%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO895^9 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/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 1.57s 1.28s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 54 ( 37 unt; 0 typ; 2 def)
% Number of atoms : 258 ( 50 equ; 0 cnn)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 294 ( 15 ~; 12 |; 13 &; 212 @)
% ( 2 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 17 usr; 7 con; 0-3 aty)
% ( 13 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 75 ( 67 ^; 8 !; 0 ?; 75 :)
% 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_14,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_28,type,
sK0: mworld > mworld ).
thf(func_def_30,type,
sK2: mworld ).
thf(f99,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f70,f84,f98]) ).
thf(f98,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[status(thm)],[f97]) ).
thf(f97,plain,
( $false
| ~ spl1_1 ),
inference(trivial_inequality_removal,[status(thm)],[f96]) ).
thf(f96,plain,
( ( $false = $true )
| ~ spl1_1 ),
inference(forward_demodulation,[status(thm)],[f89,f65]) ).
thf(f65,plain,
( ( $false
= ( q @ sK2 ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f63]) ).
thf(f63,definition,
( spl1_1
<=> ( $false
= ( q @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f89,plain,
( $true
= ( q @ sK2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f87]) ).
thf(f87,plain,
( ( $true
= ( q @ sK2 ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f60,f56]) ).
thf(f56,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( q @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( q @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( q @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( q @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( q @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( q @ Y0 ) ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
& ( q @ Y0 ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ 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 ) )
@ p
@ q ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f39,f35,f38,f42,f41,f41,f41,f42]) ).
thf(f41,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,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/sandbox2/tmp/tmp.MwZyhhcEOB/DTF2THF_5640.p',mbox_def) ).
thf(f42,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f30]) ).
thf(f30,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( mand
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X3 @ X2 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MwZyhhcEOB/DTF2THF_5640.p',mand_def) ).
thf(f38,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,
( 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/sandbox2/tmp/tmp.MwZyhhcEOB/DTF2THF_5640.p',mimplies_def) ).
thf(f35,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,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/sandbox2/tmp/tmp.MwZyhhcEOB/DTF2THF_5640.p',mlocal_def) ).
thf(f39,plain,
( ( mlocal @ ( mimplies @ ( mand @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mbox @ ( mand @ p @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( ( mlocal @ ( mimplies @ ( mand @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mbox @ ( mand @ p @ q ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f27]) ).
thf(f27,plain,
( ( mlocal @ ( mimplies @ ( mand @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mbox @ ( mand @ p @ q ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f26]) ).
thf(f26,plain,
~ ( mlocal @ ( mimplies @ ( mand @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mbox @ ( mand @ p @ q ) ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,negated_conjecture,
~ ( mlocal @ ( mimplies @ ( mand @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mbox @ ( mand @ p @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
thf(f10,conjecture,
mlocal @ ( mimplies @ ( mand @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mbox @ ( mand @ p @ q ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MwZyhhcEOB/DTF2THF_5640.p',con) ).
thf(f60,plain,
( ( mrel @ mactual @ sK2 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( $false
= ( ( mrel @ mactual @ sK2 )
=> ( ( p @ sK2 )
& ( q @ sK2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
& ( q @ Y0 ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
& ( q @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f84,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[status(thm)],[f83]) ).
thf(f83,plain,
( $false
| ~ spl1_2 ),
inference(trivial_inequality_removal,[status(thm)],[f82]) ).
thf(f82,plain,
( ( $false = $true )
| ~ spl1_2 ),
inference(forward_demodulation,[status(thm)],[f75,f69]) ).
thf(f69,plain,
( ( $false
= ( p @ sK2 ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f67]) ).
thf(f67,definition,
( spl1_2
<=> ( $false
= ( p @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f75,plain,
( $true
= ( p @ sK2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
( ( $true
= ( p @ sK2 ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f53,f60]) ).
thf(f53,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( p @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( p @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( p @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( p @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f70,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f61,f67,f63]) ).
thf(f61,plain,
( ( $false
= ( q @ sK2 ) )
| ( $false
= ( p @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( $false
= ( ( p @ sK2 )
& ( q @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO895^9 : TPTP v9.2.1. Released v8.1.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n006.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 14:53:15 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SYO895^9 : TPTP v9.2.1. Released v8.1.0.
% 0.31/0.46 % Domain : Syntactic
% 0.31/0.46 % Problem : Modal propositional logic theorems. problem 10
% 0.31/0.46 % Version : [BP13] axioms.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.31/0.46 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.31/0.46 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.31/0.46 % Source : [TPTP]
% 0.31/0.46 % Names : SYM110+1 [QMLTP]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.00 v8.2.0, 0.15 v8.1.0
% 0.31/0.46 % Syntax : Number of formulae : 23 ( 9 unt; 13 typ; 8 def)
% 0.31/0.46 % Number of atoms : 30 ( 8 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 11 ( 3 avg)
% 0.31/0.46 % Number of connectives : 35 ( 1 ~; 1 |; 2 &; 28 @)
% 0.31/0.46 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 7 ( 2 avg)
% 0.31/0.46 % Number of types : 2 ( 1 usr)
% 0.31/0.46 % Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 13 ( 12 usr; 1 con; 0-3 aty)
% 0.31/0.46 % Number of variables : 23 ( 19 ^; 2 !; 2 ?; 23 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.31/0.46 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.31/0.46 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.31/0.46 % $modal == [$constants == $rigid,$quantification == $varying,
% 0.31/0.46 % $modalities == $modal_system_D].
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(mworld,type,
% 0.31/0.46 mworld: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(mrel_type,type,
% 0.31/0.46 mrel: mworld > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mactual_type,type,
% 0.31/0.46 mactual: mworld ).
% 0.31/0.46
% 0.31/0.46 thf(mlocal_type,type,
% 0.31/0.46 mlocal: ( mworld > $o ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mlocal_def,definition,
% 0.31/0.46 ( mlocal
% 0.31/0.46 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mnot_type,type,
% 0.31/0.46 mnot: ( mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mand_type,type,
% 0.31/0.46 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mor_type,type,
% 0.31/0.46 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mimplies_type,type,
% 0.31/0.46 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mequiv_type,type,
% 0.31/0.46 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mnot_def,definition,
% 0.31/0.46 ( mnot
% 0.31/0.46 = ( ^ [A: mworld > $o,W: mworld] :
% 0.31/0.46 ~ ( A @ W ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mand_def,definition,
% 0.31/0.46 ( mand
% 0.31/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/0.46 ( ( A @ W )
% 0.31/0.46 & ( B @ W ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mor_def,definition,
% 0.31/0.46 ( mor
% 0.31/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/0.46 ( ( A @ W )
% 0.31/0.46 | ( B @ W ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mimplies_def,definition,
% 0.31/0.46 ( mimplies
% 0.31/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/0.46 ( ( A @ W )
% 0.31/0.46 => ( B @ W ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mequiv_def,definition,
% 0.31/0.46 ( mequiv
% 0.31/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/0.46 ( ( A @ W )
% 0.31/0.46 <=> ( B @ W ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mbox_type,type,
% 0.31/0.46 mbox: ( mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mbox_def,definition,
% 0.31/0.46 ( mbox
% 0.31/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.31/0.46 ! [V: mworld] :
% 0.31/0.46 ( ( mrel @ W @ V )
% 0.31/0.46 => ( Phi @ V ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mdia_type,type,
% 0.31/0.46 mdia: ( mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mdia_def,definition,
% 0.31/0.46 ( mdia
% 0.31/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.31/0.46 ? [V: mworld] :
% 0.31/0.46 ( ( mrel @ W @ V )
% 0.31/0.46 & ( Phi @ V ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mrel_serial,axiom,
% 0.31/0.46 ! [W: mworld] :
% 0.31/0.46 ? [V: mworld] : ( mrel @ W @ V ) ).
% 0.31/0.46
% 0.31/0.46 thf(p_decl,type,
% 0.31/0.46 p: mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(q_decl,type,
% 0.31/0.46 q: mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(con,conjecture,
% 0.31/0.46 mlocal @ ( mimplies @ ( mand @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mbox @ ( mand @ p @ q ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.57/1.24 ---- Embedded in THF ---
% 1.57/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.57/1.24 %%% Generated on Tue Feb 24 14:53:16 EST 2026
% 1.57/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.57/1.24 %%% Logic specification used:
% 1.57/1.24 %%% thf(spec, logic, $$dhol).
% 1.57/1.24
% 1.57/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.MwZyhhcEOB/DTF2DTF5640.p
% See solution above
% 1.57/1.24 ------------------------
% 1.57/1.25 ---- Cleaned THF ---
% 1.57/1.25 thf(mworld,type,
% 1.57/1.25 mworld: $tType ).
% 1.57/1.25
% 1.57/1.25 thf(mrel_type,type,
% 1.57/1.25 mrel: mworld > mworld > $o ).
% 1.57/1.25
% 1.57/1.25 thf(mactual_type,type,
% 1.57/1.25 mactual: mworld ).
% 1.57/1.25
% 1.57/1.25 thf(mlocal_type,type,
% 1.57/1.25 mlocal: ( mworld > $o ) > $o ).
% 1.57/1.25
% 1.57/1.25 thf(mlocal_def,definition,
% 1.57/1.25 ( mlocal
% 1.57/1.25 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.57/1.25
% 1.57/1.25 thf(mnot_type,type,
% 1.57/1.25 mnot: ( mworld > $o ) > mworld > $o ).
% 1.57/1.25
% 1.57/1.25 thf(mand_type,type,
% 1.57/1.25 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.57/1.25
% 1.57/1.25 thf(mor_type,type,
% 1.57/1.25 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.57/1.25
% 1.57/1.25 thf(mimplies_type,type,
% 1.57/1.25 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.57/1.25
% 1.57/1.25 thf(mequiv_type,type,
% 1.57/1.25 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.57/1.25
% 1.57/1.25 thf(mnot_def,definition,
% 1.57/1.25 ( mnot
% 1.57/1.25 = ( ^ [A: mworld > $o,W: mworld] :
% 1.57/1.25 ~ ( A @ W ) ) ) ).
% 1.57/1.25
% 1.57/1.25 thf(mand_def,definition,
% 1.57/1.25 ( mand
% 1.57/1.25 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.57/1.25 ( ( A @ W )
% 1.57/1.25 & ( B @ W ) ) ) ) ).
% 1.57/1.25
% 1.57/1.25 thf(mor_def,definition,
% 1.57/1.25 ( mor
% 1.57/1.25 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.57/1.25 ( ( A @ W )
% 1.57/1.25 | ( B @ W ) ) ) ) ).
% 1.57/1.25
% 1.57/1.25 thf(mimplies_def,definition,
% 1.57/1.25 ( mimplies
% 1.57/1.25 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.57/1.25 ( ( A @ W )
% 1.57/1.25 => ( B @ W ) ) ) ) ).
% 1.57/1.25
% 1.57/1.25 thf(mequiv_def,definition,
% 1.57/1.25 ( mequiv
% 1.57/1.25 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.57/1.25 ( ( A @ W )
% 1.57/1.25 <=> ( B @ W ) ) ) ) ).
% 1.57/1.25
% 1.57/1.25 thf(mbox_type,type,
% 1.57/1.25 mbox: ( mworld > $o ) > mworld > $o ).
% 1.57/1.25
% 1.57/1.25 thf(mbox_def,definition,
% 1.57/1.25 ( mbox
% 1.57/1.25 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.57/1.25 ! [V: mworld] :
% 1.57/1.25 ( ( mrel @ W @ V )
% 1.57/1.25 => ( Phi @ V ) ) ) ) ).
% 1.57/1.25
% 1.57/1.25 thf(mdia_type,type,
% 1.57/1.25 mdia: ( mworld > $o ) > mworld > $o ).
% 1.57/1.25
% 1.57/1.25 thf(mdia_def,definition,
% 1.57/1.25 ( mdia
% 1.57/1.25 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.57/1.25 ? [V: mworld] :
% 1.57/1.25 ( ( mrel @ W @ V )
% 1.57/1.25 & ( Phi @ V ) ) ) ) ).
% 1.57/1.25
% 1.57/1.25 thf(mrel_serial,axiom,
% 1.57/1.25 ! [W: mworld] :
% 1.57/1.25 ? [V: mworld] : ( mrel @ W @ V ) ).
% 1.57/1.25
% 1.57/1.25 thf(p_decl,type,
% 1.57/1.25 p: mworld > $o ).
% 1.57/1.25
% 1.57/1.25 thf(q_decl,type,
% 1.57/1.25 q: mworld > $o ).
% 1.57/1.25
% 1.57/1.25 thf(con,conjecture,
% 1.57/1.25 mlocal @ ( mimplies @ ( mand @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mbox @ ( mand @ p @ q ) ) ) ).
% 1.57/1.25 ------------------------
% 1.57/1.27 % (5795)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_5640 for (2999ds/27Mi)
% 1.57/1.27 % (5798)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_5640 for (2999ds/275Mi)
% 1.57/1.28 % (5798)Refutation not found, incomplete strategy
% 1.57/1.28 % (5798)------------------------------
% 1.57/1.28 % (5798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.28 % (5798)Termination reason: Refutation not found, incomplete strategy
% 1.57/1.28
% 1.57/1.28
% 1.57/1.28 % (5798)Memory used [KB]: 5500
% 1.57/1.28 % (5798)Time elapsed: 0.004 s
% 1.57/1.28 % (5798)Instructions burned: 3 (million)
% 1.57/1.28 % (5798)------------------------------
% 1.57/1.28 % (5798)------------------------------
% 1.57/1.28 % (5799)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5640 for (2999ds/18Mi)
% 1.57/1.28 % (5795)First to succeed.
% 1.57/1.28 % (5795)Refutation found. Thanks to Tanya!
% 1.57/1.28 % SZS status Theorem for DTF2THF_5640
% 1.57/1.28 % SZS output start Proof for DTF2THF_5640
% 1.57/1.28 thf(type_def_5, type, mworld: $tType).
% 1.57/1.28 thf(func_def_0, type, mworld: $tType).
% 1.57/1.28 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.57/1.28 thf(func_def_2, type, mactual: mworld).
% 1.57/1.28 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.57/1.28 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.57/1.28 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.57/1.28 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.57/1.28 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.57/1.28 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.57/1.28 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.57/1.28 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.57/1.28 thf(func_def_12, type, p: mworld > $o).
% 1.57/1.28 thf(func_def_13, type, q: mworld > $o).
% 1.57/1.28 thf(func_def_14, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.57/1.28 thf(func_def_28, type, sK0: mworld > mworld).
% 1.57/1.28 thf(func_def_30, type, sK2: mworld).
% 1.57/1.28 thf(f99,plain,(
% 1.57/1.28 $false),
% 1.57/1.28 inference(avatar_sat_refutation,[status(thm)],[f70,f84,f98])).
% 1.57/1.28 thf(f98,plain,(
% 1.57/1.28 ~spl1_1),
% 1.57/1.28 inference(avatar_contradiction_clause,[status(thm)],[f97])).
% 1.57/1.28 thf(f97,plain,(
% 1.57/1.28 $false | ~spl1_1),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f96])).
% 1.57/1.28 thf(f96,plain,(
% 1.57/1.28 ($false = $true) | ~spl1_1),
% 1.57/1.28 inference(forward_demodulation,[status(thm)],[f89,f65])).
% 1.57/1.28 thf(f65,plain,(
% 1.57/1.28 ($false = (q @ sK2)) | ~spl1_1),
% 1.57/1.28 inference(avatar_component_clause,[status(thm)],[f63])).
% 1.57/1.28 thf(f63,definition,(
% 1.57/1.28 spl1_1 <=> ($false = (q @ sK2))),
% 1.57/1.28 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.57/1.28 thf(f89,plain,(
% 1.57/1.28 ($true = (q @ sK2))),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f87])).
% 1.57/1.28 thf(f87,plain,(
% 1.57/1.28 ($true = (q @ sK2)) | ($false = $true)),
% 1.57/1.28 inference(superposition,[status(thm)],[f60,f56])).
% 1.57/1.28 thf(f56,plain,(
% 1.57/1.28 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = (q @ X1))) )),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.57/1.28 thf(f55,plain,(
% 1.57/1.28 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => (q @ X1)) = $true)) )),
% 1.57/1.28 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.57/1.28 thf(f54,plain,(
% 1.57/1.28 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (q @ Y0))) @ X1))) )),
% 1.57/1.28 inference(pi_clausification,[status(thm)],[f49])).
% 1.57/1.28 thf(f49,plain,(
% 1.57/1.28 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (q @ Y0)))) = $true)),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.57/1.28 thf(f48,plain,(
% 1.57/1.28 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (p @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (q @ Y0))))))),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.57/1.28 thf(f46,plain,(
% 1.57/1.28 ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (p @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (q @ Y0))))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((p @ Y0) & (q @ Y0)))))) != $true)),
% 1.57/1.28 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.57/1.28 thf(f45,plain,(
% 1.57/1.28 ($true != ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ 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))))))) @ p @ q)))))),
% 1.57/1.28 inference(definition_unfolding,[status(thm)],[f39,f35,f38,f42,f41,f41,f41,f42])).
% 1.57/1.28 thf(f41,plain,(
% 1.57/1.28 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f15])).
% 1.57/1.28 thf(f15,plain,(
% 1.57/1.28 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.57/1.28 inference(fool_elimination,[status(thm)],[f14])).
% 1.57/1.28 thf(f14,plain,(
% 1.57/1.28 (mbox = (^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 1.57/1.28 inference(rectify,[status(thm)],[f7])).
% 1.57/1.28 thf(f7,axiom,(
% 1.57/1.28 (mbox = (^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))))),
% 1.57/1.28 file('/export/starexec/sandbox2/tmp/tmp.MwZyhhcEOB/DTF2THF_5640.p',mbox_def)).
% 1.57/1.28 thf(f42,plain,(
% 1.57/1.28 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f31])).
% 1.57/1.28 thf(f31,plain,(
% 1.57/1.28 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.57/1.28 inference(fool_elimination,[status(thm)],[f30])).
% 1.57/1.28 thf(f30,plain,(
% 1.57/1.28 (mand = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X0 @ X2))))),
% 1.57/1.28 inference(rectify,[status(thm)],[f3])).
% 1.57/1.28 thf(f3,axiom,(
% 1.57/1.28 (mand = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) & (X1 @ X2))))),
% 1.57/1.28 file('/export/starexec/sandbox2/tmp/tmp.MwZyhhcEOB/DTF2THF_5640.p',mand_def)).
% 1.57/1.28 thf(f38,plain,(
% 1.57/1.28 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f29])).
% 1.57/1.28 thf(f29,plain,(
% 1.57/1.28 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.57/1.28 inference(fool_elimination,[status(thm)],[f28])).
% 1.57/1.28 thf(f28,plain,(
% 1.57/1.28 (mimplies = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 1.57/1.28 inference(rectify,[status(thm)],[f5])).
% 1.57/1.28 thf(f5,axiom,(
% 1.57/1.28 (mimplies = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))))),
% 1.57/1.28 file('/export/starexec/sandbox2/tmp/tmp.MwZyhhcEOB/DTF2THF_5640.p',mimplies_def)).
% 1.57/1.28 thf(f35,plain,(
% 1.57/1.28 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f13])).
% 1.57/1.28 thf(f13,plain,(
% 1.57/1.28 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.57/1.28 inference(fool_elimination,[status(thm)],[f1])).
% 1.57/1.28 thf(f1,axiom,(
% 1.57/1.28 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 1.57/1.28 file('/export/starexec/sandbox2/tmp/tmp.MwZyhhcEOB/DTF2THF_5640.p',mlocal_def)).
% 1.57/1.28 thf(f39,plain,(
% 1.57/1.28 ((mlocal @ (mimplies @ (mand @ (mbox @ p) @ (mbox @ q)) @ (mbox @ (mand @ p @ q)))) != $true)),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f32])).
% 1.57/1.28 thf(f32,plain,(
% 1.57/1.28 ((mlocal @ (mimplies @ (mand @ (mbox @ p) @ (mbox @ q)) @ (mbox @ (mand @ p @ q)))) != $true)),
% 1.57/1.28 inference(flattening,[status(thm)],[f27])).
% 1.57/1.28 thf(f27,plain,(
% 1.57/1.28 ~((mlocal @ (mimplies @ (mand @ (mbox @ p) @ (mbox @ q)) @ (mbox @ (mand @ p @ q)))) = $true)),
% 1.57/1.28 inference(fool_elimination,[status(thm)],[f26])).
% 1.57/1.28 thf(f26,plain,(
% 1.57/1.28 ~(mlocal @ (mimplies @ (mand @ (mbox @ p) @ (mbox @ q)) @ (mbox @ (mand @ p @ q))))),
% 1.57/1.28 inference(rectify,[status(thm)],[f11])).
% 1.57/1.28 thf(f11,negated_conjecture,(
% 1.57/1.28 ~(mlocal @ (mimplies @ (mand @ (mbox @ p) @ (mbox @ q)) @ (mbox @ (mand @ p @ q))))),
% 1.57/1.28 inference(negated_conjecture,[status(cth)],[f10])).
% 1.57/1.28 thf(f10,conjecture,(
% 1.57/1.28 (mlocal @ (mimplies @ (mand @ (mbox @ p) @ (mbox @ q)) @ (mbox @ (mand @ p @ q))))),
% 1.57/1.28 file('/export/starexec/sandbox2/tmp/tmp.MwZyhhcEOB/DTF2THF_5640.p',con)).
% 1.57/1.28 thf(f60,plain,(
% 1.57/1.28 ((mrel @ mactual @ sK2) = $true)),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.57/1.28 thf(f58,plain,(
% 1.57/1.28 ($false = ((mrel @ mactual @ sK2) => ((p @ sK2) & (q @ sK2))))),
% 1.57/1.28 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.57/1.28 thf(f57,plain,(
% 1.57/1.28 ($false = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((p @ Y0) & (q @ Y0)))) @ sK2))),
% 1.57/1.28 inference(sigma_clausification,[status(thm)],[f47])).
% 1.57/1.28 thf(f47,plain,(
% 1.57/1.28 ($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((p @ Y0) & (q @ Y0))))))),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.57/1.28 thf(f84,plain,(
% 1.57/1.28 ~spl1_2),
% 1.57/1.28 inference(avatar_contradiction_clause,[status(thm)],[f83])).
% 1.57/1.28 thf(f83,plain,(
% 1.57/1.28 $false | ~spl1_2),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f82])).
% 1.57/1.28 thf(f82,plain,(
% 1.57/1.28 ($false = $true) | ~spl1_2),
% 1.57/1.28 inference(forward_demodulation,[status(thm)],[f75,f69])).
% 1.57/1.28 thf(f69,plain,(
% 1.57/1.28 ($false = (p @ sK2)) | ~spl1_2),
% 1.57/1.28 inference(avatar_component_clause,[status(thm)],[f67])).
% 1.57/1.28 thf(f67,definition,(
% 1.57/1.28 spl1_2 <=> ($false = (p @ sK2))),
% 1.57/1.28 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.57/1.28 thf(f75,plain,(
% 1.57/1.28 ($true = (p @ sK2))),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.57/1.28 thf(f71,plain,(
% 1.57/1.28 ($true = (p @ sK2)) | ($false = $true)),
% 1.57/1.28 inference(superposition,[status(thm)],[f53,f60])).
% 1.57/1.28 thf(f53,plain,(
% 1.57/1.28 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ((p @ X1) = $true)) )),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.57/1.28 thf(f52,plain,(
% 1.57/1.28 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (p @ X1)))) )),
% 1.57/1.28 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.57/1.28 thf(f51,plain,(
% 1.57/1.28 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (p @ Y0))) @ X1))) )),
% 1.57/1.28 inference(pi_clausification,[status(thm)],[f50])).
% 1.57/1.28 thf(f50,plain,(
% 1.57/1.28 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (p @ Y0)))) = $true)),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.57/1.28 thf(f70,plain,(
% 1.57/1.28 spl1_1 | spl1_2),
% 1.57/1.28 inference(avatar_split_clause,[status(thm)],[f61,f67,f63])).
% 1.57/1.28 thf(f61,plain,(
% 1.57/1.28 ($false = (q @ sK2)) | ($false = (p @ sK2))),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.57/1.28 thf(f59,plain,(
% 1.57/1.28 ($false = ((p @ sK2) & (q @ sK2)))),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.57/1.28 % SZS output end Proof for DTF2THF_5640
% 1.57/1.28 % (5795)------------------------------
% 1.57/1.28 % (5795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.28 % (5795)Termination reason: Refutation
% 1.57/1.28
% 1.57/1.28 % (5795)Memory used [KB]: 5500
% 1.57/1.28 % (5795)Time elapsed: 0.006 s
% 1.57/1.28 % (5795)Instructions burned: 6 (million)
% 1.57/1.28 % (5795)------------------------------
% 1.57/1.28 % (5795)------------------------------
% 1.57/1.28 % (5790)Success in time 0.011 s
%------------------------------------------------------------------------------