%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO893^11 : 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 : n004.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 1.97s 1.65s
% Output : Refutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 11
% Syntax : Number of formulae : 142 ( 43 unt; 0 typ; 3 def)
% Number of atoms : 872 ( 135 equ; 0 cnn)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 1468 ( 158 ~; 100 |; 90 &; 882 @)
% ( 5 <=>; 104 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 24 usr; 17 con; 0-3 aty)
% ( 75 !!; 54 ??; 0 @@+; 0 @@-)
% Number of variables : 254 ( 204 ^; 48 !; 2 ?; 254 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(func_def_0,type,
mworld: $tType ).
thf(func_def_1,type,
mrel: mworld > mworld > $o ).
thf(func_def_2,type,
mactual: mworld ).
thf(func_def_3,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_5,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
p: mworld > $o ).
thf(func_def_27,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
sK2: mworld ).
thf(func_def_29,type,
sK3: mworld ).
thf(func_def_30,type,
sK4: mworld ).
thf(func_def_31,type,
sK5: mworld ).
thf(func_def_32,type,
sK6: mworld ).
thf(func_def_33,type,
sK7: mworld ).
thf(func_def_34,type,
sK8: mworld ).
thf(func_def_35,type,
sK9: mworld ).
thf(func_def_36,type,
sK10: mworld ).
thf(f944,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f86,f419,f423,f939]) ).
thf(f939,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[status(thm)],[f938]) ).
thf(f938,plain,
( $false
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f937]) ).
thf(f937,plain,
( ( $true = $false )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f925,f844]) ).
thf(f844,plain,
( ( ( mrel @ sK7 @ sK9 )
= $false )
| ~ spl0_4 ),
inference(not_proxy_clausification,[status(thm)],[f690]) ).
thf(f690,plain,
( ( $true
= ( ~ ( mrel @ sK7 @ sK9 ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f686]) ).
thf(f686,plain,
( ( $true
= ( ( mrel @ sK7 @ sK9 )
=> $false ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f60,f681]) ).
thf(f681,plain,
( ( ( mrel @ sK9 @ sK7 )
= $false )
| ~ spl0_4 ),
inference(not_proxy_clausification,[status(thm)],[f678]) ).
thf(f678,plain,
( ( ( ~ ( mrel @ sK9 @ sK7 ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f675]) ).
thf(f675,plain,
( ( ( ( mrel @ sK9 @ sK7 )
=> $false )
= $true )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f661,f517]) ).
thf(f517,plain,
( ( ( p @ sK7 )
= $false )
| ~ spl0_4 ),
inference(not_proxy_clausification,[status(thm)],[f513]) ).
thf(f513,plain,
( ( $true
= ( ~ ( p @ sK7 ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f512]) ).
thf(f512,plain,
( ( ( $true
& ~ ( p @ sK7 ) )
= $true )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f503,f511]) ).
thf(f511,plain,
( ( $true
= ( mrel @ sK6 @ sK7 ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f503]) ).
thf(f503,plain,
( ( ( ( mrel @ sK6 @ sK7 )
& ~ ( p @ sK7 ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f501]) ).
thf(f501,plain,
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK6 @ Y0 )
& ~ ( p @ Y0 ) )
@ sK7 )
= $true )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f499]) ).
thf(f499,plain,
( ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK6 @ Y0 )
& ~ ( p @ Y0 ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f497]) ).
thf(f497,plain,
( ( $true
= ( $true
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK6 @ Y0 )
& ~ ( p @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f486,f49]) ).
thf(f49,plain,
! [X1: mworld] :
( $true
= ( mrel @ X1 @ X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] : ( mrel @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] : ( mrel @ Y0 @ Y0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] : ( mrel @ Y0 @ Y0 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
! [X2: mworld] : ( mrel @ X2 @ X2 ),
file('/export/starexec/sandbox2/tmp/tmp.KxhdkAZLMx/DTF2THF_7388.p',mrel_reflexive) ).
thf(f486,plain,
( ! [X1: mworld] :
( ( ( mrel @ sK6 @ X1 )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ~ ( p @ Y0 ) ) ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f485]) ).
thf(f485,plain,
( ! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ sK6 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( p @ Y1 ) ) ) )
@ X1 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f434]) ).
thf(f434,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK6 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( p @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f433]) ).
thf(f433,plain,
( ( $true
= ( ( mrel @ mactual @ sK6 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK6 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( p @ Y1 ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f432]) ).
thf(f432,plain,
( ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( p @ Y2 ) ) ) ) ) )
@ sK6 )
= $true )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f428]) ).
thf(f428,plain,
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( p @ Y2 ) ) ) ) ) ) )
!= $false )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f65,f85]) ).
thf(f85,plain,
( ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f84]) ).
thf(f84,definition,
( spl0_4
<=> ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f65,plain,
( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) ) )
!= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( p @ Y2 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
( ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) ) )
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( p @ Y2 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) ) )
!= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( p @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ~ ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ p ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f35,f40,f43,f42,f37,f45,f37,f45,f37,f45,f42]) ).
thf(f45,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f31]) ).
thf(f31,plain,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( X0 @ X2 )
& ( mrel @ X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
( mdia
= ( ^ [X0: mworld > $o,X2: mworld] :
? [X4: mworld] :
( ( X0 @ X4 )
& ( mrel @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KxhdkAZLMx/DTF2THF_7388.p',mdia_def) ).
thf(f37,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f33]) ).
thf(f33,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X2: mworld] :
! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KxhdkAZLMx/DTF2THF_7388.p',mbox_def) ).
thf(f42,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X1: mworld > $o,X2: mworld] :
~ ( X1 @ X2 ) )
= mnot ),
file('/export/starexec/sandbox2/tmp/tmp.KxhdkAZLMx/DTF2THF_7388.p',mnot_def) ).
thf(f43,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( mequiv
= ( ^ [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 ) ) )
= mequiv ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
<=> ( X3 @ X2 ) ) )
= mequiv ),
file('/export/starexec/sandbox2/tmp/tmp.KxhdkAZLMx/DTF2THF_7388.p',mequiv_def) ).
thf(f40,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.KxhdkAZLMx/DTF2THF_7388.p',mlocal_def) ).
thf(f35,plain,
( $true
= ( ~ ( mlocal @ ( mequiv @ ( mnot @ ( mbox @ ( mdia @ ( mbox @ p ) ) ) ) @ ( mdia @ ( mbox @ ( mdia @ ( mnot @ p ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( $true
= ( ~ ( mlocal @ ( mequiv @ ( mnot @ ( mbox @ ( mdia @ ( mbox @ p ) ) ) ) @ ( mdia @ ( mbox @ ( mdia @ ( mnot @ p ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
~ ( mlocal @ ( mequiv @ ( mnot @ ( mbox @ ( mdia @ ( mbox @ p ) ) ) ) @ ( mdia @ ( mbox @ ( mdia @ ( mnot @ p ) ) ) ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,negated_conjecture,
~ ( mlocal @ ( mequiv @ ( mnot @ ( mbox @ ( mdia @ ( mbox @ p ) ) ) ) @ ( mdia @ ( mbox @ ( mdia @ ( mnot @ p ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
thf(f11,conjecture,
mlocal @ ( mequiv @ ( mnot @ ( mbox @ ( mdia @ ( mbox @ p ) ) ) ) @ ( mdia @ ( mbox @ ( mdia @ ( mnot @ p ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KxhdkAZLMx/DTF2THF_7388.p',con) ).
thf(f661,plain,
( ! [X1: mworld] :
( ( ( mrel @ sK9 @ X1 )
=> ( p @ X1 ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f660]) ).
thf(f660,plain,
( ! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( p @ Y0 ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f641]) ).
thf(f641,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( p @ Y0 ) ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f640]) ).
thf(f640,plain,
( ( $true
= ( $true
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( p @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f624,f639]) ).
thf(f639,plain,
( ( ( mrel @ mactual @ sK9 )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f624]) ).
thf(f624,plain,
( ( $true
= ( ( mrel @ mactual @ sK9 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK9 @ Y0 )
=> ( p @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f622]) ).
thf(f622,plain,
( ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
@ sK9 )
= $true )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f548]) ).
thf(f548,plain,
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f545]) ).
thf(f545,plain,
( ( $true
= ( $true
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f521,f49]) ).
thf(f521,plain,
( ! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f520]) ).
thf(f520,plain,
( ! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f514]) ).
thf(f514,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(not_proxy_clausification,[status(thm)],[f85]) ).
thf(f60,plain,
! [X0: mworld,X1: mworld] :
( ( ( mrel @ X0 @ X1 )
=> ( mrel @ X1 @ X0 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f58]) ).
thf(f58,plain,
! [X0: mworld,X1: mworld] :
( $true
= ( ( ( mrel @ X0 @ X1 )
& $true )
=> ( mrel @ X1 @ X0 ) ) ),
inference(superposition,[status(thm)],[f55,f49]) ).
thf(f55,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ( ( mrel @ X1 @ X3 )
& ( mrel @ X1 @ X2 ) )
=> ( mrel @ X3 @ X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: mworld,X3: mworld,X1: mworld] :
( ( ^ [Y0: mworld] :
( ( ( mrel @ X1 @ Y0 )
& ( mrel @ X1 @ X2 ) )
=> ( mrel @ Y0 @ X2 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: mworld,X1: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( ( mrel @ X1 @ Y0 )
& ( mrel @ X1 @ X2 ) )
=> ( mrel @ Y0 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: mworld,X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( ( mrel @ X1 @ Y1 )
& ( mrel @ X1 @ Y0 ) )
=> ( mrel @ Y1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X1: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( ( mrel @ X1 @ Y1 )
& ( mrel @ X1 @ Y0 ) )
=> ( mrel @ Y1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( !! @ mworld
@ ^ [Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( ( mrel @ Y0 @ Y2 )
& ( mrel @ Y0 @ Y1 ) )
=> ( mrel @ Y2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( !! @ mworld
@ ^ [Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( ( mrel @ Y0 @ Y2 )
& ( mrel @ Y0 @ Y1 ) )
=> ( mrel @ Y2 @ Y1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( !! @ mworld
@ ^ [Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( ( mrel @ Y0 @ Y2 )
& ( mrel @ Y0 @ Y1 ) )
=> ( mrel @ Y2 @ Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X2 @ X1 )
& ( mrel @ X2 @ X0 ) )
=> ( mrel @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
! [X5: mworld,X4: mworld,X2: mworld] :
( ( ( mrel @ X2 @ X4 )
& ( mrel @ X2 @ X5 ) )
=> ( mrel @ X5 @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.KxhdkAZLMx/DTF2THF_7388.p',mrel_euclidean) ).
thf(f925,plain,
( ( ( mrel @ sK7 @ sK9 )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f922]) ).
thf(f922,plain,
( ( ( $true
=> ( mrel @ sK7 @ sK9 ) )
= $true )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f564,f652]) ).
thf(f652,plain,
( ( ( mrel @ sK6 @ sK9 )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f645]) ).
thf(f645,plain,
( ( ( $true
=> ( mrel @ sK6 @ sK9 ) )
= $true )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f445,f639]) ).
thf(f445,plain,
( ! [X0: mworld] :
( ( ( mrel @ mactual @ X0 )
=> ( mrel @ sK6 @ X0 ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f440]) ).
thf(f440,plain,
( ! [X0: mworld] :
( $true
= ( ( $true
& ( mrel @ mactual @ X0 ) )
=> ( mrel @ sK6 @ X0 ) ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f55,f437]) ).
thf(f437,plain,
( ( $true
= ( mrel @ mactual @ sK6 ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f436]) ).
thf(f436,plain,
( ( ( ( mrel @ mactual @ sK6 )
& $true )
= $true )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f433,f434]) ).
thf(f564,plain,
( ! [X0: mworld] :
( ( ( mrel @ sK6 @ X0 )
=> ( mrel @ sK7 @ X0 ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f555]) ).
thf(f555,plain,
( ! [X0: mworld] :
( ( ( $true
& ( mrel @ sK6 @ X0 ) )
=> ( mrel @ sK7 @ X0 ) )
= $true )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f55,f511]) ).
thf(f423,plain,
( spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f422,f81,f77]) ).
thf(f77,definition,
( spl0_2
<=> ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f81,definition,
( spl0_3
<=> ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( p @ Y2 ) ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f422,plain,
( ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f421]) ).
thf(f421,plain,
( ( ( ~ ~ ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f420]) ).
thf(f420,plain,
( ( $true
= ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) ) )
!= $false ) )
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f47,f82]) ).
thf(f82,plain,
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( p @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f81]) ).
thf(f419,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f418]) ).
thf(f418,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f417]) ).
thf(f417,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f406,f234]) ).
thf(f234,plain,
( ( ( mrel @ sK4 @ sK3 )
= $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f233]) ).
thf(f233,plain,
( ( ( ( mrel @ sK4 @ sK3 )
& $true )
= $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f229]) ).
thf(f229,plain,
( ( ( ( mrel @ sK4 @ sK3 )
& ~ $false )
= $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f217,f158]) ).
thf(f158,plain,
( ( ( p @ sK3 )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f157]) ).
thf(f157,plain,
( ( ( ( mrel @ sK2 @ sK3 )
=> ( p @ sK3 ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f154]) ).
thf(f154,plain,
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) )
@ sK3 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f116]) ).
thf(f116,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f115]) ).
thf(f115,plain,
( ( ( $true
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f103,f49]) ).
thf(f103,plain,
( ! [X1: mworld] :
( ( ( mrel @ sK2 @ X1 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( p @ Y0 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f102]) ).
thf(f102,plain,
( ! [X1: mworld] :
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f100]) ).
thf(f100,plain,
( ( ( $true
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f97,f99]) ).
thf(f99,plain,
( ( ( mrel @ mactual @ sK2 )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
( ( ( ( mrel @ mactual @ sK2 )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f96]) ).
thf(f96,plain,
( ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) )
@ sK2 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(not_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
( ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f77]) ).
thf(f217,plain,
( ! [X1: mworld] :
( ( ( mrel @ sK4 @ X1 )
& ~ ( p @ X1 ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f216]) ).
thf(f216,plain,
( ! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ sK4 @ Y0 )
& ~ ( p @ Y0 ) )
@ X1 )
= $false )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f168]) ).
thf(f168,plain,
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK4 @ Y0 )
& ~ ( p @ Y0 ) ) )
= $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f167]) ).
thf(f167,plain,
( ( ( ( mrel @ mactual @ sK4 )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK4 @ Y0 )
& ~ ( p @ Y0 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f164]) ).
thf(f164,plain,
( ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( p @ Y1 ) ) ) )
@ sK4 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f144]) ).
thf(f144,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( p @ Y1 ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f141]) ).
thf(f141,plain,
( ( ( $true
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( p @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f130,f49]) ).
thf(f130,plain,
( ! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ~ ( p @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f129]) ).
thf(f129,plain,
( ! [X1: mworld] :
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( p @ Y2 ) ) ) ) ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f82]) ).
thf(f406,plain,
( ( ( mrel @ sK4 @ sK3 )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f403]) ).
thf(f403,plain,
( ( $true
= ( $true
=> ( mrel @ sK4 @ sK3 ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f186,f201]) ).
thf(f201,plain,
( ( ( mrel @ sK2 @ sK4 )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f188]) ).
thf(f188,plain,
( ( ( $true
=> ( mrel @ sK2 @ sK4 ) )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f112,f169]) ).
thf(f169,plain,
( ( ( mrel @ mactual @ sK4 )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f167]) ).
thf(f112,plain,
( ! [X0: mworld] :
( $true
= ( ( mrel @ mactual @ X0 )
=> ( mrel @ sK2 @ X0 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f106]) ).
thf(f106,plain,
( ! [X0: mworld] :
( ( ( $true
& ( mrel @ mactual @ X0 ) )
=> ( mrel @ sK2 @ X0 ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f55,f99]) ).
thf(f186,plain,
( ! [X0: mworld] :
( ( ( mrel @ sK2 @ X0 )
=> ( mrel @ X0 @ sK3 ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f179]) ).
thf(f179,plain,
( ! [X0: mworld] :
( $true
= ( ( ( mrel @ sK2 @ X0 )
& $true )
=> ( mrel @ X0 @ sK3 ) ) )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f55,f159]) ).
thf(f159,plain,
( ( ( mrel @ sK2 @ sK3 )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f157]) ).
thf(f86,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f72,f84,f81]) ).
thf(f72,plain,
( ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) ) )
= $false )
| ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ~ ( p @ Y2 ) ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYO893^11 : 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 : n004.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 15:01:11 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
% 0.17/0.43 ---- Original DTF file ---
% 0.17/0.43 thf(spec,logic,$$dhol).
% 0.17/0.43 %------------------------------------------------------------------------------
% 0.17/0.43 % File : SYO893^11 : TPTP v9.2.1. Released v8.1.0.
% 0.17/0.43 % Domain : Syntactic
% 0.17/0.43 % Problem : Modal propositional logic theorems. problem 1
% 0.17/0.43 % Version : [BP13] axioms.
% 0.17/0.43 % English :
% 0.17/0.43
% 0.17/0.43 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.17/0.43 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.17/0.43 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.17/0.43 % Source : [TPTP]
% 0.17/0.43 % Names : SYM101+1 [QMLTP]
% 0.17/0.43 % Status : Theorem
% 0.17/0.43 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.31 v8.1.0
% 0.17/0.43 % Syntax : Number of formulae : 23 ( 9 unt; 12 typ; 8 def)
% 0.17/0.43 % Number of atoms : 34 ( 8 equ; 0 cnn)
% 0.17/0.43 % Maximal formula atoms : 12 ( 3 avg)
% 0.17/0.43 % Number of connectives : 44 ( 1 ~; 1 |; 3 &; 35 @)
% 0.17/0.43 % ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 0.17/0.43 % Maximal formula depth : 8 ( 3 avg)
% 0.17/0.43 % Number of types : 2 ( 1 usr)
% 0.17/0.43 % Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% 0.17/0.43 % Number of symbols : 12 ( 11 usr; 1 con; 0-3 aty)
% 0.17/0.43 % Number of variables : 25 ( 19 ^; 5 !; 1 ?; 25 :)
% 0.17/0.43 % SPC : TH0_THM_EQU_NAR
% 0.17/0.43
% 0.17/0.43 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.17/0.43 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.17/0.43 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.17/0.43 % $modal == [$constants == $rigid,$quantification == $varying,
% 0.17/0.43 % $modalities == $modal_system_S5].
% 0.17/0.43 %------------------------------------------------------------------------------
% 0.17/0.43 thf(mworld,type,
% 0.17/0.43 mworld: $tType ).
% 0.17/0.43
% 0.17/0.43 thf(mrel_type,type,
% 0.17/0.43 mrel: mworld > mworld > $o ).
% 0.17/0.43
% 0.17/0.43 thf(mactual_type,type,
% 0.17/0.43 mactual: mworld ).
% 0.17/0.43
% 0.17/0.43 thf(mlocal_type,type,
% 0.17/0.43 mlocal: ( mworld > $o ) > $o ).
% 0.17/0.43
% 0.17/0.43 thf(mlocal_def,definition,
% 0.17/0.43 ( mlocal
% 0.17/0.43 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(mnot_type,type,
% 0.17/0.43 mnot: ( mworld > $o ) > mworld > $o ).
% 0.17/0.43
% 0.17/0.43 thf(mand_type,type,
% 0.17/0.43 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.17/0.43
% 0.17/0.43 thf(mor_type,type,
% 0.17/0.43 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.17/0.43
% 0.17/0.43 thf(mimplies_type,type,
% 0.17/0.43 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.17/0.43
% 0.17/0.43 thf(mequiv_type,type,
% 0.17/0.43 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.17/0.43
% 0.17/0.43 thf(mnot_def,definition,
% 0.17/0.43 ( mnot
% 0.17/0.43 = ( ^ [A: mworld > $o,W: mworld] :
% 0.17/0.43 ~ ( A @ W ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(mand_def,definition,
% 0.17/0.43 ( mand
% 0.17/0.43 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.17/0.43 ( ( A @ W )
% 0.17/0.43 & ( B @ W ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(mor_def,definition,
% 0.17/0.43 ( mor
% 0.17/0.43 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.17/0.43 ( ( A @ W )
% 0.17/0.43 | ( B @ W ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(mimplies_def,definition,
% 0.17/0.43 ( mimplies
% 0.17/0.43 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.17/0.43 ( ( A @ W )
% 0.17/0.43 => ( B @ W ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(mequiv_def,definition,
% 0.17/0.43 ( mequiv
% 0.17/0.43 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.17/0.43 ( ( A @ W )
% 0.17/0.43 <=> ( B @ W ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(mbox_type,type,
% 0.17/0.43 mbox: ( mworld > $o ) > mworld > $o ).
% 0.17/0.43
% 0.17/0.43 thf(mbox_def,definition,
% 0.17/0.43 ( mbox
% 0.17/0.43 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.17/0.43 ! [V: mworld] :
% 0.17/0.43 ( ( mrel @ W @ V )
% 0.17/0.43 => ( Phi @ V ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(mdia_type,type,
% 0.17/0.43 mdia: ( mworld > $o ) > mworld > $o ).
% 0.17/0.43
% 0.17/0.43 thf(mdia_def,definition,
% 0.17/0.43 ( mdia
% 0.17/0.43 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.17/0.43 ? [V: mworld] :
% 0.17/0.43 ( ( mrel @ W @ V )
% 0.17/0.43 & ( Phi @ V ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(mrel_reflexive,axiom,
% 0.17/0.43 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.17/0.43
% 0.17/0.43 thf(mrel_euclidean,axiom,
% 0.17/0.43 ! [W: mworld,V: mworld,U: mworld] :
% 0.17/0.43 ( ( ( mrel @ W @ U )
% 0.17/0.43 & ( mrel @ W @ V ) )
% 0.17/0.43 => ( mrel @ U @ V ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(p_decl,type,
% 0.17/0.43 p: mworld > $o ).
% 0.17/0.43
% 0.17/0.43 thf(con,conjecture,
% 0.17/0.43 mlocal @ ( mequiv @ ( mnot @ ( mbox @ ( mdia @ ( mbox @ p ) ) ) ) @ ( mdia @ ( mbox @ ( mdia @ ( mnot @ p ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 %------------------------------------------------------------------------------
% 0.17/0.43 ------------------------
% 1.94/1.52 ---- Embedded in THF ---
% 1.94/1.52 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.94/1.52 %%% Generated on Tue Feb 24 15:01:12 EST 2026
% 1.94/1.52 %%% using '$$dhol' embedding, version 1.3.0.
% 1.94/1.52 %%% Logic specification used:
% 1.94/1.52 %%% thf(spec, logic, $$dhol).
% 1.94/1.52
% 1.94/1.52 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.KxhdkAZLMx/DTF2DTF7388.p
% See solution above
% 1.94/1.52 ------------------------
% 1.94/1.53 ---- Cleaned THF ---
% 1.94/1.53 thf(mworld,type,
% 1.94/1.53 mworld: $tType ).
% 1.94/1.53
% 1.94/1.53 thf(mrel_type,type,
% 1.94/1.53 mrel: mworld > mworld > $o ).
% 1.94/1.53
% 1.94/1.53 thf(mactual_type,type,
% 1.94/1.53 mactual: mworld ).
% 1.94/1.53
% 1.94/1.53 thf(mlocal_type,type,
% 1.94/1.53 mlocal: ( mworld > $o ) > $o ).
% 1.94/1.53
% 1.94/1.53 thf(mlocal_def,definition,
% 1.94/1.53 ( mlocal
% 1.94/1.53 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.94/1.53
% 1.94/1.53 thf(mnot_type,type,
% 1.94/1.53 mnot: ( mworld > $o ) > mworld > $o ).
% 1.94/1.53
% 1.94/1.53 thf(mand_type,type,
% 1.94/1.53 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.94/1.53
% 1.94/1.53 thf(mor_type,type,
% 1.94/1.53 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.94/1.53
% 1.94/1.53 thf(mimplies_type,type,
% 1.94/1.53 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.94/1.53
% 1.94/1.53 thf(mequiv_type,type,
% 1.94/1.53 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.94/1.53
% 1.94/1.53 thf(mnot_def,definition,
% 1.94/1.53 ( mnot
% 1.94/1.53 = ( ^ [A: mworld > $o,W: mworld] :
% 1.94/1.53 ~ ( A @ W ) ) ) ).
% 1.94/1.53
% 1.94/1.53 thf(mand_def,definition,
% 1.94/1.53 ( mand
% 1.94/1.53 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.94/1.53 ( ( A @ W )
% 1.94/1.53 & ( B @ W ) ) ) ) ).
% 1.94/1.53
% 1.94/1.53 thf(mor_def,definition,
% 1.94/1.53 ( mor
% 1.94/1.53 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.94/1.53 ( ( A @ W )
% 1.94/1.53 | ( B @ W ) ) ) ) ).
% 1.94/1.53
% 1.94/1.53 thf(mimplies_def,definition,
% 1.94/1.53 ( mimplies
% 1.94/1.53 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.94/1.53 ( ( A @ W )
% 1.94/1.53 => ( B @ W ) ) ) ) ).
% 1.94/1.53
% 1.94/1.53 thf(mequiv_def,definition,
% 1.94/1.53 ( mequiv
% 1.94/1.53 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.94/1.53 ( ( A @ W )
% 1.94/1.53 <=> ( B @ W ) ) ) ) ).
% 1.94/1.53
% 1.94/1.53 thf(mbox_type,type,
% 1.94/1.53 mbox: ( mworld > $o ) > mworld > $o ).
% 1.94/1.53
% 1.94/1.53 thf(mbox_def,definition,
% 1.94/1.53 ( mbox
% 1.94/1.53 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.94/1.53 ! [V: mworld] :
% 1.94/1.53 ( ( mrel @ W @ V )
% 1.94/1.53 => ( Phi @ V ) ) ) ) ).
% 1.94/1.53
% 1.94/1.53 thf(mdia_type,type,
% 1.94/1.53 mdia: ( mworld > $o ) > mworld > $o ).
% 1.94/1.53
% 1.94/1.53 thf(mdia_def,definition,
% 1.94/1.53 ( mdia
% 1.94/1.53 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.94/1.53 ? [V: mworld] :
% 1.94/1.53 ( ( mrel @ W @ V )
% 1.94/1.53 & ( Phi @ V ) ) ) ) ).
% 1.94/1.53
% 1.94/1.53 thf(mrel_reflexive,axiom,
% 1.94/1.53 ! [W: mworld] : ( mrel @ W @ W ) ).
% 1.94/1.53
% 1.94/1.53 thf(mrel_euclidean,axiom,
% 1.94/1.53 ! [W: mworld,V: mworld,U: mworld] :
% 1.94/1.53 ( ( ( mrel @ W @ U )
% 1.94/1.53 & ( mrel @ W @ V ) )
% 1.94/1.53 => ( mrel @ U @ V ) ) ).
% 1.94/1.53
% 1.94/1.53 thf(p_decl,type,
% 1.94/1.53 p: mworld > $o ).
% 1.94/1.53
% 1.94/1.53 thf(con,conjecture,
% 1.94/1.53 mlocal @ ( mequiv @ ( mnot @ ( mbox @ ( mdia @ ( mbox @ p ) ) ) ) @ ( mdia @ ( mbox @ ( mdia @ ( mnot @ p ) ) ) ) ) ).
% 1.94/1.53 ------------------------
% 1.94/1.55 % (7488)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/2Mi)
% 1.94/1.55 % (7487)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_7388 for (2999ds/27Mi)
% 1.94/1.55 % (7485)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/183Mi)
% 1.94/1.55 % (7486)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_7388 for (2999ds/4Mi)
% 1.94/1.55 % (7489)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_7388 for (2999ds/2Mi)
% 1.94/1.55 % (7488)Instruction limit reached!
% 1.94/1.55 % (7488)------------------------------
% 1.94/1.55 % (7488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.55 % (7488)Termination reason: Unknown
% 1.94/1.55 % (7488)Termination phase: Property scanning
% 1.94/1.55 % (7489)Instruction limit reached!
% 1.94/1.55 % (7489)------------------------------
% 1.94/1.55 % (7489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.55
% 1.94/1.55 % (7488)Memory used [KB]: 1023
% 1.94/1.55 % (7488)Time elapsed: 0.003 s
% 1.94/1.55 % (7488)Instructions burned: 3 (million)
% 1.94/1.55 % (7488)------------------------------
% 1.94/1.55 % (7488)------------------------------
% 1.94/1.55 % (7489)Termination reason: Unknown
% 1.94/1.55 % (7489)Termination phase: Property scanning
% 1.94/1.55
% 1.94/1.55 % (7489)Memory used [KB]: 1023
% 1.94/1.55 % (7489)Time elapsed: 0.002 s
% 1.94/1.55 % (7489)Instructions burned: 2 (million)
% 1.94/1.55 % (7489)------------------------------
% 1.94/1.55 % (7489)------------------------------
% 1.94/1.55 % (7490)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_7388 for (2999ds/275Mi)
% 1.94/1.55 % (7491)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/18Mi)
% 1.94/1.55 % (7486)Instruction limit reached!
% 1.94/1.55 % (7486)------------------------------
% 1.94/1.55 % (7486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.55 % (7486)Termination reason: Unknown
% 1.94/1.55 % (7486)Termination phase: Saturation
% 1.94/1.55
% 1.94/1.55 % (7486)Memory used [KB]: 5500
% 1.94/1.55 % (7486)Time elapsed: 0.004 s
% 1.94/1.55 % (7486)Instructions burned: 5 (million)
% 1.94/1.55 % (7486)------------------------------
% 1.94/1.55 % (7486)------------------------------
% 1.94/1.55 % (7490)Refutation not found, incomplete strategy
% 1.94/1.55 % (7490)------------------------------
% 1.94/1.55 % (7490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.55 % (7490)Termination reason: Refutation not found, incomplete strategy
% 1.94/1.55
% 1.94/1.55
% 1.94/1.55 % (7490)Memory used [KB]: 5500
% 1.94/1.55 % (7490)Time elapsed: 0.003 s
% 1.94/1.55 % (7490)Instructions burned: 2 (million)
% 1.94/1.55 % (7490)------------------------------
% 1.94/1.55 % (7490)------------------------------
% 1.94/1.56 % (7491)Instruction limit reached!
% 1.94/1.56 % (7491)------------------------------
% 1.94/1.56 % (7491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.56 % (7491)Termination reason: Unknown
% 1.94/1.56 % (7491)Termination phase: Saturation
% 1.94/1.56
% 1.94/1.56 % (7491)Memory used [KB]: 5628
% 1.94/1.56 % (7491)Time elapsed: 0.013 s
% 1.94/1.56 % (7491)Instructions burned: 19 (million)
% 1.94/1.56 % (7491)------------------------------
% 1.94/1.56 % (7491)------------------------------
% 1.94/1.56 % (7487)Instruction limit reached!
% 1.94/1.56 % (7487)------------------------------
% 1.94/1.56 % (7487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.56 % (7487)Termination reason: Unknown
% 1.94/1.56 % (7487)Termination phase: Saturation
% 1.94/1.56
% 1.94/1.56 % (7487)Memory used [KB]: 5756
% 1.94/1.56 % (7487)Time elapsed: 0.017 s
% 1.94/1.56 % (7487)Instructions burned: 28 (million)
% 1.94/1.56 % (7487)------------------------------
% 1.94/1.56 % (7487)------------------------------
% 1.94/1.57 % (7494)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/15Mi)
% 1.94/1.57 % (7492)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/3Mi)
% 1.94/1.57 % (7493)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/37Mi)
% 1.94/1.57 % (7492)Instruction limit reached!
% 1.94/1.57 % (7492)------------------------------
% 1.94/1.57 % (7492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.57 % (7492)Termination reason: Unknown
% 1.94/1.57 % (7492)Termination phase: Saturation
% 1.94/1.57
% 1.94/1.57 % (7492)Memory used [KB]: 5500
% 1.94/1.57 % (7492)Time elapsed: 0.004 s
% 1.94/1.57 % (7492)Instructions burned: 4 (million)
% 1.94/1.57 % (7492)------------------------------
% 1.94/1.57 % (7492)------------------------------
% 1.94/1.57 % (7495)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/3Mi)
% 1.94/1.58 % (7495)Instruction limit reached!
% 1.94/1.58 % (7495)------------------------------
% 1.94/1.58 % (7495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.58 % (7495)Termination reason: Unknown
% 1.94/1.58 % (7495)Termination phase: Saturation
% 1.94/1.58
% 1.94/1.58 % (7495)Memory used [KB]: 5500
% 1.94/1.58 % (7495)Time elapsed: 0.004 s
% 1.94/1.58 % (7495)Instructions burned: 3 (million)
% 1.94/1.58 % (7495)------------------------------
% 1.94/1.58 % (7495)------------------------------
% 1.94/1.58 % (7494)Instruction limit reached!
% 1.94/1.58 % (7494)------------------------------
% 1.94/1.58 % (7494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.58 % (7494)Termination reason: Unknown
% 1.94/1.58 % (7494)Termination phase: Saturation
% 1.94/1.58
% 1.94/1.58 % (7494)Memory used [KB]: 5628
% 1.94/1.58 % (7494)Time elapsed: 0.010 s
% 1.94/1.58 % (7494)Instructions burned: 16 (million)
% 1.94/1.58 % (7494)------------------------------
% 1.94/1.58 % (7494)------------------------------
% 1.94/1.58 % (7497)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/7Mi)
% 1.94/1.58 % (7496)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/1041Mi)
% 1.94/1.58 % (7497)Instruction limit reached!
% 1.94/1.58 % (7497)------------------------------
% 1.94/1.58 % (7497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.58 % (7497)Termination reason: Unknown
% 1.94/1.58 % (7497)Termination phase: Saturation
% 1.94/1.58
% 1.94/1.58 % (7497)Memory used [KB]: 1023
% 1.94/1.58 % (7497)Time elapsed: 0.005 s
% 1.94/1.58 % (7497)Instructions burned: 7 (million)
% 1.94/1.58 % (7497)------------------------------
% 1.94/1.58 % (7497)------------------------------
% 1.94/1.59 % (7498)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/16Mi)
% 1.94/1.59 % (7493)Instruction limit reached!
% 1.94/1.59 % (7493)------------------------------
% 1.94/1.59 % (7493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.59 % (7493)Termination reason: Unknown
% 1.94/1.59 % (7493)Termination phase: Saturation
% 1.94/1.59
% 1.94/1.59 % (7493)Memory used [KB]: 5628
% 1.94/1.59 % (7493)Time elapsed: 0.022 s
% 1.94/1.59 % (7493)Instructions burned: 37 (million)
% 1.94/1.59 % (7493)------------------------------
% 1.94/1.59 % (7493)------------------------------
% 1.94/1.59 % (7500)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/3Mi)
% 1.94/1.60 % (7499)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/3Mi)
% 1.97/1.60 % (7500)Instruction limit reached!
% 1.97/1.60 % (7500)------------------------------
% 1.97/1.60 % (7500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.60 % (7500)Termination reason: Unknown
% 1.97/1.60 % (7500)Termination phase: Function definition elimination
% 1.97/1.60
% 1.97/1.60 % (7500)Memory used [KB]: 1023
% 1.97/1.60 % (7500)Time elapsed: 0.004 s
% 1.97/1.60 % (7500)Instructions burned: 3 (million)
% 1.97/1.60 % (7500)------------------------------
% 1.97/1.60 % (7500)------------------------------
% 1.97/1.60 % (7498)Instruction limit reached!
% 1.97/1.60 % (7498)------------------------------
% 1.97/1.60 % (7498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.60 % (7498)Termination reason: Unknown
% 1.97/1.60 % (7498)Termination phase: Saturation
% 1.97/1.60
% 1.97/1.60 % (7498)Memory used [KB]: 5756
% 1.97/1.60 % (7498)Time elapsed: 0.011 s
% 1.97/1.60 % (7498)Instructions burned: 16 (million)
% 1.97/1.60 % (7498)------------------------------
% 1.97/1.60 % (7498)------------------------------
% 1.97/1.60 % (7499)Instruction limit reached!
% 1.97/1.60 % (7499)------------------------------
% 1.97/1.60 % (7499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.60 % (7499)Termination reason: Unknown
% 1.97/1.60 % (7499)Termination phase: Twee Goal Transformation
% 1.97/1.60
% 1.97/1.60 % (7499)Memory used [KB]: 1023
% 1.97/1.60 % (7499)Time elapsed: 0.003 s
% 1.97/1.60 % (7499)Instructions burned: 3 (million)
% 1.97/1.60 % (7499)------------------------------
% 1.97/1.60 % (7499)------------------------------
% 1.97/1.60 % (7501)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/7Mi)
% 1.97/1.60 % (7501)Refutation not found, incomplete strategy
% 1.97/1.60 % (7501)------------------------------
% 1.97/1.60 % (7501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.60 % (7501)Termination reason: Refutation not found, incomplete strategy
% 1.97/1.60
% 1.97/1.60
% 1.97/1.60 % (7501)Memory used [KB]: 5500
% 1.97/1.60 % (7501)Time elapsed: 0.005 s
% 1.97/1.60 % (7501)Instructions burned: 6 (million)
% 1.97/1.60 % (7501)------------------------------
% 1.97/1.60 % (7501)------------------------------
% 1.97/1.61 % (7502)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/3Mi)
% 1.97/1.61 % (7502)Instruction limit reached!
% 1.97/1.61 % (7502)------------------------------
% 1.97/1.61 % (7502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.61 % (7502)Termination reason: Unknown
% 1.97/1.61 % (7502)Termination phase: Function definition elimination
% 1.97/1.61
% 1.97/1.61 % (7502)Memory used [KB]: 1023
% 1.97/1.61 % (7502)Time elapsed: 0.003 s
% 1.97/1.61 % (7502)Instructions burned: 3 (million)
% 1.97/1.61 % (7502)------------------------------
% 1.97/1.61 % (7502)------------------------------
% 1.97/1.61 % (7503)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/4Mi)
% 1.97/1.61 % (7504)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/18Mi)
% 1.97/1.62 % (7503)Instruction limit reached!
% 1.97/1.62 % (7503)------------------------------
% 1.97/1.62 % (7503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.62 % (7503)Termination reason: Unknown
% 1.97/1.62 % (7505)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/710Mi)
% 1.97/1.62 % (7503)Termination phase: Saturation
% 1.97/1.62
% 1.97/1.62 % (7503)Memory used [KB]: 5500
% 1.97/1.62 % (7503)Time elapsed: 0.004 s
% 1.97/1.62 % (7503)Instructions burned: 5 (million)
% 1.97/1.62 % (7503)------------------------------
% 1.97/1.62 % (7503)------------------------------
% 1.97/1.62 % (7506)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/6Mi)
% 1.97/1.62 % (7504)Instruction limit reached!
% 1.97/1.62 % (7504)------------------------------
% 1.97/1.62 % (7504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.62 % (7504)Termination reason: Unknown
% 1.97/1.62 % (7504)Termination phase: Saturation
% 1.97/1.62
% 1.97/1.62 % (7504)Memory used [KB]: 5628
% 1.97/1.62 % (7504)Time elapsed: 0.012 s
% 1.97/1.62 % (7504)Instructions burned: 18 (million)
% 1.97/1.62 % (7504)------------------------------
% 1.97/1.62 % (7504)------------------------------
% 1.97/1.62 % (7506)Instruction limit reached!
% 1.97/1.62 % (7506)------------------------------
% 1.97/1.62 % (7506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.62 % (7506)Termination reason: Unknown
% 1.97/1.62 % (7506)Termination phase: Saturation
% 1.97/1.62
% 1.97/1.62 % (7506)Memory used [KB]: 5500
% 1.97/1.62 % (7506)Time elapsed: 0.005 s
% 1.97/1.62 % (7506)Instructions burned: 6 (million)
% 1.97/1.62 % (7506)------------------------------
% 1.97/1.62 % (7506)------------------------------
% 1.97/1.63 % (7507)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/902Mi)
% 1.97/1.63 % (7507)Refutation not found, incomplete strategy
% 1.97/1.63 % (7507)------------------------------
% 1.97/1.63 % (7507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.63 % (7507)Termination reason: Refutation not found, incomplete strategy
% 1.97/1.63
% 1.97/1.63
% 1.97/1.63 % (7507)Memory used [KB]: 5500
% 1.97/1.63 % (7507)Time elapsed: 0.003 s
% 1.97/1.63 % (7507)Instructions burned: 3 (million)
% 1.97/1.63 % (7507)------------------------------
% 1.97/1.63 % (7507)------------------------------
% 1.97/1.63 % (7508)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/21Mi)
% 1.97/1.64 % (7510)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/6Mi)
% 1.97/1.64 % (7509)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/5Mi)
% 1.97/1.64 % (7509)Instruction limit reached!
% 1.97/1.64 % (7509)------------------------------
% 1.97/1.64 % (7509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.64 % (7509)Termination reason: Unknown
% 1.97/1.64 % (7509)Termination phase: Saturation
% 1.97/1.64
% 1.97/1.64 % (7509)Memory used [KB]: 5500
% 1.97/1.64 % (7509)Time elapsed: 0.005 s
% 1.97/1.64 % (7509)Instructions burned: 6 (million)
% 1.97/1.64 % (7509)------------------------------
% 1.97/1.64 % (7509)------------------------------
% 1.97/1.64 % (7510)Instruction limit reached!
% 1.97/1.64 % (7510)------------------------------
% 1.97/1.64 % (7510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.64 % (7510)Termination reason: Unknown
% 1.97/1.64 % (7510)Termination phase: Saturation
% 1.97/1.64
% 1.97/1.64 % (7510)Memory used [KB]: 5500
% 1.97/1.64 % (7510)Time elapsed: 0.006 s
% 1.97/1.64 % (7510)Instructions burned: 7 (million)
% 1.97/1.64 % (7510)------------------------------
% 1.97/1.64 % (7510)------------------------------
% 1.97/1.65 % (7508)Instruction limit reached!
% 1.97/1.65 % (7508)------------------------------
% 1.97/1.65 % (7508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.65 % (7508)Termination reason: Unknown
% 1.97/1.65 % (7508)Termination phase: Saturation
% 1.97/1.65
% 1.97/1.65 % (7508)Memory used [KB]: 5628
% 1.97/1.65 % (7508)Time elapsed: 0.014 s
% 1.97/1.65 % (7508)Instructions burned: 21 (million)
% 1.97/1.65 % (7508)------------------------------
% 1.97/1.65 % (7508)------------------------------
% 1.97/1.65 % (7485)Instruction limit reached!
% 1.97/1.65 % (7485)------------------------------
% 1.97/1.65 % (7485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.65 % (7485)Termination reason: Unknown
% 1.97/1.65 % (7485)Termination phase: Saturation
% 1.97/1.65
% 1.97/1.65 % (7485)Memory used [KB]: 6524
% 1.97/1.65 % (7485)Time elapsed: 0.101 s
% 1.97/1.65 % (7485)Instructions burned: 183 (million)
% 1.97/1.65 % (7485)------------------------------
% 1.97/1.65 % (7485)------------------------------
% 1.97/1.65 % (7496)First to succeed.
% 1.97/1.65 % (7511)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_7388 for (2999ds/377Mi)
% 1.97/1.65 % (7496)Refutation found. Thanks to Tanya!
% 1.97/1.65 % SZS status Theorem for DTF2THF_7388
% 1.97/1.65 % SZS output start Proof for DTF2THF_7388
% 1.97/1.65 thf(type_def_5, type, mworld: $tType).
% 1.97/1.65 thf(func_def_0, type, mworld: $tType).
% 1.97/1.65 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.97/1.65 thf(func_def_2, type, mactual: mworld).
% 1.97/1.65 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.97/1.65 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.97/1.65 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.97/1.65 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.97/1.65 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.97/1.65 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.97/1.65 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.97/1.65 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.97/1.65 thf(func_def_12, type, p: mworld > $o).
% 1.97/1.65 thf(func_def_27, type, ph1: !>[X0: $tType]:(X0)).
% 1.97/1.65 thf(func_def_28, type, sK2: mworld).
% 1.97/1.65 thf(func_def_29, type, sK3: mworld).
% 1.97/1.65 thf(func_def_30, type, sK4: mworld).
% 1.97/1.65 thf(func_def_31, type, sK5: mworld).
% 1.97/1.65 thf(func_def_32, type, sK6: mworld).
% 1.97/1.65 thf(func_def_33, type, sK7: mworld).
% 1.97/1.65 thf(func_def_34, type, sK8: mworld).
% 1.97/1.65 thf(func_def_35, type, sK9: mworld).
% 1.97/1.65 thf(func_def_36, type, sK10: mworld).
% 1.97/1.65 thf(f944,plain,(
% 1.97/1.65 $false),
% 1.97/1.65 inference(avatar_sat_refutation,[status(thm)],[f86,f419,f423,f939])).
% 1.97/1.65 thf(f939,plain,(
% 1.97/1.65 ~spl0_4),
% 1.97/1.65 inference(avatar_contradiction_clause,[status(thm)],[f938])).
% 1.97/1.65 thf(f938,plain,(
% 1.97/1.65 $false | ~spl0_4),
% 1.97/1.65 inference(trivial_inequality_removal,[status(thm)],[f937])).
% 1.97/1.65 thf(f937,plain,(
% 1.97/1.65 ($true = $false) | ~spl0_4),
% 1.97/1.65 inference(forward_demodulation,[status(thm)],[f925,f844])).
% 1.97/1.65 thf(f844,plain,(
% 1.97/1.65 ((mrel @ sK7 @ sK9) = $false) | ~spl0_4),
% 1.97/1.65 inference(not_proxy_clausification,[status(thm)],[f690])).
% 1.97/1.65 thf(f690,plain,(
% 1.97/1.65 ($true = (~ (mrel @ sK7 @ sK9))) | ~spl0_4),
% 1.97/1.65 inference(boolean_simplification,[status(thm)],[f686])).
% 1.97/1.65 thf(f686,plain,(
% 1.97/1.65 ($true = ((mrel @ sK7 @ sK9) => $false)) | ~spl0_4),
% 1.97/1.65 inference(superposition,[status(thm)],[f60,f681])).
% 1.97/1.65 thf(f681,plain,(
% 1.97/1.65 ((mrel @ sK9 @ sK7) = $false) | ~spl0_4),
% 1.97/1.65 inference(not_proxy_clausification,[status(thm)],[f678])).
% 1.97/1.65 thf(f678,plain,(
% 1.97/1.65 ((~ (mrel @ sK9 @ sK7)) = $true) | ~spl0_4),
% 1.97/1.65 inference(boolean_simplification,[status(thm)],[f675])).
% 1.97/1.65 thf(f675,plain,(
% 1.97/1.65 (((mrel @ sK9 @ sK7) => $false) = $true) | ~spl0_4),
% 1.97/1.65 inference(superposition,[status(thm)],[f661,f517])).
% 1.97/1.65 thf(f517,plain,(
% 1.97/1.65 ((p @ sK7) = $false) | ~spl0_4),
% 1.97/1.65 inference(not_proxy_clausification,[status(thm)],[f513])).
% 1.97/1.65 thf(f513,plain,(
% 1.97/1.65 ($true = (~ (p @ sK7))) | ~spl0_4),
% 1.97/1.65 inference(boolean_simplification,[status(thm)],[f512])).
% 1.97/1.65 thf(f512,plain,(
% 1.97/1.65 (($true & (~ (p @ sK7))) = $true) | ~spl0_4),
% 1.97/1.65 inference(backward_demodulation,[status(thm)],[f503,f511])).
% 1.97/1.65 thf(f511,plain,(
% 1.97/1.65 ($true = (mrel @ sK6 @ sK7)) | ~spl0_4),
% 1.97/1.65 inference(binary_proxy_clausification,[status(thm)],[f503])).
% 1.97/1.65 thf(f503,plain,(
% 1.97/1.65 (((mrel @ sK6 @ sK7) & (~ (p @ sK7))) = $true) | ~spl0_4),
% 1.97/1.65 inference(beta_eta_normalization,[status(thm)],[f501])).
% 1.97/1.65 thf(f501,plain,(
% 1.97/1.65 (((^[Y0 : mworld]: ((mrel @ sK6 @ Y0) & (~ (p @ Y0)))) @ sK7) = $true) | ~spl0_4),
% 1.97/1.65 inference(sigma_clausification,[status(thm)],[f499])).
% 1.97/1.65 thf(f499,plain,(
% 1.97/1.65 ($true = (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ sK6 @ Y0) & (~ (p @ Y0)))))) | ~spl0_4),
% 1.97/1.65 inference(boolean_simplification,[status(thm)],[f497])).
% 1.97/1.65 thf(f497,plain,(
% 1.97/1.65 ($true = ($true => (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ sK6 @ Y0) & (~ (p @ Y0))))))) | ~spl0_4),
% 1.97/1.65 inference(superposition,[status(thm)],[f486,f49])).
% 1.97/1.65 thf(f49,plain,(
% 1.97/1.65 ( ! [X1 : mworld] : (($true = (mrel @ X1 @ X1))) )),
% 1.97/1.65 inference(beta_eta_normalization,[status(thm)],[f48])).
% 1.97/1.65 thf(f48,plain,(
% 1.97/1.65 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: (mrel @ Y0 @ Y0)) @ X1))) )),
% 1.97/1.65 inference(pi_clausification,[status(thm)],[f39])).
% 1.97/1.65 thf(f39,plain,(
% 1.97/1.65 ((!! @ mworld @ (^[Y0 : mworld]: (mrel @ Y0 @ Y0))) = $true)),
% 1.97/1.65 inference(cnf_transformation,[status(thm)],[f24])).
% 1.97/1.65 thf(f24,plain,(
% 1.97/1.65 ((!! @ mworld @ (^[Y0 : mworld]: (mrel @ Y0 @ Y0))) = $true)),
% 1.97/1.65 inference(fool_elimination,[status(thm)],[f23])).
% 1.97/1.65 thf(f23,plain,(
% 1.97/1.65 ! [X0 : mworld] : (mrel @ X0 @ X0)),
% 1.97/1.65 inference(rectify,[status(thm)],[f9])).
% 1.97/1.65 thf(f9,axiom,(
% 1.97/1.65 ! [X2 : mworld] : (mrel @ X2 @ X2)),
% 1.97/1.65 file('/export/starexec/sandbox2/tmp/tmp.KxhdkAZLMx/DTF2THF_7388.p',mrel_reflexive)).
% 1.97/1.65 thf(f486,plain,(
% 1.97/1.65 ( ! [X1 : mworld] : ((((mrel @ sK6 @ X1) => (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) & (~ (p @ Y0)))))) = $true)) ) | ~spl0_4),
% 1.97/1.65 inference(beta_eta_normalization,[status(thm)],[f485])).
% 1.97/1.65 thf(f485,plain,(
% 1.97/1.65 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ sK6 @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) & (~ (p @ Y1))))))) @ X1) = $true)) ) | ~spl0_4),
% 1.97/1.65 inference(pi_clausification,[status(thm)],[f434])).
% 1.97/1.65 thf(f434,plain,(
% 1.97/1.65 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK6 @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) & (~ (p @ Y1)))))))) = $true) | ~spl0_4),
% 1.97/1.65 inference(binary_proxy_clausification,[status(thm)],[f433])).
% 1.97/1.65 thf(f433,plain,(
% 1.97/1.65 ($true = ((mrel @ mactual @ sK6) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK6 @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) & (~ (p @ Y1)))))))))) | ~spl0_4),
% 1.97/1.65 inference(beta_eta_normalization,[status(thm)],[f432])).
% 1.97/1.65 thf(f432,plain,(
% 1.97/1.65 (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (~ (p @ Y2)))))))))) @ sK6) = $true) | ~spl0_4),
% 1.97/1.65 inference(sigma_clausification,[status(thm)],[f428])).
% 1.97/1.65 thf(f428,plain,(
% 1.97/1.65 ((?? @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (~ (p @ Y2))))))))))) != $false) | ~spl0_4),
% 1.97/1.65 inference(forward_demodulation,[status(thm)],[f65,f85])).
% 1.97/1.65 thf(f85,plain,(
% 1.97/1.65 ((~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (p @ Y2))))))))))) = $false) | ~spl0_4),
% 1.97/1.65 inference(avatar_component_clause,[status(thm)],[f84])).
% 1.97/1.65 thf(f84,definition,(
% 1.97/1.65 spl0_4 <=> ((~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (p @ Y2))))))))))) = $false)),
% 1.97/1.65 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.97/1.65 thf(f65,plain,(
% 1.97/1.65 ((~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (p @ Y2))))))))))) != (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (~ (p @ Y2))))))))))))),
% 1.97/1.65 inference(binary_proxy_clausification,[status(thm)],[f64])).
% 1.97/1.65 thf(f64,plain,(
% 1.97/1.65 (((~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (p @ Y2))))))))))) = (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (~ (p @ Y2)))))))))))) = $false)),
% 1.97/1.65 inference(not_proxy_clausification,[status(thm)],[f47])).
% 1.97/1.65 thf(f47,plain,(
% 1.97/1.65 ((~ ((~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (p @ Y2))))))))))) = (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (~ (p @ Y2))))))))))))) = $true)),
% 1.97/1.65 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.97/1.65 thf(f46,plain,(
% 1.97/1.65 ((~ ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ p)))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ p))))))) = $true)),
% 1.97/1.65 inference(definition_unfolding,[status(thm)],[f35,f40,f43,f42,f37,f45,f37,f45,f37,f45,f42])).
% 1.97/1.65 thf(f45,plain,(
% 1.97/1.65 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.97/1.65 inference(cnf_transformation,[status(thm)],[f32])).
% 1.97/1.65 thf(f32,plain,(
% 1.97/1.65 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.97/1.65 inference(fool_elimination,[status(thm)],[f31])).
% 1.97/1.65 thf(f31,plain,(
% 1.97/1.65 (mdia = (^[X0 : mworld > $o, X1 : mworld] : (? [X2 : mworld] : ((X0 @ X2) & (mrel @ X1 @ X2)))))),
% 1.97/1.65 inference(rectify,[status(thm)],[f8])).
% 1.97/1.65 thf(f8,axiom,(
% 1.97/1.65 (mdia = (^[X0 : mworld > $o, X2 : mworld] : (? [X4 : mworld] : ((X0 @ X4) & (mrel @ X2 @ X4)))))),
% 1.97/1.65 file('/export/starexec/sandbox2/tmp/tmp.KxhdkAZLMx/DTF2THF_7388.p',mdia_def)).
% 1.97/1.65 thf(f37,plain,(
% 1.97/1.65 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.97/1.65 inference(cnf_transformation,[status(thm)],[f34])).
% 1.97/1.65 thf(f34,plain,(
% 1.97/1.65 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.97/1.65 inference(fool_elimination,[status(thm)],[f33])).
% 1.97/1.65 thf(f33,plain,(
% 1.97/1.65 (mbox = (^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 1.97/1.65 inference(rectify,[status(thm)],[f7])).
% 1.97/1.65 thf(f7,axiom,(
% 1.97/1.65 (mbox = (^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))))),
% 1.97/1.65 file('/export/starexec/sandbox2/tmp/tmp.KxhdkAZLMx/DTF2THF_7388.p',mbox_def)).
% 1.97/1.65 thf(f42,plain,(
% 1.97/1.65 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 1.97/1.65 inference(cnf_transformation,[status(thm)],[f18])).
% 1.97/1.65 thf(f18,plain,(
% 1.97/1.65 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 1.97/1.65 inference(fool_elimination,[status(thm)],[f17])).
% 1.97/1.65 thf(f17,plain,(
% 1.97/1.65 ((^[X0 : mworld > $o, X1 : mworld] : (~(X0 @ X1))) = mnot)),
% 1.97/1.65 inference(rectify,[status(thm)],[f2])).
% 1.97/1.65 thf(f2,axiom,(
% 1.97/1.65 ((^[X1 : mworld > $o, X2 : mworld] : (~(X1 @ X2))) = mnot)),
% 1.97/1.65 file('/export/starexec/sandbox2/tmp/tmp.KxhdkAZLMx/DTF2THF_7388.p',mnot_def)).
% 1.97/1.65 thf(f43,plain,(
% 1.97/1.65 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 1.97/1.65 inference(cnf_transformation,[status(thm)],[f16])).
% 1.97/1.65 thf(f16,plain,(
% 1.97/1.65 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 1.97/1.65 inference(fool_elimination,[status(thm)],[f15])).
% 1.97/1.65 thf(f15,plain,(
% 1.97/1.65 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) <=> (X1 @ X2))) = mequiv)),
% 1.97/1.65 inference(rectify,[status(thm)],[f6])).
% 1.97/1.65 thf(f6,axiom,(
% 1.97/1.65 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) <=> (X3 @ X2))) = mequiv)),
% 1.97/1.65 file('/export/starexec/sandbox2/tmp/tmp.KxhdkAZLMx/DTF2THF_7388.p',mequiv_def)).
% 1.97/1.65 thf(f40,plain,(
% 1.97/1.65 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.97/1.65 inference(cnf_transformation,[status(thm)],[f14])).
% 1.97/1.65 thf(f14,plain,(
% 1.97/1.65 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.97/1.65 inference(fool_elimination,[status(thm)],[f1])).
% 1.97/1.65 thf(f1,axiom,(
% 1.97/1.65 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 1.97/1.65 file('/export/starexec/sandbox2/tmp/tmp.KxhdkAZLMx/DTF2THF_7388.p',mlocal_def)).
% 1.97/1.65 thf(f35,plain,(
% 1.97/1.65 ($true = (~ (mlocal @ (mequiv @ (mnot @ (mbox @ (mdia @ (mbox @ p)))) @ (mdia @ (mbox @ (mdia @ (mnot @ p))))))))),
% 1.97/1.65 inference(cnf_transformation,[status(thm)],[f20])).
% 1.97/1.65 thf(f20,plain,(
% 1.97/1.65 ($true = (~ (mlocal @ (mequiv @ (mnot @ (mbox @ (mdia @ (mbox @ p)))) @ (mdia @ (mbox @ (mdia @ (mnot @ p))))))))),
% 1.97/1.65 inference(fool_elimination,[status(thm)],[f19])).
% 1.97/1.65 thf(f19,plain,(
% 1.97/1.65 ~(mlocal @ (mequiv @ (mnot @ (mbox @ (mdia @ (mbox @ p)))) @ (mdia @ (mbox @ (mdia @ (mnot @ p))))))),
% 1.97/1.65 inference(rectify,[status(thm)],[f12])).
% 1.97/1.65 thf(f12,negated_conjecture,(
% 1.97/1.65 ~(mlocal @ (mequiv @ (mnot @ (mbox @ (mdia @ (mbox @ p)))) @ (mdia @ (mbox @ (mdia @ (mnot @ p))))))),
% 1.97/1.65 inference(negated_conjecture,[status(cth)],[f11])).
% 1.97/1.65 thf(f11,conjecture,(
% 1.97/1.65 (mlocal @ (mequiv @ (mnot @ (mbox @ (mdia @ (mbox @ p)))) @ (mdia @ (mbox @ (mdia @ (mnot @ p))))))),
% 1.97/1.65 file('/export/starexec/sandbox2/tmp/tmp.KxhdkAZLMx/DTF2THF_7388.p',con)).
% 1.97/1.65 thf(f661,plain,(
% 1.97/1.65 ( ! [X1 : mworld] : ((((mrel @ sK9 @ X1) => (p @ X1)) = $true)) ) | ~spl0_4),
% 1.97/1.65 inference(beta_eta_normalization,[status(thm)],[f660])).
% 1.97/1.65 thf(f660,plain,(
% 1.97/1.65 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ sK9 @ Y0) => (p @ Y0))) @ X1))) ) | ~spl0_4),
% 1.97/1.65 inference(pi_clausification,[status(thm)],[f641])).
% 1.97/1.65 thf(f641,plain,(
% 1.97/1.65 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK9 @ Y0) => (p @ Y0)))) = $true) | ~spl0_4),
% 1.97/1.65 inference(boolean_simplification,[status(thm)],[f640])).
% 1.97/1.65 thf(f640,plain,(
% 1.97/1.65 ($true = ($true & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK9 @ Y0) => (p @ Y0)))))) | ~spl0_4),
% 1.97/1.65 inference(backward_demodulation,[status(thm)],[f624,f639])).
% 1.97/1.65 thf(f639,plain,(
% 1.97/1.65 ((mrel @ mactual @ sK9) = $true) | ~spl0_4),
% 1.97/1.65 inference(binary_proxy_clausification,[status(thm)],[f624])).
% 1.97/1.65 thf(f624,plain,(
% 1.97/1.65 ($true = ((mrel @ mactual @ sK9) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK9 @ Y0) => (p @ Y0)))))) | ~spl0_4),
% 1.97/1.65 inference(beta_eta_normalization,[status(thm)],[f622])).
% 1.97/1.65 thf(f622,plain,(
% 1.97/1.65 (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (p @ Y1)))))) @ sK9) = $true) | ~spl0_4),
% 1.97/1.65 inference(sigma_clausification,[status(thm)],[f548])).
% 1.97/1.65 thf(f548,plain,(
% 1.97/1.65 ((?? @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (p @ Y1))))))) = $true) | ~spl0_4),
% 1.97/1.65 inference(boolean_simplification,[status(thm)],[f545])).
% 1.97/1.65 thf(f545,plain,(
% 1.97/1.65 ($true = ($true => (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (p @ Y1))))))))) | ~spl0_4),
% 1.97/1.65 inference(superposition,[status(thm)],[f521,f49])).
% 1.97/1.65 thf(f521,plain,(
% 1.97/1.65 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (p @ Y1)))))))) = $true)) ) | ~spl0_4),
% 1.97/1.65 inference(beta_eta_normalization,[status(thm)],[f520])).
% 1.97/1.65 thf(f520,plain,(
% 1.97/1.65 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (p @ Y2))))))))) @ X1))) ) | ~spl0_4),
% 1.97/1.65 inference(pi_clausification,[status(thm)],[f514])).
% 1.97/1.65 thf(f514,plain,(
% 1.97/1.65 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (p @ Y2))))))))))) | ~spl0_4),
% 1.97/1.65 inference(not_proxy_clausification,[status(thm)],[f85])).
% 1.97/1.65 thf(f60,plain,(
% 1.97/1.65 ( ! [X0 : mworld,X1 : mworld] : ((((mrel @ X0 @ X1) => (mrel @ X1 @ X0)) = $true)) )),
% 1.97/1.65 inference(boolean_simplification,[status(thm)],[f58])).
% 1.97/1.65 thf(f58,plain,(
% 1.97/1.65 ( ! [X0 : mworld,X1 : mworld] : (($true = (((mrel @ X0 @ X1) & $true) => (mrel @ X1 @ X0)))) )),
% 1.97/1.65 inference(superposition,[status(thm)],[f55,f49])).
% 1.97/1.65 thf(f55,plain,(
% 1.97/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ X1 @ X3) & (mrel @ X1 @ X2)) => (mrel @ X3 @ X2)) = $true)) )),
% 1.97/1.65 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.97/1.65 thf(f54,plain,(
% 1.97/1.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: (((mrel @ X1 @ Y0) & (mrel @ X1 @ X2)) => (mrel @ Y0 @ X2))) @ X3) = $true)) )),
% 1.97/1.65 inference(pi_clausification,[status(thm)],[f53])).
% 1.97/1.65 thf(f53,plain,(
% 1.97/1.65 ( ! [X2 : mworld,X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: (((mrel @ X1 @ Y0) & (mrel @ X1 @ X2)) => (mrel @ Y0 @ X2)))))) )),
% 1.97/1.65 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.97/1.65 thf(f52,plain,(
% 1.97/1.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: (!! @ mworld @ (^[Y1 : mworld]: (((mrel @ X1 @ Y1) & (mrel @ X1 @ Y0)) => (mrel @ Y1 @ Y0))))) @ X2))) )),
% 1.97/1.65 inference(pi_clausification,[status(thm)],[f51])).
% 1.97/1.65 thf(f51,plain,(
% 1.97/1.65 ( ! [X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: (!! @ mworld @ (^[Y1 : mworld]: (((mrel @ X1 @ Y1) & (mrel @ X1 @ Y0)) => (mrel @ Y1 @ Y0)))))))) )),
% 1.97/1.65 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.97/1.65 thf(f50,plain,(
% 1.97/1.65 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: (!! @ mworld @ (^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: (((mrel @ Y0 @ Y2) & (mrel @ Y0 @ Y1)) => (mrel @ Y2 @ Y1))))))) @ X1))) )),
% 1.97/1.65 inference(pi_clausification,[status(thm)],[f44])).
% 1.97/1.65 thf(f44,plain,(
% 1.97/1.65 ((!! @ mworld @ (^[Y0 : mworld]: (!! @ mworld @ (^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: (((mrel @ Y0 @ Y2) & (mrel @ Y0 @ Y1)) => (mrel @ Y2 @ Y1)))))))) = $true)),
% 1.97/1.65 inference(cnf_transformation,[status(thm)],[f22])).
% 1.97/1.65 thf(f22,plain,(
% 1.97/1.65 ((!! @ mworld @ (^[Y0 : mworld]: (!! @ mworld @ (^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: (((mrel @ Y0 @ Y2) & (mrel @ Y0 @ Y1)) => (mrel @ Y2 @ Y1)))))))) = $true)),
% 1.97/1.65 inference(fool_elimination,[status(thm)],[f21])).
% 1.97/1.65 thf(f21,plain,(
% 1.97/1.65 ! [X0 : mworld,X1 : mworld,X2 : mworld] : (((mrel @ X2 @ X1) & (mrel @ X2 @ X0)) => (mrel @ X0 @ X1))),
% 1.97/1.65 inference(rectify,[status(thm)],[f10])).
% 1.97/1.65 thf(f10,axiom,(
% 1.97/1.65 ! [X5 : mworld,X4 : mworld,X2 : mworld] : (((mrel @ X2 @ X4) & (mrel @ X2 @ X5)) => (mrel @ X5 @ X4))),
% 1.97/1.65 file('/export/starexec/sandbox2/tmp/tmp.KxhdkAZLMx/DTF2THF_7388.p',mrel_euclidean)).
% 1.97/1.65 thf(f925,plain,(
% 1.97/1.65 ((mrel @ sK7 @ sK9) = $true) | ~spl0_4),
% 1.97/1.65 inference(boolean_simplification,[status(thm)],[f922])).
% 1.97/1.65 thf(f922,plain,(
% 1.97/1.65 (($true => (mrel @ sK7 @ sK9)) = $true) | ~spl0_4),
% 1.97/1.65 inference(superposition,[status(thm)],[f564,f652])).
% 1.97/1.65 thf(f652,plain,(
% 1.97/1.65 ((mrel @ sK6 @ sK9) = $true) | ~spl0_4),
% 1.97/1.65 inference(boolean_simplification,[status(thm)],[f645])).
% 1.97/1.65 thf(f645,plain,(
% 1.97/1.65 (($true => (mrel @ sK6 @ sK9)) = $true) | ~spl0_4),
% 1.97/1.65 inference(superposition,[status(thm)],[f445,f639])).
% 1.97/1.65 thf(f445,plain,(
% 1.97/1.65 ( ! [X0 : mworld] : ((((mrel @ mactual @ X0) => (mrel @ sK6 @ X0)) = $true)) ) | ~spl0_4),
% 1.97/1.65 inference(boolean_simplification,[status(thm)],[f440])).
% 1.97/1.65 thf(f440,plain,(
% 1.97/1.65 ( ! [X0 : mworld] : (($true = (($true & (mrel @ mactual @ X0)) => (mrel @ sK6 @ X0)))) ) | ~spl0_4),
% 1.97/1.65 inference(superposition,[status(thm)],[f55,f437])).
% 1.97/1.65 thf(f437,plain,(
% 1.97/1.65 ($true = (mrel @ mactual @ sK6)) | ~spl0_4),
% 1.97/1.65 inference(boolean_simplification,[status(thm)],[f436])).
% 1.97/1.65 thf(f436,plain,(
% 1.97/1.65 (((mrel @ mactual @ sK6) & $true) = $true) | ~spl0_4),
% 1.97/1.65 inference(backward_demodulation,[status(thm)],[f433,f434])).
% 1.97/1.65 thf(f564,plain,(
% 1.97/1.65 ( ! [X0 : mworld] : ((((mrel @ sK6 @ X0) => (mrel @ sK7 @ X0)) = $true)) ) | ~spl0_4),
% 1.97/1.65 inference(boolean_simplification,[status(thm)],[f555])).
% 1.97/1.65 thf(f555,plain,(
% 1.97/1.65 ( ! [X0 : mworld] : (((($true & (mrel @ sK6 @ X0)) => (mrel @ sK7 @ X0)) = $true)) ) | ~spl0_4),
% 1.97/1.65 inference(superposition,[status(thm)],[f55,f511])).
% 1.97/1.65 thf(f423,plain,(
% 1.97/1.65 spl0_2 | ~spl0_3),
% 1.97/1.65 inference(avatar_split_clause,[status(thm)],[f422,f81,f77])).
% 1.97/1.65 thf(f77,definition,(
% 1.97/1.65 spl0_2 <=> ((~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (p @ Y2))))))))))) = $true)),
% 1.97/1.65 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.97/1.65 thf(f81,definition,(
% 1.97/1.65 spl0_3 <=> ((?? @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (~ (p @ Y2))))))))))) = $false)),
% 1.97/1.65 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.97/1.65 thf(f422,plain,(
% 1.97/1.65 ((~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (p @ Y2))))))))))) = $true) | ~spl0_3),
% 1.97/1.65 inference(boolean_simplification,[status(thm)],[f421])).
% 1.97/1.65 thf(f421,plain,(
% 1.97/1.65 ((~ (~ (~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (p @ Y2))))))))))))) = $true) | ~spl0_3),
% 1.97/1.65 inference(boolean_simplification,[status(thm)],[f420])).
% 1.97/1.65 thf(f420,plain,(
% 1.97/1.65 ($true = (~ ((~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (p @ Y2))))))))))) = $false))) | ~spl0_3),
% 1.97/1.65 inference(forward_demodulation,[status(thm)],[f47,f82])).
% 1.97/1.65 thf(f82,plain,(
% 1.97/1.65 ((?? @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (~ (p @ Y2))))))))))) = $false) | ~spl0_3),
% 1.97/1.65 inference(avatar_component_clause,[status(thm)],[f81])).
% 1.97/1.65 thf(f419,plain,(
% 1.97/1.65 ~spl0_2 | ~spl0_3),
% 1.97/1.65 inference(avatar_contradiction_clause,[status(thm)],[f418])).
% 1.97/1.65 thf(f418,plain,(
% 1.97/1.65 $false | (~spl0_2 | ~spl0_3)),
% 1.97/1.65 inference(trivial_inequality_removal,[status(thm)],[f417])).
% 1.97/1.65 thf(f417,plain,(
% 1.97/1.65 ($true = $false) | (~spl0_2 | ~spl0_3)),
% 1.97/1.65 inference(forward_demodulation,[status(thm)],[f406,f234])).
% 1.97/1.65 thf(f234,plain,(
% 1.97/1.65 ((mrel @ sK4 @ sK3) = $false) | (~spl0_2 | ~spl0_3)),
% 1.97/1.65 inference(boolean_simplification,[status(thm)],[f233])).
% 1.97/1.65 thf(f233,plain,(
% 1.97/1.65 (((mrel @ sK4 @ sK3) & $true) = $false) | (~spl0_2 | ~spl0_3)),
% 1.97/1.65 inference(boolean_simplification,[status(thm)],[f229])).
% 1.97/1.65 thf(f229,plain,(
% 1.97/1.65 (((mrel @ sK4 @ sK3) & (~ $false)) = $false) | (~spl0_2 | ~spl0_3)),
% 1.97/1.65 inference(superposition,[status(thm)],[f217,f158])).
% 1.97/1.65 thf(f158,plain,(
% 1.97/1.65 ((p @ sK3) = $false) | ~spl0_2),
% 1.97/1.65 inference(binary_proxy_clausification,[status(thm)],[f157])).
% 1.97/1.65 thf(f157,plain,(
% 1.97/1.65 (((mrel @ sK2 @ sK3) => (p @ sK3)) = $false) | ~spl0_2),
% 1.97/1.65 inference(beta_eta_normalization,[status(thm)],[f154])).
% 1.97/1.65 thf(f154,plain,(
% 1.97/1.65 (((^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (p @ Y0))) @ sK3) = $false) | ~spl0_2),
% 1.97/1.65 inference(sigma_clausification,[status(thm)],[f116])).
% 1.97/1.65 thf(f116,plain,(
% 1.97/1.65 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (p @ Y0)))) = $false) | ~spl0_2),
% 1.97/1.65 inference(boolean_simplification,[status(thm)],[f115])).
% 1.97/1.65 thf(f115,plain,(
% 1.97/1.65 (($true & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (p @ Y0))))) = $false) | ~spl0_2),
% 1.97/1.65 inference(superposition,[status(thm)],[f103,f49])).
% 1.97/1.65 thf(f103,plain,(
% 1.97/1.65 ( ! [X1 : mworld] : ((((mrel @ sK2 @ X1) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (p @ Y0))))) = $false)) ) | ~spl0_2),
% 1.97/1.65 inference(beta_eta_normalization,[status(thm)],[f102])).
% 1.97/1.65 thf(f102,plain,(
% 1.97/1.65 ( ! [X1 : mworld] : (($false = ((^[Y0 : mworld]: ((mrel @ sK2 @ Y0) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (p @ Y1)))))) @ X1))) ) | ~spl0_2),
% 1.97/1.65 inference(pi_clausification,[status(thm)],[f101])).
% 1.97/1.65 thf(f101,plain,(
% 1.97/1.65 ((?? @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (p @ Y1))))))) = $false) | ~spl0_2),
% 1.97/1.65 inference(boolean_simplification,[status(thm)],[f100])).
% 1.97/1.65 thf(f100,plain,(
% 1.97/1.65 (($true => (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (p @ Y1)))))))) = $false) | ~spl0_2),
% 1.97/1.66 inference(backward_demodulation,[status(thm)],[f97,f99])).
% 1.97/1.66 thf(f99,plain,(
% 1.97/1.66 ((mrel @ mactual @ sK2) = $true) | ~spl0_2),
% 1.97/1.66 inference(binary_proxy_clausification,[status(thm)],[f97])).
% 1.97/1.66 thf(f97,plain,(
% 1.97/1.66 (((mrel @ mactual @ sK2) => (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (p @ Y1)))))))) = $false) | ~spl0_2),
% 1.97/1.66 inference(beta_eta_normalization,[status(thm)],[f96])).
% 1.97/1.66 thf(f96,plain,(
% 1.97/1.66 (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (p @ Y2))))))))) @ sK2) = $false) | ~spl0_2),
% 1.97/1.66 inference(sigma_clausification,[status(thm)],[f93])).
% 1.97/1.66 thf(f93,plain,(
% 1.97/1.66 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (p @ Y2)))))))))) = $false) | ~spl0_2),
% 1.97/1.66 inference(not_proxy_clausification,[status(thm)],[f78])).
% 1.97/1.66 thf(f78,plain,(
% 1.97/1.66 ((~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (p @ Y2))))))))))) = $true) | ~spl0_2),
% 1.97/1.66 inference(avatar_component_clause,[status(thm)],[f77])).
% 1.97/1.66 thf(f217,plain,(
% 1.97/1.66 ( ! [X1 : mworld] : ((((mrel @ sK4 @ X1) & (~ (p @ X1))) = $false)) ) | ~spl0_3),
% 1.97/1.66 inference(beta_eta_normalization,[status(thm)],[f216])).
% 1.97/1.66 thf(f216,plain,(
% 1.97/1.66 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ sK4 @ Y0) & (~ (p @ Y0)))) @ X1) = $false)) ) | ~spl0_3),
% 1.97/1.66 inference(pi_clausification,[status(thm)],[f168])).
% 1.97/1.66 thf(f168,plain,(
% 1.97/1.66 ((?? @ mworld @ (^[Y0 : mworld]: ((mrel @ sK4 @ Y0) & (~ (p @ Y0))))) = $false) | ~spl0_3),
% 1.97/1.66 inference(binary_proxy_clausification,[status(thm)],[f167])).
% 1.97/1.66 thf(f167,plain,(
% 1.97/1.66 (((mrel @ mactual @ sK4) => (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ sK4 @ Y0) & (~ (p @ Y0)))))) = $false) | ~spl0_3),
% 1.97/1.66 inference(beta_eta_normalization,[status(thm)],[f164])).
% 1.97/1.66 thf(f164,plain,(
% 1.97/1.66 (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) & (~ (p @ Y1))))))) @ sK4) = $false) | ~spl0_3),
% 1.97/1.66 inference(sigma_clausification,[status(thm)],[f144])).
% 1.97/1.66 thf(f144,plain,(
% 1.97/1.66 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) & (~ (p @ Y1)))))))) = $false) | ~spl0_3),
% 1.97/1.66 inference(boolean_simplification,[status(thm)],[f141])).
% 1.97/1.66 thf(f141,plain,(
% 1.97/1.66 (($true & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) & (~ (p @ Y1))))))))) = $false) | ~spl0_3),
% 1.97/1.66 inference(superposition,[status(thm)],[f130,f49])).
% 1.97/1.66 thf(f130,plain,(
% 1.97/1.66 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) & (~ (p @ Y1))))))))) = $false)) ) | ~spl0_3),
% 1.97/1.66 inference(beta_eta_normalization,[status(thm)],[f129])).
% 1.97/1.66 thf(f129,plain,(
% 1.97/1.66 ( ! [X1 : mworld] : (($false = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (~ (p @ Y2)))))))))) @ X1))) ) | ~spl0_3),
% 1.97/1.66 inference(pi_clausification,[status(thm)],[f82])).
% 1.97/1.66 thf(f406,plain,(
% 1.97/1.66 ((mrel @ sK4 @ sK3) = $true) | (~spl0_2 | ~spl0_3)),
% 1.97/1.66 inference(boolean_simplification,[status(thm)],[f403])).
% 1.97/1.66 thf(f403,plain,(
% 1.97/1.66 ($true = ($true => (mrel @ sK4 @ sK3))) | (~spl0_2 | ~spl0_3)),
% 1.97/1.66 inference(superposition,[status(thm)],[f186,f201])).
% 1.97/1.66 thf(f201,plain,(
% 1.97/1.66 ((mrel @ sK2 @ sK4) = $true) | (~spl0_2 | ~spl0_3)),
% 1.97/1.66 inference(boolean_simplification,[status(thm)],[f188])).
% 1.97/1.66 thf(f188,plain,(
% 1.97/1.66 (($true => (mrel @ sK2 @ sK4)) = $true) | (~spl0_2 | ~spl0_3)),
% 1.97/1.66 inference(superposition,[status(thm)],[f112,f169])).
% 1.97/1.66 thf(f169,plain,(
% 1.97/1.66 ((mrel @ mactual @ sK4) = $true) | ~spl0_3),
% 1.97/1.66 inference(binary_proxy_clausification,[status(thm)],[f167])).
% 1.97/1.66 thf(f112,plain,(
% 1.97/1.66 ( ! [X0 : mworld] : (($true = ((mrel @ mactual @ X0) => (mrel @ sK2 @ X0)))) ) | ~spl0_2),
% 1.97/1.66 inference(boolean_simplification,[status(thm)],[f106])).
% 1.97/1.66 thf(f106,plain,(
% 1.97/1.66 ( ! [X0 : mworld] : (((($true & (mrel @ mactual @ X0)) => (mrel @ sK2 @ X0)) = $true)) ) | ~spl0_2),
% 1.97/1.66 inference(superposition,[status(thm)],[f55,f99])).
% 1.97/1.66 thf(f186,plain,(
% 1.97/1.66 ( ! [X0 : mworld] : ((((mrel @ sK2 @ X0) => (mrel @ X0 @ sK3)) = $true)) ) | ~spl0_2),
% 1.97/1.66 inference(boolean_simplification,[status(thm)],[f179])).
% 1.97/1.66 thf(f179,plain,(
% 1.97/1.66 ( ! [X0 : mworld] : (($true = (((mrel @ sK2 @ X0) & $true) => (mrel @ X0 @ sK3)))) ) | ~spl0_2),
% 1.97/1.66 inference(superposition,[status(thm)],[f55,f159])).
% 1.97/1.66 thf(f159,plain,(
% 1.97/1.66 ((mrel @ sK2 @ sK3) = $true) | ~spl0_2),
% 1.97/1.66 inference(binary_proxy_clausification,[status(thm)],[f157])).
% 1.97/1.66 thf(f86,plain,(
% 1.97/1.66 spl0_3 | spl0_4),
% 1.97/1.66 inference(avatar_split_clause,[status(thm)],[f72,f84,f81])).
% 1.97/1.66 thf(f72,plain,(
% 1.97/1.66 ((~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (p @ Y2))))))))))) = $false) | ((?? @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (~ (p @ Y2))))))))))) = $false)),
% 1.97/1.66 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 1.97/1.66 % SZS output end Proof for DTF2THF_7388
% 1.97/1.66 % (7496)------------------------------
% 1.97/1.66 % (7496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.66 % (7496)Termination reason: Refutation
% 1.97/1.66
% 1.97/1.66 % (7496)Memory used [KB]: 6140
% 1.97/1.66 % (7496)Time elapsed: 0.072 s
% 1.97/1.66 % (7496)Instructions burned: 117 (million)
% 1.97/1.66 % (7496)------------------------------
% 1.97/1.66 % (7496)------------------------------
% 1.97/1.66 % (7484)Success in time 0.111 s
%------------------------------------------------------------------------------