%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO902^8 : 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 : n021.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 09:55:10 AM UTC 2026
% Result : Theorem 1.70s 1.31s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 56 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 315 ( 66 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 421 ( 7 ~; 16 |; 33 &; 316 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 13 usr; 6 con; 0-3 aty)
% ( 8 !!; 23 ??; 0 @@+; 0 @@-)
% Number of variables : 107 ( 81 ^; 24 !; 2 ?; 107 :)
% 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 > mworld ).
thf(f107,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f106]) ).
thf(f106,plain,
$true = $false,
inference(backward_demodulation,[status(thm)],[f67,f104]) ).
thf(f104,plain,
( $false
= ( p @ ( sK2 @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f98]) ).
thf(f98,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK2 @ sK1 ) ) ) ),
inference(superposition,[status(thm)],[f89,f71]) ).
thf(f71,plain,
( $true
= ( mrel @ sK1 @ ( sK2 @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ( $true = $false )
| ( $true
= ( mrel @ sK1 @ ( sK2 @ sK1 ) ) ) ),
inference(superposition,[status(thm)],[f42,f56]) ).
thf(f56,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( mrel @ X1 @ ( sK2 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( ( p @ ( sK2 @ X1 ) )
& ( mrel @ X1 @ ( sK2 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ X1 @ Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $false
= ( mrel @ sK1 @ X1 ) ) ),
inference(sigma_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ X1 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ sK1 @ X1 )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ X1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( p @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( p @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( p @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) )
& ( mrel @ mactual @ sK1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( p @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) )
& ( mrel @ mactual @ Y0 ) )
@ sK1 )
= $true ),
inference(sigma_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( p @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) )
& ( mrel @ mactual @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( $true
!= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( p @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) )
& ( mrel @ mactual @ Y0 ) ) )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( p @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( 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] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ p ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ p ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f38,f41,f40,f33,f34,f33,f33,f33]) ).
thf(f34,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f27]) ).
thf(f27,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.T1TUnQspu6/DTF2THF_15326.p',mbox_def) ).
thf(f33,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( mrel @ X1 @ X2 )
& ( X0 @ X2 ) ) )
= mdia ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
( ( ^ [X0: mworld > $o,X2: mworld] :
? [X4: mworld] :
( ( mrel @ X2 @ X4 )
& ( X0 @ X4 ) ) )
= mdia ),
file('/export/starexec/sandbox/tmp/tmp.T1TUnQspu6/DTF2THF_15326.p',mdia_def) ).
thf(f40,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,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.T1TUnQspu6/DTF2THF_15326.p',mimplies_def) ).
thf(f41,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,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.T1TUnQspu6/DTF2THF_15326.p',mlocal_def) ).
thf(f38,plain,
( ( mlocal @ ( mimplies @ ( mdia @ ( mbox @ ( mdia @ p ) ) ) @ ( mdia @ ( mdia @ p ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( ( mlocal @ ( mimplies @ ( mdia @ ( mbox @ ( mdia @ p ) ) ) @ ( mdia @ ( mdia @ p ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f24]) ).
thf(f24,plain,
( ( mlocal @ ( mimplies @ ( mdia @ ( mbox @ ( mdia @ p ) ) ) @ ( mdia @ ( mdia @ p ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
~ ( mlocal @ ( mimplies @ ( mdia @ ( mbox @ ( mdia @ p ) ) ) @ ( mdia @ ( mdia @ p ) ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,negated_conjecture,
~ ( mlocal @ ( mimplies @ ( mdia @ ( mbox @ ( mdia @ p ) ) ) @ ( mdia @ ( mdia @ p ) ) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
thf(f10,conjecture,
mlocal @ ( mimplies @ ( mdia @ ( mbox @ ( mdia @ p ) ) ) @ ( mdia @ ( mdia @ p ) ) ),
file('/export/starexec/sandbox/tmp/tmp.T1TUnQspu6/DTF2THF_15326.p',con) ).
thf(f42,plain,
! [X0: mworld] :
( $true
= ( mrel @ X0 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: mworld] :
( $true
= ( mrel @ X0 @ X0 ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
! [X2: mworld] : ( mrel @ X2 @ X2 ),
file('/export/starexec/sandbox/tmp/tmp.T1TUnQspu6/DTF2THF_15326.p',mrel_reflexive) ).
thf(f89,plain,
! [X0: mworld] :
( ( $false
= ( mrel @ sK1 @ X0 ) )
| ( $false
= ( p @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f82]) ).
thf(f82,plain,
! [X0: mworld] :
( ( $false
= ( p @ X0 ) )
| ( $false
= ( mrel @ sK1 @ X0 ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f49,f63]) ).
thf(f63,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( mrel @ X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( ( p @ X2 )
& ( mrel @ X1 @ X2 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ X1 @ Y0 ) )
@ X2 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ X1 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X1: mworld] :
( $false
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ X1 @ Y0 ) ) )
& ( mrel @ mactual @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
! [X1: mworld] :
( $false
= ( ^ [Y0: mworld] :
( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( p @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( mrel @ mactual @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( p @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( mrel @ mactual @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f49,plain,
( $true
= ( mrel @ mactual @ sK1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f67,plain,
( $true
= ( p @ ( sK2 @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK2 @ sK1 ) ) ) ),
inference(superposition,[status(thm)],[f57,f42]) ).
thf(f57,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( p @ ( sK2 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO902^8 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n021.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 14:53:39 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SYO902^8 : TPTP v9.2.1. Released v8.1.0.
% 0.18/0.45 % Domain : Syntactic
% 0.18/0.45 % Problem : Popcorn problem
% 0.18/0.45 % Version : [BP13] axioms.
% 0.18/0.45 % English :
% 0.18/0.45
% 0.18/0.45 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.18/0.45 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.18/0.45 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.18/0.45 % Source : [TPTP]
% 0.18/0.45 % Names : SYM190+1 [QMLTP]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.00 v8.2.0, 0.15 v8.1.0
% 0.18/0.45 % Syntax : Number of formulae : 22 ( 9 unt; 12 typ; 8 def)
% 0.18/0.45 % Number of atoms : 28 ( 8 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 9 ( 2 avg)
% 0.18/0.45 % Number of connectives : 33 ( 1 ~; 1 |; 2 &; 26 @)
% 0.18/0.45 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 7 ( 2 avg)
% 0.18/0.45 % Number of types : 2 ( 1 usr)
% 0.18/0.45 % Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 12 ( 11 usr; 1 con; 0-3 aty)
% 0.18/0.45 % Number of variables : 22 ( 19 ^; 2 !; 1 ?; 22 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.18/0.45 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.18/0.45 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.18/0.45 % $modal == [$constants == $rigid,$quantification == $varying,
% 0.18/0.45 % $modalities == $modal_system_T].
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(mworld,type,
% 0.18/0.45 mworld: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(mrel_type,type,
% 0.18/0.45 mrel: mworld > mworld > $o ).
% 0.18/0.45
% 0.18/0.45 thf(mactual_type,type,
% 0.18/0.45 mactual: mworld ).
% 0.18/0.45
% 0.18/0.45 thf(mlocal_type,type,
% 0.18/0.45 mlocal: ( mworld > $o ) > $o ).
% 0.18/0.45
% 0.18/0.45 thf(mlocal_def,definition,
% 0.18/0.45 ( mlocal
% 0.18/0.45 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(mnot_type,type,
% 0.18/0.45 mnot: ( mworld > $o ) > mworld > $o ).
% 0.18/0.45
% 0.18/0.45 thf(mand_type,type,
% 0.18/0.45 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.18/0.45
% 0.18/0.45 thf(mor_type,type,
% 0.18/0.45 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.18/0.45
% 0.18/0.45 thf(mimplies_type,type,
% 0.18/0.45 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.18/0.45
% 0.18/0.45 thf(mequiv_type,type,
% 0.18/0.45 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.18/0.45
% 0.18/0.45 thf(mnot_def,definition,
% 0.18/0.45 ( mnot
% 0.18/0.45 = ( ^ [A: mworld > $o,W: mworld] :
% 0.18/0.45 ~ ( A @ W ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(mand_def,definition,
% 0.18/0.45 ( mand
% 0.18/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.18/0.45 ( ( A @ W )
% 0.18/0.45 & ( B @ W ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(mor_def,definition,
% 0.18/0.45 ( mor
% 0.18/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.18/0.45 ( ( A @ W )
% 0.18/0.45 | ( B @ W ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(mimplies_def,definition,
% 0.18/0.45 ( mimplies
% 0.18/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.18/0.45 ( ( A @ W )
% 0.18/0.45 => ( B @ W ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(mequiv_def,definition,
% 0.18/0.45 ( mequiv
% 0.18/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.18/0.45 ( ( A @ W )
% 0.18/0.45 <=> ( B @ W ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(mbox_type,type,
% 0.18/0.45 mbox: ( mworld > $o ) > mworld > $o ).
% 0.18/0.45
% 0.18/0.45 thf(mbox_def,definition,
% 0.18/0.45 ( mbox
% 0.18/0.45 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.18/0.45 ! [V: mworld] :
% 0.18/0.45 ( ( mrel @ W @ V )
% 0.18/0.45 => ( Phi @ V ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(mdia_type,type,
% 0.18/0.45 mdia: ( mworld > $o ) > mworld > $o ).
% 0.18/0.45
% 0.18/0.45 thf(mdia_def,definition,
% 0.18/0.45 ( mdia
% 0.18/0.45 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.18/0.45 ? [V: mworld] :
% 0.18/0.45 ( ( mrel @ W @ V )
% 0.18/0.45 & ( Phi @ V ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(mrel_reflexive,axiom,
% 0.18/0.45 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.18/0.45
% 0.18/0.45 thf(p_decl,type,
% 0.18/0.45 p: mworld > $o ).
% 0.18/0.45
% 0.18/0.45 thf(con,conjecture,
% 0.18/0.45 mlocal @ ( mimplies @ ( mdia @ ( mbox @ ( mdia @ p ) ) ) @ ( mdia @ ( mdia @ p ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.55/1.27 ---- Embedded in THF ---
% 1.55/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.55/1.27 %%% Generated on Tue Feb 24 14:53:39 EST 2026
% 1.55/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.55/1.27 %%% Logic specification used:
% 1.55/1.27 %%% thf(spec, logic, $$dhol).
% 1.55/1.27
% 1.55/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.T1TUnQspu6/DTF2DTF15326.p
% See solution above
% 1.55/1.27 ------------------------
% 1.55/1.28 ---- Cleaned THF ---
% 1.55/1.28 thf(mworld,type,
% 1.55/1.28 mworld: $tType ).
% 1.55/1.28
% 1.55/1.28 thf(mrel_type,type,
% 1.55/1.28 mrel: mworld > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mactual_type,type,
% 1.55/1.28 mactual: mworld ).
% 1.55/1.28
% 1.55/1.28 thf(mlocal_type,type,
% 1.55/1.28 mlocal: ( mworld > $o ) > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mlocal_def,definition,
% 1.55/1.28 ( mlocal
% 1.55/1.28 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mnot_type,type,
% 1.55/1.28 mnot: ( mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mand_type,type,
% 1.55/1.28 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mor_type,type,
% 1.55/1.28 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mimplies_type,type,
% 1.55/1.28 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mequiv_type,type,
% 1.55/1.28 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mnot_def,definition,
% 1.55/1.28 ( mnot
% 1.55/1.28 = ( ^ [A: mworld > $o,W: mworld] :
% 1.55/1.28 ~ ( A @ W ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mand_def,definition,
% 1.55/1.28 ( mand
% 1.55/1.28 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.55/1.28 ( ( A @ W )
% 1.55/1.28 & ( B @ W ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mor_def,definition,
% 1.55/1.28 ( mor
% 1.55/1.28 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.55/1.28 ( ( A @ W )
% 1.55/1.28 | ( B @ W ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mimplies_def,definition,
% 1.55/1.28 ( mimplies
% 1.55/1.28 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.55/1.28 ( ( A @ W )
% 1.55/1.28 => ( B @ W ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mequiv_def,definition,
% 1.55/1.28 ( mequiv
% 1.55/1.28 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.55/1.28 ( ( A @ W )
% 1.55/1.28 <=> ( B @ W ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mbox_type,type,
% 1.55/1.28 mbox: ( mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mbox_def,definition,
% 1.55/1.28 ( mbox
% 1.55/1.28 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.55/1.28 ! [V: mworld] :
% 1.55/1.28 ( ( mrel @ W @ V )
% 1.55/1.28 => ( Phi @ V ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mdia_type,type,
% 1.55/1.28 mdia: ( mworld > $o ) > mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(mdia_def,definition,
% 1.55/1.28 ( mdia
% 1.55/1.28 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.55/1.28 ? [V: mworld] :
% 1.55/1.28 ( ( mrel @ W @ V )
% 1.55/1.28 & ( Phi @ V ) ) ) ) ).
% 1.55/1.28
% 1.55/1.28 thf(mrel_reflexive,axiom,
% 1.55/1.28 ! [W: mworld] : ( mrel @ W @ W ) ).
% 1.55/1.28
% 1.55/1.28 thf(p_decl,type,
% 1.55/1.28 p: mworld > $o ).
% 1.55/1.28
% 1.55/1.28 thf(con,conjecture,
% 1.55/1.28 mlocal @ ( mimplies @ ( mdia @ ( mbox @ ( mdia @ p ) ) ) @ ( mdia @ ( mdia @ p ) ) ) ).
% 1.55/1.28 ------------------------
% 1.55/1.29 % (15426)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15326 for (2999ds/2Mi)
% 1.55/1.30 % (15426)Instruction limit reached!
% 1.55/1.30 % (15426)------------------------------
% 1.55/1.30 % (15426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.30 % (15426)Termination reason: Unknown
% 1.55/1.30 % (15426)Termination phase: Clausification
% 1.55/1.30
% 1.55/1.30 % (15426)Memory used [KB]: 895
% 1.55/1.30 % (15426)Time elapsed: 0.002 s
% 1.55/1.30 % (15426)Instructions burned: 2 (million)
% 1.55/1.30 % (15426)------------------------------
% 1.55/1.30 % (15426)------------------------------
% 1.55/1.30 % (15424)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_15326 for (2999ds/4Mi)
% 1.70/1.30 % (15424)Instruction limit reached!
% 1.70/1.30 % (15424)------------------------------
% 1.70/1.30 % (15424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.30 % (15424)Termination reason: Unknown
% 1.70/1.30 % (15424)Termination phase: Saturation
% 1.70/1.30
% 1.70/1.30 % (15424)Memory used [KB]: 5500
% 1.70/1.30 % (15424)Time elapsed: 0.003 s
% 1.70/1.30 % (15424)Instructions burned: 5 (million)
% 1.70/1.30 % (15424)------------------------------
% 1.70/1.30 % (15424)------------------------------
% 1.70/1.30 % (15423)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15326 for (2999ds/183Mi)
% 1.70/1.30 % (15427)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_15326 for (2999ds/2Mi)
% 1.70/1.30 % (15428)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_15326 for (2999ds/275Mi)
% 1.70/1.30 % (15429)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15326 for (2999ds/18Mi)
% 1.70/1.30 % (15425)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_15326 for (2999ds/27Mi)
% 1.70/1.30 % (15427)Instruction limit reached!
% 1.70/1.30 % (15427)------------------------------
% 1.70/1.30 % (15427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.30 % (15427)Termination reason: Unknown
% 1.70/1.30 % (15427)Termination phase: Property scanning
% 1.70/1.30
% 1.70/1.30 % (15427)Memory used [KB]: 1023
% 1.70/1.30 % (15427)Time elapsed: 0.003 s
% 1.70/1.30 % (15427)Instructions burned: 2 (million)
% 1.70/1.30 % (15427)------------------------------
% 1.70/1.30 % (15427)------------------------------
% 1.70/1.30 % (15428)Refutation not found, incomplete strategy
% 1.70/1.30 % (15428)------------------------------
% 1.70/1.30 % (15428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.30 % (15428)Termination reason: Refutation not found, incomplete strategy
% 1.70/1.30
% 1.70/1.30
% 1.70/1.30 % (15428)Memory used [KB]: 5500
% 1.70/1.30 % (15428)Time elapsed: 0.004 s
% 1.70/1.30 % (15428)Instructions burned: 2 (million)
% 1.70/1.30 % (15430)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15326 for (2999ds/3Mi)
% 1.70/1.30 % (15428)------------------------------
% 1.70/1.30 % (15428)------------------------------
% 1.70/1.31 % (15430)Instruction limit reached!
% 1.70/1.31 % (15430)------------------------------
% 1.70/1.31 % (15430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.31 % (15430)Termination reason: Unknown
% 1.70/1.31 % (15430)Termination phase: Saturation
% 1.70/1.31
% 1.70/1.31 % (15430)Memory used [KB]: 5500
% 1.70/1.31 % (15430)Time elapsed: 0.002 s
% 1.70/1.31 % (15430)Instructions burned: 4 (million)
% 1.70/1.31 % (15430)------------------------------
% 1.70/1.31 % (15430)------------------------------
% 1.70/1.31 % (15431)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_15326 for (2999ds/37Mi)
% 1.70/1.31 % (15429)First to succeed.
% 1.70/1.31 % (15423)Also succeeded, but the first one will report.
% 1.70/1.31 % (15429)Refutation found. Thanks to Tanya!
% 1.70/1.31 % SZS status Theorem for DTF2THF_15326
% 1.70/1.31 % SZS output start Proof for DTF2THF_15326
% 1.70/1.31 thf(type_def_5, type, mworld: $tType).
% 1.70/1.31 thf(func_def_0, type, mworld: $tType).
% 1.70/1.31 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.70/1.31 thf(func_def_2, type, mactual: mworld).
% 1.70/1.31 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.70/1.31 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.70/1.31 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.70/1.31 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.70/1.31 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.70/1.31 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.70/1.31 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.70/1.31 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.70/1.31 thf(func_def_12, type, p: mworld > $o).
% 1.70/1.31 thf(func_def_27, type, sK1: mworld).
% 1.70/1.31 thf(func_def_28, type, sK2: mworld > mworld).
% 1.70/1.31 thf(f107,plain,(
% 1.70/1.31 $false),
% 1.70/1.31 inference(trivial_inequality_removal,[status(thm)],[f106])).
% 1.70/1.31 thf(f106,plain,(
% 1.70/1.31 ($true = $false)),
% 1.70/1.31 inference(backward_demodulation,[status(thm)],[f67,f104])).
% 1.70/1.31 thf(f104,plain,(
% 1.70/1.31 ($false = (p @ (sK2 @ sK1)))),
% 1.70/1.31 inference(trivial_inequality_removal,[status(thm)],[f98])).
% 1.70/1.31 thf(f98,plain,(
% 1.70/1.31 ($true = $false) | ($false = (p @ (sK2 @ sK1)))),
% 1.70/1.31 inference(superposition,[status(thm)],[f89,f71])).
% 1.70/1.31 thf(f71,plain,(
% 1.70/1.31 ($true = (mrel @ sK1 @ (sK2 @ sK1)))),
% 1.70/1.31 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.70/1.31 thf(f69,plain,(
% 1.70/1.31 ($true = $false) | ($true = (mrel @ sK1 @ (sK2 @ sK1)))),
% 1.70/1.31 inference(superposition,[status(thm)],[f42,f56])).
% 1.70/1.31 thf(f56,plain,(
% 1.70/1.31 ( ! [X1 : mworld] : (($false = (mrel @ sK1 @ X1)) | ($true = (mrel @ X1 @ (sK2 @ X1)))) )),
% 1.70/1.31 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.70/1.31 thf(f55,plain,(
% 1.70/1.31 ( ! [X1 : mworld] : (($false = (mrel @ sK1 @ X1)) | ($true = ((p @ (sK2 @ X1)) & (mrel @ X1 @ (sK2 @ X1))))) )),
% 1.70/1.31 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.70/1.31 thf(f54,plain,(
% 1.70/1.31 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((p @ Y0) & (mrel @ X1 @ Y0))) @ (sK2 @ X1))) | ($false = (mrel @ sK1 @ X1))) )),
% 1.70/1.31 inference(sigma_clausification,[status(thm)],[f53])).
% 1.70/1.31 thf(f53,plain,(
% 1.70/1.31 ( ! [X1 : mworld] : (($false = (mrel @ sK1 @ X1)) | ($true = (?? @ mworld @ (^[Y0 : mworld]: ((p @ Y0) & (mrel @ X1 @ Y0)))))) )),
% 1.70/1.31 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.70/1.31 thf(f52,plain,(
% 1.70/1.31 ( ! [X1 : mworld] : (($true = ((mrel @ sK1 @ X1) => (?? @ mworld @ (^[Y0 : mworld]: ((p @ Y0) & (mrel @ X1 @ Y0))))))) )),
% 1.70/1.31 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.70/1.31 thf(f51,plain,(
% 1.70/1.31 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((p @ Y1) & (mrel @ Y0 @ Y1)))))) @ X1))) )),
% 1.70/1.31 inference(pi_clausification,[status(thm)],[f50])).
% 1.70/1.31 thf(f50,plain,(
% 1.70/1.31 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((p @ Y1) & (mrel @ Y0 @ Y1))))))))),
% 1.70/1.31 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.70/1.31 thf(f48,plain,(
% 1.70/1.31 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((p @ Y1) & (mrel @ Y0 @ Y1))))))) & (mrel @ mactual @ sK1)))),
% 1.70/1.31 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.70/1.31 thf(f47,plain,(
% 1.70/1.31 (((^[Y0 : mworld]: ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (?? @ mworld @ (^[Y2 : mworld]: ((p @ Y2) & (mrel @ Y1 @ Y2))))))) & (mrel @ mactual @ Y0))) @ sK1) = $true)),
% 1.70/1.31 inference(sigma_clausification,[status(thm)],[f46])).
% 1.70/1.31 thf(f46,plain,(
% 1.70/1.31 ($true = (?? @ mworld @ (^[Y0 : mworld]: ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (?? @ mworld @ (^[Y2 : mworld]: ((p @ Y2) & (mrel @ Y1 @ Y2))))))) & (mrel @ mactual @ Y0)))))),
% 1.70/1.31 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.70/1.31 thf(f44,plain,(
% 1.70/1.31 ($true != ((?? @ mworld @ (^[Y0 : mworld]: ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (?? @ mworld @ (^[Y2 : mworld]: ((p @ Y2) & (mrel @ Y1 @ Y2))))))) & (mrel @ mactual @ Y0)))) => (?? @ mworld @ (^[Y0 : mworld]: ((?? @ mworld @ (^[Y1 : mworld]: ((p @ Y1) & (mrel @ Y0 @ Y1)))) & (mrel @ mactual @ Y0))))))),
% 1.70/1.31 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.70/1.31 thf(f43,plain,(
% 1.70/1.31 ($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]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ p))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ p)))))),
% 1.70/1.31 inference(definition_unfolding,[status(thm)],[f38,f41,f40,f33,f34,f33,f33,f33])).
% 1.70/1.31 thf(f34,plain,(
% 1.70/1.31 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.70/1.31 inference(cnf_transformation,[status(thm)],[f28])).
% 1.70/1.31 thf(f28,plain,(
% 1.70/1.31 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.70/1.31 inference(fool_elimination,[status(thm)],[f27])).
% 1.70/1.31 thf(f27,plain,(
% 1.70/1.31 (mbox = (^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 1.70/1.31 inference(rectify,[status(thm)],[f7])).
% 1.70/1.31 thf(f7,axiom,(
% 1.70/1.31 (mbox = (^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))))),
% 1.70/1.31 file('/export/starexec/sandbox/tmp/tmp.T1TUnQspu6/DTF2THF_15326.p',mbox_def)).
% 1.70/1.31 thf(f33,plain,(
% 1.70/1.31 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))))),
% 1.70/1.31 inference(cnf_transformation,[status(thm)],[f14])).
% 1.70/1.31 thf(f14,plain,(
% 1.70/1.31 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))))),
% 1.70/1.31 inference(fool_elimination,[status(thm)],[f13])).
% 1.70/1.31 thf(f13,plain,(
% 1.70/1.31 ((^[X0 : mworld > $o, X1 : mworld] : (? [X2 : mworld] : ((mrel @ X1 @ X2) & (X0 @ X2)))) = mdia)),
% 1.70/1.31 inference(rectify,[status(thm)],[f8])).
% 1.70/1.31 thf(f8,axiom,(
% 1.70/1.31 ((^[X0 : mworld > $o, X2 : mworld] : (? [X4 : mworld] : ((mrel @ X2 @ X4) & (X0 @ X4)))) = mdia)),
% 1.70/1.31 file('/export/starexec/sandbox/tmp/tmp.T1TUnQspu6/DTF2THF_15326.p',mdia_def)).
% 1.70/1.31 thf(f40,plain,(
% 1.70/1.31 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.70/1.31 inference(cnf_transformation,[status(thm)],[f16])).
% 1.70/1.31 thf(f16,plain,(
% 1.70/1.31 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.70/1.31 inference(fool_elimination,[status(thm)],[f15])).
% 1.70/1.31 thf(f15,plain,(
% 1.70/1.31 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 1.70/1.31 inference(rectify,[status(thm)],[f5])).
% 1.70/1.31 thf(f5,axiom,(
% 1.70/1.31 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))) = mimplies)),
% 1.70/1.31 file('/export/starexec/sandbox/tmp/tmp.T1TUnQspu6/DTF2THF_15326.p',mimplies_def)).
% 1.70/1.31 thf(f41,plain,(
% 1.70/1.31 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.70/1.31 inference(cnf_transformation,[status(thm)],[f31])).
% 1.70/1.31 thf(f31,plain,(
% 1.70/1.31 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.70/1.31 inference(fool_elimination,[status(thm)],[f1])).
% 1.70/1.31 thf(f1,axiom,(
% 1.70/1.31 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 1.70/1.31 file('/export/starexec/sandbox/tmp/tmp.T1TUnQspu6/DTF2THF_15326.p',mlocal_def)).
% 1.70/1.31 thf(f38,plain,(
% 1.70/1.31 ((mlocal @ (mimplies @ (mdia @ (mbox @ (mdia @ p))) @ (mdia @ (mdia @ p)))) != $true)),
% 1.70/1.31 inference(cnf_transformation,[status(thm)],[f32])).
% 1.70/1.31 thf(f32,plain,(
% 1.70/1.31 ((mlocal @ (mimplies @ (mdia @ (mbox @ (mdia @ p))) @ (mdia @ (mdia @ p)))) != $true)),
% 1.70/1.31 inference(flattening,[status(thm)],[f24])).
% 1.70/1.31 thf(f24,plain,(
% 1.70/1.31 ~((mlocal @ (mimplies @ (mdia @ (mbox @ (mdia @ p))) @ (mdia @ (mdia @ p)))) = $true)),
% 1.70/1.31 inference(fool_elimination,[status(thm)],[f23])).
% 1.70/1.31 thf(f23,plain,(
% 1.70/1.31 ~(mlocal @ (mimplies @ (mdia @ (mbox @ (mdia @ p))) @ (mdia @ (mdia @ p))))),
% 1.70/1.31 inference(rectify,[status(thm)],[f11])).
% 1.70/1.31 thf(f11,negated_conjecture,(
% 1.70/1.31 ~(mlocal @ (mimplies @ (mdia @ (mbox @ (mdia @ p))) @ (mdia @ (mdia @ p))))),
% 1.70/1.31 inference(negated_conjecture,[status(cth)],[f10])).
% 1.70/1.31 thf(f10,conjecture,(
% 1.70/1.31 (mlocal @ (mimplies @ (mdia @ (mbox @ (mdia @ p))) @ (mdia @ (mdia @ p))))),
% 1.70/1.31 file('/export/starexec/sandbox/tmp/tmp.T1TUnQspu6/DTF2THF_15326.p',con)).
% 1.70/1.31 thf(f42,plain,(
% 1.70/1.31 ( ! [X0 : mworld] : (($true = (mrel @ X0 @ X0))) )),
% 1.70/1.31 inference(cnf_transformation,[status(thm)],[f20])).
% 1.70/1.31 thf(f20,plain,(
% 1.70/1.31 ! [X0 : mworld] : ($true = (mrel @ X0 @ X0))),
% 1.70/1.31 inference(fool_elimination,[status(thm)],[f19])).
% 1.70/1.31 thf(f19,plain,(
% 1.70/1.31 ! [X0 : mworld] : (mrel @ X0 @ X0)),
% 1.70/1.31 inference(rectify,[status(thm)],[f9])).
% 1.70/1.31 thf(f9,axiom,(
% 1.70/1.31 ! [X2 : mworld] : (mrel @ X2 @ X2)),
% 1.70/1.31 file('/export/starexec/sandbox/tmp/tmp.T1TUnQspu6/DTF2THF_15326.p',mrel_reflexive)).
% 1.70/1.31 thf(f89,plain,(
% 1.70/1.31 ( ! [X0 : mworld] : (($false = (mrel @ sK1 @ X0)) | ($false = (p @ X0))) )),
% 1.70/1.31 inference(trivial_inequality_removal,[status(thm)],[f82])).
% 1.70/1.31 thf(f82,plain,(
% 1.70/1.31 ( ! [X0 : mworld] : (($false = (p @ X0)) | ($false = (mrel @ sK1 @ X0)) | ($true = $false)) )),
% 1.70/1.31 inference(superposition,[status(thm)],[f49,f63])).
% 1.70/1.31 thf(f63,plain,(
% 1.70/1.31 ( ! [X2 : mworld,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($false = (p @ X2)) | ($false = (mrel @ X1 @ X2))) )),
% 1.70/1.31 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 1.70/1.31 thf(f62,plain,(
% 1.70/1.31 ( ! [X2 : mworld,X1 : mworld] : (($false = ((p @ X2) & (mrel @ X1 @ X2))) | ($false = (mrel @ mactual @ X1))) )),
% 1.70/1.31 inference(beta_eta_normalization,[status(thm)],[f61])).
% 1.70/1.31 thf(f61,plain,(
% 1.70/1.31 ( ! [X2 : mworld,X1 : mworld] : (($false = ((^[Y0 : mworld]: ((p @ Y0) & (mrel @ X1 @ Y0))) @ X2)) | ($false = (mrel @ mactual @ X1))) )),
% 1.70/1.31 inference(pi_clausification,[status(thm)],[f60])).
% 1.70/1.31 thf(f60,plain,(
% 1.70/1.31 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($false = (?? @ mworld @ (^[Y0 : mworld]: ((p @ Y0) & (mrel @ X1 @ Y0)))))) )),
% 1.70/1.31 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.70/1.31 thf(f59,plain,(
% 1.70/1.31 ( ! [X1 : mworld] : (($false = ((?? @ mworld @ (^[Y0 : mworld]: ((p @ Y0) & (mrel @ X1 @ Y0)))) & (mrel @ mactual @ X1)))) )),
% 1.70/1.31 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.70/1.31 thf(f58,plain,(
% 1.70/1.31 ( ! [X1 : mworld] : (($false = ((^[Y0 : mworld]: ((?? @ mworld @ (^[Y1 : mworld]: ((p @ Y1) & (mrel @ Y0 @ Y1)))) & (mrel @ mactual @ Y0))) @ X1))) )),
% 1.70/1.31 inference(pi_clausification,[status(thm)],[f45])).
% 1.70/1.31 thf(f45,plain,(
% 1.70/1.31 ($false = (?? @ mworld @ (^[Y0 : mworld]: ((?? @ mworld @ (^[Y1 : mworld]: ((p @ Y1) & (mrel @ Y0 @ Y1)))) & (mrel @ mactual @ Y0)))))),
% 1.70/1.31 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.70/1.31 thf(f49,plain,(
% 1.70/1.31 ($true = (mrel @ mactual @ sK1))),
% 1.70/1.31 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.70/1.31 thf(f67,plain,(
% 1.70/1.31 ($true = (p @ (sK2 @ sK1)))),
% 1.70/1.31 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.70/1.31 thf(f64,plain,(
% 1.70/1.31 ($true = $false) | ($true = (p @ (sK2 @ sK1)))),
% 1.70/1.31 inference(superposition,[status(thm)],[f57,f42])).
% 1.70/1.31 thf(f57,plain,(
% 1.70/1.31 ( ! [X1 : mworld] : (($false = (mrel @ sK1 @ X1)) | ($true = (p @ (sK2 @ X1)))) )),
% 1.70/1.31 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.70/1.31 % SZS output end Proof for DTF2THF_15326
% 1.70/1.31 % (15429)------------------------------
% 1.70/1.31 % (15429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.31 % (15429)Termination reason: Refutation
% 1.70/1.31
% 1.70/1.31 % (15429)Memory used [KB]: 5628
% 1.70/1.31 % (15429)Time elapsed: 0.009 s
% 1.70/1.31 % (15429)Instructions burned: 9 (million)
% 1.70/1.31 % (15429)------------------------------
% 1.70/1.31 % (15429)------------------------------
% 1.70/1.31 % (15422)Success in time 0.017 s
%------------------------------------------------------------------------------