%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO900^11 : 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 : n023.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 09:55:09 AM UTC 2026
% Result : Theorem 0.30s 1.33s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of formulae : 67 ( 41 unt; 0 typ; 2 def)
% Number of atoms : 435 ( 85 equ; 0 cnn)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 595 ( 45 ~; 41 |; 3 &; 407 @)
% ( 2 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 18 usr; 10 con; 0-3 aty)
% ( 34 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 132 ( 95 ^; 37 !; 0 ?; 132 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(func_def_0,type,
mworld: $tType ).
thf(func_def_1,type,
mrel: mworld > mworld > $o ).
thf(func_def_2,type,
mactual: mworld ).
thf(func_def_3,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_5,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
p: mworld > $o ).
thf(func_def_13,type,
q: mworld > $o ).
thf(func_def_28,type,
sK1: mworld ).
thf(func_def_29,type,
sK2: mworld ).
thf(func_def_30,type,
sK3: mworld ).
thf(func_def_31,type,
sK4: mworld ).
thf(f224,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f186,f212,f223]) ).
thf(f223,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f222]) ).
thf(f222,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f218]) ).
thf(f218,plain,
( ( $false = $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f182,f77]) ).
thf(f77,plain,
( $false
= ( p @ sK4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
( ( ( mrel @ sK3 @ sK4 )
=> ( p @ sK4 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
( ( ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( p @ Y0 ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( p @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( p @ Y0 ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
( $false
= ( ( mrel @ mactual @ sK3 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( p @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f66]) ).
thf(f66,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ^ [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 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p ) ) ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f45,f46,f43,f44,f38,f44,f44,f44,f38,f44,f44]) ).
thf(f38,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f25]) ).
thf(f25,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( mimplies
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.edocsbdCrN/DTF2THF_22872.p',mimplies_def) ).
thf(f44,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X2: mworld] :
! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( X0 @ X4 ) ) )
= mbox ),
file('/export/starexec/sandbox/tmp/tmp.edocsbdCrN/DTF2THF_22872.p',mbox_def) ).
thf(f43,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X3 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/tmp/tmp.edocsbdCrN/DTF2THF_22872.p',mor_def) ).
thf(f46,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,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.edocsbdCrN/DTF2THF_22872.p',mlocal_def) ).
thf(f45,plain,
( ( mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ( mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ( mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
~ ( mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,negated_conjecture,
~ ( mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
thf(f11,conjecture,
mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.edocsbdCrN/DTF2THF_22872.p',con) ).
thf(f182,plain,
( ( ( p @ sK4 )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f180]) ).
thf(f180,definition,
( spl0_1
<=> ( ( p @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f212,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f211]) ).
thf(f211,plain,
( $false
| ~ spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f208,f56]) ).
thf(f56,plain,
( $true
= ( mrel @ mactual @ sK1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( $false
= ( ( mrel @ mactual @ sK1 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) )
@ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f208,plain,
( ( $true
!= ( mrel @ mactual @ sK1 ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f203]) ).
thf(f203,plain,
( ( $true
!= ( mrel @ mactual @ sK1 ) )
| ( $true != $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f185,f69]) ).
thf(f69,plain,
( ( mrel @ mactual @ sK3 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f67]) ).
thf(f185,plain,
( ! [X0: mworld] :
( ( ( mrel @ X0 @ sK3 )
!= $true )
| ( ( mrel @ X0 @ sK1 )
!= $true ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f184]) ).
thf(f184,definition,
( spl0_2
<=> ! [X0: mworld] :
( ( ( mrel @ X0 @ sK3 )
!= $true )
| ( ( mrel @ X0 @ sK1 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f186,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f173,f184,f180]) ).
thf(f173,plain,
! [X0: mworld] :
( ( ( p @ sK4 )
= $true )
| ( ( mrel @ X0 @ sK3 )
!= $true )
| ( ( mrel @ X0 @ sK1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f170]) ).
thf(f170,plain,
! [X0: mworld] :
( ( ( mrel @ X0 @ sK3 )
!= $true )
| ( ( mrel @ X0 @ sK1 )
!= $true )
| ( $true != $true )
| ( ( p @ sK4 )
= $true ) ),
inference(superposition,[status(thm)],[f108,f78]) ).
thf(f78,plain,
( ( mrel @ sK3 @ sK4 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f108,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( $true
!= ( mrel @ X0 @ X1 ) )
| ( ( p @ X1 )
= $true )
| ( ( mrel @ X2 @ X0 )
!= $true )
| ( ( mrel @ X2 @ sK1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f107]) ).
thf(f107,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( ( mrel @ X2 @ X0 )
!= $true )
| ( ( p @ X1 )
= $true )
| ( ( mrel @ X2 @ sK1 )
!= $true )
| ( $true
!= ( mrel @ X0 @ X1 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f90,f40]) ).
thf(f40,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( ( mrel @ X0 @ X2 )
= $true )
| ( ( mrel @ X1 @ X0 )
!= $true )
| ( ( mrel @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X1 @ X0 )
!= $true )
| ( ( mrel @ X1 @ X2 )
!= $true )
| ( ( mrel @ X0 @ X2 )
= $true ) ),
inference(flattening,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X0 @ X2 )
= $true )
| ( ( mrel @ X1 @ X2 )
!= $true )
| ( ( mrel @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( ( mrel @ X1 @ X2 )
= $true )
& ( ( mrel @ X1 @ X0 )
= $true ) )
=> ( ( mrel @ X0 @ X2 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X1 @ X0 )
& ( mrel @ X1 @ X2 ) )
=> ( mrel @ X0 @ X2 ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
! [X5: mworld,X2: mworld,X4: mworld] :
( ( ( mrel @ X2 @ X5 )
& ( mrel @ X2 @ X4 ) )
=> ( mrel @ X5 @ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.edocsbdCrN/DTF2THF_22872.p',mrel_euclidean) ).
thf(f90,plain,
! [X0: mworld,X1: mworld] :
( ( ( mrel @ X1 @ sK1 )
!= $true )
| ( ( p @ X0 )
= $true )
| ( ( mrel @ X1 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
! [X0: mworld,X1: mworld] :
( ( ( mrel @ X1 @ sK1 )
!= $true )
| ( ( p @ X0 )
= $true )
| ( $false = $true )
| ( ( mrel @ X1 @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f61,f40]) ).
thf(f61,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( ( p @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
! [X1: mworld] :
( ( ( mrel @ sK1 @ X1 )
=> ( p @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( q @ Y0 ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO900^11 : TPTP v9.2.1. Released v8.1.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n023.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:54:19 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SYO900^11 : TPTP v9.2.1. Released v8.1.0.
% 0.30/0.46 % Domain : Syntactic
% 0.30/0.46 % Problem : Modal propositional logic theorems. problem 57
% 0.30/0.46 % Version : [BP13] axioms.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.30/0.46 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.30/0.46 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.30/0.46 % Source : [TPTP]
% 0.30/0.46 % Names : SYM157+1 [QMLTP]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v8.2.0, 0.15 v8.1.0
% 0.30/0.46 % Syntax : Number of formulae : 24 ( 9 unt; 13 typ; 8 def)
% 0.30/0.46 % Number of atoms : 36 ( 8 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 14 ( 3 avg)
% 0.30/0.46 % Number of connectives : 46 ( 1 ~; 1 |; 3 &; 37 @)
% 0.30/0.46 % ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 8 ( 3 avg)
% 0.30/0.46 % Number of types : 2 ( 1 usr)
% 0.30/0.46 % Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 13 ( 12 usr; 1 con; 0-3 aty)
% 0.30/0.46 % Number of variables : 25 ( 19 ^; 5 !; 1 ?; 25 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.30/0.46 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.30/0.46 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.30/0.46 % $modal == [$constants == $rigid,$quantification == $varying,
% 0.30/0.46 % $modalities == $modal_system_S5].
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(mworld,type,
% 0.30/0.46 mworld: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(mrel_type,type,
% 0.30/0.46 mrel: mworld > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mactual_type,type,
% 0.30/0.46 mactual: mworld ).
% 0.30/0.46
% 0.30/0.46 thf(mlocal_type,type,
% 0.30/0.46 mlocal: ( mworld > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mlocal_def,definition,
% 0.30/0.46 ( mlocal
% 0.30/0.46 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mnot_type,type,
% 0.30/0.46 mnot: ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mand_type,type,
% 0.30/0.46 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mor_type,type,
% 0.30/0.46 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mimplies_type,type,
% 0.30/0.46 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mequiv_type,type,
% 0.30/0.46 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mnot_def,definition,
% 0.30/0.46 ( mnot
% 0.30/0.46 = ( ^ [A: mworld > $o,W: mworld] :
% 0.30/0.46 ~ ( A @ W ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mand_def,definition,
% 0.30/0.46 ( mand
% 0.30/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.46 ( ( A @ W )
% 0.30/0.46 & ( B @ W ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mor_def,definition,
% 0.30/0.46 ( mor
% 0.30/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.46 ( ( A @ W )
% 0.30/0.46 | ( B @ W ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mimplies_def,definition,
% 0.30/0.46 ( mimplies
% 0.30/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.46 ( ( A @ W )
% 0.30/0.46 => ( B @ W ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mequiv_def,definition,
% 0.30/0.46 ( mequiv
% 0.30/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.46 ( ( A @ W )
% 0.30/0.46 <=> ( B @ W ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mbox_type,type,
% 0.30/0.46 mbox: ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mbox_def,definition,
% 0.30/0.46 ( mbox
% 0.30/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.30/0.46 ! [V: mworld] :
% 0.30/0.46 ( ( mrel @ W @ V )
% 0.30/0.46 => ( Phi @ V ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mdia_type,type,
% 0.30/0.46 mdia: ( mworld > $o ) > mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(mdia_def,definition,
% 0.30/0.46 ( mdia
% 0.30/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.30/0.46 ? [V: mworld] :
% 0.30/0.46 ( ( mrel @ W @ V )
% 0.30/0.46 & ( Phi @ V ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(mrel_reflexive,axiom,
% 0.30/0.46 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.30/0.46
% 0.30/0.46 thf(mrel_euclidean,axiom,
% 0.30/0.46 ! [W: mworld,V: mworld,U: mworld] :
% 0.30/0.46 ( ( ( mrel @ W @ U )
% 0.30/0.46 & ( mrel @ W @ V ) )
% 0.30/0.46 => ( mrel @ U @ V ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(p_decl,type,
% 0.30/0.46 p: mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(q_decl,type,
% 0.30/0.46 q: mworld > $o ).
% 0.30/0.46
% 0.30/0.46 thf(con,conjecture,
% 0.30/0.46 mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 0.30/1.30 ---- Embedded in THF ---
% 0.30/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.30/1.30 %%% Generated on Tue Feb 24 14:54:20 EST 2026
% 0.30/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.30/1.30 %%% Logic specification used:
% 0.30/1.30 %%% thf(spec, logic, $$dhol).
% 0.30/1.30
% 0.30/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.edocsbdCrN/DTF2DTF22872.p
% See solution above
% 0.30/1.30 ------------------------
% 0.30/1.31 ---- Cleaned THF ---
% 0.30/1.31 thf(mworld,type,
% 0.30/1.31 mworld: $tType ).
% 0.30/1.31
% 0.30/1.31 thf(mrel_type,type,
% 0.30/1.31 mrel: mworld > mworld > $o ).
% 0.30/1.31
% 0.30/1.31 thf(mactual_type,type,
% 0.30/1.31 mactual: mworld ).
% 0.30/1.31
% 0.30/1.31 thf(mlocal_type,type,
% 0.30/1.31 mlocal: ( mworld > $o ) > $o ).
% 0.30/1.31
% 0.30/1.31 thf(mlocal_def,definition,
% 0.30/1.31 ( mlocal
% 0.30/1.31 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.30/1.31
% 0.30/1.31 thf(mnot_type,type,
% 0.30/1.31 mnot: ( mworld > $o ) > mworld > $o ).
% 0.30/1.31
% 0.30/1.31 thf(mand_type,type,
% 0.30/1.31 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/1.31
% 0.30/1.31 thf(mor_type,type,
% 0.30/1.31 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/1.31
% 0.30/1.31 thf(mimplies_type,type,
% 0.30/1.31 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/1.31
% 0.30/1.31 thf(mequiv_type,type,
% 0.30/1.31 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/1.31
% 0.30/1.31 thf(mnot_def,definition,
% 0.30/1.31 ( mnot
% 0.30/1.31 = ( ^ [A: mworld > $o,W: mworld] :
% 0.30/1.31 ~ ( A @ W ) ) ) ).
% 0.30/1.31
% 0.30/1.31 thf(mand_def,definition,
% 0.30/1.31 ( mand
% 0.30/1.31 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/1.31 ( ( A @ W )
% 0.30/1.31 & ( B @ W ) ) ) ) ).
% 0.30/1.31
% 0.30/1.31 thf(mor_def,definition,
% 0.30/1.31 ( mor
% 0.30/1.31 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/1.31 ( ( A @ W )
% 0.30/1.31 | ( B @ W ) ) ) ) ).
% 0.30/1.31
% 0.30/1.31 thf(mimplies_def,definition,
% 0.30/1.31 ( mimplies
% 0.30/1.31 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/1.31 ( ( A @ W )
% 0.30/1.31 => ( B @ W ) ) ) ) ).
% 0.30/1.31
% 0.30/1.31 thf(mequiv_def,definition,
% 0.30/1.31 ( mequiv
% 0.30/1.31 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/1.31 ( ( A @ W )
% 0.30/1.31 <=> ( B @ W ) ) ) ) ).
% 0.30/1.31
% 0.30/1.31 thf(mbox_type,type,
% 0.30/1.31 mbox: ( mworld > $o ) > mworld > $o ).
% 0.30/1.31
% 0.30/1.31 thf(mbox_def,definition,
% 0.30/1.31 ( mbox
% 0.30/1.31 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.30/1.31 ! [V: mworld] :
% 0.30/1.31 ( ( mrel @ W @ V )
% 0.30/1.31 => ( Phi @ V ) ) ) ) ).
% 0.30/1.31
% 0.30/1.31 thf(mdia_type,type,
% 0.30/1.31 mdia: ( mworld > $o ) > mworld > $o ).
% 0.30/1.31
% 0.30/1.31 thf(mdia_def,definition,
% 0.30/1.31 ( mdia
% 0.30/1.31 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.30/1.31 ? [V: mworld] :
% 0.30/1.31 ( ( mrel @ W @ V )
% 0.30/1.31 & ( Phi @ V ) ) ) ) ).
% 0.30/1.31
% 0.30/1.31 thf(mrel_reflexive,axiom,
% 0.30/1.31 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.30/1.31
% 0.30/1.31 thf(mrel_euclidean,axiom,
% 0.30/1.31 ! [W: mworld,V: mworld,U: mworld] :
% 0.30/1.31 ( ( ( mrel @ W @ U )
% 0.30/1.31 & ( mrel @ W @ V ) )
% 0.30/1.31 => ( mrel @ U @ V ) ) ).
% 0.30/1.31
% 0.30/1.31 thf(p_decl,type,
% 0.30/1.31 p: mworld > $o ).
% 0.30/1.31
% 0.30/1.31 thf(q_decl,type,
% 0.30/1.31 q: mworld > $o ).
% 0.30/1.31
% 0.30/1.31 thf(con,conjecture,
% 0.30/1.31 mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) ).
% 0.30/1.31 ------------------------
% 0.30/1.32 % (22969)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22872 for (2999ds/183Mi)
% 0.30/1.33 % (22970)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_22872 for (2999ds/4Mi)
% 0.30/1.33 % (22970)Instruction limit reached!
% 0.30/1.33 % (22970)------------------------------
% 0.30/1.33 % (22970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.33 % (22970)Termination reason: Unknown
% 0.30/1.33 % (22970)Termination phase: Saturation
% 0.30/1.33
% 0.30/1.33 % (22970)Memory used [KB]: 5500
% 0.30/1.33 % (22970)Time elapsed: 0.003 s
% 0.30/1.33 % (22970)Instructions burned: 5 (million)
% 0.30/1.33 % (22970)------------------------------
% 0.30/1.33 % (22970)------------------------------
% 0.30/1.33 % (22969)First to succeed.
% 0.30/1.33 % (22971)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_22872 for (2999ds/27Mi)
% 0.30/1.33 % (22972)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22872 for (2999ds/2Mi)
% 0.30/1.33 % (22973)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_22872 for (2999ds/2Mi)
% 0.30/1.33 % (22974)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_22872 for (2999ds/275Mi)
% 0.30/1.33 % (22975)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22872 for (2999ds/18Mi)
% 0.30/1.33 % (22972)Instruction limit reached!
% 0.30/1.33 % (22972)------------------------------
% 0.30/1.33 % (22972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.33 % (22972)Termination reason: Unknown
% 0.30/1.33 % (22972)Termination phase: shuffling
% 0.30/1.33
% 0.30/1.33 % (22972)Memory used [KB]: 895
% 0.30/1.33 % (22972)Time elapsed: 0.003 s
% 0.30/1.33 % (22972)Instructions burned: 2 (million)
% 0.30/1.33 % (22972)------------------------------
% 0.30/1.33 % (22972)------------------------------
% 0.30/1.33 % (22973)Instruction limit reached!
% 0.30/1.33 % (22973)------------------------------
% 0.30/1.33 % (22973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.33 % (22973)Termination reason: Unknown
% 0.30/1.33 % (22973)Termination phase: shuffling
% 0.30/1.33
% 0.30/1.33 % (22973)Memory used [KB]: 1023
% 0.30/1.33 % (22973)Time elapsed: 0.003 s
% 0.30/1.33 % (22973)Instructions burned: 2 (million)
% 0.30/1.33 % (22973)------------------------------
% 0.30/1.33 % (22973)------------------------------
% 0.30/1.33 % (22969)Refutation found. Thanks to Tanya!
% 0.30/1.33 % SZS status Theorem for DTF2THF_22872
% 0.30/1.33 % SZS output start Proof for DTF2THF_22872
% 0.30/1.33 thf(type_def_5, type, mworld: $tType).
% 0.30/1.33 thf(func_def_0, type, mworld: $tType).
% 0.30/1.33 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 0.30/1.33 thf(func_def_2, type, mactual: mworld).
% 0.30/1.33 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 0.30/1.33 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 0.30/1.33 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.30/1.33 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.30/1.33 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.30/1.33 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.30/1.33 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 0.30/1.33 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 0.30/1.33 thf(func_def_12, type, p: mworld > $o).
% 0.30/1.33 thf(func_def_13, type, q: mworld > $o).
% 0.30/1.33 thf(func_def_28, type, sK1: mworld).
% 0.30/1.33 thf(func_def_29, type, sK2: mworld).
% 0.30/1.33 thf(func_def_30, type, sK3: mworld).
% 0.30/1.33 thf(func_def_31, type, sK4: mworld).
% 0.30/1.33 thf(f224,plain,(
% 0.30/1.33 $false),
% 0.30/1.33 inference(avatar_sat_refutation,[status(thm)],[f186,f212,f223])).
% 0.30/1.33 thf(f223,plain,(
% 0.30/1.33 ~spl0_1),
% 0.30/1.33 inference(avatar_contradiction_clause,[status(thm)],[f222])).
% 0.30/1.33 thf(f222,plain,(
% 0.30/1.33 $false | ~spl0_1),
% 0.30/1.33 inference(trivial_inequality_removal,[status(thm)],[f218])).
% 0.30/1.33 thf(f218,plain,(
% 0.30/1.33 ($false = $true) | ~spl0_1),
% 0.30/1.33 inference(superposition,[status(thm)],[f182,f77])).
% 0.30/1.33 thf(f77,plain,(
% 0.30/1.33 ($false = (p @ sK4))),
% 0.30/1.33 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 0.30/1.33 thf(f76,plain,(
% 0.30/1.33 (((mrel @ sK3 @ sK4) => (p @ sK4)) = $false)),
% 0.30/1.33 inference(beta_eta_normalization,[status(thm)],[f75])).
% 0.30/1.33 thf(f75,plain,(
% 0.30/1.33 (((^[Y0 : mworld]: ((mrel @ sK3 @ Y0) => (p @ Y0))) @ sK4) = $false)),
% 0.30/1.33 inference(sigma_clausification,[status(thm)],[f70])).
% 0.30/1.33 thf(f70,plain,(
% 0.30/1.33 ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK3 @ Y0) => (p @ Y0)))))),
% 0.30/1.33 inference(binary_proxy_clausification,[status(thm)],[f68])).
% 0.30/1.33 thf(f68,plain,(
% 0.30/1.33 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK3 @ Y0) => (q @ Y0)))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK3 @ Y0) => (p @ Y0))))) = $false)),
% 0.30/1.33 inference(binary_proxy_clausification,[status(thm)],[f67])).
% 0.30/1.33 thf(f67,plain,(
% 0.30/1.33 ($false = ((mrel @ mactual @ sK3) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK3 @ Y0) => (q @ Y0)))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK3 @ Y0) => (p @ Y0)))))))),
% 0.30/1.33 inference(beta_eta_normalization,[status(thm)],[f66])).
% 0.30/1.33 thf(f66,plain,(
% 0.30/1.33 ($false = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (q @ Y1)))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (p @ Y1))))))) @ sK3))),
% 0.30/1.33 inference(sigma_clausification,[status(thm)],[f51])).
% 0.30/1.33 thf(f51,plain,(
% 0.30/1.33 ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (q @ Y1)))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (p @ Y1)))))))))),
% 0.30/1.33 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 0.30/1.33 thf(f50,plain,(
% 0.30/1.33 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (p @ Y1)))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (q @ Y1)))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (q @ Y1)))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (p @ Y1))))))))) != $true)),
% 0.30/1.33 inference(beta_eta_normalization,[status(thm)],[f49])).
% 0.30/1.33 thf(f49,plain,(
% 0.30/1.33 (((^[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))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ p) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ q))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ q) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ p))))) != $true)),
% 0.30/1.33 inference(definition_unfolding,[status(thm)],[f45,f46,f43,f44,f38,f44,f44,f44,f38,f44,f44])).
% 0.30/1.33 thf(f38,plain,(
% 0.30/1.33 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.30/1.33 inference(cnf_transformation,[status(thm)],[f26])).
% 0.30/1.33 thf(f26,plain,(
% 0.30/1.33 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.30/1.33 inference(fool_elimination,[status(thm)],[f25])).
% 0.30/1.33 thf(f25,plain,(
% 0.30/1.33 (mimplies = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 0.30/1.33 inference(rectify,[status(thm)],[f5])).
% 0.30/1.33 thf(f5,axiom,(
% 0.30/1.33 (mimplies = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))))),
% 0.30/1.33 file('/export/starexec/sandbox/tmp/tmp.edocsbdCrN/DTF2THF_22872.p',mimplies_def)).
% 0.30/1.33 thf(f44,plain,(
% 0.30/1.33 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.30/1.33 inference(cnf_transformation,[status(thm)],[f34])).
% 0.30/1.33 thf(f34,plain,(
% 0.30/1.33 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.30/1.33 inference(fool_elimination,[status(thm)],[f33])).
% 0.30/1.33 thf(f33,plain,(
% 0.30/1.33 ((^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 0.30/1.33 inference(rectify,[status(thm)],[f7])).
% 0.30/1.33 thf(f7,axiom,(
% 0.30/1.33 ((^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))) = mbox)),
% 0.30/1.33 file('/export/starexec/sandbox/tmp/tmp.edocsbdCrN/DTF2THF_22872.p',mbox_def)).
% 0.30/1.33 thf(f43,plain,(
% 0.30/1.33 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.30/1.33 inference(cnf_transformation,[status(thm)],[f28])).
% 0.30/1.33 thf(f28,plain,(
% 0.30/1.33 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.30/1.33 inference(fool_elimination,[status(thm)],[f27])).
% 0.30/1.33 thf(f27,plain,(
% 0.30/1.33 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.30/1.33 inference(rectify,[status(thm)],[f4])).
% 0.30/1.33 thf(f4,axiom,(
% 0.30/1.33 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) | (X1 @ X2))) = mor)),
% 0.30/1.33 file('/export/starexec/sandbox/tmp/tmp.edocsbdCrN/DTF2THF_22872.p',mor_def)).
% 0.30/1.33 thf(f46,plain,(
% 0.30/1.33 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.30/1.33 inference(cnf_transformation,[status(thm)],[f16])).
% 0.30/1.33 thf(f16,plain,(
% 0.30/1.33 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.30/1.33 inference(fool_elimination,[status(thm)],[f1])).
% 0.30/1.33 thf(f1,axiom,(
% 0.30/1.33 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 0.30/1.33 file('/export/starexec/sandbox/tmp/tmp.edocsbdCrN/DTF2THF_22872.p',mlocal_def)).
% 0.30/1.33 thf(f45,plain,(
% 0.30/1.33 ((mlocal @ (mor @ (mbox @ (mimplies @ (mbox @ p) @ (mbox @ q))) @ (mbox @ (mimplies @ (mbox @ q) @ (mbox @ p))))) != $true)),
% 0.30/1.33 inference(cnf_transformation,[status(thm)],[f35])).
% 0.30/1.33 thf(f35,plain,(
% 0.30/1.33 ((mlocal @ (mor @ (mbox @ (mimplies @ (mbox @ p) @ (mbox @ q))) @ (mbox @ (mimplies @ (mbox @ q) @ (mbox @ p))))) != $true)),
% 0.30/1.33 inference(flattening,[status(thm)],[f18])).
% 0.30/1.33 thf(f18,plain,(
% 0.30/1.33 ~((mlocal @ (mor @ (mbox @ (mimplies @ (mbox @ p) @ (mbox @ q))) @ (mbox @ (mimplies @ (mbox @ q) @ (mbox @ p))))) = $true)),
% 0.30/1.33 inference(fool_elimination,[status(thm)],[f17])).
% 0.30/1.33 thf(f17,plain,(
% 0.30/1.33 ~(mlocal @ (mor @ (mbox @ (mimplies @ (mbox @ p) @ (mbox @ q))) @ (mbox @ (mimplies @ (mbox @ q) @ (mbox @ p)))))),
% 0.30/1.33 inference(rectify,[status(thm)],[f12])).
% 0.30/1.33 thf(f12,negated_conjecture,(
% 0.30/1.33 ~(mlocal @ (mor @ (mbox @ (mimplies @ (mbox @ p) @ (mbox @ q))) @ (mbox @ (mimplies @ (mbox @ q) @ (mbox @ p)))))),
% 0.30/1.33 inference(negated_conjecture,[status(cth)],[f11])).
% 0.30/1.33 thf(f11,conjecture,(
% 0.30/1.33 (mlocal @ (mor @ (mbox @ (mimplies @ (mbox @ p) @ (mbox @ q))) @ (mbox @ (mimplies @ (mbox @ q) @ (mbox @ p)))))),
% 0.30/1.33 file('/export/starexec/sandbox/tmp/tmp.edocsbdCrN/DTF2THF_22872.p',con)).
% 0.30/1.33 thf(f182,plain,(
% 0.30/1.33 ((p @ sK4) = $true) | ~spl0_1),
% 0.30/1.33 inference(avatar_component_clause,[status(thm)],[f180])).
% 0.30/1.33 thf(f180,definition,(
% 0.30/1.33 spl0_1 <=> ((p @ sK4) = $true)),
% 0.30/1.33 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 0.30/1.33 thf(f212,plain,(
% 0.30/1.33 ~spl0_2),
% 0.30/1.33 inference(avatar_contradiction_clause,[status(thm)],[f211])).
% 0.30/1.33 thf(f211,plain,(
% 0.30/1.33 $false | ~spl0_2),
% 0.30/1.33 inference(subsumption_resolution,[status(thm)],[f208,f56])).
% 0.30/1.33 thf(f56,plain,(
% 0.30/1.33 ($true = (mrel @ mactual @ sK1))),
% 0.30/1.33 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 0.30/1.33 thf(f54,plain,(
% 0.30/1.33 ($false = ((mrel @ mactual @ sK1) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (p @ Y0)))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (q @ Y0)))))))),
% 0.30/1.33 inference(beta_eta_normalization,[status(thm)],[f53])).
% 0.30/1.33 thf(f53,plain,(
% 0.30/1.33 ($false = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (p @ Y1)))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (q @ Y1))))))) @ sK1))),
% 0.30/1.33 inference(sigma_clausification,[status(thm)],[f52])).
% 0.30/1.33 thf(f52,plain,(
% 0.30/1.33 ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (p @ Y1)))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (q @ Y1)))))))))),
% 0.30/1.33 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 0.30/1.33 thf(f208,plain,(
% 0.30/1.33 ($true != (mrel @ mactual @ sK1)) | ~spl0_2),
% 0.30/1.33 inference(trivial_inequality_removal,[status(thm)],[f203])).
% 0.30/1.33 thf(f203,plain,(
% 0.30/1.33 ($true != (mrel @ mactual @ sK1)) | ($true != $true) | ~spl0_2),
% 0.30/1.33 inference(superposition,[status(thm)],[f185,f69])).
% 0.30/1.33 thf(f69,plain,(
% 0.30/1.33 ((mrel @ mactual @ sK3) = $true)),
% 0.30/1.33 inference(binary_proxy_clausification,[status(thm)],[f67])).
% 0.30/1.33 thf(f185,plain,(
% 0.30/1.33 ( ! [X0 : mworld] : (((mrel @ X0 @ sK3) != $true) | ((mrel @ X0 @ sK1) != $true)) ) | ~spl0_2),
% 0.30/1.33 inference(avatar_component_clause,[status(thm)],[f184])).
% 0.30/1.33 thf(f184,definition,(
% 0.30/1.33 spl0_2 <=> ! [X0 : mworld] : (((mrel @ X0 @ sK3) != $true) | ((mrel @ X0 @ sK1) != $true))),
% 0.30/1.33 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 0.30/1.33 thf(f186,plain,(
% 0.30/1.33 spl0_1 | spl0_2),
% 0.30/1.33 inference(avatar_split_clause,[status(thm)],[f173,f184,f180])).
% 0.30/1.33 thf(f173,plain,(
% 0.30/1.33 ( ! [X0 : mworld] : (((p @ sK4) = $true) | ((mrel @ X0 @ sK3) != $true) | ((mrel @ X0 @ sK1) != $true)) )),
% 0.30/1.33 inference(trivial_inequality_removal,[status(thm)],[f170])).
% 0.30/1.33 thf(f170,plain,(
% 0.30/1.33 ( ! [X0 : mworld] : (((mrel @ X0 @ sK3) != $true) | ((mrel @ X0 @ sK1) != $true) | ($true != $true) | ((p @ sK4) = $true)) )),
% 0.30/1.33 inference(superposition,[status(thm)],[f108,f78])).
% 0.30/1.33 thf(f78,plain,(
% 0.30/1.33 ((mrel @ sK3 @ sK4) = $true)),
% 0.30/1.33 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 0.30/1.33 thf(f108,plain,(
% 0.30/1.33 ( ! [X2 : mworld,X0 : mworld,X1 : mworld] : (($true != (mrel @ X0 @ X1)) | ((p @ X1) = $true) | ((mrel @ X2 @ X0) != $true) | ((mrel @ X2 @ sK1) != $true)) )),
% 0.30/1.33 inference(trivial_inequality_removal,[status(thm)],[f107])).
% 0.30/1.33 thf(f107,plain,(
% 0.30/1.33 ( ! [X2 : mworld,X0 : mworld,X1 : mworld] : (((mrel @ X2 @ X0) != $true) | ((p @ X1) = $true) | ((mrel @ X2 @ sK1) != $true) | ($true != (mrel @ X0 @ X1)) | ($true != $true)) )),
% 0.30/1.33 inference(superposition,[status(thm)],[f90,f40])).
% 0.30/1.33 thf(f40,plain,(
% 0.30/1.33 ( ! [X2 : mworld,X0 : mworld,X1 : mworld] : (((mrel @ X0 @ X2) = $true) | ((mrel @ X1 @ X0) != $true) | ((mrel @ X1 @ X2) != $true)) )),
% 0.30/1.33 inference(cnf_transformation,[status(thm)],[f37])).
% 0.30/1.33 thf(f37,plain,(
% 0.30/1.33 ! [X0 : mworld,X1 : mworld,X2 : mworld] : (((mrel @ X1 @ X0) != $true) | ((mrel @ X1 @ X2) != $true) | ((mrel @ X0 @ X2) = $true))),
% 0.30/1.33 inference(flattening,[status(thm)],[f36])).
% 0.30/1.33 thf(f36,plain,(
% 0.30/1.33 ! [X0 : mworld,X1 : mworld,X2 : mworld] : (((mrel @ X0 @ X2) = $true) | (((mrel @ X1 @ X2) != $true) | ((mrel @ X1 @ X0) != $true)))),
% 0.30/1.33 inference(ennf_transformation,[status(thm)],[f24])).
% 0.30/1.33 thf(f24,plain,(
% 0.30/1.33 ! [X0 : mworld,X1 : mworld,X2 : mworld] : ((((mrel @ X1 @ X2) = $true) & ((mrel @ X1 @ X0) = $true)) => ((mrel @ X0 @ X2) = $true))),
% 0.30/1.33 inference(fool_elimination,[status(thm)],[f23])).
% 0.30/1.33 thf(f23,plain,(
% 0.30/1.33 ! [X0 : mworld,X1 : mworld,X2 : mworld] : (((mrel @ X1 @ X0) & (mrel @ X1 @ X2)) => (mrel @ X0 @ X2))),
% 0.30/1.33 inference(rectify,[status(thm)],[f10])).
% 0.30/1.33 thf(f10,axiom,(
% 0.30/1.33 ! [X5 : mworld,X2 : mworld,X4 : mworld] : (((mrel @ X2 @ X5) & (mrel @ X2 @ X4)) => (mrel @ X5 @ X4))),
% 0.30/1.33 file('/export/starexec/sandbox/tmp/tmp.edocsbdCrN/DTF2THF_22872.p',mrel_euclidean)).
% 0.30/1.33 thf(f90,plain,(
% 0.30/1.33 ( ! [X0 : mworld,X1 : mworld] : (((mrel @ X1 @ sK1) != $true) | ((p @ X0) = $true) | ((mrel @ X1 @ X0) != $true)) )),
% 0.30/1.33 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 0.30/1.33 thf(f88,plain,(
% 0.30/1.33 ( ! [X0 : mworld,X1 : mworld] : (((mrel @ X1 @ sK1) != $true) | ((p @ X0) = $true) | ($false = $true) | ((mrel @ X1 @ X0) != $true)) )),
% 0.30/1.33 inference(superposition,[status(thm)],[f61,f40])).
% 0.30/1.33 thf(f61,plain,(
% 0.30/1.33 ( ! [X1 : mworld] : (($false = (mrel @ sK1 @ X1)) | ((p @ X1) = $true)) )),
% 0.30/1.33 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 0.30/1.33 thf(f60,plain,(
% 0.30/1.33 ( ! [X1 : mworld] : ((((mrel @ sK1 @ X1) => (p @ X1)) = $true)) )),
% 0.30/1.33 inference(beta_eta_normalization,[status(thm)],[f59])).
% 0.30/1.33 thf(f59,plain,(
% 0.30/1.33 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (p @ Y0))) @ X1) = $true)) )),
% 0.30/1.33 inference(pi_clausification,[status(thm)],[f58])).
% 0.30/1.33 thf(f58,plain,(
% 0.30/1.33 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (p @ Y0)))))),
% 0.30/1.33 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 0.30/1.33 thf(f55,plain,(
% 0.30/1.33 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (p @ Y0)))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (q @ Y0))))) = $false)),
% 0.30/1.33 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 0.30/1.33 % SZS output end Proof for DTF2THF_22872
% 0.30/1.33 % (22969)------------------------------
% 0.30/1.33 % (22969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.33 % (22969)Termination reason: Refutation
% 0.30/1.33
% 0.30/1.33 % (22969)Memory used [KB]: 5628
% 0.30/1.33 % (22969)Time elapsed: 0.010 s
% 0.30/1.33 % (22969)Instructions burned: 21 (million)
% 0.30/1.33 % (22969)------------------------------
% 0.30/1.33 % (22969)------------------------------
% 0.30/1.33 % (22968)Success in time 0.018 s
%------------------------------------------------------------------------------