%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO897^6 : 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 : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:55:09 AM UTC 2026
% Result : Theorem 1.69s 1.51s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 200 ( 40 equ; 0 cnn)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 244 ( 7 ~; 4 |; 12 &; 188 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 14 usr; 6 con; 0-3 aty)
% ( 6 !!; 8 ??; 0 @@+; 0 @@-)
% Number of variables : 82 ( 60 ^; 20 !; 2 ?; 82 :)
% 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_29,type,
sK1: mworld ).
thf(f67,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
$false = $true,
inference(superposition,[status(thm)],[f64,f36]) ).
thf(f36,plain,
! [X0: mworld,X1: mworld] :
( $true
= ( mrel @ X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: mworld,X1: mworld] :
( $true
= ( mrel @ X1 @ X0 ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: mworld,X1: mworld] : ( mrel @ X1 @ X0 ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
! [X4: mworld,X2: mworld] : ( mrel @ X2 @ X4 ),
file('/export/starexec/sandbox/tmp/tmp.bogbYEE8Yk/DTF2THF_28554.p',mrel_universal) ).
thf(f64,plain,
! [X1: mworld] :
( $false
= ( mrel @ mactual @ X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[status(thm)],[f58,f61]) ).
thf(f61,plain,
! [X0: mworld] :
( $true
= ( q @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
! [X0: mworld] :
( ( $true
= ( q @ X0 ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f55,f36]) ).
thf(f55,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( q @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( q @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( q @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( q @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( q @ Y0 ) ) )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( q @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ Y0 )
& ( mrel @ mactual @ Y0 ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( q @ Y0 ) ) )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( q @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ q ) ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f41,f35,f39,f40,f39,f34,f40]) ).
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.bogbYEE8Yk/DTF2THF_28554.p',mbox_def) ).
thf(f40,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.bogbYEE8Yk/DTF2THF_28554.p',mdia_def) ).
thf(f39,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.bogbYEE8Yk/DTF2THF_28554.p',mimplies_def) ).
thf(f35,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.bogbYEE8Yk/DTF2THF_28554.p',mlocal_def) ).
thf(f41,plain,
( ( mlocal @ ( mimplies @ ( mdia @ p ) @ ( mimplies @ ( mbox @ q ) @ ( mdia @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( ( mlocal @ ( mimplies @ ( mdia @ p ) @ ( mimplies @ ( mbox @ q ) @ ( mdia @ q ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f30]) ).
thf(f30,plain,
( ( mlocal @ ( mimplies @ ( mdia @ p ) @ ( mimplies @ ( mbox @ q ) @ ( mdia @ q ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f29]) ).
thf(f29,plain,
~ ( mlocal @ ( mimplies @ ( mdia @ p ) @ ( mimplies @ ( mbox @ q ) @ ( mdia @ q ) ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,negated_conjecture,
~ ( mlocal @ ( mimplies @ ( mdia @ p ) @ ( mimplies @ ( mbox @ q ) @ ( mdia @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
thf(f10,conjecture,
mlocal @ ( mimplies @ ( mdia @ p ) @ ( mimplies @ ( mbox @ q ) @ ( mdia @ q ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bogbYEE8Yk/DTF2THF_28554.p',con) ).
thf(f58,plain,
! [X1: mworld] :
( ( ( q @ X1 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
! [X1: mworld] :
( $false
= ( ( q @ X1 )
& ( mrel @ mactual @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
! [X1: mworld] :
( $false
= ( ^ [Y0: mworld] :
( ( q @ Y0 )
& ( mrel @ mactual @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( q @ Y0 )
& ( mrel @ mactual @ Y0 ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO897^6 : TPTP v9.2.1. Released v8.1.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n001.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:54:05 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SYO897^6 : TPTP v9.2.1. Released v8.1.0.
% 0.29/0.46 % Domain : Syntactic
% 0.29/0.46 % Problem : Modal propositional logic theorems. problem 22
% 0.29/0.46 % Version : [BP13] axioms.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.29/0.46 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.29/0.46 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.29/0.46 % Source : [TPTP]
% 0.29/0.46 % Names : SYM122+1 [QMLTP]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.00 v8.2.0, 0.15 v8.1.0
% 0.29/0.46 % Syntax : Number of formulae : 23 ( 9 unt; 13 typ; 8 def)
% 0.29/0.46 % Number of atoms : 28 ( 8 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 9 ( 2 avg)
% 0.29/0.46 % Number of connectives : 33 ( 1 ~; 1 |; 2 &; 26 @)
% 0.29/0.46 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 6 ( 2 avg)
% 0.29/0.46 % Number of types : 2 ( 1 usr)
% 0.29/0.46 % Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 13 ( 12 usr; 1 con; 0-3 aty)
% 0.29/0.46 % Number of variables : 23 ( 19 ^; 3 !; 1 ?; 23 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.29/0.46 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.29/0.46 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.29/0.46 % $modal == [$constants == $rigid,$quantification == $constant,
% 0.29/0.46 % $modalities == $modal_system_S5U].
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(mworld,type,
% 0.29/0.46 mworld: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(mrel_type,type,
% 0.29/0.46 mrel: mworld > mworld > $o ).
% 0.29/0.46
% 0.29/0.46 thf(mactual_type,type,
% 0.29/0.46 mactual: mworld ).
% 0.29/0.46
% 0.29/0.46 thf(mlocal_type,type,
% 0.29/0.46 mlocal: ( mworld > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(mlocal_def,definition,
% 0.29/0.46 ( mlocal
% 0.29/0.46 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(mnot_type,type,
% 0.29/0.46 mnot: ( mworld > $o ) > mworld > $o ).
% 0.29/0.46
% 0.29/0.46 thf(mand_type,type,
% 0.29/0.46 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/0.46
% 0.29/0.46 thf(mor_type,type,
% 0.29/0.46 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/0.46
% 0.29/0.46 thf(mimplies_type,type,
% 0.29/0.46 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/0.46
% 0.29/0.46 thf(mequiv_type,type,
% 0.29/0.46 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/0.46
% 0.29/0.46 thf(mnot_def,definition,
% 0.29/0.46 ( mnot
% 0.29/0.46 = ( ^ [A: mworld > $o,W: mworld] :
% 0.29/0.46 ~ ( A @ W ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(mand_def,definition,
% 0.29/0.46 ( mand
% 0.29/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/0.46 ( ( A @ W )
% 0.29/0.46 & ( B @ W ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(mor_def,definition,
% 0.29/0.46 ( mor
% 0.29/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/0.46 ( ( A @ W )
% 0.29/0.46 | ( B @ W ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(mimplies_def,definition,
% 0.29/0.46 ( mimplies
% 0.29/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/0.46 ( ( A @ W )
% 0.29/0.46 => ( B @ W ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(mequiv_def,definition,
% 0.29/0.46 ( mequiv
% 0.29/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/0.46 ( ( A @ W )
% 0.29/0.46 <=> ( B @ W ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(mbox_type,type,
% 0.29/0.46 mbox: ( mworld > $o ) > mworld > $o ).
% 0.29/0.46
% 0.29/0.46 thf(mbox_def,definition,
% 0.29/0.46 ( mbox
% 0.29/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.29/0.46 ! [V: mworld] :
% 0.29/0.46 ( ( mrel @ W @ V )
% 0.29/0.46 => ( Phi @ V ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(mdia_type,type,
% 0.29/0.46 mdia: ( mworld > $o ) > mworld > $o ).
% 0.29/0.46
% 0.29/0.46 thf(mdia_def,definition,
% 0.29/0.46 ( mdia
% 0.29/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.29/0.46 ? [V: mworld] :
% 0.29/0.46 ( ( mrel @ W @ V )
% 0.29/0.46 & ( Phi @ V ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(mrel_universal,axiom,
% 0.29/0.46 ! [W: mworld,V: mworld] : ( mrel @ W @ V ) ).
% 0.29/0.46
% 0.29/0.46 %%% This output was generated by tptputils, version 1.2.
% 0.29/0.46 %%% Generated on Wed Apr 27 15:39:34 CEST 2022 using command 'downgrade(tff)'.
% 0.29/0.46 thf(p_decl,type,
% 0.29/0.46 p: mworld > $o ).
% 0.29/0.46
% 0.29/0.46 thf(q_decl,type,
% 0.29/0.46 q: mworld > $o ).
% 0.29/0.46
% 0.29/0.46 thf(con,conjecture,
% 0.29/0.46 mlocal @ ( mimplies @ ( mdia @ p ) @ ( mimplies @ ( mbox @ q ) @ ( mdia @ q ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.49/1.29 ---- Embedded in THF ---
% 1.49/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.29 %%% Generated on Tue Feb 24 14:54:06 EST 2026
% 1.49/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.29 %%% Logic specification used:
% 1.49/1.29 %%% thf(spec, logic, $$dhol).
% 1.49/1.29
% 1.49/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.bogbYEE8Yk/DTF2DTF28554.p
% See solution above
% 1.49/1.29 ------------------------
% 1.69/1.30 ---- Cleaned THF ---
% 1.69/1.30 thf(mworld,type,
% 1.69/1.30 mworld: $tType ).
% 1.69/1.30
% 1.69/1.30 thf(mrel_type,type,
% 1.69/1.30 mrel: mworld > mworld > $o ).
% 1.69/1.30
% 1.69/1.30 thf(mactual_type,type,
% 1.69/1.30 mactual: mworld ).
% 1.69/1.30
% 1.69/1.30 thf(mlocal_type,type,
% 1.69/1.30 mlocal: ( mworld > $o ) > $o ).
% 1.69/1.30
% 1.69/1.30 thf(mlocal_def,definition,
% 1.69/1.30 ( mlocal
% 1.69/1.30 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(mnot_type,type,
% 1.69/1.30 mnot: ( mworld > $o ) > mworld > $o ).
% 1.69/1.30
% 1.69/1.30 thf(mand_type,type,
% 1.69/1.30 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.69/1.30
% 1.69/1.30 thf(mor_type,type,
% 1.69/1.30 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.69/1.30
% 1.69/1.30 thf(mimplies_type,type,
% 1.69/1.30 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.69/1.30
% 1.69/1.30 thf(mequiv_type,type,
% 1.69/1.30 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.69/1.30
% 1.69/1.30 thf(mnot_def,definition,
% 1.69/1.30 ( mnot
% 1.69/1.30 = ( ^ [A: mworld > $o,W: mworld] :
% 1.69/1.30 ~ ( A @ W ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(mand_def,definition,
% 1.69/1.30 ( mand
% 1.69/1.30 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.69/1.30 ( ( A @ W )
% 1.69/1.30 & ( B @ W ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(mor_def,definition,
% 1.69/1.30 ( mor
% 1.69/1.30 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.69/1.30 ( ( A @ W )
% 1.69/1.30 | ( B @ W ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(mimplies_def,definition,
% 1.69/1.30 ( mimplies
% 1.69/1.30 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.69/1.30 ( ( A @ W )
% 1.69/1.30 => ( B @ W ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(mequiv_def,definition,
% 1.69/1.30 ( mequiv
% 1.69/1.30 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.69/1.30 ( ( A @ W )
% 1.69/1.30 <=> ( B @ W ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(mbox_type,type,
% 1.69/1.30 mbox: ( mworld > $o ) > mworld > $o ).
% 1.69/1.30
% 1.69/1.30 thf(mbox_def,definition,
% 1.69/1.30 ( mbox
% 1.69/1.30 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.69/1.30 ! [V: mworld] :
% 1.69/1.30 ( ( mrel @ W @ V )
% 1.69/1.30 => ( Phi @ V ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(mdia_type,type,
% 1.69/1.30 mdia: ( mworld > $o ) > mworld > $o ).
% 1.69/1.30
% 1.69/1.30 thf(mdia_def,definition,
% 1.69/1.30 ( mdia
% 1.69/1.30 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.69/1.30 ? [V: mworld] :
% 1.69/1.30 ( ( mrel @ W @ V )
% 1.69/1.30 & ( Phi @ V ) ) ) ) ).
% 1.69/1.30
% 1.69/1.30 thf(mrel_universal,axiom,
% 1.69/1.30 ! [W: mworld,V: mworld] : ( mrel @ W @ V ) ).
% 1.69/1.30
% 1.69/1.30 thf(p_decl,type,
% 1.69/1.30 p: mworld > $o ).
% 1.69/1.30
% 1.69/1.30 thf(q_decl,type,
% 1.69/1.30 q: mworld > $o ).
% 1.69/1.30
% 1.69/1.30 thf(con,conjecture,
% 1.69/1.30 mlocal @ ( mimplies @ ( mdia @ p ) @ ( mimplies @ ( mbox @ q ) @ ( mdia @ q ) ) ) ).
% 1.69/1.30 ------------------------
% 1.69/1.34 ipcrm: permission denied for id (294916)
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% 1.69/1.43 ipcrm: permission denied for id (3670094)
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% 1.69/1.44 ipcrm: permission denied for id (3997782)
% 1.69/1.44 ipcrm: permission denied for id (4030551)
% 1.69/1.44 ipcrm: permission denied for id (4161627)
% 1.69/1.44 ipcrm: permission denied for id (4227164)
% 1.69/1.45 ipcrm: permission denied for id (4292702)
% 1.69/1.45 ipcrm: permission denied for id (4358240)
% 1.69/1.45 ipcrm: permission denied for id (4391009)
% 1.69/1.45 ipcrm: permission denied for id (4423778)
% 1.69/1.46 ipcrm: permission denied for id (4554853)
% 1.69/1.46 ipcrm: permission denied for id (4718697)
% 1.69/1.46 ipcrm: permission denied for id (4751466)
% 1.69/1.46 ipcrm: permission denied for id (4817004)
% 1.69/1.47 ipcrm: permission denied for id (4882542)
% 1.69/1.47 ipcrm: permission denied for id (5177457)
% 1.69/1.48 ipcrm: permission denied for id (5537912)
% 1.69/1.48 ipcrm: permission denied for id (5570681)
% 1.69/1.48 ipcrm: permission denied for id (5603450)
% 1.69/1.50 % (28789)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_28554 for (2998ds/27Mi)
% 1.69/1.51 % (28789)First to succeed.
% 1.69/1.51 % (28787)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28554 for (2998ds/183Mi)
% 1.69/1.51 % (28788)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_28554 for (2998ds/4Mi)
% 1.69/1.51 % (28791)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_28554 for (2998ds/2Mi)
% 1.69/1.51 % (28792)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_28554 for (2998ds/275Mi)
% 1.69/1.51 % (28793)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28554 for (2998ds/18Mi)
% 1.69/1.51 % (28790)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28554 for (2998ds/2Mi)
% 1.69/1.51 % (28791)Instruction limit reached!
% 1.69/1.51 % (28791)------------------------------
% 1.69/1.51 % (28791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.51 % (28791)Termination reason: Unknown
% 1.69/1.51 % (28791)Termination phase: shuffling
% 1.69/1.51
% 1.69/1.51 % (28791)Memory used [KB]: 895
% 1.69/1.51 % (28791)Time elapsed: 0.003 s
% 1.69/1.51 % (28791)Instructions burned: 2 (million)
% 1.69/1.51 % (28791)------------------------------
% 1.69/1.51 % (28791)------------------------------
% 1.69/1.51 % (28790)Instruction limit reached!
% 1.69/1.51 % (28790)------------------------------
% 1.69/1.51 % (28790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.51 % (28790)Termination reason: Unknown
% 1.69/1.51 % (28790)Termination phase: Function definition elimination
% 1.69/1.51
% 1.69/1.51 % (28790)Memory used [KB]: 1023
% 1.69/1.51 % (28790)Time elapsed: 0.003 s
% 1.69/1.51 % (28790)Instructions burned: 2 (million)
% 1.69/1.51 % (28790)------------------------------
% 1.69/1.51 % (28790)------------------------------
% 1.69/1.51 % (28789)Refutation found. Thanks to Tanya!
% 1.69/1.51 % SZS status Theorem for DTF2THF_28554
% 1.69/1.51 % SZS output start Proof for DTF2THF_28554
% 1.69/1.51 thf(type_def_5, type, mworld: $tType).
% 1.69/1.51 thf(func_def_0, type, mworld: $tType).
% 1.69/1.51 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.69/1.51 thf(func_def_2, type, mactual: mworld).
% 1.69/1.51 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.69/1.51 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.69/1.51 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.69/1.51 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.69/1.51 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.69/1.51 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.69/1.51 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.69/1.51 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.69/1.51 thf(func_def_12, type, p: mworld > $o).
% 1.69/1.51 thf(func_def_13, type, q: mworld > $o).
% 1.69/1.51 thf(func_def_14, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.69/1.51 thf(func_def_29, type, sK1: mworld).
% 1.69/1.51 thf(f67,plain,(
% 1.69/1.51 $false),
% 1.69/1.51 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.69/1.51 thf(f65,plain,(
% 1.69/1.51 ($false = $true)),
% 1.69/1.51 inference(superposition,[status(thm)],[f64,f36])).
% 1.69/1.51 thf(f36,plain,(
% 1.69/1.51 ( ! [X0 : mworld,X1 : mworld] : (($true = (mrel @ X1 @ X0))) )),
% 1.69/1.51 inference(cnf_transformation,[status(thm)],[f18])).
% 1.69/1.51 thf(f18,plain,(
% 1.69/1.51 ! [X0 : mworld,X1 : mworld] : ($true = (mrel @ X1 @ X0))),
% 1.69/1.51 inference(fool_elimination,[status(thm)],[f17])).
% 1.69/1.51 thf(f17,plain,(
% 1.69/1.51 ! [X0 : mworld,X1 : mworld] : (mrel @ X1 @ X0)),
% 1.69/1.51 inference(rectify,[status(thm)],[f9])).
% 1.69/1.51 thf(f9,axiom,(
% 1.69/1.51 ! [X4 : mworld,X2 : mworld] : (mrel @ X2 @ X4)),
% 1.69/1.51 file('/export/starexec/sandbox/tmp/tmp.bogbYEE8Yk/DTF2THF_28554.p',mrel_universal)).
% 1.69/1.51 thf(f64,plain,(
% 1.69/1.51 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1))) )),
% 1.69/1.51 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.69/1.51 thf(f63,plain,(
% 1.69/1.51 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($false = $true)) )),
% 1.69/1.51 inference(forward_demodulation,[status(thm)],[f58,f61])).
% 1.69/1.51 thf(f61,plain,(
% 1.69/1.51 ( ! [X0 : mworld] : (($true = (q @ X0))) )),
% 1.69/1.51 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.69/1.51 thf(f59,plain,(
% 1.69/1.51 ( ! [X0 : mworld] : (($true = (q @ X0)) | ($false = $true)) )),
% 1.69/1.51 inference(superposition,[status(thm)],[f55,f36])).
% 1.69/1.51 thf(f55,plain,(
% 1.69/1.51 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ((q @ X1) = $true)) )),
% 1.69/1.51 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.69/1.51 thf(f54,plain,(
% 1.69/1.51 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => (q @ X1)) = $true)) )),
% 1.69/1.51 inference(beta_eta_normalization,[status(thm)],[f53])).
% 1.69/1.51 thf(f53,plain,(
% 1.69/1.51 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (q @ Y0))) @ X1))) )),
% 1.69/1.51 inference(pi_clausification,[status(thm)],[f52])).
% 1.69/1.51 thf(f52,plain,(
% 1.69/1.51 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (q @ Y0)))))),
% 1.69/1.51 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.69/1.51 thf(f45,plain,(
% 1.69/1.51 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (q @ Y0)))) => (?? @ mworld @ (^[Y0 : mworld]: ((q @ Y0) & (mrel @ mactual @ Y0))))))),
% 1.69/1.51 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.69/1.51 thf(f44,plain,(
% 1.69/1.51 (((?? @ mworld @ (^[Y0 : mworld]: ((p @ Y0) & (mrel @ mactual @ Y0)))) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (q @ Y0)))) => (?? @ mworld @ (^[Y0 : mworld]: ((q @ Y0) & (mrel @ mactual @ Y0)))))) != $true)),
% 1.69/1.51 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.69/1.51 thf(f43,plain,(
% 1.69/1.51 (((^[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))))))) @ p) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ q) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ q)))) != $true)),
% 1.69/1.51 inference(definition_unfolding,[status(thm)],[f41,f35,f39,f40,f39,f34,f40])).
% 1.69/1.51 thf(f34,plain,(
% 1.69/1.51 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.69/1.51 inference(cnf_transformation,[status(thm)],[f28])).
% 1.69/1.51 thf(f28,plain,(
% 1.69/1.51 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.69/1.51 inference(fool_elimination,[status(thm)],[f27])).
% 1.69/1.51 thf(f27,plain,(
% 1.69/1.51 (mbox = (^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 1.69/1.51 inference(rectify,[status(thm)],[f7])).
% 1.69/1.51 thf(f7,axiom,(
% 1.69/1.51 (mbox = (^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))))),
% 1.69/1.51 file('/export/starexec/sandbox/tmp/tmp.bogbYEE8Yk/DTF2THF_28554.p',mbox_def)).
% 1.69/1.51 thf(f40,plain,(
% 1.69/1.51 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))))),
% 1.69/1.51 inference(cnf_transformation,[status(thm)],[f14])).
% 1.69/1.51 thf(f14,plain,(
% 1.69/1.51 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))))),
% 1.69/1.51 inference(fool_elimination,[status(thm)],[f13])).
% 1.69/1.51 thf(f13,plain,(
% 1.69/1.51 ((^[X0 : mworld > $o, X1 : mworld] : (? [X2 : mworld] : ((mrel @ X1 @ X2) & (X0 @ X2)))) = mdia)),
% 1.69/1.51 inference(rectify,[status(thm)],[f8])).
% 1.69/1.51 thf(f8,axiom,(
% 1.69/1.51 ((^[X0 : mworld > $o, X2 : mworld] : (? [X4 : mworld] : ((mrel @ X2 @ X4) & (X0 @ X4)))) = mdia)),
% 1.69/1.51 file('/export/starexec/sandbox/tmp/tmp.bogbYEE8Yk/DTF2THF_28554.p',mdia_def)).
% 1.69/1.51 thf(f39,plain,(
% 1.69/1.51 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.69/1.51 inference(cnf_transformation,[status(thm)],[f16])).
% 1.69/1.51 thf(f16,plain,(
% 1.69/1.51 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.69/1.51 inference(fool_elimination,[status(thm)],[f15])).
% 1.69/1.51 thf(f15,plain,(
% 1.69/1.51 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 1.69/1.51 inference(rectify,[status(thm)],[f5])).
% 1.69/1.51 thf(f5,axiom,(
% 1.69/1.51 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))) = mimplies)),
% 1.69/1.51 file('/export/starexec/sandbox/tmp/tmp.bogbYEE8Yk/DTF2THF_28554.p',mimplies_def)).
% 1.69/1.51 thf(f35,plain,(
% 1.69/1.51 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.69/1.51 inference(cnf_transformation,[status(thm)],[f31])).
% 1.69/1.51 thf(f31,plain,(
% 1.69/1.51 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.69/1.51 inference(fool_elimination,[status(thm)],[f1])).
% 1.69/1.51 thf(f1,axiom,(
% 1.69/1.51 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 1.69/1.51 file('/export/starexec/sandbox/tmp/tmp.bogbYEE8Yk/DTF2THF_28554.p',mlocal_def)).
% 1.69/1.51 thf(f41,plain,(
% 1.69/1.51 ((mlocal @ (mimplies @ (mdia @ p) @ (mimplies @ (mbox @ q) @ (mdia @ q)))) != $true)),
% 1.69/1.51 inference(cnf_transformation,[status(thm)],[f32])).
% 1.69/1.51 thf(f32,plain,(
% 1.69/1.51 ((mlocal @ (mimplies @ (mdia @ p) @ (mimplies @ (mbox @ q) @ (mdia @ q)))) != $true)),
% 1.69/1.51 inference(flattening,[status(thm)],[f30])).
% 1.69/1.51 thf(f30,plain,(
% 1.69/1.51 ~((mlocal @ (mimplies @ (mdia @ p) @ (mimplies @ (mbox @ q) @ (mdia @ q)))) = $true)),
% 1.69/1.51 inference(fool_elimination,[status(thm)],[f29])).
% 1.69/1.51 thf(f29,plain,(
% 1.69/1.51 ~(mlocal @ (mimplies @ (mdia @ p) @ (mimplies @ (mbox @ q) @ (mdia @ q))))),
% 1.69/1.51 inference(rectify,[status(thm)],[f11])).
% 1.69/1.51 thf(f11,negated_conjecture,(
% 1.69/1.51 ~(mlocal @ (mimplies @ (mdia @ p) @ (mimplies @ (mbox @ q) @ (mdia @ q))))),
% 1.69/1.51 inference(negated_conjecture,[status(cth)],[f10])).
% 1.69/1.51 thf(f10,conjecture,(
% 1.69/1.51 (mlocal @ (mimplies @ (mdia @ p) @ (mimplies @ (mbox @ q) @ (mdia @ q))))),
% 1.69/1.51 file('/export/starexec/sandbox/tmp/tmp.bogbYEE8Yk/DTF2THF_28554.p',con)).
% 1.69/1.51 thf(f58,plain,(
% 1.69/1.51 ( ! [X1 : mworld] : (((q @ X1) = $false) | ($false = (mrel @ mactual @ X1))) )),
% 1.69/1.51 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.69/1.51 thf(f57,plain,(
% 1.69/1.51 ( ! [X1 : mworld] : (($false = ((q @ X1) & (mrel @ mactual @ X1)))) )),
% 1.69/1.51 inference(beta_eta_normalization,[status(thm)],[f56])).
% 1.69/1.51 thf(f56,plain,(
% 1.69/1.51 ( ! [X1 : mworld] : (($false = ((^[Y0 : mworld]: ((q @ Y0) & (mrel @ mactual @ Y0))) @ X1))) )),
% 1.69/1.51 inference(pi_clausification,[status(thm)],[f51])).
% 1.69/1.51 thf(f51,plain,(
% 1.69/1.51 ((?? @ mworld @ (^[Y0 : mworld]: ((q @ Y0) & (mrel @ mactual @ Y0)))) = $false)),
% 1.69/1.51 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.69/1.51 % SZS output end Proof for DTF2THF_28554
% 1.69/1.51 % (28789)------------------------------
% 1.69/1.51 % (28789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.51 % (28789)Termination reason: Refutation
% 1.69/1.51
% 1.69/1.51 % (28789)Memory used [KB]: 5500
% 1.69/1.51 % (28789)Time elapsed: 0.006 s
% 1.69/1.51 % (28789)Instructions burned: 5 (million)
% 1.69/1.51 % (28789)------------------------------
% 1.69/1.51 % (28789)------------------------------
% 1.69/1.51 % (28651)Success in time 0.205 s
%------------------------------------------------------------------------------