( p @ sK1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f89,plain,
( spl0_2
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f62,f86,f77]) ).
thf(f62,plain,
( ( $true
= ( mrel @ mactual @ sK1 ) )
| ( $true
= ( mrel @ mactual @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ( $true
= ( mrel @ mactual @ sK1 ) )
| ( $false
= ( ( mrel @ mactual @ sK3 )
=> ~ ( p @ sK3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
( ( $true
= ( mrel @ mactual @ sK1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( p @ Y0 ) )
@ sK3 ) ) ),
inference(sigma_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( $true
= ( mrel @ mactual @ sK1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( p @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f84,plain,
( spl0_2
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f63,f81,f77]) ).
thf(f63,plain,
( ( $true
= ( p @ sK3 ) )
| ( $true
= ( mrel @ mactual @ sK1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
( ( $false
= ( ~ ( p @ sK3 ) ) )
| ( $true
= ( mrel @ mactual @ sK1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f75,plain,
( spl0_1
| spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f71,f73,f73]) ).
thf(f71,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( p @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( p @ X1 ) )
| ( $false
= ( ( p @ X2 )
& ( mrel @ mactual @ X2 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) )
@ X2 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) )
| ( $false
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ~ ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) ) )
| ( $false
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
! [X1: mworld] :
( ( $true
= ( ~ ( p @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ~ ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ mactual @ X1 )
=> ~ ( p @ X1 ) ) )
| ( $true
= ( ~ ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f64]) ).
thf(f64,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( p @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ~ ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO894^8 : TPTP v9.2.1. Released v8.1.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n006.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 14:53:15 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.26/0.46 ---- Original DTF file ---
% 0.26/0.46 thf(spec,logic,$$dhol).
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 % File : SYO894^8 : TPTP v9.2.1. Released v8.1.0.
% 0.26/0.46 % Domain : Syntactic
% 0.26/0.46 % Problem : Modal propositional logic theorems. problem 5
% 0.26/0.46 % Version : [BP13] axioms.
% 0.26/0.46 % English :
% 0.26/0.46
% 0.26/0.46 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.26/0.46 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.26/0.46 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.26/0.46 % Source : [TPTP]
% 0.26/0.46 % Names : SYM105+1 [QMLTP]
% 0.26/0.46
% 0.26/0.46 % Status : Theorem
% 0.26/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0
% 0.26/0.46 % Syntax : Number of formulae : 22 ( 9 unt; 12 typ; 8 def)
% 0.26/0.46 % Number of atoms : 29 ( 8 equ; 0 cnn)
% 0.26/0.46 % Maximal formula atoms : 10 ( 2 avg)
% 0.26/0.46 % Number of connectives : 34 ( 1 ~; 1 |; 2 &; 27 @)
% 0.26/0.46 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.26/0.46 % Maximal formula depth : 7 ( 2 avg)
% 0.26/0.46 % Number of types : 2 ( 1 usr)
% 0.26/0.46 % Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% 0.26/0.46 % Number of symbols : 12 ( 11 usr; 1 con; 0-3 aty)
% 0.26/0.46 % Number of variables : 22 ( 19 ^; 2 !; 1 ?; 22 :)
% 0.26/0.46 % SPC : TH0_THM_EQU_NAR
% 0.26/0.46
% 0.26/0.46 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.26/0.46 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.26/0.46 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.26/0.46 % $modal == [$constants == $rigid,$quantification == $varying,
% 0.26/0.46 % $modalities == $modal_system_T].
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 thf(mworld,type,
% 0.26/0.46 mworld: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(mrel_type,type,
% 0.26/0.46 mrel: mworld > mworld > $o ).
% 0.26/0.46
% 0.26/0.46 thf(mactual_type,type,
% 0.26/0.46 mactual: mworld ).
% 0.26/0.46
% 0.26/0.46 thf(mlocal_type,type,
% 0.26/0.46 mlocal: ( mworld > $o ) > $o ).
% 0.26/0.46
% 0.26/0.46 thf(mlocal_def,definition,
% 0.26/0.46 ( mlocal
% 0.26/0.46 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(mnot_type,type,
% 0.26/0.46 mnot: ( mworld > $o ) > mworld > $o ).
% 0.26/0.46
% 0.26/0.46 thf(mand_type,type,
% 0.26/0.46 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.26/0.46
% 0.26/0.46 thf(mor_type,type,
% 0.26/0.46 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.26/0.46
% 0.26/0.46 thf(mimplies_type,type,
% 0.26/0.46 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.26/0.46
% 0.26/0.46 thf(mequiv_type,type,
% 0.26/0.46 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.26/0.46
% 0.26/0.46 thf(mnot_def,definition,
% 0.26/0.46 ( mnot
% 0.26/0.46 = ( ^ [A: mworld > $o,W: mworld] :
% 0.26/0.46 ~ ( A @ W ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(mand_def,definition,
% 0.26/0.46 ( mand
% 0.26/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.26/0.46 ( ( A @ W )
% 0.26/0.46 & ( B @ W ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(mor_def,definition,
% 0.26/0.46 ( mor
% 0.26/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.26/0.46 ( ( A @ W )
% 0.26/0.46 | ( B @ W ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(mimplies_def,definition,
% 0.26/0.46 ( mimplies
% 0.26/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.26/0.46 ( ( A @ W )
% 0.26/0.46 => ( B @ W ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(mequiv_def,definition,
% 0.26/0.46 ( mequiv
% 0.26/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.26/0.46 ( ( A @ W )
% 0.26/0.46 <=> ( B @ W ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(mbox_type,type,
% 0.26/0.46 mbox: ( mworld > $o ) > mworld > $o ).
% 0.26/0.46
% 0.26/0.46 thf(mbox_def,definition,
% 0.26/0.46 ( mbox
% 0.26/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.26/0.46 ! [V: mworld] :
% 0.26/0.46 ( ( mrel @ W @ V )
% 0.26/0.46 => ( Phi @ V ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(mdia_type,type,
% 0.26/0.46 mdia: ( mworld > $o ) > mworld > $o ).
% 0.26/0.46
% 0.26/0.46 thf(mdia_def,definition,
% 0.26/0.46 ( mdia
% 0.26/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.26/0.46 ? [V: mworld] :
% 0.26/0.46 ( ( mrel @ W @ V )
% 0.26/0.46 & ( Phi @ V ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(mrel_reflexive,axiom,
% 0.26/0.46 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.26/0.46
% 0.26/0.46 thf(p_decl,type,
% 0.26/0.46 p: mworld > $o ).
% 0.26/0.46
% 0.26/0.46 thf(con,conjecture,
% 0.26/0.46 mlocal @ ( mequiv @ ( mbox @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia @ p ) ) ) ).
% 0.26/0.46
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 ------------------------
% 1.71/1.31 ---- Embedded in THF ---
% 1.71/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.71/1.31 %%% Generated on Tue Feb 24 14:53:16 EST 2026
% 1.71/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.71/1.31 %%% Logic specification used:
% 1.71/1.31 %%% thf(spec, logic, $$dhol).
% 1.71/1.31
% 1.71/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.1yFxI6HofA/DTF2DTF5598.p
% See solution above
% 1.71/1.31 ------------------------
% 1.71/1.32 ---- Cleaned THF ---
% 1.71/1.32 thf(mworld,type,
% 1.71/1.32 mworld: $tType ).
% 1.71/1.32
% 1.71/1.32 thf(mrel_type,type,
% 1.71/1.32 mrel: mworld > mworld > $o ).
% 1.71/1.32
% 1.71/1.32 thf(mactual_type,type,
% 1.71/1.32 mactual: mworld ).
% 1.71/1.32
% 1.71/1.32 thf(mlocal_type,type,
% 1.71/1.32 mlocal: ( mworld > $o ) > $o ).
% 1.71/1.32
% 1.71/1.32 thf(mlocal_def,definition,
% 1.71/1.32 ( mlocal
% 1.71/1.32 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.71/1.32
% 1.71/1.32 thf(mnot_type,type,
% 1.71/1.32 mnot: ( mworld > $o ) > mworld > $o ).
% 1.71/1.32
% 1.71/1.32 thf(mand_type,type,
% 1.71/1.32 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.71/1.32
% 1.71/1.32 thf(mor_type,type,
% 1.71/1.32 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.71/1.32
% 1.71/1.32 thf(mimplies_type,type,
% 1.71/1.32 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.71/1.32
% 1.71/1.32 thf(mequiv_type,type,
% 1.71/1.32 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.71/1.32
% 1.71/1.32 thf(mnot_def,definition,
% 1.71/1.32 ( mnot
% 1.71/1.32 = ( ^ [A: mworld > $o,W: mworld] :
% 1.71/1.32 ~ ( A @ W ) ) ) ).
% 1.71/1.32
% 1.71/1.32 thf(mand_def,definition,
% 1.71/1.32 ( mand
% 1.71/1.32 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.71/1.32 ( ( A @ W )
% 1.71/1.32 & ( B @ W ) ) ) ) ).
% 1.71/1.32
% 1.71/1.32 thf(mor_def,definition,
% 1.71/1.32 ( mor
% 1.71/1.32 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.71/1.32 ( ( A @ W )
% 1.71/1.32 | ( B @ W ) ) ) ) ).
% 1.71/1.32
% 1.71/1.32 thf(mimplies_def,definition,
% 1.71/1.32 ( mimplies
% 1.71/1.32 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.71/1.32 ( ( A @ W )
% 1.71/1.32 => ( B @ W ) ) ) ) ).
% 1.71/1.32
% 1.71/1.32 thf(mequiv_def,definition,
% 1.71/1.32 ( mequiv
% 1.71/1.32 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.71/1.32 ( ( A @ W )
% 1.71/1.32 <=> ( B @ W ) ) ) ) ).
% 1.71/1.32
% 1.71/1.32 thf(mbox_type,type,
% 1.71/1.32 mbox: ( mworld > $o ) > mworld > $o ).
% 1.71/1.32
% 1.71/1.32 thf(mbox_def,definition,
% 1.71/1.32 ( mbox
% 1.71/1.32 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.71/1.32 ! [V: mworld] :
% 1.71/1.32 ( ( mrel @ W @ V )
% 1.71/1.32 => ( Phi @ V ) ) ) ) ).
% 1.71/1.32
% 1.71/1.32 thf(mdia_type,type,
% 1.71/1.32 mdia: ( mworld > $o ) > mworld > $o ).
% 1.71/1.32
% 1.71/1.32 thf(mdia_def,definition,
% 1.71/1.32 ( mdia
% 1.71/1.32 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.71/1.32 ? [V: mworld] :
% 1.71/1.32 ( ( mrel @ W @ V )
% 1.71/1.32 & ( Phi @ V ) ) ) ) ).
% 1.71/1.32
% 1.71/1.32 thf(mrel_reflexive,axiom,
% 1.71/1.32 ! [W: mworld] : ( mrel @ W @ W ) ).
% 1.71/1.32
% 1.71/1.32 thf(p_decl,type,
% 1.71/1.32 p: mworld > $o ).
% 1.71/1.32
% 1.71/1.32 thf(con,conjecture,
% 1.71/1.32 mlocal @ ( mequiv @ ( mbox @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia @ p ) ) ) ).
% 1.71/1.32 ------------------------
% 1.71/1.35 % (5800)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5598 for (2999ds/183Mi)
% 1.71/1.35 % (5804)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_5598 for (2999ds/2Mi)
% 1.71/1.35 % (5804)Instruction limit reached!
% 1.71/1.35 % (5804)------------------------------
% 1.71/1.35 % (5804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.35 % (5804)Termination reason: Unknown
% 1.71/1.35 % (5804)Termination phase: Saturation
% 1.71/1.35
% 1.71/1.35 % (5804)Memory used [KB]: 5500
% 1.71/1.35 % (5804)Time elapsed: 0.003 s
% 1.71/1.35 % (5804)Instructions burned: 3 (million)
% 1.71/1.35 % (5804)------------------------------
% 1.71/1.35 % (5804)------------------------------
% 1.71/1.35 % (5806)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5598 for (2999ds/18Mi)
% 1.71/1.35 % (5800)First to succeed.
% 1.71/1.35 % (5800)Refutation found. Thanks to Tanya!
% 1.71/1.35 % SZS status Theorem for DTF2THF_5598
% 1.71/1.35 % SZS output start Proof for DTF2THF_5598
% 1.71/1.35 thf(type_def_5, type, mworld: $tType).
% 1.71/1.35 thf(func_def_0, type, mworld: $tType).
% 1.71/1.35 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.71/1.35 thf(func_def_2, type, mactual: mworld).
% 1.71/1.35 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.71/1.35 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.71/1.35 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.71/1.35 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.71/1.35 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.71/1.35 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.71/1.35 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.71/1.35 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.71/1.35 thf(func_def_12, type, p: mworld > $o).
% 1.71/1.35 thf(func_def_27, type, sK1: mworld).
% 1.71/1.35 thf(func_def_28, type, sK2: mworld).
% 1.71/1.35 thf(func_def_29, type, sK3: mworld).
% 1.71/1.35 thf(f140,plain,(
% 1.71/1.35 $false),
% 1.71/1.35 inference(avatar_sat_refutation,[status(thm)],[f75,f84,f89,f98,f103,f117,f127,f139])).
% 1.71/1.35 thf(f139,plain,(
% 1.71/1.35 ~spl0_1 | ~spl0_5 | ~spl0_7),
% 1.71/1.35 inference(avatar_contradiction_clause,[status(thm)],[f138])).
% 1.71/1.35 thf(f138,plain,(
% 1.71/1.35 $false | (~spl0_1 | ~spl0_5 | ~spl0_7)),
% 1.71/1.35 inference(trivial_inequality_removal,[status(thm)],[f135])).
% 1.71/1.35 thf(f135,plain,(
% 1.71/1.35 ($false = $true) | (~spl0_1 | ~spl0_5 | ~spl0_7)),
% 1.71/1.35 inference(superposition,[status(thm)],[f93,f133])).
% 1.71/1.35 thf(f133,plain,(
% 1.71/1.35 ($false = (p @ sK2)) | (~spl0_1 | ~spl0_7)),
% 1.71/1.35 inference(trivial_inequality_removal,[status(thm)],[f131])).
% 1.71/1.35 thf(f131,plain,(
% 1.71/1.35 ($false = $true) | ($false = (p @ sK2)) | (~spl0_1 | ~spl0_7)),
% 1.71/1.35 inference(superposition,[status(thm)],[f74,f102])).
% 1.71/1.35 thf(f102,plain,(
% 1.71/1.35 ($true = (mrel @ mactual @ sK2)) | ~spl0_7),
% 1.71/1.35 inference(avatar_component_clause,[status(thm)],[f100])).
% 1.71/1.35 thf(f100,definition,(
% 1.71/1.35 spl0_7 <=> ($true = (mrel @ mactual @ sK2))),
% 1.71/1.35 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.71/1.35 thf(f74,plain,(
% 1.71/1.35 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($false = (p @ X1))) ) | ~spl0_1),
% 1.71/1.35 inference(avatar_component_clause,[status(thm)],[f73])).
% 1.71/1.35 thf(f73,definition,(
% 1.71/1.35 spl0_1 <=> ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($false = (p @ X1)))),
% 1.71/1.35 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.71/1.35 thf(f93,plain,(
% 1.71/1.35 ($true = (p @ sK2)) | ~spl0_5),
% 1.71/1.35 inference(avatar_component_clause,[status(thm)],[f91])).
% 1.71/1.35 thf(f91,definition,(
% 1.71/1.35 spl0_5 <=> ($true = (p @ sK2))),
% 1.71/1.35 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.71/1.35 thf(f127,plain,(
% 1.71/1.35 ~spl0_1 | ~spl0_2 | ~spl0_6),
% 1.71/1.35 inference(avatar_contradiction_clause,[status(thm)],[f126])).
% 1.71/1.35 thf(f126,plain,(
% 1.71/1.35 $false | (~spl0_1 | ~spl0_2 | ~spl0_6)),
% 1.71/1.35 inference(trivial_inequality_removal,[status(thm)],[f123])).
% 1.71/1.35 thf(f123,plain,(
% 1.71/1.35 ($false = $true) | (~spl0_1 | ~spl0_2 | ~spl0_6)),
% 1.71/1.35 inference(superposition,[status(thm)],[f97,f121])).
% 1.71/1.35 thf(f121,plain,(
% 1.71/1.35 ($false = (p @ sK1)) | (~spl0_1 | ~spl0_2)),
% 1.71/1.35 inference(trivial_inequality_removal,[status(thm)],[f119])).
% 1.71/1.35 thf(f119,plain,(
% 1.71/1.35 ($false = $true) | ($false = (p @ sK1)) | (~spl0_1 | ~spl0_2)),
% 1.71/1.35 inference(superposition,[status(thm)],[f74,f79])).
% 1.71/1.35 thf(f79,plain,(
% 1.71/1.35 ($true = (mrel @ mactual @ sK1)) | ~spl0_2),
% 1.71/1.35 inference(avatar_component_clause,[status(thm)],[f77])).
% 1.71/1.35 thf(f77,definition,(
% 1.71/1.35 spl0_2 <=> ($true = (mrel @ mactual @ sK1))),
% 1.71/1.35 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.71/1.35 thf(f97,plain,(
% 1.71/1.35 ($true = (p @ sK1)) | ~spl0_6),
% 1.71/1.35 inference(avatar_component_clause,[status(thm)],[f95])).
% 1.71/1.35 thf(f95,definition,(
% 1.71/1.35 spl0_6 <=> ($true = (p @ sK1))),
% 1.71/1.35 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.71/1.35 thf(f117,plain,(
% 1.71/1.35 ~spl0_1 | ~spl0_3 | ~spl0_4),
% 1.71/1.35 inference(avatar_contradiction_clause,[status(thm)],[f116])).
% 1.71/1.35 thf(f116,plain,(
% 1.71/1.35 $false | (~spl0_1 | ~spl0_3 | ~spl0_4)),
% 1.71/1.35 inference(trivial_inequality_removal,[status(thm)],[f113])).
% 1.71/1.35 thf(f113,plain,(
% 1.71/1.35 ($false = $true) | (~spl0_1 | ~spl0_3 | ~spl0_4)),
% 1.71/1.35 inference(superposition,[status(thm)],[f83,f109])).
% 1.71/1.35 thf(f109,plain,(
% 1.71/1.35 ($false = (p @ sK3)) | (~spl0_1 | ~spl0_4)),
% 1.71/1.35 inference(trivial_inequality_removal,[status(thm)],[f105])).
% 1.71/1.35 thf(f105,plain,(
% 1.71/1.35 ($false = (p @ sK3)) | ($false = $true) | (~spl0_1 | ~spl0_4)),
% 1.71/1.35 inference(superposition,[status(thm)],[f74,f88])).
% 1.71/1.35 thf(f88,plain,(
% 1.71/1.35 ($true = (mrel @ mactual @ sK3)) | ~spl0_4),
% 1.71/1.35 inference(avatar_component_clause,[status(thm)],[f86])).
% 1.71/1.35 thf(f86,definition,(
% 1.71/1.35 spl0_4 <=> ($true = (mrel @ mactual @ sK3))),
% 1.71/1.35 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.71/1.35 thf(f83,plain,(
% 1.71/1.35 ($true = (p @ sK3)) | ~spl0_3),
% 1.71/1.35 inference(avatar_component_clause,[status(thm)],[f81])).
% 1.71/1.35 thf(f81,definition,(
% 1.71/1.35 spl0_3 <=> ($true = (p @ sK3))),
% 1.71/1.35 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.71/1.35 thf(f103,plain,(
% 1.71/1.35 spl0_7 | spl0_6),
% 1.71/1.35 inference(avatar_split_clause,[status(thm)],[f57,f95,f100])).
% 1.71/1.35 thf(f57,plain,(
% 1.71/1.35 ($true = (p @ sK1)) | ($true = (mrel @ mactual @ sK2))),
% 1.71/1.35 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.71/1.35 thf(f55,plain,(
% 1.71/1.35 ($true = (p @ sK1)) | ($false = ((mrel @ mactual @ sK2) => (~ (p @ sK2))))),
% 1.71/1.35 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.71/1.35 thf(f54,plain,(
% 1.71/1.35 ($false = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (p @ Y0)))) @ sK2)) | ($true = (p @ sK1))),
% 1.71/1.35 inference(sigma_clausification,[status(thm)],[f53])).
% 1.71/1.35 thf(f53,plain,(
% 1.71/1.35 ($true = (p @ sK1)) | ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (p @ Y0))))))),
% 1.71/1.35 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 1.71/1.35 thf(f51,plain,(
% 1.71/1.35 ($true = ((p @ sK1) & (mrel @ mactual @ sK1))) | ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (p @ Y0))))))),
% 1.71/1.35 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.71/1.35 thf(f50,plain,(
% 1.71/1.35 ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (p @ Y0)))))) | ($true = ((^[Y0 : mworld]: ((p @ Y0) & (mrel @ mactual @ Y0))) @ sK1))),
% 1.71/1.35 inference(sigma_clausification,[status(thm)],[f49])).
% 1.71/1.35 thf(f49,plain,(
% 1.71/1.35 ((?? @ mworld @ (^[Y0 : mworld]: ((p @ Y0) & (mrel @ mactual @ Y0)))) = $true) | ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (p @ Y0))))))),
% 1.71/1.35 inference(not_proxy_clausification,[status(thm)],[f48])).
% 1.71/1.35 thf(f48,plain,(
% 1.71/1.35 ($false = (~ (?? @ mworld @ (^[Y0 : mworld]: ((p @ Y0) & (mrel @ mactual @ Y0)))))) | ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (p @ Y0))))))),
% 1.71/1.35 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.71/1.35 thf(f46,plain,(
% 1.71/1.35 ((~ (?? @ mworld @ (^[Y0 : mworld]: ((p @ Y0) & (mrel @ mactual @ Y0))))) != (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (p @ Y0))))))),
% 1.71/1.35 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.71/1.35 thf(f45,plain,(
% 1.71/1.35 ($true != ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (p @ Y0))))) = (~ (?? @ mworld @ (^[Y0 : mworld]: ((p @ Y0) & (mrel @ mactual @ Y0)))))))),
% 1.71/1.35 inference(boolean_simplification,[status(thm)],[f44])).
% 1.71/1.35 thf(f44,plain,(
% 1.71/1.35 ($true != ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((p @ Y0) => (~ (p @ Y0)))))) = (~ (?? @ mworld @ (^[Y0 : mworld]: ((p @ Y0) & (mrel @ mactual @ Y0)))))))),
% 1.71/1.35 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.71/1.35 thf(f43,plain,(
% 1.71/1.35 ($true != ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ p @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ p))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ p)))))),
% 1.71/1.35 inference(definition_unfolding,[status(thm)],[f39,f35,f38,f37,f33,f36,f36,f40])).
% 1.71/1.35 thf(f40,plain,(
% 1.71/1.35 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))))),
% 1.71/1.35 inference(cnf_transformation,[status(thm)],[f21])).
% 1.71/1.35 thf(f21,plain,(
% 1.71/1.35 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))))),
% 1.71/1.35 inference(fool_elimination,[status(thm)],[f20])).
% 1.71/1.35 thf(f20,plain,(
% 1.71/1.35 (mdia = (^[X0 : mworld > $o, X1 : mworld] : (? [X2 : mworld] : ((mrel @ X1 @ X2) & (X0 @ X2)))))),
% 1.71/1.35 inference(rectify,[status(thm)],[f8])).
% 1.71/1.35 thf(f8,axiom,(
% 1.71/1.35 (mdia = (^[X0 : mworld > $o, X2 : mworld] : (? [X4 : mworld] : ((mrel @ X2 @ X4) & (X0 @ X4)))))),
% 1.71/1.35 file('/export/starexec/sandbox/tmp/tmp.1yFxI6HofA/DTF2THF_5598.p',mdia_def)).
% 1.71/1.35 thf(f36,plain,(
% 1.71/1.35 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 1.71/1.35 inference(cnf_transformation,[status(thm)],[f23])).
% 1.71/1.35 thf(f23,plain,(
% 1.71/1.35 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 1.71/1.35 inference(fool_elimination,[status(thm)],[f22])).
% 1.71/1.35 thf(f22,plain,(
% 1.71/1.35 (mnot = (^[X0 : mworld > $o, X1 : mworld] : (~(X0 @ X1))))),
% 1.71/1.35 inference(rectify,[status(thm)],[f2])).
% 1.71/1.35 thf(f2,axiom,(
% 1.71/1.35 (mnot = (^[X1 : mworld > $o, X2 : mworld] : (~(X1 @ X2))))),
% 1.71/1.35 file('/export/starexec/sandbox/tmp/tmp.1yFxI6HofA/DTF2THF_5598.p',mnot_def)).
% 1.71/1.35 thf(f33,plain,(
% 1.71/1.35 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.71/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.71/1.35 thf(f29,plain,(
% 1.71/1.35 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.71/1.35 inference(fool_elimination,[status(thm)],[f28])).
% 1.71/1.35 thf(f28,plain,(
% 1.71/1.35 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 1.71/1.35 inference(rectify,[status(thm)],[f5])).
% 1.71/1.35 thf(f5,axiom,(
% 1.71/1.35 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))) = mimplies)),
% 1.71/1.35 file('/export/starexec/sandbox/tmp/tmp.1yFxI6HofA/DTF2THF_5598.p',mimplies_def)).
% 1.71/1.35 thf(f37,plain,(
% 1.71/1.35 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.71/1.35 inference(cnf_transformation,[status(thm)],[f31])).
% 1.71/1.35 thf(f31,plain,(
% 1.71/1.35 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.71/1.35 inference(fool_elimination,[status(thm)],[f30])).
% 1.71/1.35 thf(f30,plain,(
% 1.71/1.35 (mbox = (^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 1.71/1.35 inference(rectify,[status(thm)],[f7])).
% 1.71/1.35 thf(f7,axiom,(
% 1.71/1.35 (mbox = (^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))))),
% 1.71/1.35 file('/export/starexec/sandbox/tmp/tmp.1yFxI6HofA/DTF2THF_5598.p',mbox_def)).
% 1.71/1.35 thf(f38,plain,(
% 1.71/1.35 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 1.71/1.35 inference(cnf_transformation,[status(thm)],[f27])).
% 1.71/1.35 thf(f27,plain,(
% 1.71/1.35 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 1.71/1.35 inference(fool_elimination,[status(thm)],[f26])).
% 1.71/1.35 thf(f26,plain,(
% 1.71/1.35 (mequiv = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) <=> (X1 @ X2))))),
% 1.71/1.35 inference(rectify,[status(thm)],[f6])).
% 1.71/1.35 thf(f6,axiom,(
% 1.71/1.35 (mequiv = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) <=> (X3 @ X2))))),
% 1.71/1.35 file('/export/starexec/sandbox/tmp/tmp.1yFxI6HofA/DTF2THF_5598.p',mequiv_def)).
% 1.71/1.35 thf(f35,plain,(
% 1.71/1.35 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.71/1.35 inference(cnf_transformation,[status(thm)],[f19])).
% 1.71/1.35 thf(f19,plain,(
% 1.71/1.35 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.71/1.35 inference(fool_elimination,[status(thm)],[f1])).
% 1.71/1.35 thf(f1,axiom,(
% 1.71/1.35 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 1.71/1.35 file('/export/starexec/sandbox/tmp/tmp.1yFxI6HofA/DTF2THF_5598.p',mlocal_def)).
% 1.71/1.35 thf(f39,plain,(
% 1.71/1.35 ((mlocal @ (mequiv @ (mbox @ (mimplies @ p @ (mnot @ p))) @ (mnot @ (mdia @ p)))) != $true)),
% 1.71/1.35 inference(cnf_transformation,[status(thm)],[f32])).
% 1.71/1.35 thf(f32,plain,(
% 1.71/1.35 ((mlocal @ (mequiv @ (mbox @ (mimplies @ p @ (mnot @ p))) @ (mnot @ (mdia @ p)))) != $true)),
% 1.71/1.35 inference(flattening,[status(thm)],[f14])).
% 1.71/1.35 thf(f14,plain,(
% 1.71/1.35 ~((mlocal @ (mequiv @ (mbox @ (mimplies @ p @ (mnot @ p))) @ (mnot @ (mdia @ p)))) = $true)),
% 1.71/1.35 inference(fool_elimination,[status(thm)],[f13])).
% 1.71/1.35 thf(f13,plain,(
% 1.71/1.35 ~(mlocal @ (mequiv @ (mbox @ (mimplies @ p @ (mnot @ p))) @ (mnot @ (mdia @ p))))),
% 1.71/1.35 inference(rectify,[status(thm)],[f11])).
% 1.71/1.35 thf(f11,negated_conjecture,(
% 1.71/1.35 ~(mlocal @ (mequiv @ (mbox @ (mimplies @ p @ (mnot @ p))) @ (mnot @ (mdia @ p))))),
% 1.71/1.35 inference(negated_conjecture,[status(cth)],[f10])).
% 1.71/1.35 thf(f10,conjecture,(
% 1.71/1.35 (mlocal @ (mequiv @ (mbox @ (mimplies @ p @ (mnot @ p))) @ (mnot @ (mdia @ p))))),
% 1.71/1.35 file('/export/starexec/sandbox/tmp/tmp.1yFxI6HofA/DTF2THF_5598.p',con)).
% 1.71/1.35 thf(f98,plain,(
% 1.71/1.35 spl0_5 | spl0_6),
% 1.71/1.35 inference(avatar_split_clause,[status(thm)],[f58,f95,f91])).
% 1.71/1.35 thf(f58,plain,(
% 1.71/1.35 ($true = (p @ sK1)) | ($true = (p @ sK2))),
% 1.71/1.35 inference(not_proxy_clausification,[status(thm)],[f56])).
% 1.71/1.35 thf(f56,plain,(
% 1.71/1.35 ($false = (~ (p @ sK2))) | ($true = (p @ sK1))),
% 1.71/1.35 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.71/1.35 thf(f89,plain,(
% 1.71/1.35 spl0_2 | spl0_4),
% 1.71/1.35 inference(avatar_split_clause,[status(thm)],[f62,f86,f77])).
% 1.71/1.35 thf(f62,plain,(
% 1.71/1.35 ($true = (mrel @ mactual @ sK1)) | ($true = (mrel @ mactual @ sK3))),
% 1.71/1.35 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.71/1.35 thf(f60,plain,(
% 1.71/1.35 ($true = (mrel @ mactual @ sK1)) | ($false = ((mrel @ mactual @ sK3) => (~ (p @ sK3))))),
% 1.71/1.35 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.71/1.35 thf(f59,plain,(
% 1.71/1.35 ($true = (mrel @ mactual @ sK1)) | ($false = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (p @ Y0)))) @ sK3))),
% 1.71/1.35 inference(sigma_clausification,[status(thm)],[f52])).
% 1.71/1.35 thf(f52,plain,(
% 1.71/1.35 ($true = (mrel @ mactual @ sK1)) | ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (p @ Y0))))))),
% 1.71/1.35 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 1.71/1.35 thf(f84,plain,(
% 1.71/1.35 spl0_2 | spl0_3),
% 1.71/1.35 inference(avatar_split_clause,[status(thm)],[f63,f81,f77])).
% 1.71/1.35 thf(f63,plain,(
% 1.71/1.35 ($true = (p @ sK3)) | ($true = (mrel @ mactual @ sK1))),
% 1.71/1.35 inference(not_proxy_clausification,[status(thm)],[f61])).
% 1.71/1.35 thf(f61,plain,(
% 1.71/1.35 ($false = (~ (p @ sK3))) | ($true = (mrel @ mactual @ sK1))),
% 1.71/1.35 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.71/1.35 thf(f75,plain,(
% 1.71/1.35 spl0_1 | spl0_1),
% 1.71/1.35 inference(avatar_split_clause,[status(thm)],[f71,f73,f73])).
% 1.71/1.35 thf(f71,plain,(
% 1.71/1.35 ( ! [X2 : mworld,X1 : mworld] : (($false = (mrel @ mactual @ X2)) | ($false = (mrel @ mactual @ X1)) | ($false = (p @ X1)) | ($false = (p @ X2))) )),
% 1.71/1.35 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.71/1.35 thf(f70,plain,(
% 1.71/1.35 ( ! [X2 : mworld,X1 : mworld] : (($false = (p @ X1)) | ($false = ((p @ X2) & (mrel @ mactual @ X2))) | ($false = (mrel @ mactual @ X1))) )),
% 1.71/1.35 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.71/1.35 thf(f69,plain,(
% 1.71/1.35 ( ! [X2 : mworld,X1 : mworld] : (($false = ((^[Y0 : mworld]: ((p @ Y0) & (mrel @ mactual @ Y0))) @ X2)) | ($false = (p @ X1)) | ($false = (mrel @ mactual @ X1))) )),
% 1.71/1.35 inference(pi_clausification,[status(thm)],[f68])).
% 1.71/1.35 thf(f68,plain,(
% 1.71/1.35 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($false = (?? @ mworld @ (^[Y0 : mworld]: ((p @ Y0) & (mrel @ mactual @ Y0))))) | ($false = (p @ X1))) )),
% 1.71/1.35 inference(not_proxy_clausification,[status(thm)],[f67])).
% 1.71/1.35 thf(f67,plain,(
% 1.71/1.35 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = (~ (?? @ mworld @ (^[Y0 : mworld]: ((p @ Y0) & (mrel @ mactual @ Y0)))))) | ($false = (p @ X1))) )),
% 1.71/1.35 inference(not_proxy_clausification,[status(thm)],[f66])).
% 1.71/1.35 thf(f66,plain,(
% 1.71/1.35 ( ! [X1 : mworld] : (($true = (~ (p @ X1))) | ($false = (mrel @ mactual @ X1)) | ($true = (~ (?? @ mworld @ (^[Y0 : mworld]: ((p @ Y0) & (mrel @ mactual @ Y0))))))) )),
% 1.71/1.35 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 1.71/1.35 thf(f65,plain,(
% 1.71/1.35 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (~ (p @ X1)))) | ($true = (~ (?? @ mworld @ (^[Y0 : mworld]: ((p @ Y0) & (mrel @ mactual @ Y0))))))) )),
% 1.71/1.35 inference(beta_eta_normalization,[status(thm)],[f64])).
% 1.71/1.35 thf(f64,plain,(
% 1.71/1.35 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (p @ Y0)))) @ X1)) | ($true = (~ (?? @ mworld @ (^[Y0 : mworld]: ((p @ Y0) & (mrel @ mactual @ Y0))))))) )),
% 1.71/1.35 inference(pi_clausification,[status(thm)],[f47])).
% 1.71/1.35 thf(f47,plain,(
% 1.71/1.35 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (p @ Y0)))))) | ($true = (~ (?? @ mworld @ (^[Y0 : mworld]: ((p @ Y0) & (mrel @ mactual @ Y0))))))),
% 1.71/1.35 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.71/1.35 % SZS output end Proof for DTF2THF_5598
% 1.71/1.35 % (5800)------------------------------
% 1.71/1.35 % (5800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.35 % (5800)Termination reason: Refutation
% 1.71/1.35
% 1.71/1.35 % (5800)Memory used [KB]: 5628
% 1.71/1.35 % (5800)Time elapsed: 0.007 s
% 1.71/1.35 % (5800)Instructions burned: 6 (million)
% 1.71/1.35 % (5800)------------------------------
% 1.71/1.35 % (5800)------------------------------
% 1.71/1.35 % (5792)Success in time 0.022 s
%------------------------------------------------------------------------------