%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO896^7 : 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 : n016.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 1.77s 1.50s
% Output : Refutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 339 ( 71 equ; 0 cnn)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 397 ( 22 ~; 16 |; 17 &; 290 @)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 13 usr; 6 con; 0-3 aty)
% ( 10 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 106 ( 93 ^; 11 !; 2 ?; 106 :)
% 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(f72,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
$true = $false,
inference(forward_demodulation,[status(thm)],[f70,f64]) ).
thf(f64,plain,
( $false
= ( q @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( $true = $false )
| ( $false
= ( q @ sK1 ) ) ),
inference(forward_demodulation,[status(thm)],[f62,f57]) ).
thf(f57,plain,
( ( p @ sK1 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( ( mrel @ mactual @ sK1 )
& ( p @ sK1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( p @ Y0 ) )
@ sK1 )
= $true ),
inference(sigma_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( p @ Y0 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( $false
= ( ~ ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( p @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( $true
!= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
=> ~ ( q @ Y0 ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
=> ( q @ Y0 ) ) ) ) )
=> ~ ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( p @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,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] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ p
@ 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
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ q ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ p ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f31,f35,f32,f30,f36,f32,f36,f32,f34,f34,f33]) ).
thf(f33,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( X0 @ X2 )
& ( mrel @ X1 @ X2 ) ) )
= mdia ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
( ( ^ [X0: mworld > $o,X2: mworld] :
? [X4: mworld] :
( ( X0 @ X4 )
& ( mrel @ X2 @ X4 ) ) )
= mdia ),
file('/export/starexec/sandbox2/tmp/tmp.9uDMIUsq1Y/DTF2THF_30427.p',mdia_def) ).
thf(f34,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( mnot
= ( ^ [X1: mworld > $o,X2: mworld] :
~ ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9uDMIUsq1Y/DTF2THF_30427.p',mnot_def) ).
thf(f36,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,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/sandbox2/tmp/tmp.9uDMIUsq1Y/DTF2THF_30427.p',mbox_def) ).
thf(f30,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( mand
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9uDMIUsq1Y/DTF2THF_30427.p',mand_def) ).
thf(f32,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,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.9uDMIUsq1Y/DTF2THF_30427.p',mimplies_def) ).
thf(f35,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,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.9uDMIUsq1Y/DTF2THF_30427.p',mlocal_def) ).
thf(f31,plain,
( ( mlocal @ ( mimplies @ ( mand @ ( mbox @ ( mimplies @ p @ q ) ) @ ( mbox @ ( mimplies @ p @ ( mnot @ q ) ) ) ) @ ( mnot @ ( mdia @ p ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( mlocal @ ( mimplies @ ( mand @ ( mbox @ ( mimplies @ p @ q ) ) @ ( mbox @ ( mimplies @ p @ ( mnot @ q ) ) ) ) @ ( mnot @ ( mdia @ p ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f28]) ).
thf(f28,plain,
( ( mlocal @ ( mimplies @ ( mand @ ( mbox @ ( mimplies @ p @ q ) ) @ ( mbox @ ( mimplies @ p @ ( mnot @ q ) ) ) ) @ ( mnot @ ( mdia @ p ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f27]) ).
thf(f27,plain,
~ ( mlocal @ ( mimplies @ ( mand @ ( mbox @ ( mimplies @ p @ q ) ) @ ( mbox @ ( mimplies @ p @ ( mnot @ q ) ) ) ) @ ( mnot @ ( mdia @ p ) ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,negated_conjecture,
~ ( mlocal @ ( mimplies @ ( mand @ ( mbox @ ( mimplies @ p @ q ) ) @ ( mbox @ ( mimplies @ p @ ( mnot @ q ) ) ) ) @ ( mnot @ ( mdia @ p ) ) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
thf(f9,conjecture,
mlocal @ ( mimplies @ ( mand @ ( mbox @ ( mimplies @ p @ q ) ) @ ( mbox @ ( mimplies @ p @ ( mnot @ q ) ) ) ) @ ( mnot @ ( mdia @ p ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9uDMIUsq1Y/DTF2THF_30427.p',con) ).
thf(f62,plain,
( ( ( p @ sK1 )
= $false )
| ( $false
= ( q @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
( ( $true = $false )
| ( ( p @ sK1 )
= $false )
| ( $false
= ( q @ sK1 ) ) ),
inference(superposition,[status(thm)],[f49,f58]) ).
thf(f58,plain,
( $true
= ( mrel @ mactual @ sK1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f49,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( q @ X1 )
= $false )
| ( $false
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: mworld] :
( ( ( ~ ( q @ X1 ) )
= $true )
| ( $false
= ( p @ X1 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X1: mworld] :
( ( $true
= ( ( p @ X1 )
=> ~ ( q @ X1 ) ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ( p @ X1 )
=> ~ ( q @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
=> ~ ( q @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
=> ~ ( q @ Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
=> ~ ( q @ Y0 ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
=> ( q @ Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f70,plain,
( $true
= ( q @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ( $true = $false )
| ( $true
= ( q @ sK1 ) ) ),
inference(forward_demodulation,[status(thm)],[f68,f57]) ).
thf(f68,plain,
( ( ( p @ sK1 )
= $false )
| ( $true
= ( q @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ( ( p @ sK1 )
= $false )
| ( $true = $false )
| ( $true
= ( q @ sK1 ) ) ),
inference(superposition,[status(thm)],[f58,f53]) ).
thf(f53,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( q @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ( p @ X1 )
=> ( q @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ( p @ X1 )
=> ( q @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
=> ( q @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
=> ( q @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYO896^7 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.32 % Computer : n016.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue Feb 24 14:53:51 EST 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.43 ---- Original DTF file ---
% 0.16/0.43 thf(spec,logic,$$dhol).
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 % File : SYO896^7 : TPTP v9.2.1. Released v8.1.0.
% 0.16/0.43 % Domain : Syntactic
% 0.16/0.43 % Problem : Modal propositional logic theorems. problem 14
% 0.16/0.43 % Version : [BP13] axioms.
% 0.16/0.43 % English :
% 0.16/0.43
% 0.16/0.43 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.16/0.43 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.16/0.43 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.16/0.43 % Source : [TPTP]
% 0.16/0.43 % Names : SYM114+1 [QMLTP]
% 0.16/0.43
% 0.16/0.43 % Status : Theorem
% 0.16/0.43 % Rating : 0.00 v8.2.0, 0.15 v8.1.0
% 0.16/0.43 % Syntax : Number of formulae : 22 ( 8 unt; 13 typ; 8 def)
% 0.16/0.43 % Number of atoms : 33 ( 8 equ; 0 cnn)
% 0.16/0.43 % Maximal formula atoms : 15 ( 3 avg)
% 0.16/0.43 % Number of connectives : 37 ( 1 ~; 1 |; 2 &; 30 @)
% 0.16/0.43 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.16/0.43 % Maximal formula depth : 9 ( 2 avg)
% 0.16/0.43 % Number of types : 2 ( 1 usr)
% 0.16/0.43 % Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% 0.16/0.43 % Number of symbols : 13 ( 12 usr; 1 con; 0-3 aty)
% 0.16/0.43 % Number of variables : 21 ( 19 ^; 1 !; 1 ?; 21 :)
% 0.16/0.43 % SPC : TH0_THM_EQU_NAR
% 0.16/0.43
% 0.16/0.43 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.16/0.43 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.16/0.43 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.16/0.43 % $modal == [$constants == $rigid,$quantification == $varying,
% 0.16/0.43 % $modalities == $modal_system_K].
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 thf(mworld,type,
% 0.16/0.43 mworld: $tType ).
% 0.16/0.43
% 0.16/0.43 thf(mrel_type,type,
% 0.16/0.43 mrel: mworld > mworld > $o ).
% 0.16/0.43
% 0.16/0.43 thf(mactual_type,type,
% 0.16/0.43 mactual: mworld ).
% 0.16/0.43
% 0.16/0.43 thf(mlocal_type,type,
% 0.16/0.43 mlocal: ( mworld > $o ) > $o ).
% 0.16/0.43
% 0.16/0.43 thf(mlocal_def,definition,
% 0.16/0.43 ( mlocal
% 0.16/0.43 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(mnot_type,type,
% 0.16/0.43 mnot: ( mworld > $o ) > mworld > $o ).
% 0.16/0.43
% 0.16/0.43 thf(mand_type,type,
% 0.16/0.43 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.16/0.43
% 0.16/0.43 thf(mor_type,type,
% 0.16/0.43 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.16/0.43
% 0.16/0.43 thf(mimplies_type,type,
% 0.16/0.43 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.16/0.43
% 0.16/0.43 thf(mequiv_type,type,
% 0.16/0.43 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.16/0.43
% 0.16/0.43 thf(mnot_def,definition,
% 0.16/0.43 ( mnot
% 0.16/0.43 = ( ^ [A: mworld > $o,W: mworld] :
% 0.16/0.43 ~ ( A @ W ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(mand_def,definition,
% 0.16/0.43 ( mand
% 0.16/0.43 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.16/0.43 ( ( A @ W )
% 0.16/0.43 & ( B @ W ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(mor_def,definition,
% 0.16/0.43 ( mor
% 0.16/0.43 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.16/0.43 ( ( A @ W )
% 0.16/0.43 | ( B @ W ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(mimplies_def,definition,
% 0.16/0.43 ( mimplies
% 0.16/0.43 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.16/0.43 ( ( A @ W )
% 0.16/0.43 => ( B @ W ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(mequiv_def,definition,
% 0.16/0.43 ( mequiv
% 0.16/0.43 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.16/0.43 ( ( A @ W )
% 0.16/0.43 <=> ( B @ W ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(mbox_type,type,
% 0.16/0.43 mbox: ( mworld > $o ) > mworld > $o ).
% 0.16/0.43
% 0.16/0.43 thf(mbox_def,definition,
% 0.16/0.43 ( mbox
% 0.16/0.43 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.16/0.43 ! [V: mworld] :
% 0.16/0.43 ( ( mrel @ W @ V )
% 0.16/0.43 => ( Phi @ V ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(mdia_type,type,
% 0.16/0.43 mdia: ( mworld > $o ) > mworld > $o ).
% 0.16/0.43
% 0.16/0.43 thf(mdia_def,definition,
% 0.16/0.43 ( mdia
% 0.16/0.43 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.16/0.43 ? [V: mworld] :
% 0.16/0.43 ( ( mrel @ W @ V )
% 0.16/0.43 & ( Phi @ V ) ) ) ) ).
% 0.16/0.43
% 0.16/0.43 thf(p_decl,type,
% 0.16/0.43 p: mworld > $o ).
% 0.16/0.43
% 0.16/0.43 thf(q_decl,type,
% 0.16/0.43 q: mworld > $o ).
% 0.16/0.43
% 0.16/0.43 thf(con,conjecture,
% 0.16/0.43 mlocal @ ( mimplies @ ( mand @ ( mbox @ ( mimplies @ p @ q ) ) @ ( mbox @ ( mimplies @ p @ ( mnot @ q ) ) ) ) @ ( mnot @ ( mdia @ p ) ) ) ).
% 0.16/0.43
% 0.16/0.43 %------------------------------------------------------------------------------
% 0.16/0.43 ------------------------
% 1.77/1.46 ---- Embedded in THF ---
% 1.77/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.77/1.46 %%% Generated on Tue Feb 24 14:53:52 EST 2026
% 1.77/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 1.77/1.46 %%% Logic specification used:
% 1.77/1.46 %%% thf(spec, logic, $$dhol).
% 1.77/1.46
% 1.77/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.9uDMIUsq1Y/DTF2DTF30427.p
% See solution above
% 1.77/1.46 ------------------------
% 1.77/1.47 ---- Cleaned THF ---
% 1.77/1.47 thf(mworld,type,
% 1.77/1.47 mworld: $tType ).
% 1.77/1.47
% 1.77/1.47 thf(mrel_type,type,
% 1.77/1.47 mrel: mworld > mworld > $o ).
% 1.77/1.47
% 1.77/1.47 thf(mactual_type,type,
% 1.77/1.47 mactual: mworld ).
% 1.77/1.47
% 1.77/1.47 thf(mlocal_type,type,
% 1.77/1.47 mlocal: ( mworld > $o ) > $o ).
% 1.77/1.47
% 1.77/1.47 thf(mlocal_def,definition,
% 1.77/1.47 ( mlocal
% 1.77/1.47 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.77/1.47
% 1.77/1.47 thf(mnot_type,type,
% 1.77/1.47 mnot: ( mworld > $o ) > mworld > $o ).
% 1.77/1.47
% 1.77/1.47 thf(mand_type,type,
% 1.77/1.47 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.77/1.47
% 1.77/1.47 thf(mor_type,type,
% 1.77/1.47 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.77/1.47
% 1.77/1.47 thf(mimplies_type,type,
% 1.77/1.47 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.77/1.47
% 1.77/1.47 thf(mequiv_type,type,
% 1.77/1.47 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.77/1.47
% 1.77/1.47 thf(mnot_def,definition,
% 1.77/1.47 ( mnot
% 1.77/1.47 = ( ^ [A: mworld > $o,W: mworld] :
% 1.77/1.47 ~ ( A @ W ) ) ) ).
% 1.77/1.47
% 1.77/1.47 thf(mand_def,definition,
% 1.77/1.47 ( mand
% 1.77/1.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.77/1.47 ( ( A @ W )
% 1.77/1.47 & ( B @ W ) ) ) ) ).
% 1.77/1.47
% 1.77/1.47 thf(mor_def,definition,
% 1.77/1.47 ( mor
% 1.77/1.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.77/1.47 ( ( A @ W )
% 1.77/1.47 | ( B @ W ) ) ) ) ).
% 1.77/1.47
% 1.77/1.47 thf(mimplies_def,definition,
% 1.77/1.47 ( mimplies
% 1.77/1.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.77/1.47 ( ( A @ W )
% 1.77/1.47 => ( B @ W ) ) ) ) ).
% 1.77/1.47
% 1.77/1.47 thf(mequiv_def,definition,
% 1.77/1.47 ( mequiv
% 1.77/1.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.77/1.47 ( ( A @ W )
% 1.77/1.47 <=> ( B @ W ) ) ) ) ).
% 1.77/1.47
% 1.77/1.47 thf(mbox_type,type,
% 1.77/1.47 mbox: ( mworld > $o ) > mworld > $o ).
% 1.77/1.47
% 1.77/1.47 thf(mbox_def,definition,
% 1.77/1.47 ( mbox
% 1.77/1.47 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.77/1.47 ! [V: mworld] :
% 1.77/1.47 ( ( mrel @ W @ V )
% 1.77/1.47 => ( Phi @ V ) ) ) ) ).
% 1.77/1.47
% 1.77/1.47 thf(mdia_type,type,
% 1.77/1.47 mdia: ( mworld > $o ) > mworld > $o ).
% 1.77/1.47
% 1.77/1.47 thf(mdia_def,definition,
% 1.77/1.47 ( mdia
% 1.77/1.47 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.77/1.47 ? [V: mworld] :
% 1.77/1.47 ( ( mrel @ W @ V )
% 1.77/1.47 & ( Phi @ V ) ) ) ) ).
% 1.77/1.47
% 1.77/1.47 thf(p_decl,type,
% 1.77/1.47 p: mworld > $o ).
% 1.77/1.47
% 1.77/1.47 thf(q_decl,type,
% 1.77/1.47 q: mworld > $o ).
% 1.77/1.47
% 1.77/1.47 thf(con,conjecture,
% 1.77/1.47 mlocal @ ( mimplies @ ( mand @ ( mbox @ ( mimplies @ p @ q ) ) @ ( mbox @ ( mimplies @ p @ ( mnot @ q ) ) ) ) @ ( mnot @ ( mdia @ p ) ) ) ).
% 1.77/1.47 ------------------------
% 1.77/1.49 % (30531)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30427 for (2999ds/18Mi)
% 1.77/1.49 % (30528)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30427 for (2999ds/2Mi)
% 1.77/1.49 % (30526)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_30427 for (2999ds/4Mi)
% 1.77/1.49 % (30527)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_30427 for (2999ds/27Mi)
% 1.77/1.49 % (30530)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_30427 for (2999ds/275Mi)
% 1.77/1.49 % (30525)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30427 for (2999ds/183Mi)
% 1.77/1.49 % (30529)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_30427 for (2999ds/2Mi)
% 1.77/1.49 % (30528)Instruction limit reached!
% 1.77/1.49 % (30528)------------------------------
% 1.77/1.49 % (30528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.49 % (30528)Termination reason: Unknown
% 1.77/1.49 % (30528)Termination phase: shuffling
% 1.77/1.49
% 1.77/1.49 % (30528)Memory used [KB]: 895
% 1.77/1.49 % (30528)Time elapsed: 0.003 s
% 1.77/1.49 % (30528)Instructions burned: 2 (million)
% 1.77/1.49 % (30528)------------------------------
% 1.77/1.49 % (30528)------------------------------
% 1.77/1.49 % (30529)Instruction limit reached!
% 1.77/1.49 % (30529)------------------------------
% 1.77/1.49 % (30529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.49 % (30529)Termination reason: Unknown
% 1.77/1.49 % (30529)Termination phase: Saturation
% 1.77/1.49
% 1.77/1.49 % (30529)Memory used [KB]: 1023
% 1.77/1.49 % (30529)Time elapsed: 0.003 s
% 1.77/1.49 % (30529)Instructions burned: 3 (million)
% 1.77/1.49 % (30529)------------------------------
% 1.77/1.49 % (30529)------------------------------
% 1.77/1.49 % (30530)Refutation not found, incomplete strategy
% 1.77/1.49 % (30530)------------------------------
% 1.77/1.49 % (30530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.49 % (30530)Termination reason: Refutation not found, incomplete strategy
% 1.77/1.49
% 1.77/1.49
% 1.77/1.49 % (30530)Memory used [KB]: 5500
% 1.77/1.49 % (30530)Time elapsed: 0.004 s
% 1.77/1.49 % (30530)Instructions burned: 3 (million)
% 1.77/1.49 % (30530)------------------------------
% 1.77/1.49 % (30530)------------------------------
% 1.77/1.49 % (30526)Instruction limit reached!
% 1.77/1.49 % (30526)------------------------------
% 1.77/1.49 % (30526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.49 % (30526)Termination reason: Unknown
% 1.77/1.49 % (30526)Termination phase: Saturation
% 1.77/1.49
% 1.77/1.49 % (30526)Memory used [KB]: 5500
% 1.77/1.49 % (30526)Time elapsed: 0.004 s
% 1.77/1.49 % (30526)Instructions burned: 5 (million)
% 1.77/1.49 % (30526)------------------------------
% 1.77/1.49 % (30526)------------------------------
% 1.77/1.49 % (30531)First to succeed.
% 1.77/1.50 % (30525)Also succeeded, but the first one will report.
% 1.77/1.50 % (30527)Also succeeded, but the first one will report.
% 1.77/1.50 % (30531)Refutation found. Thanks to Tanya!
% 1.77/1.50 % SZS status Theorem for DTF2THF_30427
% 1.77/1.50 % SZS output start Proof for DTF2THF_30427
% 1.77/1.50 thf(type_def_5, type, mworld: $tType).
% 1.77/1.50 thf(func_def_0, type, mworld: $tType).
% 1.77/1.50 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.77/1.50 thf(func_def_2, type, mactual: mworld).
% 1.77/1.50 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.77/1.50 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.77/1.50 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.77/1.50 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.77/1.50 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.77/1.50 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.77/1.50 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.77/1.50 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.77/1.50 thf(func_def_12, type, p: mworld > $o).
% 1.77/1.50 thf(func_def_13, type, q: mworld > $o).
% 1.77/1.50 thf(func_def_28, type, sK1: mworld).
% 1.77/1.50 thf(f72,plain,(
% 1.77/1.50 $false),
% 1.77/1.50 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.90/1.50 thf(f71,plain,(
% 1.90/1.50 ($true = $false)),
% 1.90/1.50 inference(forward_demodulation,[status(thm)],[f70,f64])).
% 1.90/1.50 thf(f64,plain,(
% 1.90/1.50 ($false = (q @ sK1))),
% 1.90/1.50 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.90/1.50 thf(f63,plain,(
% 1.90/1.50 ($true = $false) | ($false = (q @ sK1))),
% 1.90/1.50 inference(forward_demodulation,[status(thm)],[f62,f57])).
% 1.90/1.50 thf(f57,plain,(
% 1.90/1.50 ((p @ sK1) = $true)),
% 1.90/1.50 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.90/1.50 thf(f56,plain,(
% 1.90/1.50 (((mrel @ mactual @ sK1) & (p @ sK1)) = $true)),
% 1.90/1.50 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.90/1.50 thf(f55,plain,(
% 1.90/1.50 (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (p @ Y0))) @ sK1) = $true)),
% 1.90/1.50 inference(sigma_clausification,[status(thm)],[f54])).
% 1.90/1.50 thf(f54,plain,(
% 1.90/1.50 ($true = (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (p @ Y0)))))),
% 1.90/1.50 inference(not_proxy_clausification,[status(thm)],[f41])).
% 1.90/1.50 thf(f41,plain,(
% 1.90/1.50 ($false = (~ (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (p @ Y0))))))),
% 1.90/1.50 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.90/1.50 thf(f40,plain,(
% 1.90/1.50 ($true != (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((p @ Y0) => (~ (q @ Y0)))))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((p @ Y0) => (q @ Y0)))))) => (~ (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (p @ Y0)))))))),
% 1.90/1.50 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.90/1.50 thf(f39,plain,(
% 1.90/1.50 ($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]: ((Y1 @ Y2) & (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ p @ 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 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ q)))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (Y0 @ Y2))))))) @ p)))))),
% 1.90/1.50 inference(definition_unfolding,[status(thm)],[f31,f35,f32,f30,f36,f32,f36,f32,f34,f34,f33])).
% 1.90/1.50 thf(f33,plain,(
% 1.90/1.50 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.90/1.50 inference(cnf_transformation,[status(thm)],[f16])).
% 1.90/1.50 thf(f16,plain,(
% 1.90/1.50 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.90/1.50 inference(fool_elimination,[status(thm)],[f15])).
% 1.90/1.50 thf(f15,plain,(
% 1.90/1.50 ((^[X0 : mworld > $o, X1 : mworld] : (? [X2 : mworld] : ((X0 @ X2) & (mrel @ X1 @ X2)))) = mdia)),
% 1.90/1.50 inference(rectify,[status(thm)],[f8])).
% 1.90/1.50 thf(f8,axiom,(
% 1.90/1.50 ((^[X0 : mworld > $o, X2 : mworld] : (? [X4 : mworld] : ((X0 @ X4) & (mrel @ X2 @ X4)))) = mdia)),
% 1.90/1.50 file('/export/starexec/sandbox2/tmp/tmp.9uDMIUsq1Y/DTF2THF_30427.p',mdia_def)).
% 1.90/1.50 thf(f34,plain,(
% 1.90/1.50 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 1.90/1.50 inference(cnf_transformation,[status(thm)],[f13])).
% 1.90/1.50 thf(f13,plain,(
% 1.90/1.50 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 1.90/1.50 inference(fool_elimination,[status(thm)],[f12])).
% 1.90/1.50 thf(f12,plain,(
% 1.90/1.50 (mnot = (^[X0 : mworld > $o, X1 : mworld] : (~(X0 @ X1))))),
% 1.90/1.50 inference(rectify,[status(thm)],[f2])).
% 1.90/1.50 thf(f2,axiom,(
% 1.90/1.50 (mnot = (^[X1 : mworld > $o, X2 : mworld] : (~(X1 @ X2))))),
% 1.90/1.50 file('/export/starexec/sandbox2/tmp/tmp.9uDMIUsq1Y/DTF2THF_30427.p',mnot_def)).
% 1.90/1.50 thf(f36,plain,(
% 1.90/1.50 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.90/1.50 inference(cnf_transformation,[status(thm)],[f24])).
% 1.90/1.50 thf(f24,plain,(
% 1.90/1.50 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.90/1.50 inference(fool_elimination,[status(thm)],[f23])).
% 1.90/1.50 thf(f23,plain,(
% 1.90/1.50 ((^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 1.90/1.50 inference(rectify,[status(thm)],[f7])).
% 1.90/1.50 thf(f7,axiom,(
% 1.90/1.50 ((^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))) = mbox)),
% 1.90/1.50 file('/export/starexec/sandbox2/tmp/tmp.9uDMIUsq1Y/DTF2THF_30427.p',mbox_def)).
% 1.90/1.50 thf(f30,plain,(
% 1.90/1.50 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.90/1.50 inference(cnf_transformation,[status(thm)],[f18])).
% 1.90/1.50 thf(f18,plain,(
% 1.90/1.50 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.90/1.50 inference(fool_elimination,[status(thm)],[f17])).
% 1.90/1.50 thf(f17,plain,(
% 1.90/1.50 (mand = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) & (X1 @ X2))))),
% 1.90/1.50 inference(rectify,[status(thm)],[f3])).
% 1.90/1.50 thf(f3,axiom,(
% 1.90/1.50 (mand = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X3 @ X2))))),
% 1.90/1.50 file('/export/starexec/sandbox2/tmp/tmp.9uDMIUsq1Y/DTF2THF_30427.p',mand_def)).
% 1.90/1.50 thf(f32,plain,(
% 1.90/1.50 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.90/1.50 inference(cnf_transformation,[status(thm)],[f20])).
% 1.90/1.50 thf(f20,plain,(
% 1.90/1.50 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.90/1.50 inference(fool_elimination,[status(thm)],[f19])).
% 1.90/1.50 thf(f19,plain,(
% 1.90/1.50 (mimplies = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 1.90/1.50 inference(rectify,[status(thm)],[f5])).
% 1.90/1.50 thf(f5,axiom,(
% 1.90/1.50 (mimplies = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))))),
% 1.90/1.50 file('/export/starexec/sandbox2/tmp/tmp.9uDMIUsq1Y/DTF2THF_30427.p',mimplies_def)).
% 1.90/1.50 thf(f35,plain,(
% 1.90/1.50 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.90/1.50 inference(cnf_transformation,[status(thm)],[f14])).
% 1.90/1.50 thf(f14,plain,(
% 1.90/1.50 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.90/1.50 inference(fool_elimination,[status(thm)],[f1])).
% 1.90/1.50 thf(f1,axiom,(
% 1.90/1.50 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 1.90/1.50 file('/export/starexec/sandbox2/tmp/tmp.9uDMIUsq1Y/DTF2THF_30427.p',mlocal_def)).
% 1.90/1.50 thf(f31,plain,(
% 1.90/1.50 ((mlocal @ (mimplies @ (mand @ (mbox @ (mimplies @ p @ q)) @ (mbox @ (mimplies @ p @ (mnot @ q)))) @ (mnot @ (mdia @ p)))) != $true)),
% 1.90/1.50 inference(cnf_transformation,[status(thm)],[f29])).
% 1.90/1.50 thf(f29,plain,(
% 1.90/1.50 ((mlocal @ (mimplies @ (mand @ (mbox @ (mimplies @ p @ q)) @ (mbox @ (mimplies @ p @ (mnot @ q)))) @ (mnot @ (mdia @ p)))) != $true)),
% 1.90/1.50 inference(flattening,[status(thm)],[f28])).
% 1.90/1.50 thf(f28,plain,(
% 1.90/1.50 ~((mlocal @ (mimplies @ (mand @ (mbox @ (mimplies @ p @ q)) @ (mbox @ (mimplies @ p @ (mnot @ q)))) @ (mnot @ (mdia @ p)))) = $true)),
% 1.90/1.50 inference(fool_elimination,[status(thm)],[f27])).
% 1.90/1.50 thf(f27,plain,(
% 1.90/1.50 ~(mlocal @ (mimplies @ (mand @ (mbox @ (mimplies @ p @ q)) @ (mbox @ (mimplies @ p @ (mnot @ q)))) @ (mnot @ (mdia @ p))))),
% 1.90/1.50 inference(rectify,[status(thm)],[f10])).
% 1.90/1.50 thf(f10,negated_conjecture,(
% 1.90/1.50 ~(mlocal @ (mimplies @ (mand @ (mbox @ (mimplies @ p @ q)) @ (mbox @ (mimplies @ p @ (mnot @ q)))) @ (mnot @ (mdia @ p))))),
% 1.90/1.50 inference(negated_conjecture,[status(cth)],[f9])).
% 1.90/1.50 thf(f9,conjecture,(
% 1.90/1.50 (mlocal @ (mimplies @ (mand @ (mbox @ (mimplies @ p @ q)) @ (mbox @ (mimplies @ p @ (mnot @ q)))) @ (mnot @ (mdia @ p))))),
% 1.90/1.50 file('/export/starexec/sandbox2/tmp/tmp.9uDMIUsq1Y/DTF2THF_30427.p',con)).
% 1.90/1.50 thf(f62,plain,(
% 1.90/1.50 ((p @ sK1) = $false) | ($false = (q @ sK1))),
% 1.90/1.50 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.90/1.50 thf(f59,plain,(
% 1.90/1.50 ($true = $false) | ((p @ sK1) = $false) | ($false = (q @ sK1))),
% 1.90/1.50 inference(superposition,[status(thm)],[f49,f58])).
% 1.90/1.50 thf(f58,plain,(
% 1.90/1.50 ($true = (mrel @ mactual @ sK1))),
% 1.90/1.50 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.90/1.50 thf(f49,plain,(
% 1.90/1.50 ( ! [X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ((q @ X1) = $false) | ($false = (p @ X1))) )),
% 1.90/1.50 inference(not_proxy_clausification,[status(thm)],[f48])).
% 1.90/1.50 thf(f48,plain,(
% 1.90/1.50 ( ! [X1 : mworld] : (((~ (q @ X1)) = $true) | ($false = (p @ X1)) | ((mrel @ mactual @ X1) = $false)) )),
% 1.90/1.50 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.90/1.50 thf(f47,plain,(
% 1.90/1.50 ( ! [X1 : mworld] : (($true = ((p @ X1) => (~ (q @ X1)))) | ((mrel @ mactual @ X1) = $false)) )),
% 1.90/1.50 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.90/1.50 thf(f46,plain,(
% 1.90/1.50 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => ((p @ X1) => (~ (q @ X1)))))) )),
% 1.90/1.50 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.90/1.50 thf(f45,plain,(
% 1.90/1.50 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((p @ Y0) => (~ (q @ Y0))))) @ X1) = $true)) )),
% 1.90/1.50 inference(pi_clausification,[status(thm)],[f44])).
% 1.90/1.50 thf(f44,plain,(
% 1.90/1.50 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((p @ Y0) => (~ (q @ Y0)))))) = $true)),
% 1.90/1.50 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.90/1.50 thf(f42,plain,(
% 1.90/1.50 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((p @ Y0) => (~ (q @ Y0)))))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((p @ Y0) => (q @ Y0)))))) = $true)),
% 1.90/1.50 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.90/1.50 thf(f70,plain,(
% 1.90/1.50 ($true = (q @ sK1))),
% 1.90/1.50 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.90/1.50 thf(f69,plain,(
% 1.90/1.50 ($true = $false) | ($true = (q @ sK1))),
% 1.90/1.50 inference(forward_demodulation,[status(thm)],[f68,f57])).
% 1.90/1.50 thf(f68,plain,(
% 1.90/1.50 ((p @ sK1) = $false) | ($true = (q @ sK1))),
% 1.90/1.50 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.90/1.50 thf(f66,plain,(
% 1.90/1.50 ((p @ sK1) = $false) | ($true = $false) | ($true = (q @ sK1))),
% 1.90/1.50 inference(superposition,[status(thm)],[f58,f53])).
% 1.90/1.50 thf(f53,plain,(
% 1.90/1.50 ( ! [X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($false = (p @ X1)) | ($true = (q @ X1))) )),
% 1.90/1.50 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.90/1.50 thf(f52,plain,(
% 1.90/1.50 ( ! [X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = ((p @ X1) => (q @ X1)))) )),
% 1.90/1.50 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 1.90/1.50 thf(f51,plain,(
% 1.90/1.50 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => ((p @ X1) => (q @ X1))))) )),
% 1.90/1.50 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.90/1.50 thf(f50,plain,(
% 1.90/1.50 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((p @ Y0) => (q @ Y0)))) @ X1) = $true)) )),
% 1.90/1.50 inference(pi_clausification,[status(thm)],[f43])).
% 1.90/1.50 thf(f43,plain,(
% 1.90/1.50 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((p @ Y0) => (q @ Y0))))))),
% 1.90/1.50 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.90/1.50 % SZS output end Proof for DTF2THF_30427
% 1.90/1.50 % (30531)------------------------------
% 1.90/1.50 % (30531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/1.50 % (30531)Termination reason: Refutation
% 1.90/1.50
% 1.90/1.50 % (30531)Memory used [KB]: 5500
% 1.90/1.50 % (30531)Time elapsed: 0.007 s
% 1.90/1.50 % (30531)Instructions burned: 5 (million)
% 1.90/1.50 % (30531)------------------------------
% 1.90/1.50 % (30531)------------------------------
% 1.90/1.50 % (30524)Success in time 0.021 s
%------------------------------------------------------------------------------