%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM810^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 09:24:49 AM UTC 2026
% Result : Theorem 1.52s 1.27s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 4
% Syntax : Number of formulae : 53 ( 31 unt; 0 typ; 2 def)
% Number of atoms : 365 ( 45 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 694 ( 24 ~; 17 |; 37 &; 459 @)
% ( 2 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 9 usr; 10 con; 0-2 aty)
% ( 61 !!; 34 ??; 0 @@+; 0 @@-)
% Number of variables : 93 ( 65 ^; 25 !; 3 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cDOUBLE: $i > $i > $o ).
thf(func_def_2,type,
cS: $i > $i ).
thf(func_def_16,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f154,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f109,f117,f153]) ).
thf(f153,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[status(thm)],[f152]) ).
thf(f152,plain,
( $false
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f151]) ).
thf(f151,plain,
( ( $false = $true )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f149,f150]) ).
thf(f150,plain,
( ! [X1: $i] :
( $false
= ( cDOUBLE @ ( cS @ sK4 ) @ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f141]) ).
thf(f141,plain,
( ( ( ?? @ $i @ ( cDOUBLE @ ( cS @ sK4 ) ) )
= $false )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f136]) ).
thf(f136,plain,
( ( $false
= ( ( ?? @ $i @ ( cDOUBLE @ sK4 ) )
=> ( ?? @ $i @ ( cDOUBLE @ ( cS @ sK4 ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f132]) ).
thf(f132,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ?? @ $i @ ( cDOUBLE @ Y0 ) )
=> ( ?? @ $i @ ( cDOUBLE @ ( cS @ Y0 ) ) ) )
@ sK4 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f108]) ).
thf(f108,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i @ ( cDOUBLE @ Y0 ) )
=> ( ?? @ $i @ ( cDOUBLE @ ( cS @ Y0 ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f107]) ).
thf(f107,definition,
( spl0_4
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i @ ( cDOUBLE @ Y0 ) )
=> ( ?? @ $i @ ( cDOUBLE @ ( cS @ Y0 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f149,plain,
( ( ( cDOUBLE @ ( cS @ sK4 ) @ ( cS @ ( cS @ sK5 ) ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f148]) ).
thf(f148,plain,
( ( $true
= ( $true
=> ( cDOUBLE @ ( cS @ sK4 ) @ ( cS @ ( cS @ sK5 ) ) ) ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f34,f147]) ).
thf(f147,plain,
( ( ( cDOUBLE @ sK4 @ sK5 )
= $true )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f142]) ).
thf(f142,plain,
( ( ( ?? @ $i @ ( cDOUBLE @ sK4 ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f136]) ).
thf(f34,plain,
! [X2: $i,X1: $i] :
( ( ( cDOUBLE @ X2 @ X1 )
=> ( cDOUBLE @ ( cS @ X2 ) @ ( cS @ ( cS @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( cDOUBLE @ Y0 @ X1 )
=> ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ ( cS @ X1 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( cDOUBLE @ Y0 @ X1 )
=> ( cDOUBLE @ ( cS @ Y0 ) @ ( cS @ ( cS @ X1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( $true
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f26,f28]) ).
thf(f28,plain,
( ( cDOUBLE @ c0 @ c0 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( cDOUBLE @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( cDOUBLE @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) ) )
& $true )
= $true ),
inference(backward_demodulation,[status(thm)],[f17,f23]) ).
thf(f23,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( cDOUBLE @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i @ Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( ( cDOUBLE @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i @ Y0 ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( cDOUBLE @ Y0 ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ~ ( ( ( cDOUBLE @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i @ Y0 ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( cDOUBLE @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ~ ( ( ( cDOUBLE @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) ) )
& ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( cDOUBLE @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f10,f9]) ).
thf(f9,plain,
( cIND
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( cIND
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
! [X0: $i > $o] :
( ( ( ( X0 @ c0 )
& ! [X1: $i] :
( ( X0 @ X1 )
=> ( X0 @ ( cS @ X1 ) ) ) )
=> ! [X2: $i] : ( X0 @ X2 ) )
= cIND ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i > $o] :
( ( ( ( X0 @ c0 )
& ! [X1: $i] :
( ( X0 @ X1 )
=> ( X0 @ ( cS @ X1 ) ) ) )
=> ! [X1: $i] : ( X0 @ X1 ) )
= cIND ),
file('/export/starexec/sandbox/tmp/tmp.pqs0QRzIdW/DTF2THF_8977.p',cIND_def) ).
thf(f10,plain,
( ( ~ ( ( ( cDOUBLE @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) ) )
& cIND )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( cDOUBLE @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ~ ( ( ( cDOUBLE @ c0 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cDOUBLE @ Y1 @ Y0 )
=> ( cDOUBLE @ ( cS @ Y1 ) @ ( cS @ ( cS @ Y0 ) ) ) ) ) )
& cIND )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( cDOUBLE @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( cIND
& ! [X0: $i,X1: $i] :
( ( cDOUBLE @ X0 @ X1 )
=> ( cDOUBLE @ ( cS @ X0 ) @ ( cS @ ( cS @ X1 ) ) ) )
& ( cDOUBLE @ c0 @ c0 ) )
=> ! [X2: $i] :
? [X3: $i] : ( cDOUBLE @ X2 @ X3 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( ( cIND
& ! [X1: $i,X2: $i] :
( ( cDOUBLE @ X1 @ X2 )
=> ( cDOUBLE @ ( cS @ X1 ) @ ( cS @ ( cS @ X2 ) ) ) )
& ( cDOUBLE @ c0 @ c0 ) )
=> ! [X1: $i] :
? [X2: $i] : ( cDOUBLE @ X1 @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( ( cIND
& ! [X1: $i,X2: $i] :
( ( cDOUBLE @ X1 @ X2 )
=> ( cDOUBLE @ ( cS @ X1 ) @ ( cS @ ( cS @ X2 ) ) ) )
& ( cDOUBLE @ c0 @ c0 ) )
=> ! [X1: $i] :
? [X2: $i] : ( cDOUBLE @ X1 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.pqs0QRzIdW/DTF2THF_8977.p',cTHM140) ).
thf(f117,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[status(thm)],[f116]) ).
thf(f116,plain,
( $false
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f113]) ).
thf(f113,plain,
( ( $false = $true )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f28,f112]) ).
thf(f112,plain,
( ! [X1: $i] :
( $false
= ( cDOUBLE @ c0 @ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
( ( ( ?? @ $i @ ( cDOUBLE @ c0 ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f104]) ).
thf(f104,definition,
( spl0_3
<=> ( ( ?? @ $i @ ( cDOUBLE @ c0 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f109,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f102,f107,f104]) ).
thf(f102,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i @ ( cDOUBLE @ Y0 ) )
=> ( ?? @ $i @ ( cDOUBLE @ ( cS @ Y0 ) ) ) ) )
= $false )
| ( ( ?? @ $i @ ( cDOUBLE @ c0 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i @ ( cDOUBLE @ Y0 ) )
=> ( ?? @ $i @ ( cDOUBLE @ ( cS @ Y0 ) ) ) ) )
& ( ?? @ $i @ ( cDOUBLE @ c0 ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i @ ( cDOUBLE @ Y0 ) )
=> ( ?? @ $i @ ( cDOUBLE @ ( cS @ Y0 ) ) ) ) )
& ( ?? @ $i @ ( cDOUBLE @ c0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i @ ( cDOUBLE @ Y0 ) )
=> ( ?? @ $i @ ( cDOUBLE @ ( cS @ Y0 ) ) ) ) )
& ( ?? @ $i @ ( cDOUBLE @ c0 ) ) )
=> $false )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] : ( ?? @ $i @ ( cDOUBLE @ Y1 ) )
@ Y0 )
=> ( ^ [Y1: $i] : ( ?? @ $i @ ( cDOUBLE @ Y1 ) )
@ ( cS @ Y0 ) ) ) )
& ( ^ [Y0: $i] : ( ?? @ $i @ ( cDOUBLE @ Y0 ) )
@ c0 ) )
=> $false )
= $true ),
inference(superposition,[status(thm)],[f45,f19]) ).
thf(f19,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( cDOUBLE @ Y0 ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( cDOUBLE @ Y0 ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f13,f17]) ).
thf(f45,plain,
! [X1: $i > $o] :
( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) ) )
& ( X1 @ c0 ) )
=> ( !! @ $i @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM810^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n026.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 11:15:10 EST 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : NUM810^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.29/0.45 % Domain : Number Theory (Induction on naturals)
% 0.29/0.45 % Problem : TPS problem THM140
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English : Existence of doubles of naturals.
% 0.29/0.45
% 0.29/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Bro09]
% 0.29/0.45 % Names : tps_0347 [Bro09]
% 0.29/0.45 % : THM140 [TPS]
% 0.29/0.45 % : THM579 [TPS]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.67 v9.1.0, 0.62 v9.0.0, 0.70 v8.2.0, 0.77 v8.1.0, 0.82 v7.5.0, 0.71 v7.4.0, 0.67 v7.2.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.60 v5.3.0, 0.80 v5.2.0
% 0.29/0.45 % Syntax : Number of formulae : 6 ( 1 unt; 4 typ; 1 def)
% 0.29/0.45 % Number of atoms : 7 ( 1 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 5 ( 3 avg)
% 0.29/0.45 % Number of connectives : 23 ( 0 ~; 0 |; 3 &; 16 @)
% 0.29/0.45 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 10 ( 6 avg)
% 0.29/0.45 % Number of types : 2 ( 0 usr)
% 0.29/0.45 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.29/0.45 % Number of variables : 7 ( 0 ^; 6 !; 1 ?; 7 :)
% 0.29/0.45 % SPC : TH0_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.45 % :
% 0.29/0.45 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(c0_type,type,
% 0.29/0.45 c0: $i ).
% 0.29/0.45
% 0.29/0.45 thf(cDOUBLE_type,type,
% 0.29/0.45 cDOUBLE: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(cS_type,type,
% 0.29/0.45 cS: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(cIND_type,type,
% 0.29/0.45 cIND: $o ).
% 0.29/0.45
% 0.29/0.45 thf(cIND_def,definition,
% 0.29/0.45 ( cIND
% 0.29/0.45 = ( ! [Xp: $i > $o] :
% 0.29/0.45 ( ( ( Xp @ c0 )
% 0.29/0.45 & ! [Xx: $i] :
% 0.29/0.45 ( ( Xp @ Xx )
% 0.29/0.45 => ( Xp @ ( cS @ Xx ) ) ) )
% 0.29/0.45 => ! [Xx: $i] : ( Xp @ Xx ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(cTHM140,conjecture,
% 0.29/0.45 ( ( cIND
% 0.29/0.45 & ( cDOUBLE @ c0 @ c0 )
% 0.29/0.45 & ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( cDOUBLE @ Xx @ Xy )
% 0.29/0.45 => ( cDOUBLE @ ( cS @ Xx ) @ ( cS @ ( cS @ Xy ) ) ) ) )
% 0.29/0.45 => ! [Xx: $i] :
% 0.29/0.45 ? [Xy: $i] : ( cDOUBLE @ Xx @ Xy ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.36/1.19 ---- Embedded in THF ---
% 1.36/1.19 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.36/1.19 %%% Generated on Tue Feb 24 11:15:11 EST 2026
% 1.36/1.19 %%% using '$$dhol' embedding, version 1.3.0.
% 1.36/1.19 %%% Logic specification used:
% 1.36/1.19 %%% thf(spec, logic, $$dhol).
% 1.36/1.19
% 1.36/1.19 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.pqs0QRzIdW/DTF2DTF8977.p
% See solution above
% 1.36/1.19 ------------------------
% 1.52/1.20 ---- Cleaned THF ---
% 1.52/1.20 thf(c0_type,type,
% 1.52/1.20 c0: $i ).
% 1.52/1.20
% 1.52/1.20 thf(cDOUBLE_type,type,
% 1.52/1.20 cDOUBLE: $i > $i > $o ).
% 1.52/1.20
% 1.52/1.20 thf(cS_type,type,
% 1.52/1.20 cS: $i > $i ).
% 1.52/1.20
% 1.52/1.20 thf(cIND_type,type,
% 1.52/1.20 cIND: $o ).
% 1.52/1.20
% 1.52/1.20 thf(cIND_def,definition,
% 1.52/1.20 ( cIND
% 1.52/1.20 = ( ! [Xp: $i > $o] :
% 1.52/1.20 ( ( ( Xp @ c0 )
% 1.52/1.20 & ! [Xx: $i] :
% 1.52/1.20 ( ( Xp @ Xx )
% 1.52/1.20 => ( Xp @ ( cS @ Xx ) ) ) )
% 1.52/1.20 => ! [Xx: $i] : ( Xp @ Xx ) ) ) ) ).
% 1.52/1.20
% 1.52/1.20 thf(cTHM140,conjecture,
% 1.52/1.20 ( ( cIND
% 1.52/1.20 & ( cDOUBLE @ c0 @ c0 )
% 1.52/1.20 & ! [Xx: $i,Xy: $i] :
% 1.52/1.20 ( ( cDOUBLE @ Xx @ Xy )
% 1.52/1.20 => ( cDOUBLE @ ( cS @ Xx ) @ ( cS @ ( cS @ Xy ) ) ) ) )
% 1.52/1.20 => ! [Xx: $i] :
% 1.52/1.20 ? [Xy: $i] : ( cDOUBLE @ Xx @ Xy ) ) ).
% 1.52/1.20 ------------------------
% 1.52/1.21 % (9266)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_8977 for (2999ds/27Mi)
% 1.52/1.21 % (9264)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8977 for (2999ds/183Mi)
% 1.52/1.22 % (9265)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_8977 for (2999ds/4Mi)
% 1.52/1.22 % (9267)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8977 for (2999ds/2Mi)
% 1.52/1.22 % (9268)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_8977 for (2999ds/2Mi)
% 1.52/1.22 % (9269)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_8977 for (2999ds/275Mi)
% 1.52/1.22 % (9270)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8977 for (2999ds/18Mi)
% 1.52/1.22 % (9267)Instruction limit reached!
% 1.52/1.22 % (9267)------------------------------
% 1.52/1.22 % (9267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.22 % (9267)Termination reason: Unknown
% 1.52/1.22 % (9267)Termination phase: Preprocessing 3
% 1.52/1.22
% 1.52/1.22 % (9267)Memory used [KB]: 895
% 1.52/1.22 % (9267)Time elapsed: 0.003 s
% 1.52/1.22 % (9267)Instructions burned: 2 (million)
% 1.52/1.22 % (9267)------------------------------
% 1.52/1.22 % (9267)------------------------------
% 1.52/1.22 % (9268)Instruction limit reached!
% 1.52/1.22 % (9268)------------------------------
% 1.52/1.22 % (9268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.22 % (9268)Termination reason: Unknown
% 1.52/1.22 % (9268)Termination phase: Property scanning
% 1.52/1.22
% 1.52/1.22 % (9268)Memory used [KB]: 895
% 1.52/1.22 % (9268)Time elapsed: 0.003 s
% 1.52/1.22 % (9268)Instructions burned: 2 (million)
% 1.52/1.22 % (9268)------------------------------
% 1.52/1.22 % (9268)------------------------------
% 1.52/1.22 % (9266)Instruction limit reached!
% 1.52/1.22 % (9266)------------------------------
% 1.52/1.22 % (9266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.22 % (9266)Termination reason: Unknown
% 1.52/1.22 % (9266)Termination phase: Saturation
% 1.52/1.22
% 1.52/1.22 % (9266)Memory used [KB]: 5628
% 1.52/1.22 % (9266)Time elapsed: 0.011 s
% 1.52/1.22 % (9266)Instructions burned: 29 (million)
% 1.52/1.22 % (9266)------------------------------
% 1.52/1.22 % (9266)------------------------------
% 1.52/1.22 % (9265)Instruction limit reached!
% 1.52/1.22 % (9265)------------------------------
% 1.52/1.22 % (9265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.22 % (9265)Termination reason: Unknown
% 1.52/1.22 % (9265)Termination phase: Saturation
% 1.52/1.22
% 1.52/1.22 % (9265)Memory used [KB]: 5500
% 1.52/1.22 % (9265)Time elapsed: 0.005 s
% 1.52/1.22 % (9265)Instructions burned: 4 (million)
% 1.52/1.22 % (9265)------------------------------
% 1.52/1.22 % (9265)------------------------------
% 1.52/1.23 % (9273)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_8977 for (2999ds/15Mi)
% 1.52/1.23 % (9270)Instruction limit reached!
% 1.52/1.23 % (9270)------------------------------
% 1.52/1.23 % (9270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.23 % (9270)Termination reason: Unknown
% 1.52/1.23 % (9270)Termination phase: Saturation
% 1.52/1.23
% 1.52/1.23 % (9270)Memory used [KB]: 5628
% 1.52/1.23 % (9270)Time elapsed: 0.014 s
% 1.52/1.23 % (9270)Instructions burned: 18 (million)
% 1.52/1.23 % (9270)------------------------------
% 1.52/1.23 % (9270)------------------------------
% 1.52/1.24 % (9273)Instruction limit reached!
% 1.52/1.24 % (9273)------------------------------
% 1.52/1.24 % (9273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.24 % (9273)Termination reason: Unknown
% 1.52/1.24 % (9273)Termination phase: Saturation
% 1.52/1.24
% 1.52/1.24 % (9273)Memory used [KB]: 5628
% 1.52/1.24 % (9273)Time elapsed: 0.007 s
% 1.52/1.24 % (9273)Instructions burned: 17 (million)
% 1.52/1.24 % (9273)------------------------------
% 1.52/1.24 % (9273)------------------------------
% 1.52/1.24 % (9271)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8977 for (2999ds/3Mi)
% 1.52/1.24 % (9272)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_8977 for (2999ds/37Mi)
% 1.52/1.24 % (9274)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_8977 for (2999ds/3Mi)
% 1.52/1.24 % (9271)Instruction limit reached!
% 1.52/1.24 % (9271)------------------------------
% 1.52/1.24 % (9271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.24 % (9271)Termination reason: Unknown
% 1.52/1.24 % (9271)Termination phase: Saturation
% 1.52/1.24
% 1.52/1.24 % (9271)Memory used [KB]: 5500
% 1.52/1.24 % (9271)Time elapsed: 0.004 s
% 1.52/1.24 % (9271)Instructions burned: 3 (million)
% 1.52/1.24 % (9271)------------------------------
% 1.52/1.24 % (9271)------------------------------
% 1.52/1.24 % (9274)Instruction limit reached!
% 1.52/1.24 % (9274)------------------------------
% 1.52/1.24 % (9274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.24 % (9274)Termination reason: Unknown
% 1.52/1.24 % (9274)Termination phase: Saturation
% 1.52/1.24
% 1.52/1.24 % (9274)Memory used [KB]: 5500
% 1.52/1.24 % (9274)Time elapsed: 0.004 s
% 1.52/1.24 % (9274)Instructions burned: 3 (million)
% 1.52/1.24 % (9274)------------------------------
% 1.52/1.24 % (9274)------------------------------
% 1.52/1.25 % (9276)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_8977 for (2999ds/7Mi)
% 1.52/1.25 % (9276)Instruction limit reached!
% 1.52/1.25 % (9276)------------------------------
% 1.52/1.25 % (9276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.25 % (9276)Termination reason: Unknown
% 1.52/1.25 % (9276)Termination phase: Saturation
% 1.52/1.25
% 1.52/1.25 % (9276)Memory used [KB]: 1023
% 1.52/1.25 % (9276)Time elapsed: 0.004 s
% 1.52/1.25 % (9276)Instructions burned: 9 (million)
% 1.52/1.25 % (9276)------------------------------
% 1.52/1.25 % (9276)------------------------------
% 1.52/1.25 % (9275)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_8977 for (2999ds/1041Mi)
% 1.52/1.26 % (9277)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_8977 for (2999ds/16Mi)
% 1.52/1.26 % (9279)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_8977 for (2999ds/3Mi)
% 1.52/1.26 % (9272)Instruction limit reached!
% 1.52/1.26 % (9272)------------------------------
% 1.52/1.26 % (9272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.26 % (9272)Termination reason: Unknown
% 1.52/1.26 % (9272)Termination phase: Saturation
% 1.52/1.26
% 1.52/1.26 % (9272)Memory used [KB]: 5884
% 1.52/1.26 % (9278)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_8977 for (2999ds/3Mi)
% 1.52/1.26 % (9272)Time elapsed: 0.023 s
% 1.52/1.26 % (9272)Instructions burned: 37 (million)
% 1.52/1.26 % (9272)------------------------------
% 1.52/1.26 % (9272)------------------------------
% 1.52/1.26 % (9279)Instruction limit reached!
% 1.52/1.26 % (9279)------------------------------
% 1.52/1.26 % (9279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.26 % (9279)Termination reason: Unknown
% 1.52/1.26 % (9279)Termination phase: Saturation
% 1.52/1.26
% 1.52/1.26 % (9279)Memory used [KB]: 1023
% 1.52/1.26 % (9279)Time elapsed: 0.002 s
% 1.52/1.26 % (9279)Instructions burned: 3 (million)
% 1.52/1.26 % (9279)------------------------------
% 1.52/1.26 % (9279)------------------------------
% 1.52/1.26 % (9278)Instruction limit reached!
% 1.52/1.26 % (9278)------------------------------
% 1.52/1.26 % (9278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.26 % (9278)Termination reason: Unknown
% 1.52/1.26 % (9278)Termination phase: Saturation
% 1.52/1.26
% 1.52/1.26 % (9278)Memory used [KB]: 5500
% 1.52/1.26 % (9278)Time elapsed: 0.004 s
% 1.52/1.26 % (9278)Instructions burned: 3 (million)
% 1.52/1.26 % (9278)------------------------------
% 1.52/1.26 % (9278)------------------------------
% 1.52/1.27 % (9275)First to succeed.
% 1.52/1.27 % (9277)Instruction limit reached!
% 1.52/1.27 % (9277)------------------------------
% 1.52/1.27 % (9277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.27 % (9277)Termination reason: Unknown
% 1.52/1.27 % (9277)Termination phase: Saturation
% 1.52/1.27
% 1.52/1.27 % (9277)Memory used [KB]: 5756
% 1.52/1.27 % (9277)Time elapsed: 0.013 s
% 1.52/1.27 % (9277)Instructions burned: 16 (million)
% 1.52/1.27 % (9277)------------------------------
% 1.52/1.27 % (9277)------------------------------
% 1.52/1.27 % (9280)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_8977 for (2999ds/7Mi)
% 1.52/1.27 % (9275)Refutation found. Thanks to Tanya!
% 1.52/1.27 % SZS status Theorem for DTF2THF_8977
% 1.52/1.27 % SZS output start Proof for DTF2THF_8977
% 1.52/1.27 thf(func_def_1, type, cDOUBLE: $i > $i > $o).
% 1.52/1.27 thf(func_def_2, type, cS: $i > $i).
% 1.52/1.27 thf(func_def_16, type, ph1: !>[X0: $tType]:(X0)).
% 1.52/1.27 thf(f154,plain,(
% 1.52/1.27 $false),
% 1.52/1.27 inference(avatar_sat_refutation,[status(thm)],[f109,f117,f153])).
% 1.52/1.27 thf(f153,plain,(
% 1.52/1.27 ~spl0_4),
% 1.52/1.27 inference(avatar_contradiction_clause,[status(thm)],[f152])).
% 1.52/1.27 thf(f152,plain,(
% 1.52/1.27 $false | ~spl0_4),
% 1.52/1.27 inference(trivial_inequality_removal,[status(thm)],[f151])).
% 1.52/1.27 thf(f151,plain,(
% 1.52/1.27 ($false = $true) | ~spl0_4),
% 1.52/1.27 inference(backward_demodulation,[status(thm)],[f149,f150])).
% 1.52/1.27 thf(f150,plain,(
% 1.52/1.27 ( ! [X1 : $i] : (($false = (cDOUBLE @ (cS @ sK4) @ X1))) ) | ~spl0_4),
% 1.52/1.27 inference(pi_clausification,[status(thm)],[f141])).
% 1.52/1.27 thf(f141,plain,(
% 1.52/1.27 ((?? @ $i @ (cDOUBLE @ (cS @ sK4))) = $false) | ~spl0_4),
% 1.52/1.27 inference(binary_proxy_clausification,[status(thm)],[f136])).
% 1.52/1.27 thf(f136,plain,(
% 1.52/1.27 ($false = ((?? @ $i @ (cDOUBLE @ sK4)) => (?? @ $i @ (cDOUBLE @ (cS @ sK4))))) | ~spl0_4),
% 1.52/1.27 inference(beta_eta_normalization,[status(thm)],[f132])).
% 1.52/1.27 thf(f132,plain,(
% 1.52/1.27 ($false = ((^[Y0 : $i]: ((?? @ $i @ (cDOUBLE @ Y0)) => (?? @ $i @ (cDOUBLE @ (cS @ Y0))))) @ sK4)) | ~spl0_4),
% 1.52/1.27 inference(sigma_clausification,[status(thm)],[f108])).
% 1.52/1.27 thf(f108,plain,(
% 1.52/1.27 ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (cDOUBLE @ Y0)) => (?? @ $i @ (cDOUBLE @ (cS @ Y0)))))) = $false) | ~spl0_4),
% 1.52/1.27 inference(avatar_component_clause,[status(thm)],[f107])).
% 1.52/1.27 thf(f107,definition,(
% 1.52/1.27 spl0_4 <=> ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (cDOUBLE @ Y0)) => (?? @ $i @ (cDOUBLE @ (cS @ Y0)))))) = $false)),
% 1.52/1.27 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.52/1.27 thf(f149,plain,(
% 1.52/1.27 ((cDOUBLE @ (cS @ sK4) @ (cS @ (cS @ sK5))) = $true) | ~spl0_4),
% 1.52/1.27 inference(boolean_simplification,[status(thm)],[f148])).
% 1.52/1.27 thf(f148,plain,(
% 1.52/1.27 ($true = ($true => (cDOUBLE @ (cS @ sK4) @ (cS @ (cS @ sK5))))) | ~spl0_4),
% 1.52/1.27 inference(superposition,[status(thm)],[f34,f147])).
% 1.52/1.27 thf(f147,plain,(
% 1.52/1.27 ((cDOUBLE @ sK4 @ sK5) = $true) | ~spl0_4),
% 1.52/1.27 inference(sigma_clausification,[status(thm)],[f142])).
% 1.52/1.27 thf(f142,plain,(
% 1.52/1.27 ((?? @ $i @ (cDOUBLE @ sK4)) = $true) | ~spl0_4),
% 1.52/1.27 inference(binary_proxy_clausification,[status(thm)],[f136])).
% 1.52/1.27 thf(f34,plain,(
% 1.52/1.27 ( ! [X2 : $i,X1 : $i] : ((((cDOUBLE @ X2 @ X1) => (cDOUBLE @ (cS @ X2) @ (cS @ (cS @ X1)))) = $true)) )),
% 1.52/1.27 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.52/1.27 thf(f33,plain,(
% 1.52/1.27 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((cDOUBLE @ Y0 @ X1) => (cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ X1))))) @ X2) = $true)) )),
% 1.52/1.27 inference(pi_clausification,[status(thm)],[f32])).
% 1.52/1.27 thf(f32,plain,(
% 1.52/1.27 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((cDOUBLE @ Y0 @ X1) => (cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ X1)))))) = $true)) )),
% 1.52/1.27 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.52/1.27 thf(f31,plain,(
% 1.52/1.27 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0))))))) @ X1) = $true)) )),
% 1.52/1.27 inference(pi_clausification,[status(thm)],[f30])).
% 1.52/1.27 thf(f30,plain,(
% 1.52/1.27 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0)))))))) = $true)),
% 1.52/1.27 inference(boolean_simplification,[status(thm)],[f29])).
% 1.52/1.27 thf(f29,plain,(
% 1.52/1.27 (($true & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0))))))))) = $true)),
% 1.52/1.27 inference(backward_demodulation,[status(thm)],[f26,f28])).
% 1.52/1.27 thf(f28,plain,(
% 1.52/1.27 ((cDOUBLE @ c0 @ c0) = $true)),
% 1.52/1.27 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.52/1.27 thf(f26,plain,(
% 1.52/1.27 (((cDOUBLE @ c0 @ c0) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0))))))))) = $true)),
% 1.52/1.27 inference(boolean_simplification,[status(thm)],[f25])).
% 1.52/1.27 thf(f25,plain,(
% 1.52/1.27 ((((cDOUBLE @ c0 @ c0) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0))))))))) & $true) = $true)),
% 1.52/1.27 inference(backward_demodulation,[status(thm)],[f17,f23])).
% 1.52/1.27 thf(f23,plain,(
% 1.52/1.27 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ Y0)))))),
% 1.52/1.27 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.52/1.27 thf(f17,plain,(
% 1.52/1.27 ((((cDOUBLE @ c0 @ c0) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0))))))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ Y0))))) = $true)),
% 1.52/1.27 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.52/1.27 thf(f13,plain,(
% 1.52/1.27 (((((cDOUBLE @ c0 @ c0) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0))))))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ Y0))))) => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (cDOUBLE @ Y0))))) = $false)),
% 1.52/1.27 inference(not_proxy_clausification,[status(thm)],[f12])).
% 1.52/1.27 thf(f12,plain,(
% 1.52/1.27 ((~ ((((cDOUBLE @ c0 @ c0) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0))))))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ Y0))))) => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (cDOUBLE @ Y0)))))) = $true)),
% 1.52/1.27 inference(beta_eta_normalization,[status(thm)],[f11])).
% 1.52/1.27 thf(f11,plain,(
% 1.52/1.27 ((~ ((((cDOUBLE @ c0 @ c0) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0))))))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))) => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (cDOUBLE @ Y0 @ Y1))))))) = $true)),
% 1.52/1.27 inference(definition_unfolding,[status(thm)],[f10,f9])).
% 1.52/1.27 thf(f9,plain,(
% 1.52/1.27 (cIND = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 1.52/1.27 inference(cnf_transformation,[status(thm)],[f6])).
% 1.52/1.27 thf(f6,plain,(
% 1.52/1.27 (cIND = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 1.52/1.27 inference(fool_elimination,[status(thm)],[f5])).
% 1.52/1.27 thf(f5,plain,(
% 1.52/1.27 (! [X0 : $i > $o] : (((X0 @ c0) & ! [X1 : $i] : ((X0 @ X1) => (X0 @ (cS @ X1)))) => ! [X2 : $i] : (X0 @ X2)) = cIND)),
% 1.52/1.27 inference(rectify,[status(thm)],[f1])).
% 1.52/1.27 thf(f1,axiom,(
% 1.52/1.27 (! [X0 : $i > $o] : (((X0 @ c0) & ! [X1 : $i] : ((X0 @ X1) => (X0 @ (cS @ X1)))) => ! [X1 : $i] : (X0 @ X1)) = cIND)),
% 1.52/1.27 file('/export/starexec/sandbox/tmp/tmp.pqs0QRzIdW/DTF2THF_8977.p',cIND_def)).
% 1.52/1.27 thf(f10,plain,(
% 1.52/1.27 ((~ ((((cDOUBLE @ c0 @ c0) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0))))))))) & cIND) => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (cDOUBLE @ Y0 @ Y1))))))) = $true)),
% 1.52/1.27 inference(cnf_transformation,[status(thm)],[f8])).
% 1.52/1.27 thf(f8,plain,(
% 1.52/1.27 ((~ ((((cDOUBLE @ c0 @ c0) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y1 @ Y0) => (cDOUBLE @ (cS @ Y1) @ (cS @ (cS @ Y0))))))))) & cIND) => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (cDOUBLE @ Y0 @ Y1))))))) = $true)),
% 1.52/1.27 inference(fool_elimination,[status(thm)],[f7])).
% 1.52/1.27 thf(f7,plain,(
% 1.52/1.27 ~((cIND & ! [X0 : $i,X1 : $i] : ((cDOUBLE @ X0 @ X1) => (cDOUBLE @ (cS @ X0) @ (cS @ (cS @ X1)))) & (cDOUBLE @ c0 @ c0)) => ! [X2 : $i] : ? [X3 : $i] : (cDOUBLE @ X2 @ X3))),
% 1.52/1.27 inference(rectify,[status(thm)],[f3])).
% 1.52/1.27 thf(f3,negated_conjecture,(
% 1.52/1.27 ~((cIND & ! [X1 : $i,X2 : $i] : ((cDOUBLE @ X1 @ X2) => (cDOUBLE @ (cS @ X1) @ (cS @ (cS @ X2)))) & (cDOUBLE @ c0 @ c0)) => ! [X1 : $i] : ? [X2 : $i] : (cDOUBLE @ X1 @ X2))),
% 1.52/1.27 inference(negated_conjecture,[status(cth)],[f2])).
% 1.52/1.27 thf(f2,conjecture,(
% 1.52/1.27 (cIND & ! [X1 : $i,X2 : $i] : ((cDOUBLE @ X1 @ X2) => (cDOUBLE @ (cS @ X1) @ (cS @ (cS @ X2)))) & (cDOUBLE @ c0 @ c0)) => ! [X1 : $i] : ? [X2 : $i] : (cDOUBLE @ X1 @ X2)),
% 1.52/1.27 file('/export/starexec/sandbox/tmp/tmp.pqs0QRzIdW/DTF2THF_8977.p',cTHM140)).
% 1.52/1.27 thf(f117,plain,(
% 1.52/1.27 ~spl0_3),
% 1.52/1.27 inference(avatar_contradiction_clause,[status(thm)],[f116])).
% 1.52/1.27 thf(f116,plain,(
% 1.52/1.27 $false | ~spl0_3),
% 1.52/1.27 inference(trivial_inequality_removal,[status(thm)],[f113])).
% 1.52/1.27 thf(f113,plain,(
% 1.52/1.27 ($false = $true) | ~spl0_3),
% 1.52/1.27 inference(backward_demodulation,[status(thm)],[f28,f112])).
% 1.52/1.27 thf(f112,plain,(
% 1.52/1.27 ( ! [X1 : $i] : (($false = (cDOUBLE @ c0 @ X1))) ) | ~spl0_3),
% 1.52/1.27 inference(pi_clausification,[status(thm)],[f105])).
% 1.52/1.27 thf(f105,plain,(
% 1.52/1.27 ((?? @ $i @ (cDOUBLE @ c0)) = $false) | ~spl0_3),
% 1.52/1.27 inference(avatar_component_clause,[status(thm)],[f104])).
% 1.52/1.27 thf(f104,definition,(
% 1.52/1.27 spl0_3 <=> ((?? @ $i @ (cDOUBLE @ c0)) = $false)),
% 1.52/1.27 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.52/1.27 thf(f109,plain,(
% 1.52/1.27 spl0_3 | spl0_4),
% 1.52/1.27 inference(avatar_split_clause,[status(thm)],[f102,f107,f104])).
% 1.52/1.27 thf(f102,plain,(
% 1.52/1.27 ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (cDOUBLE @ Y0)) => (?? @ $i @ (cDOUBLE @ (cS @ Y0)))))) = $false) | ((?? @ $i @ (cDOUBLE @ c0)) = $false)),
% 1.52/1.27 inference(binary_proxy_clausification,[status(thm)],[f97])).
% 1.52/1.27 thf(f97,plain,(
% 1.52/1.27 (((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (cDOUBLE @ Y0)) => (?? @ $i @ (cDOUBLE @ (cS @ Y0)))))) & (?? @ $i @ (cDOUBLE @ c0))) = $false)),
% 1.52/1.27 inference(not_proxy_clausification,[status(thm)],[f59])).
% 1.52/1.27 thf(f59,plain,(
% 1.52/1.27 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (cDOUBLE @ Y0)) => (?? @ $i @ (cDOUBLE @ (cS @ Y0)))))) & (?? @ $i @ (cDOUBLE @ c0)))))),
% 1.52/1.27 inference(boolean_simplification,[status(thm)],[f58])).
% 1.52/1.27 thf(f58,plain,(
% 1.52/1.27 ((((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (cDOUBLE @ Y0)) => (?? @ $i @ (cDOUBLE @ (cS @ Y0)))))) & (?? @ $i @ (cDOUBLE @ c0))) => $false) = $true)),
% 1.52/1.27 inference(beta_eta_normalization,[status(thm)],[f53])).
% 1.52/1.27 thf(f53,plain,(
% 1.52/1.27 ((((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (?? @ $i @ (cDOUBLE @ Y1))) @ Y0) => ((^[Y1 : $i]: (?? @ $i @ (cDOUBLE @ Y1))) @ (cS @ Y0))))) & ((^[Y0 : $i]: (?? @ $i @ (cDOUBLE @ Y0))) @ c0)) => $false) = $true)),
% 1.52/1.27 inference(superposition,[status(thm)],[f45,f19])).
% 1.52/1.27 thf(f19,plain,(
% 1.52/1.27 ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (cDOUBLE @ Y0)))) = $false)),
% 1.52/1.27 inference(boolean_simplification,[status(thm)],[f18])).
% 1.52/1.27 thf(f18,plain,(
% 1.52/1.27 (($true => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (cDOUBLE @ Y0))))) = $false)),
% 1.52/1.27 inference(backward_demodulation,[status(thm)],[f13,f17])).
% 1.52/1.27 thf(f45,plain,(
% 1.52/1.27 ( ! [X1 : $i > $o] : (($true = (((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ Y0))))) & (X1 @ c0)) => (!! @ $i @ X1)))) )),
% 1.52/1.27 inference(beta_eta_normalization,[status(thm)],[f44])).
% 1.52/1.27 thf(f44,plain,(
% 1.52/1.27 ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ Y0))) @ X1))) )),
% 1.52/1.27 inference(pi_clausification,[status(thm)],[f23])).
% 1.52/1.27 % SZS output end Proof for DTF2THF_8977
% 1.52/1.27 % (9275)------------------------------
% 1.52/1.27 % (9275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.27 % (9275)Termination reason: Refutation
% 1.52/1.27
% 1.52/1.27 % (9275)Memory used [KB]: 5628
% 1.52/1.27 % (9275)Time elapsed: 0.021 s
% 1.52/1.27 % (9275)Instructions burned: 27 (million)
% 1.52/1.27 % (9275)------------------------------
% 1.52/1.27 % (9275)------------------------------
% 1.52/1.27 % (9263)Success in time 0.061 s
%------------------------------------------------------------------------------