%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO891^16 : 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 09:55:07 AM UTC 2026
% Result : Theorem 2.31s 1.80s
% Output : Refutation 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 63 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 400 ( 78 equ; 0 cnn)
% Maximal formula atoms : 13 ( 6 avg)
% Number of connectives : 598 ( 20 ~; 19 |; 43 &; 456 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 19 usr; 7 con; 0-3 aty)
% ( 8 !!; 28 ??; 0 @@+; 0 @@-)
% Number of variables : 175 ( 136 ^; 35 !; 4 ?; 175 :)
% 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,
eiw_di: $i > mworld > $o ).
thf(func_def_13,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_14,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_15,type,
qmltpeq: $i > $i > mworld > $o ).
thf(func_def_16,type,
p: $i > mworld > $o ).
thf(func_def_30,type,
sK0: mworld > $i ).
thf(func_def_34,type,
sK2: $i > mworld > $i ).
thf(func_def_36,type,
sK4: mworld ).
thf(f181,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f180,f133]) ).
thf(f133,plain,
( $true
= ( eiw_di @ sK3 @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f131]) ).
thf(f131,plain,
( $true
= ( ( eiw_di @ sK3 @ mactual )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ sK3 @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f130]) ).
thf(f130,plain,
( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( p @ Y0 @ Y1 )
& ( mrel @ mactual @ Y1 ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f129]) ).
thf(f129,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( p @ Y0 @ Y1 )
& ( mrel @ mactual @ Y1 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f116]) ).
thf(f116,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( p @ Y0 @ Y1 )
& ( mrel @ mactual @ Y1 ) ) ) ) )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( p @ Y1 @ Y0 ) ) )
& ( mrel @ mactual @ Y0 ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f115]) ).
thf(f115,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( qmltpeq @ Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( p @ Y0 @ Y1 )
& ( mrel @ mactual @ Y1 ) ) ) ) )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( p @ Y1 @ Y0 ) ) )
& ( mrel @ mactual @ Y0 ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f85]) ).
thf(f85,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
& ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] : ( qmltpeq @ Y0 @ Y1 ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( ?? @ mworld
@ ^ [Y3: mworld] :
( ( Y1 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
@ ( p @ Y0 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] : ( p @ Y0 ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f67,f81,f82,f76,f68,f69,f82,f69,f70,f70,f69]) ).
thf(f70,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f32]) ).
thf(f32,plain,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( mrel @ X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
( mdia
= ( ^ [X0: mworld > $o,X2: mworld] :
? [X4: mworld] :
( ( mrel @ X2 @ X4 )
& ( X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.65HT4npiqv/DTF2THF_508.p',mdia_def) ).
thf(f69,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
thf(f58,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) )
= mexists_di ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
( ( ^ [X1: $i > mworld > $o,X2: mworld] :
? [X6: $i] :
( ( X1 @ X6 @ X2 )
& ( eiw_di @ X6 @ X2 ) ) )
= mexists_di ),
file('/export/starexec/sandbox2/tmp/tmp.65HT4npiqv/DTF2THF_508.p',mexists_di_def) ).
thf(f68,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f26]) ).
thf(f26,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.65HT4npiqv/DTF2THF_508.p',mbox_def) ).
thf(f76,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_di ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,axiom,
( ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X6: $i] :
( ( eiw_di @ X6 @ X2 )
=> ( X1 @ X6 @ X2 ) ) )
= mforall_di ),
file('/export/starexec/sandbox2/tmp/tmp.65HT4npiqv/DTF2THF_508.p',mforall_di_def) ).
thf(f82,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f24]) ).
thf(f24,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/sandbox2/tmp/tmp.65HT4npiqv/DTF2THF_508.p',mimplies_def) ).
thf(f81,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
thf(f50,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.65HT4npiqv/DTF2THF_508.p',mlocal_def) ).
thf(f67,plain,
( ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mexists_di
@ ^ [Y1: $i] : ( qmltpeq @ Y0 @ Y1 ) ) ) )
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] : ( mdia @ ( p @ Y0 ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [Y0: $i] : ( p @ Y0 ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f59]) ).
thf(f59,plain,
( ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mexists_di
@ ^ [Y1: $i] : ( qmltpeq @ Y0 @ Y1 ) ) ) )
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] : ( mdia @ ( p @ Y0 ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [Y0: $i] : ( p @ Y0 ) ) ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f31]) ).
thf(f31,plain,
( ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [Y0: $i] :
( mbox
@ ( mexists_di
@ ^ [Y1: $i] : ( qmltpeq @ Y0 @ Y1 ) ) ) )
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] : ( mdia @ ( p @ Y0 ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [Y0: $i] : ( p @ Y0 ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f30]) ).
thf(f30,plain,
~ ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [X0: $i] :
( mbox
@ ( mexists_di
@ ^ [X1: $i] : ( qmltpeq @ X0 @ X1 ) ) ) )
@ ( mimplies
@ ( mexists_di
@ ^ [X2: $i] : ( mdia @ ( p @ X2 ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [X3: $i] : ( p @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,negated_conjecture,
~ ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [X6: $i] :
( mbox
@ ( mexists_di
@ ^ [X7: $i] : ( qmltpeq @ X6 @ X7 ) ) ) )
@ ( mimplies
@ ( mexists_di
@ ^ [X6: $i] : ( mdia @ ( p @ X6 ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [X6: $i] : ( p @ X6 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
thf(f19,conjecture,
( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [X6: $i] :
( mbox
@ ( mexists_di
@ ^ [X7: $i] : ( qmltpeq @ X6 @ X7 ) ) ) )
@ ( mimplies
@ ( mexists_di
@ ^ [X6: $i] : ( mdia @ ( p @ X6 ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [X6: $i] : ( p @ X6 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.65HT4npiqv/DTF2THF_508.p',con) ).
thf(f180,plain,
( $true
!= ( eiw_di @ sK3 @ mactual ) ),
inference(trivial_inequality_removal,[status(thm)],[f176]) ).
thf(f176,plain,
( ( $true != $true )
| ( $true
!= ( eiw_di @ sK3 @ mactual ) ) ),
inference(superposition,[status(thm)],[f173,f136]) ).
thf(f136,plain,
( ( mrel @ mactual @ sK4 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f135]) ).
thf(f135,plain,
( $true
= ( ( p @ sK3 @ sK4 )
& ( mrel @ mactual @ sK4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f134]) ).
thf(f134,plain,
( $true
= ( ^ [Y0: mworld] :
( ( p @ sK3 @ Y0 )
& ( mrel @ mactual @ Y0 ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f132]) ).
thf(f132,plain,
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( p @ sK3 @ Y0 )
& ( mrel @ mactual @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f131]) ).
thf(f173,plain,
! [X0: mworld] :
( ( $true
!= ( mrel @ X0 @ sK4 ) )
| ( ( eiw_di @ sK3 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f171]) ).
thf(f171,plain,
! [X0: mworld] :
( ( $true = $false )
| ( $true
!= ( mrel @ X0 @ sK4 ) )
| ( ( eiw_di @ sK3 @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f77,f169]) ).
thf(f169,plain,
( ( eiw_di @ sK3 @ sK4 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f167]) ).
thf(f167,plain,
( ( ( eiw_di @ sK3 @ sK4 )
= $false )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f137,f163]) ).
thf(f163,plain,
! [X0: $i] :
( ( ( p @ X0 @ sK4 )
= $false )
| ( ( eiw_di @ X0 @ sK4 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f155]) ).
thf(f155,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( p @ X0 @ sK4 )
= $false )
| ( ( eiw_di @ X0 @ sK4 )
= $false ) ),
inference(superposition,[status(thm)],[f136,f143]) ).
thf(f143,plain,
! [X2: $i,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( eiw_di @ X2 @ X1 )
= $false )
| ( ( p @ X2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f142]) ).
thf(f142,plain,
! [X2: $i,X1: mworld] :
( ( ( ( eiw_di @ X2 @ X1 )
& ( p @ X2 @ X1 ) )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f141]) ).
thf(f141,plain,
! [X2: $i,X1: mworld] :
( ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( p @ Y0 @ X1 ) )
@ X2 )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f140]) ).
thf(f140,plain,
! [X1: mworld] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( p @ Y0 @ X1 ) ) )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f139]) ).
thf(f139,plain,
! [X1: mworld] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( p @ Y0 @ X1 ) ) )
& ( mrel @ mactual @ X1 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f138]) ).
thf(f138,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( p @ Y1 @ Y0 ) ) )
& ( mrel @ mactual @ Y0 ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f128]) ).
thf(f128,plain,
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( p @ Y1 @ Y0 ) ) )
& ( mrel @ mactual @ Y0 ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f116]) ).
thf(f137,plain,
( ( p @ sK3 @ sK4 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f135]) ).
thf(f77,plain,
! [X2: mworld,X0: mworld,X1: $i] :
( ( ( eiw_di @ X1 @ X2 )
= $true )
| ( $true
!= ( mrel @ X0 @ X2 ) )
| ( ( eiw_di @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
thf(f63,plain,
! [X0: mworld,X1: $i,X2: mworld] :
( ( ( eiw_di @ X1 @ X2 )
= $true )
| ( ( eiw_di @ X1 @ X0 )
!= $true )
| ( $true
!= ( mrel @ X0 @ X2 ) ) ),
inference(flattening,[status(thm)],[f62]) ).
thf(f62,plain,
! [X0: mworld,X1: $i,X2: mworld] :
( ( ( eiw_di @ X1 @ X2 )
= $true )
| ( ( eiw_di @ X1 @ X0 )
!= $true )
| ( $true
!= ( mrel @ X0 @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: mworld,X1: $i,X2: mworld] :
( ( ( ( eiw_di @ X1 @ X0 )
= $true )
& ( $true
= ( mrel @ X0 @ X2 ) ) )
=> ( ( eiw_di @ X1 @ X2 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: mworld,X1: $i,X2: mworld] :
( ( ( mrel @ X0 @ X2 )
& ( eiw_di @ X1 @ X0 ) )
=> ( eiw_di @ X1 @ X2 ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,axiom,
! [X2: mworld,X6: $i,X4: mworld] :
( ( ( mrel @ X2 @ X4 )
& ( eiw_di @ X6 @ X2 ) )
=> ( eiw_di @ X6 @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.65HT4npiqv/DTF2THF_508.p',eiw_di_cumul) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO891^16 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.32 % Computer : n016.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Feb 24 14:54:36 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.44 ---- Original DTF file ---
% 0.18/0.44 thf(spec,logic,$$dhol).
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 % File : SYO891^16 : TPTP v9.2.1. Released v8.1.0.
% 0.18/0.44 % Domain : Syntactic
% 0.18/0.44 % Problem : Fitting and Mendelsohn problem
% 0.18/0.44 % Version : [BP13] axioms.
% 0.18/0.44 % English :
% 0.18/0.44
% 0.18/0.44 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.18/0.44 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.18/0.44 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.18/0.44 % Source : [TPTP]
% 0.18/0.44 % Names : SYM056+1 [QMLTP]
% 0.18/0.44
% 0.18/0.44 % Status : Theorem
% 0.18/0.44 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0
% 0.18/0.44 % Syntax : Number of formulae : 35 ( 12 unt; 16 typ; 10 def)
% 0.18/0.44 % Number of atoms : 71 ( 10 equ; 0 cnn)
% 0.18/0.44 % Maximal formula atoms : 13 ( 3 avg)
% 0.18/0.44 % Number of connectives : 107 ( 1 ~; 1 |; 5 &; 94 @)
% 0.18/0.44 % ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% 0.18/0.44 % Maximal formula depth : 14 ( 5 avg)
% 0.18/0.44 % Number of types : 3 ( 1 usr)
% 0.18/0.44 % Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% 0.18/0.44 % Number of symbols : 16 ( 15 usr; 1 con; 0-3 aty)
% 0.18/0.44 % Number of variables : 48 ( 35 ^; 10 !; 3 ?; 48 :)
% 0.18/0.44 % SPC : TH0_THM_EQU_NAR
% 0.18/0.44
% 0.18/0.44 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.18/0.44 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.18/0.44 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.18/0.44 % $modal == [$constants == $rigid,$quantification == $cumulative,
% 0.18/0.44 % $modalities == $modal_system_S4].
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 thf(mworld,type,
% 0.18/0.44 mworld: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(mrel_type,type,
% 0.18/0.44 mrel: mworld > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(mactual_type,type,
% 0.18/0.44 mactual: mworld ).
% 0.18/0.44
% 0.18/0.44 thf(mlocal_type,type,
% 0.18/0.44 mlocal: ( mworld > $o ) > $o ).
% 0.18/0.44
% 0.18/0.44 thf(mlocal_def,definition,
% 0.18/0.44 ( mlocal
% 0.18/0.44 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(mnot_type,type,
% 0.18/0.44 mnot: ( mworld > $o ) > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(mand_type,type,
% 0.18/0.44 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(mor_type,type,
% 0.18/0.44 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(mimplies_type,type,
% 0.18/0.44 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(mequiv_type,type,
% 0.18/0.44 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(mnot_def,definition,
% 0.18/0.44 ( mnot
% 0.18/0.44 = ( ^ [A: mworld > $o,W: mworld] :
% 0.18/0.44 ~ ( A @ W ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(mand_def,definition,
% 0.18/0.44 ( mand
% 0.18/0.44 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.18/0.44 ( ( A @ W )
% 0.18/0.44 & ( B @ W ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(mor_def,definition,
% 0.18/0.44 ( mor
% 0.18/0.44 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.18/0.44 ( ( A @ W )
% 0.18/0.44 | ( B @ W ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(mimplies_def,definition,
% 0.18/0.44 ( mimplies
% 0.18/0.44 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.18/0.44 ( ( A @ W )
% 0.18/0.44 => ( B @ W ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(mequiv_def,definition,
% 0.18/0.44 ( mequiv
% 0.18/0.44 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.18/0.44 ( ( A @ W )
% 0.18/0.44 <=> ( B @ W ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(mbox_type,type,
% 0.18/0.44 mbox: ( mworld > $o ) > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(mbox_def,definition,
% 0.18/0.44 ( mbox
% 0.18/0.44 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.18/0.44 ! [V: mworld] :
% 0.18/0.44 ( ( mrel @ W @ V )
% 0.18/0.44 => ( Phi @ V ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(mdia_type,type,
% 0.18/0.44 mdia: ( mworld > $o ) > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(mdia_def,definition,
% 0.18/0.44 ( mdia
% 0.18/0.44 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.18/0.44 ? [V: mworld] :
% 0.18/0.44 ( ( mrel @ W @ V )
% 0.18/0.44 & ( Phi @ V ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(mrel_reflexive,axiom,
% 0.18/0.44 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.18/0.44
% 0.18/0.44 thf(mrel_transitive,axiom,
% 0.18/0.44 ! [W: mworld,V: mworld,U: mworld] :
% 0.18/0.44 ( ( ( mrel @ W @ V )
% 0.18/0.44 & ( mrel @ V @ U ) )
% 0.18/0.44 => ( mrel @ W @ U ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(eiw_di_type,type,
% 0.18/0.44 eiw_di: $i > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(eiw_di_nonempty,axiom,
% 0.18/0.44 ! [W: mworld] :
% 0.18/0.44 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 0.18/0.44
% 0.18/0.44 thf(eiw_di_cumul,axiom,
% 0.18/0.44 ! [W: mworld,V: mworld,X: $i] :
% 0.18/0.44 ( ( ( eiw_di @ X @ W )
% 0.18/0.44 & ( mrel @ W @ V ) )
% 0.18/0.44 => ( eiw_di @ X @ V ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(mforall_di_type,type,
% 0.18/0.44 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(mforall_di_def,definition,
% 0.18/0.44 ( mforall_di
% 0.18/0.44 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.18/0.44 ! [X: $i] :
% 0.18/0.44 ( ( eiw_di @ X @ W )
% 0.18/0.44 => ( A @ X @ W ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(mexists_di_type,type,
% 0.18/0.44 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(mexists_di_def,definition,
% 0.18/0.44 ( mexists_di
% 0.18/0.44 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.18/0.44 ? [X: $i] :
% 0.18/0.44 ( ( eiw_di @ X @ W )
% 0.18/0.44 & ( A @ X @ W ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(qmltpeq_decl,type,
% 0.18/0.44 qmltpeq: $i > $i > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(p_decl,type,
% 0.18/0.44 p: $i > mworld > $o ).
% 0.18/0.44
% 0.18/0.44 thf(reflexivity,axiom,
% 0.18/0.44 ( mlocal
% 0.18/0.44 @ ( mforall_di
% 0.18/0.44 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(symmetry,axiom,
% 0.18/0.44 ( mlocal
% 0.18/0.44 @ ( mforall_di
% 0.18/0.44 @ ^ [X: $i] :
% 0.18/0.44 ( mforall_di
% 0.18/0.44 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(transitivity,axiom,
% 0.18/0.44 ( mlocal
% 0.18/0.44 @ ( mforall_di
% 0.18/0.44 @ ^ [X: $i] :
% 0.18/0.44 ( mforall_di
% 0.18/0.44 @ ^ [Y: $i] :
% 0.18/0.44 ( mforall_di
% 0.18/0.44 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(p_substitution_1,axiom,
% 0.18/0.44 ( mlocal
% 0.18/0.44 @ ( mforall_di
% 0.18/0.44 @ ^ [A: $i] :
% 0.18/0.44 ( mforall_di
% 0.18/0.44 @ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( p @ A ) ) @ ( p @ B ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(con,conjecture,
% 0.18/0.44 ( mlocal
% 0.18/0.44 @ ( mimplies
% 0.18/0.44 @ ( mforall_di
% 0.18/0.44 @ ^ [X: $i] :
% 0.18/0.44 ( mbox
% 0.18/0.44 @ ( mexists_di
% 0.18/0.44 @ ^ [Y: $i] : ( qmltpeq @ X @ Y ) ) ) )
% 0.18/0.44 @ ( mimplies
% 0.18/0.44 @ ( mexists_di
% 0.18/0.44 @ ^ [X: $i] : ( mdia @ ( p @ X ) ) )
% 0.18/0.44 @ ( mdia
% 0.18/0.44 @ ( mexists_di
% 0.18/0.44 @ ^ [X: $i] : ( p @ X ) ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 ------------------------
% 2.21/1.75 ---- Embedded in THF ---
% 2.21/1.75 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.21/1.75 %%% Generated on Tue Feb 24 14:54:37 EST 2026
% 2.21/1.75 %%% using '$$dhol' embedding, version 1.3.0.
% 2.21/1.75 %%% Logic specification used:
% 2.21/1.75 %%% thf(spec, logic, $$dhol).
% 2.21/1.75
% 2.21/1.75 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.65HT4npiqv/DTF2DTF508.p
% See solution above
% 2.21/1.75 ------------------------
% 2.21/1.76 ---- Cleaned THF ---
% 2.21/1.76 thf(mworld,type,
% 2.21/1.76 mworld: $tType ).
% 2.21/1.76
% 2.21/1.76 thf(mrel_type,type,
% 2.21/1.76 mrel: mworld > mworld > $o ).
% 2.21/1.76
% 2.21/1.76 thf(mactual_type,type,
% 2.21/1.76 mactual: mworld ).
% 2.21/1.76
% 2.21/1.76 thf(mlocal_type,type,
% 2.21/1.76 mlocal: ( mworld > $o ) > $o ).
% 2.21/1.76
% 2.21/1.76 thf(mlocal_def,definition,
% 2.21/1.76 ( mlocal
% 2.21/1.76 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 2.21/1.76
% 2.21/1.76 thf(mnot_type,type,
% 2.21/1.76 mnot: ( mworld > $o ) > mworld > $o ).
% 2.21/1.76
% 2.21/1.76 thf(mand_type,type,
% 2.21/1.76 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 2.21/1.76
% 2.21/1.76 thf(mor_type,type,
% 2.21/1.76 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 2.21/1.76
% 2.21/1.76 thf(mimplies_type,type,
% 2.21/1.76 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 2.21/1.76
% 2.21/1.76 thf(mequiv_type,type,
% 2.21/1.76 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 2.21/1.76
% 2.21/1.76 thf(mnot_def,definition,
% 2.21/1.76 ( mnot
% 2.21/1.76 = ( ^ [A: mworld > $o,W: mworld] :
% 2.21/1.76 ~ ( A @ W ) ) ) ).
% 2.21/1.76
% 2.21/1.76 thf(mand_def,definition,
% 2.21/1.76 ( mand
% 2.21/1.76 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 2.21/1.76 ( ( A @ W )
% 2.21/1.76 & ( B @ W ) ) ) ) ).
% 2.21/1.76
% 2.21/1.76 thf(mor_def,definition,
% 2.21/1.76 ( mor
% 2.21/1.76 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 2.21/1.76 ( ( A @ W )
% 2.21/1.76 | ( B @ W ) ) ) ) ).
% 2.21/1.76
% 2.21/1.76 thf(mimplies_def,definition,
% 2.21/1.76 ( mimplies
% 2.21/1.76 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 2.21/1.76 ( ( A @ W )
% 2.21/1.76 => ( B @ W ) ) ) ) ).
% 2.21/1.76
% 2.21/1.76 thf(mequiv_def,definition,
% 2.21/1.76 ( mequiv
% 2.21/1.76 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 2.21/1.76 ( ( A @ W )
% 2.21/1.76 <=> ( B @ W ) ) ) ) ).
% 2.21/1.76
% 2.21/1.76 thf(mbox_type,type,
% 2.21/1.76 mbox: ( mworld > $o ) > mworld > $o ).
% 2.21/1.76
% 2.21/1.76 thf(mbox_def,definition,
% 2.21/1.76 ( mbox
% 2.21/1.76 = ( ^ [Phi: mworld > $o,W: mworld] :
% 2.21/1.76 ! [V: mworld] :
% 2.21/1.76 ( ( mrel @ W @ V )
% 2.21/1.76 => ( Phi @ V ) ) ) ) ).
% 2.21/1.76
% 2.21/1.76 thf(mdia_type,type,
% 2.21/1.76 mdia: ( mworld > $o ) > mworld > $o ).
% 2.21/1.76
% 2.21/1.76 thf(mdia_def,definition,
% 2.21/1.76 ( mdia
% 2.21/1.76 = ( ^ [Phi: mworld > $o,W: mworld] :
% 2.21/1.76 ? [V: mworld] :
% 2.21/1.76 ( ( mrel @ W @ V )
% 2.21/1.76 & ( Phi @ V ) ) ) ) ).
% 2.21/1.76
% 2.21/1.76 thf(mrel_reflexive,axiom,
% 2.21/1.76 ! [W: mworld] : ( mrel @ W @ W ) ).
% 2.21/1.76
% 2.21/1.76 thf(mrel_transitive,axiom,
% 2.21/1.76 ! [W: mworld,V: mworld,U: mworld] :
% 2.21/1.76 ( ( ( mrel @ W @ V )
% 2.21/1.76 & ( mrel @ V @ U ) )
% 2.21/1.76 => ( mrel @ W @ U ) ) ).
% 2.21/1.76
% 2.21/1.76 thf(eiw_di_type,type,
% 2.21/1.76 eiw_di: $i > mworld > $o ).
% 2.21/1.76
% 2.21/1.76 thf(eiw_di_nonempty,axiom,
% 2.21/1.76 ! [W: mworld] :
% 2.21/1.76 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 2.21/1.76
% 2.21/1.76 thf(eiw_di_cumul,axiom,
% 2.21/1.76 ! [W: mworld,V: mworld,X: $i] :
% 2.21/1.76 ( ( ( eiw_di @ X @ W )
% 2.21/1.76 & ( mrel @ W @ V ) )
% 2.21/1.76 => ( eiw_di @ X @ V ) ) ).
% 2.21/1.76
% 2.21/1.76 thf(mforall_di_type,type,
% 2.21/1.76 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 2.21/1.76
% 2.21/1.76 thf(mforall_di_def,definition,
% 2.21/1.76 ( mforall_di
% 2.21/1.76 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 2.21/1.76 ! [X: $i] :
% 2.21/1.76 ( ( eiw_di @ X @ W )
% 2.21/1.76 => ( A @ X @ W ) ) ) ) ).
% 2.21/1.76
% 2.21/1.76 thf(mexists_di_type,type,
% 2.21/1.76 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 2.21/1.76
% 2.21/1.76 thf(mexists_di_def,definition,
% 2.21/1.76 ( mexists_di
% 2.21/1.76 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 2.21/1.76 ? [X: $i] :
% 2.21/1.76 ( ( eiw_di @ X @ W )
% 2.21/1.76 & ( A @ X @ W ) ) ) ) ).
% 2.21/1.76
% 2.21/1.76 thf(qmltpeq_decl,type,
% 2.21/1.76 qmltpeq: $i > $i > mworld > $o ).
% 2.21/1.76
% 2.21/1.76 thf(p_decl,type,
% 2.21/1.76 p: $i > mworld > $o ).
% 2.21/1.76
% 2.21/1.76 thf(reflexivity,axiom,
% 2.21/1.76 ( mlocal
% 2.21/1.76 @ ( mforall_di
% 2.21/1.76 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 2.21/1.76
% 2.21/1.76 thf(symmetry,axiom,
% 2.21/1.76 ( mlocal
% 2.21/1.76 @ ( mforall_di
% 2.21/1.76 @ ^ [X: $i] :
% 2.21/1.76 ( mforall_di
% 2.21/1.76 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 2.21/1.76
% 2.21/1.76 thf(transitivity,axiom,
% 2.21/1.76 ( mlocal
% 2.21/1.76 @ ( mforall_di
% 2.21/1.76 @ ^ [X: $i] :
% 2.21/1.76 ( mforall_di
% 2.21/1.76 @ ^ [Y: $i] :
% 2.21/1.76 ( mforall_di
% 2.21/1.76 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 2.21/1.76
% 2.21/1.76 thf(p_substitution_1,axiom,
% 2.21/1.76 ( mlocal
% 2.21/1.76 @ ( mforall_di
% 2.21/1.76 @ ^ [A: $i] :
% 2.21/1.76 ( mforall_di
% 2.21/1.76 @ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( p @ A ) ) @ ( p @ B ) ) ) ) ) ).
% 2.21/1.76
% 2.21/1.76 thf(con,conjecture,
% 2.21/1.76 ( mlocal
% 2.21/1.76 @ ( mimplies
% 2.21/1.76 @ ( mforall_di
% 2.21/1.76 @ ^ [X: $i] :
% 2.21/1.76 ( mbox
% 2.21/1.76 @ ( mexists_di
% 2.21/1.76 @ ^ [Y: $i] : ( qmltpeq @ X @ Y ) ) ) )
% 2.21/1.76 @ ( mimplies
% 2.21/1.76 @ ( mexists_di
% 2.21/1.76 @ ^ [X: $i] : ( mdia @ ( p @ X ) ) )
% 2.21/1.76 @ ( mdia
% 2.21/1.76 @ ( mexists_di
% 2.21/1.76 @ ^ [X: $i] : ( p @ X ) ) ) ) ) ) ).
% 2.21/1.76 ------------------------
% 2.21/1.78 % (663)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_508 for (2999ds/4Mi)
% 2.21/1.78 % (666)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_508 for (2999ds/2Mi)
% 2.21/1.78 % (665)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_508 for (2999ds/2Mi)
% 2.21/1.78 % (667)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_508 for (2999ds/275Mi)
% 2.21/1.78 % (665)Instruction limit reached!
% 2.21/1.78 % (665)------------------------------
% 2.21/1.78 % (665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.78 % (665)Termination reason: Unknown
% 2.21/1.78 % (665)Termination phase: shuffling
% 2.21/1.78
% 2.21/1.78 % (666)Instruction limit reached!
% 2.21/1.78 % (666)------------------------------
% 2.21/1.78 % (666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.78 % (666)Termination reason: Unknown
% 2.21/1.78 % (666)Termination phase: shuffling
% 2.21/1.78
% 2.21/1.78 % (666)Memory used [KB]: 1023
% 2.21/1.78 % (666)Time elapsed: 0.003 s
% 2.21/1.78 % (666)Instructions burned: 3 (million)
% 2.21/1.78 % (666)------------------------------
% 2.21/1.78 % (666)------------------------------
% 2.21/1.78 % (665)Memory used [KB]: 1023
% 2.21/1.78 % (665)Time elapsed: 0.003 s
% 2.21/1.78 % (665)Instructions burned: 2 (million)
% 2.21/1.78 % (665)------------------------------
% 2.21/1.78 % (665)------------------------------
% 2.21/1.79 % (668)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_508 for (2999ds/18Mi)
% 2.21/1.79 % (663)Instruction limit reached!
% 2.21/1.79 % (663)------------------------------
% 2.21/1.79 % (663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.79 % (664)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_508 for (2999ds/27Mi)
% 2.21/1.79 % (663)Termination reason: Unknown
% 2.21/1.79 % (663)Termination phase: Property scanning
% 2.21/1.79 % (662)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_508 for (2999ds/183Mi)
% 2.21/1.79
% 2.21/1.79 % (663)Memory used [KB]: 1023
% 2.21/1.79 % (663)Time elapsed: 0.004 s
% 2.21/1.79 % (663)Instructions burned: 4 (million)
% 2.21/1.79 % (663)------------------------------
% 2.21/1.79 % (663)------------------------------
% 2.21/1.79 % (667)Refutation not found, incomplete strategy
% 2.21/1.79 % (667)------------------------------
% 2.21/1.79 % (667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.79 % (667)Termination reason: Refutation not found, incomplete strategy
% 2.21/1.79
% 2.21/1.79
% 2.21/1.79 % (667)Memory used [KB]: 5628
% 2.21/1.79 % (667)Time elapsed: 0.007 s
% 2.21/1.79 % (667)Instructions burned: 10 (million)
% 2.21/1.79 % (667)------------------------------
% 2.21/1.79 % (667)------------------------------
% 2.21/1.80 % (668)Instruction limit reached!
% 2.21/1.80 % (668)------------------------------
% 2.21/1.80 % (668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.80 % (668)Termination reason: Unknown
% 2.21/1.80 % (668)Termination phase: Saturation
% 2.21/1.80
% 2.21/1.80 % (668)Memory used [KB]: 5628
% 2.21/1.80 % (668)Time elapsed: 0.012 s
% 2.21/1.80 % (668)Instructions burned: 19 (million)
% 2.21/1.80 % (668)------------------------------
% 2.21/1.80 % (668)------------------------------
% 2.31/1.80 % (662)First to succeed.
% 2.31/1.80 % (662)Refutation found. Thanks to Tanya!
% 2.31/1.80 % SZS status Theorem for DTF2THF_508
% 2.31/1.80 % SZS output start Proof for DTF2THF_508
% 2.31/1.80 thf(type_def_5, type, mworld: $tType).
% 2.31/1.80 thf(func_def_0, type, mworld: $tType).
% 2.31/1.80 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 2.31/1.80 thf(func_def_2, type, mactual: mworld).
% 2.31/1.80 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 2.31/1.80 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 2.31/1.80 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 2.31/1.80 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 2.31/1.80 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 2.31/1.80 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 2.31/1.80 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 2.31/1.80 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 2.31/1.80 thf(func_def_12, type, eiw_di: $i > mworld > $o).
% 2.31/1.80 thf(func_def_13, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 2.31/1.80 thf(func_def_14, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 2.31/1.80 thf(func_def_15, type, qmltpeq: $i > $i > mworld > $o).
% 2.31/1.80 thf(func_def_16, type, p: $i > mworld > $o).
% 2.31/1.80 thf(func_def_30, type, sK0: mworld > $i).
% 2.31/1.80 thf(func_def_34, type, sK2: $i > mworld > $i).
% 2.31/1.80 thf(func_def_36, type, sK4: mworld).
% 2.31/1.80 thf(f181,plain,(
% 2.31/1.80 $false),
% 2.31/1.80 inference(subsumption_resolution,[status(thm)],[f180,f133])).
% 2.31/1.80 thf(f133,plain,(
% 2.31/1.80 ($true = (eiw_di @ sK3 @ mactual))),
% 2.31/1.80 inference(binary_proxy_clausification,[status(thm)],[f131])).
% 2.31/1.80 thf(f131,plain,(
% 2.31/1.80 ($true = ((eiw_di @ sK3 @ mactual) & (?? @ mworld @ (^[Y0 : mworld]: ((p @ sK3 @ Y0) & (mrel @ mactual @ Y0))))))),
% 2.31/1.80 inference(beta_eta_normalization,[status(thm)],[f130])).
% 2.31/1.80 thf(f130,plain,(
% 2.31/1.80 ($true = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) & (?? @ mworld @ (^[Y1 : mworld]: ((p @ Y0 @ Y1) & (mrel @ mactual @ Y1)))))) @ sK3))),
% 2.31/1.80 inference(sigma_clausification,[status(thm)],[f129])).
% 2.31/1.80 thf(f129,plain,(
% 2.31/1.80 ((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) & (?? @ mworld @ (^[Y1 : mworld]: ((p @ Y0 @ Y1) & (mrel @ mactual @ Y1))))))) = $true)),
% 2.31/1.80 inference(binary_proxy_clausification,[status(thm)],[f116])).
% 2.31/1.80 thf(f116,plain,(
% 2.31/1.80 (((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) & (?? @ mworld @ (^[Y1 : mworld]: ((p @ Y0 @ Y1) & (mrel @ mactual @ Y1))))))) => (?? @ mworld @ (^[Y0 : mworld]: ((?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (p @ Y1 @ Y0)))) & (mrel @ mactual @ Y0))))) = $false)),
% 2.31/1.80 inference(binary_proxy_clausification,[status(thm)],[f115])).
% 2.31/1.80 thf(f115,plain,(
% 2.31/1.80 (((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (qmltpeq @ Y0 @ Y2 @ Y1)))))))))) => ((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) & (?? @ mworld @ (^[Y1 : mworld]: ((p @ Y0 @ Y1) & (mrel @ mactual @ Y1))))))) => (?? @ mworld @ (^[Y0 : mworld]: ((?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (p @ Y1 @ Y0)))) & (mrel @ mactual @ Y0)))))) != $true)),
% 2.31/1.80 inference(beta_eta_normalization,[status(thm)],[f85])).
% 2.31/1.80 thf(f85,plain,(
% 2.31/1.80 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (?? @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) & (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : $i]: (qmltpeq @ Y0 @ Y1)))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (?? @ mworld @ (^[Y3 : mworld]: ((Y1 @ Y3) & (mrel @ Y2 @ Y3))))))) @ (p @ Y0)))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: (p @ Y0))))))) != $true)),
% 2.31/1.80 inference(definition_unfolding,[status(thm)],[f67,f81,f82,f76,f68,f69,f82,f69,f70,f70,f69])).
% 2.31/1.80 thf(f70,plain,(
% 2.31/1.80 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))))),
% 2.31/1.80 inference(cnf_transformation,[status(thm)],[f33])).
% 2.31/1.80 thf(f33,plain,(
% 2.31/1.80 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))))),
% 2.31/1.80 inference(fool_elimination,[status(thm)],[f32])).
% 2.31/1.80 thf(f32,plain,(
% 2.31/1.80 (mdia = (^[X0 : mworld > $o, X1 : mworld] : (? [X2 : mworld] : ((mrel @ X1 @ X2) & (X0 @ X2)))))),
% 2.31/1.80 inference(rectify,[status(thm)],[f8])).
% 2.31/1.80 thf(f8,axiom,(
% 2.31/1.80 (mdia = (^[X0 : mworld > $o, X2 : mworld] : (? [X4 : mworld] : ((mrel @ X2 @ X4) & (X0 @ X4)))))),
% 2.31/1.80 file('/export/starexec/sandbox2/tmp/tmp.65HT4npiqv/DTF2THF_508.p',mdia_def)).
% 2.31/1.80 thf(f69,plain,(
% 2.31/1.80 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))))),
% 2.31/1.80 inference(cnf_transformation,[status(thm)],[f58])).
% 2.31/1.80 thf(f58,plain,(
% 2.31/1.80 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))))),
% 2.31/1.80 inference(fool_elimination,[status(thm)],[f57])).
% 2.31/1.80 thf(f57,plain,(
% 2.31/1.80 ((^[X0 : $i > mworld > $o, X1 : mworld] : (? [X2 : $i] : ((X0 @ X2 @ X1) & (eiw_di @ X2 @ X1)))) = mexists_di)),
% 2.31/1.80 inference(rectify,[status(thm)],[f14])).
% 2.31/1.80 thf(f14,axiom,(
% 2.31/1.80 ((^[X1 : $i > mworld > $o, X2 : mworld] : (? [X6 : $i] : ((X1 @ X6 @ X2) & (eiw_di @ X6 @ X2)))) = mexists_di)),
% 2.31/1.80 file('/export/starexec/sandbox2/tmp/tmp.65HT4npiqv/DTF2THF_508.p',mexists_di_def)).
% 2.31/1.80 thf(f68,plain,(
% 2.31/1.80 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 2.31/1.80 inference(cnf_transformation,[status(thm)],[f27])).
% 2.31/1.80 thf(f27,plain,(
% 2.31/1.80 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 2.31/1.80 inference(fool_elimination,[status(thm)],[f26])).
% 2.31/1.80 thf(f26,plain,(
% 2.31/1.80 ((^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 2.31/1.80 inference(rectify,[status(thm)],[f7])).
% 2.31/1.80 thf(f7,axiom,(
% 2.31/1.80 ((^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))) = mbox)),
% 2.31/1.80 file('/export/starexec/sandbox2/tmp/tmp.65HT4npiqv/DTF2THF_508.p',mbox_def)).
% 2.31/1.80 thf(f76,plain,(
% 2.31/1.80 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 2.31/1.80 inference(cnf_transformation,[status(thm)],[f35])).
% 2.31/1.80 thf(f35,plain,(
% 2.31/1.80 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 2.31/1.80 inference(fool_elimination,[status(thm)],[f34])).
% 2.31/1.80 thf(f34,plain,(
% 2.31/1.80 ((^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2 : $i] : ((eiw_di @ X2 @ X1) => (X0 @ X2 @ X1)))) = mforall_di)),
% 2.31/1.80 inference(rectify,[status(thm)],[f13])).
% 2.31/1.80 thf(f13,axiom,(
% 2.31/1.80 ((^[X1 : $i > mworld > $o, X2 : mworld] : (! [X6 : $i] : ((eiw_di @ X6 @ X2) => (X1 @ X6 @ X2)))) = mforall_di)),
% 2.31/1.80 file('/export/starexec/sandbox2/tmp/tmp.65HT4npiqv/DTF2THF_508.p',mforall_di_def)).
% 2.31/1.80 thf(f82,plain,(
% 2.31/1.80 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 2.31/1.80 inference(cnf_transformation,[status(thm)],[f25])).
% 2.31/1.80 thf(f25,plain,(
% 2.31/1.80 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 2.31/1.80 inference(fool_elimination,[status(thm)],[f24])).
% 2.31/1.80 thf(f24,plain,(
% 2.31/1.80 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 2.31/1.80 inference(rectify,[status(thm)],[f5])).
% 2.31/1.80 thf(f5,axiom,(
% 2.31/1.80 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))) = mimplies)),
% 2.31/1.80 file('/export/starexec/sandbox2/tmp/tmp.65HT4npiqv/DTF2THF_508.p',mimplies_def)).
% 2.31/1.80 thf(f81,plain,(
% 2.31/1.80 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 2.31/1.80 inference(cnf_transformation,[status(thm)],[f50])).
% 2.31/1.80 thf(f50,plain,(
% 2.31/1.80 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 2.31/1.80 inference(fool_elimination,[status(thm)],[f1])).
% 2.31/1.80 thf(f1,axiom,(
% 2.31/1.80 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 2.31/1.80 file('/export/starexec/sandbox2/tmp/tmp.65HT4npiqv/DTF2THF_508.p',mlocal_def)).
% 2.31/1.80 thf(f67,plain,(
% 2.31/1.80 ((mlocal @ (mimplies @ (mforall_di @ (^[Y0 : $i]: (mbox @ (mexists_di @ (^[Y1 : $i]: (qmltpeq @ Y0 @ Y1)))))) @ (mimplies @ (mexists_di @ (^[Y0 : $i]: (mdia @ (p @ Y0)))) @ (mdia @ (mexists_di @ (^[Y0 : $i]: (p @ Y0))))))) != $true)),
% 2.31/1.80 inference(cnf_transformation,[status(thm)],[f59])).
% 2.31/1.80 thf(f59,plain,(
% 2.31/1.80 ((mlocal @ (mimplies @ (mforall_di @ (^[Y0 : $i]: (mbox @ (mexists_di @ (^[Y1 : $i]: (qmltpeq @ Y0 @ Y1)))))) @ (mimplies @ (mexists_di @ (^[Y0 : $i]: (mdia @ (p @ Y0)))) @ (mdia @ (mexists_di @ (^[Y0 : $i]: (p @ Y0))))))) != $true)),
% 2.31/1.80 inference(flattening,[status(thm)],[f31])).
% 2.31/1.80 thf(f31,plain,(
% 2.31/1.80 ~((mlocal @ (mimplies @ (mforall_di @ (^[Y0 : $i]: (mbox @ (mexists_di @ (^[Y1 : $i]: (qmltpeq @ Y0 @ Y1)))))) @ (mimplies @ (mexists_di @ (^[Y0 : $i]: (mdia @ (p @ Y0)))) @ (mdia @ (mexists_di @ (^[Y0 : $i]: (p @ Y0))))))) = $true)),
% 2.31/1.80 inference(fool_elimination,[status(thm)],[f30])).
% 2.31/1.80 thf(f30,plain,(
% 2.31/1.80 ~(mlocal @ (mimplies @ (mforall_di @ (^[X0 : $i] : (mbox @ (mexists_di @ (^[X1 : $i] : (qmltpeq @ X0 @ X1)))))) @ (mimplies @ (mexists_di @ (^[X2 : $i] : (mdia @ (p @ X2)))) @ (mdia @ (mexists_di @ (^[X3 : $i] : (p @ X3)))))))),
% 2.31/1.80 inference(rectify,[status(thm)],[f20])).
% 2.31/1.80 thf(f20,negated_conjecture,(
% 2.31/1.80 ~(mlocal @ (mimplies @ (mforall_di @ (^[X6 : $i] : (mbox @ (mexists_di @ (^[X7 : $i] : (qmltpeq @ X6 @ X7)))))) @ (mimplies @ (mexists_di @ (^[X6 : $i] : (mdia @ (p @ X6)))) @ (mdia @ (mexists_di @ (^[X6 : $i] : (p @ X6)))))))),
% 2.31/1.80 inference(negated_conjecture,[status(cth)],[f19])).
% 2.31/1.80 thf(f19,conjecture,(
% 2.31/1.80 (mlocal @ (mimplies @ (mforall_di @ (^[X6 : $i] : (mbox @ (mexists_di @ (^[X7 : $i] : (qmltpeq @ X6 @ X7)))))) @ (mimplies @ (mexists_di @ (^[X6 : $i] : (mdia @ (p @ X6)))) @ (mdia @ (mexists_di @ (^[X6 : $i] : (p @ X6)))))))),
% 2.31/1.80 file('/export/starexec/sandbox2/tmp/tmp.65HT4npiqv/DTF2THF_508.p',con)).
% 2.31/1.80 thf(f180,plain,(
% 2.31/1.80 ($true != (eiw_di @ sK3 @ mactual))),
% 2.31/1.80 inference(trivial_inequality_removal,[status(thm)],[f176])).
% 2.31/1.80 thf(f176,plain,(
% 2.31/1.80 ($true != $true) | ($true != (eiw_di @ sK3 @ mactual))),
% 2.31/1.80 inference(superposition,[status(thm)],[f173,f136])).
% 2.31/1.80 thf(f136,plain,(
% 2.31/1.80 ((mrel @ mactual @ sK4) = $true)),
% 2.31/1.80 inference(binary_proxy_clausification,[status(thm)],[f135])).
% 2.31/1.80 thf(f135,plain,(
% 2.31/1.80 ($true = ((p @ sK3 @ sK4) & (mrel @ mactual @ sK4)))),
% 2.31/1.80 inference(beta_eta_normalization,[status(thm)],[f134])).
% 2.31/1.80 thf(f134,plain,(
% 2.31/1.80 ($true = ((^[Y0 : mworld]: ((p @ sK3 @ Y0) & (mrel @ mactual @ Y0))) @ sK4))),
% 2.31/1.80 inference(sigma_clausification,[status(thm)],[f132])).
% 2.31/1.80 thf(f132,plain,(
% 2.31/1.80 ((?? @ mworld @ (^[Y0 : mworld]: ((p @ sK3 @ Y0) & (mrel @ mactual @ Y0)))) = $true)),
% 2.31/1.80 inference(binary_proxy_clausification,[status(thm)],[f131])).
% 2.31/1.80 thf(f173,plain,(
% 2.31/1.80 ( ! [X0 : mworld] : (($true != (mrel @ X0 @ sK4)) | ((eiw_di @ sK3 @ X0) != $true)) )),
% 2.31/1.80 inference(trivial_inequality_removal,[status(thm)],[f171])).
% 2.31/1.80 thf(f171,plain,(
% 2.31/1.80 ( ! [X0 : mworld] : (($true = $false) | ($true != (mrel @ X0 @ sK4)) | ((eiw_di @ sK3 @ X0) != $true)) )),
% 2.31/1.80 inference(superposition,[status(thm)],[f77,f169])).
% 2.31/1.80 thf(f169,plain,(
% 2.31/1.80 ((eiw_di @ sK3 @ sK4) = $false)),
% 2.31/1.80 inference(trivial_inequality_removal,[status(thm)],[f167])).
% 2.31/1.80 thf(f167,plain,(
% 2.31/1.80 ((eiw_di @ sK3 @ sK4) = $false) | ($true = $false)),
% 2.31/1.80 inference(superposition,[status(thm)],[f137,f163])).
% 2.31/1.80 thf(f163,plain,(
% 2.31/1.80 ( ! [X0 : $i] : (((p @ X0 @ sK4) = $false) | ((eiw_di @ X0 @ sK4) = $false)) )),
% 2.31/1.80 inference(trivial_inequality_removal,[status(thm)],[f155])).
% 2.31/1.80 thf(f155,plain,(
% 2.31/1.80 ( ! [X0 : $i] : (($true = $false) | ((p @ X0 @ sK4) = $false) | ((eiw_di @ X0 @ sK4) = $false)) )),
% 2.31/1.80 inference(superposition,[status(thm)],[f136,f143])).
% 2.31/1.80 thf(f143,plain,(
% 2.31/1.80 ( ! [X2 : $i,X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ((eiw_di @ X2 @ X1) = $false) | ((p @ X2 @ X1) = $false)) )),
% 2.31/1.80 inference(binary_proxy_clausification,[status(thm)],[f142])).
% 2.31/1.80 thf(f142,plain,(
% 2.31/1.80 ( ! [X2 : $i,X1 : mworld] : ((((eiw_di @ X2 @ X1) & (p @ X2 @ X1)) = $false) | ((mrel @ mactual @ X1) = $false)) )),
% 2.31/1.80 inference(beta_eta_normalization,[status(thm)],[f141])).
% 2.31/1.80 thf(f141,plain,(
% 2.31/1.80 ( ! [X2 : $i,X1 : mworld] : ((((^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (p @ Y0 @ X1))) @ X2) = $false) | ((mrel @ mactual @ X1) = $false)) )),
% 2.31/1.80 inference(pi_clausification,[status(thm)],[f140])).
% 2.31/1.80 thf(f140,plain,(
% 2.31/1.80 ( ! [X1 : mworld] : (((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (p @ Y0 @ X1)))) = $false) | ((mrel @ mactual @ X1) = $false)) )),
% 2.31/1.80 inference(binary_proxy_clausification,[status(thm)],[f139])).
% 2.31/1.80 thf(f139,plain,(
% 2.31/1.80 ( ! [X1 : mworld] : ((((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (p @ Y0 @ X1)))) & (mrel @ mactual @ X1)) = $false)) )),
% 2.31/1.80 inference(beta_eta_normalization,[status(thm)],[f138])).
% 2.31/1.80 thf(f138,plain,(
% 2.31/1.80 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (p @ Y1 @ Y0)))) & (mrel @ mactual @ Y0))) @ X1) = $false)) )),
% 2.31/1.80 inference(pi_clausification,[status(thm)],[f128])).
% 2.31/1.80 thf(f128,plain,(
% 2.31/1.80 ((?? @ mworld @ (^[Y0 : mworld]: ((?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (p @ Y1 @ Y0)))) & (mrel @ mactual @ Y0)))) = $false)),
% 2.31/1.80 inference(binary_proxy_clausification,[status(thm)],[f116])).
% 2.31/1.80 thf(f137,plain,(
% 2.31/1.80 ((p @ sK3 @ sK4) = $true)),
% 2.31/1.80 inference(binary_proxy_clausification,[status(thm)],[f135])).
% 2.31/1.80 thf(f77,plain,(
% 2.31/1.80 ( ! [X2 : mworld,X0 : mworld,X1 : $i] : (((eiw_di @ X1 @ X2) = $true) | ($true != (mrel @ X0 @ X2)) | ((eiw_di @ X1 @ X0) != $true)) )),
% 2.31/1.80 inference(cnf_transformation,[status(thm)],[f63])).
% 2.31/1.80 thf(f63,plain,(
% 2.31/1.80 ! [X0 : mworld,X1 : $i,X2 : mworld] : (((eiw_di @ X1 @ X2) = $true) | ((eiw_di @ X1 @ X0) != $true) | ($true != (mrel @ X0 @ X2)))),
% 2.31/1.80 inference(flattening,[status(thm)],[f62])).
% 2.31/1.80 thf(f62,plain,(
% 2.31/1.80 ! [X0 : mworld,X1 : $i,X2 : mworld] : (((eiw_di @ X1 @ X2) = $true) | (((eiw_di @ X1 @ X0) != $true) | ($true != (mrel @ X0 @ X2))))),
% 2.31/1.80 inference(ennf_transformation,[status(thm)],[f39])).
% 2.31/1.80 thf(f39,plain,(
% 2.31/1.80 ! [X0 : mworld,X1 : $i,X2 : mworld] : ((((eiw_di @ X1 @ X0) = $true) & ($true = (mrel @ X0 @ X2))) => ((eiw_di @ X1 @ X2) = $true))),
% 2.31/1.80 inference(fool_elimination,[status(thm)],[f38])).
% 2.31/1.80 thf(f38,plain,(
% 2.31/1.80 ! [X0 : mworld,X1 : $i,X2 : mworld] : (((mrel @ X0 @ X2) & (eiw_di @ X1 @ X0)) => (eiw_di @ X1 @ X2))),
% 2.31/1.80 inference(rectify,[status(thm)],[f12])).
% 2.31/1.80 thf(f12,axiom,(
% 2.31/1.80 ! [X2 : mworld,X6 : $i,X4 : mworld] : (((mrel @ X2 @ X4) & (eiw_di @ X6 @ X2)) => (eiw_di @ X6 @ X4))),
% 2.31/1.80 file('/export/starexec/sandbox2/tmp/tmp.65HT4npiqv/DTF2THF_508.p',eiw_di_cumul)).
% 2.31/1.80 % SZS output end Proof for DTF2THF_508
% 2.31/1.80 % (662)------------------------------
% 2.31/1.80 % (662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.31/1.80 % (662)Termination reason: Refutation
% 2.31/1.80
% 2.31/1.80 % (662)Memory used [KB]: 5756
% 2.31/1.80 % (662)Time elapsed: 0.016 s
% 2.31/1.80 % (662)Instructions burned: 20 (million)
% 2.31/1.80 % (662)------------------------------
% 2.31/1.80 % (662)------------------------------
% 2.31/1.80 % (661)Success in time 0.031 s
%------------------------------------------------------------------------------