%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM809^5 : 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 : n017.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 1.56s 1.39s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 14 unt; 0 typ; 3 def)
% Number of atoms : 342 ( 84 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 468 ( 30 ~; 42 |; 30 &; 313 @)
% ( 3 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 9 con; 0-2 aty)
% ( 20 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 126 ( 60 ^; 58 !; 8 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cS: $i > $i ).
thf(func_def_2,type,
r: $i > $i > $o ).
thf(func_def_15,type,
sK2: ( $i > $o ) > $i ).
thf(func_def_17,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
sK4: $i > $i ).
thf(func_def_21,type,
sK5: $i > $i ).
thf(func_def_22,type,
sK6: $i > $i ).
thf(f852,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f143,f701,f825,f851]) ).
thf(f851,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[status(thm)],[f850]) ).
thf(f850,plain,
( $false
| ~ spl1_4 ),
inference(trivial_inequality_removal,[status(thm)],[f830]) ).
thf(f830,plain,
( ( $true = $false )
| ~ spl1_4 ),
inference(superposition,[status(thm)],[f16,f134]) ).
thf(f134,plain,
( ( ( r @ c0 @ c0 )
= $false )
| ~ spl1_4 ),
inference(avatar_component_clause,[status(thm)],[f132]) ).
thf(f132,definition,
( spl1_4
<=> ( ( r @ c0 @ c0 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition]) ).
thf(f16,plain,
( ( r @ c0 @ c0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X1: $i] :
( $true
!= ( r @ sK0 @ X1 ) )
& ( ( r @ c0 @ c0 )
= $true )
& ( cIND = $true )
& ! [X2: $i,X3: $i] :
( ( $true
!= ( r @ X3 @ X2 ) )
| ( $true
= ( r @ ( cS @ X3 ) @ ( cS @ X2 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f11,f12]) ).
thf(f12,plain,
( ? [X0: $i] :
! [X1: $i] :
( $true
!= ( r @ X0 @ X1 ) )
=> ! [X1: $i] :
( $true
!= ( r @ sK0 @ X1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X0: $i] :
! [X1: $i] :
( $true
!= ( r @ X0 @ X1 ) )
& ( ( r @ c0 @ c0 )
= $true )
& ( cIND = $true )
& ! [X2: $i,X3: $i] :
( ( $true
!= ( r @ X3 @ X2 ) )
| ( $true
= ( r @ ( cS @ X3 ) @ ( cS @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
( ? [X2: $i] :
! [X3: $i] :
( $true
!= ( r @ X2 @ X3 ) )
& ( ( r @ c0 @ c0 )
= $true )
& ( cIND = $true )
& ! [X0: $i,X1: $i] :
( ( $true
!= ( r @ X1 @ X0 ) )
| ( $true
= ( r @ ( cS @ X1 ) @ ( cS @ X0 ) ) ) ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ? [X2: $i] :
! [X3: $i] :
( $true
!= ( r @ X2 @ X3 ) )
& ! [X0: $i,X1: $i] :
( ( $true
!= ( r @ X1 @ X0 ) )
| ( $true
= ( r @ ( cS @ X1 ) @ ( cS @ X0 ) ) ) )
& ( ( r @ c0 @ c0 )
= $true )
& ( cIND = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( ! [X0: $i,X1: $i] :
( ( $true
= ( r @ X1 @ X0 ) )
=> ( $true
= ( r @ ( cS @ X1 ) @ ( cS @ X0 ) ) ) )
& ( ( r @ c0 @ c0 )
= $true )
& ( cIND = $true ) )
=> ! [X2: $i] :
? [X3: $i] :
( $true
= ( r @ X2 @ X3 ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( ! [X0: $i,X1: $i] :
( ( r @ X1 @ X0 )
=> ( r @ ( cS @ X1 ) @ ( cS @ X0 ) ) )
& cIND
& ( r @ c0 @ c0 ) )
=> ! [X2: $i] :
? [X3: $i] : ( r @ X2 @ X3 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( ( ! [X2: $i,X1: $i] :
( ( r @ X1 @ X2 )
=> ( r @ ( cS @ X1 ) @ ( cS @ X2 ) ) )
& cIND
& ( r @ c0 @ c0 ) )
=> ! [X1: $i] :
? [X2: $i] : ( r @ X1 @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( ( ! [X2: $i,X1: $i] :
( ( r @ X1 @ X2 )
=> ( r @ ( cS @ X1 ) @ ( cS @ X2 ) ) )
& cIND
& ( r @ c0 @ c0 ) )
=> ! [X1: $i] :
? [X2: $i] : ( r @ X1 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.RWmZR1h96a/DTF2THF_20686.p',cTHM130) ).
thf(f825,plain,
( spl1_4
| spl1_5
| spl1_6 ),
inference(avatar_split_clause,[status(thm)],[f814,f139,f136,f132]) ).
thf(f136,definition,
( spl1_5
<=> ! [X0: $i] :
( $true
= ( r @ X0 @ X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_5])],[avatar_definition]) ).
thf(f139,definition,
( spl1_6
<=> ( $true
= ( r
@ ( sK2
@ ^ [Y0: $i] : ( r @ Y0 @ Y0 ) )
@ ( sK2
@ ^ [Y0: $i] : ( r @ Y0 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition]) ).
thf(f814,plain,
( ! [X0: $i] :
( ( $true
= ( r @ X0 @ X0 ) )
| ( ( r @ c0 @ c0 )
= $false ) )
| spl1_6 ),
inference(beta_eta_normalization,[status(thm)],[f813]) ).
thf(f813,plain,
( ! [X0: $i] :
( ( $false
= ( ^ [Y0: $i] :
( r
@ ( ^ [Y1: $i] : Y1
@ Y0 )
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ c0 ) )
| ( $true
= ( ^ [Y0: $i] :
( r
@ ( ^ [Y1: $i] : Y1
@ Y0 )
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ X0 ) ) )
| spl1_6 ),
inference(trivial_inequality_removal,[status(thm)],[f812]) ).
thf(f812,plain,
( ! [X0: $i] :
( ( $true
= ( ^ [Y0: $i] :
( r
@ ( ^ [Y1: $i] : Y1
@ Y0 )
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ X0 ) )
| ( $true != $true )
| ( $false
= ( ^ [Y0: $i] :
( r
@ ( ^ [Y1: $i] : Y1
@ Y0 )
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ c0 ) ) )
| spl1_6 ),
inference(superposition,[status(thm)],[f141,f29]) ).
thf(f29,plain,
! [X2: $i,X1: $i > $o] :
( ( $true
= ( X1 @ ( sK2 @ X1 ) ) )
| ( ( X1 @ c0 )
= $false )
| ( $true
= ( X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X1: $i > $o] :
( ( $true
= ( X1 @ X2 ) )
| ( ( X1 @ c0 )
= $false )
| ( ( ( X1 @ ( sK2 @ X1 ) )
=> ( X1 @ ( cS @ ( sK2 @ X1 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: $i,X1: $i > $o] :
( ( $true
= ( X1 @ X2 ) )
| ( ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) )
@ ( sK2 @ X1 ) )
= $false )
| ( ( X1 @ c0 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X2: $i,X1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) ) )
= $false )
| ( $true
= ( X1 @ X2 ) )
| ( ( X1 @ c0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X2: $i,X1: $i > $o] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) ) )
& ( X1 @ c0 ) )
= $false )
| ( $true
= ( X1 @ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: $i > $o] :
( ( $true
= ( !! @ $i @ X1 ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) ) )
& ( X1 @ c0 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: $i > $o] :
( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) ) )
& ( X1 @ c0 ) )
=> ( !! @ $i @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,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)],[f20]) ).
thf(f20,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) )
& ( Y0 @ c0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f18,f15]) ).
thf(f15,plain,
cIND = $true,
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f18,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,
( cIND
= ( ! [X0: $i > $o] :
( ( ( X0 @ c0 )
& ! [X1: $i] :
( ( X0 @ X1 )
=> ( X0 @ ( cS @ X1 ) ) ) )
=> ! [X2: $i] : ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( cIND
= ( ! [X0: $i > $o] :
( ( ( X0 @ c0 )
& ! [X1: $i] :
( ( X0 @ X1 )
=> ( X0 @ ( cS @ X1 ) ) ) )
=> ! [X1: $i] : ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RWmZR1h96a/DTF2THF_20686.p',cIND_def) ).
thf(f141,plain,
( ( $true
!= ( r
@ ( sK2
@ ^ [Y0: $i] : ( r @ Y0 @ Y0 ) )
@ ( sK2
@ ^ [Y0: $i] : ( r @ Y0 @ Y0 ) ) ) )
| spl1_6 ),
inference(avatar_component_clause,[status(thm)],[f139]) ).
thf(f701,plain,
~ spl1_5,
inference(avatar_contradiction_clause,[status(thm)],[f700]) ).
thf(f700,plain,
( $false
| ~ spl1_5 ),
inference(trivial_inequality_removal,[status(thm)],[f683]) ).
thf(f683,plain,
( ( $true != $true )
| ~ spl1_5 ),
inference(superposition,[status(thm)],[f17,f137]) ).
thf(f137,plain,
( ! [X0: $i] :
( $true
= ( r @ X0 @ X0 ) )
| ~ spl1_5 ),
inference(avatar_component_clause,[status(thm)],[f136]) ).
thf(f17,plain,
! [X1: $i] :
( $true
!= ( r @ sK0 @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f143,plain,
( ~ spl1_6
| spl1_5
| spl1_4 ),
inference(avatar_split_clause,[status(thm)],[f128,f132,f136,f139]) ).
thf(f128,plain,
! [X0: $i] :
( ( $true
= ( r @ X0 @ X0 ) )
| ( ( r @ c0 @ c0 )
= $false )
| ( $true
!= ( r
@ ( sK2
@ ^ [Y0: $i] : ( r @ Y0 @ Y0 ) )
@ ( sK2
@ ^ [Y0: $i] : ( r @ Y0 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f127]) ).
thf(f127,plain,
! [X0: $i] :
( ( $true
!= ( r
@ ( sK2
@ ^ [Y0: $i] :
( r
@ ( ^ [Y1: $i] : Y1
@ Y0 )
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) )
@ ( sK2
@ ^ [Y0: $i] :
( r
@ ( ^ [Y1: $i] : Y1
@ Y0 )
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( r
@ ( ^ [Y1: $i] : Y1
@ Y0 )
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ c0 ) )
| ( $true
= ( ^ [Y0: $i] :
( r
@ ( ^ [Y1: $i] : Y1
@ Y0 )
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f125]) ).
thf(f125,plain,
! [X0: $i] :
( ( $false
= ( ^ [Y0: $i] :
( r
@ ( ^ [Y1: $i] : Y1
@ Y0 )
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ c0 ) )
| ( $true = $false )
| ( $true
= ( ^ [Y0: $i] :
( r
@ ( ^ [Y1: $i] : Y1
@ Y0 )
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ X0 ) )
| ( $true
!= ( r
@ ( sK2
@ ^ [Y0: $i] :
( r
@ ( ^ [Y1: $i] : Y1
@ Y0 )
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) )
@ ( sK2
@ ^ [Y0: $i] :
( r
@ ( ^ [Y1: $i] : Y1
@ Y0 )
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f14,f28]) ).
thf(f28,plain,
! [X2: $i,X1: $i > $o] :
( ( $false
= ( X1 @ ( cS @ ( sK2 @ X1 ) ) ) )
| ( $true
= ( X1 @ X2 ) )
| ( ( X1 @ c0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f14,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( r @ ( cS @ X3 ) @ ( cS @ X2 ) ) )
| ( $true
!= ( r @ X3 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM809^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n017.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 11:13:11 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.49 ---- Original DTF file ---
% 0.27/0.49 thf(spec,logic,$$dhol).
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 % File : NUM809^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.27/0.49 % Domain : Number Theory (Induction on naturals)
% 0.27/0.49 % Problem : TPS problem THM130
% 0.27/0.49 % Version : Especial.
% 0.27/0.49 % English : Induction theorem in which the conclusion is weaker than the
% 0.27/0.49 % statement which must be proved by induction.
% 0.27/0.49
% 0.27/0.49 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.49 % Source : [Bro09]
% 0.27/0.49 % Names : tps_0235 [Bro09]
% 0.27/0.49 % : THM130 [TPS]
% 0.27/0.49
% 0.27/0.49 % Status : Theorem
% 0.27/0.49 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.62 v8.1.0, 0.55 v7.5.0, 0.29 v7.4.0, 0.56 v7.3.0, 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, 0.40 v5.2.0
% 0.27/0.49 % Syntax : Number of formulae : 6 ( 1 unt; 4 typ; 1 def)
% 0.27/0.49 % Number of atoms : 7 ( 1 equ; 0 cnn)
% 0.27/0.49 % Maximal formula atoms : 5 ( 3 avg)
% 0.27/0.49 % Number of connectives : 22 ( 0 ~; 0 |; 3 &; 15 @)
% 0.27/0.49 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.27/0.49 % Maximal formula depth : 10 ( 6 avg)
% 0.27/0.49 % Number of types : 2 ( 0 usr)
% 0.27/0.49 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.27/0.49 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.27/0.49 % Number of variables : 7 ( 0 ^; 6 !; 1 ?; 7 :)
% 0.27/0.49 % SPC : TH0_THM_EQU_NAR
% 0.27/0.49
% 0.27/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.49 % :
% 0.27/0.49 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 thf(c0_type,type,
% 0.27/0.49 c0: $i ).
% 0.27/0.49
% 0.27/0.49 thf(cS_type,type,
% 0.27/0.49 cS: $i > $i ).
% 0.27/0.49
% 0.27/0.49 thf(r_type,type,
% 0.27/0.49 r: $i > $i > $o ).
% 0.27/0.49
% 0.27/0.49 thf(cIND_type,type,
% 0.27/0.49 cIND: $o ).
% 0.27/0.49
% 0.27/0.49 thf(cIND_def,definition,
% 0.27/0.49 ( cIND
% 0.27/0.49 = ( ! [Xp: $i > $o] :
% 0.27/0.49 ( ( ( Xp @ c0 )
% 0.27/0.49 & ! [Xx: $i] :
% 0.27/0.49 ( ( Xp @ Xx )
% 0.27/0.49 => ( Xp @ ( cS @ Xx ) ) ) )
% 0.27/0.49 => ! [Xx: $i] : ( Xp @ Xx ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf(cTHM130,conjecture,
% 0.27/0.49 ( ( cIND
% 0.27/0.49 & ( r @ c0 @ c0 )
% 0.27/0.49 & ! [Xx: $i,Xy: $i] :
% 0.27/0.49 ( ( r @ Xx @ Xy )
% 0.27/0.49 => ( r @ ( cS @ Xx ) @ ( cS @ Xy ) ) ) )
% 0.27/0.49 => ! [Xx: $i] :
% 0.27/0.49 ? [Xy: $i] : ( r @ Xx @ Xy ) ) ).
% 0.27/0.49
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 ------------------------
% 1.56/1.33 ---- Embedded in THF ---
% 1.56/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.56/1.33 %%% Generated on Tue Feb 24 11:13:12 EST 2026
% 1.56/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.56/1.33 %%% Logic specification used:
% 1.56/1.33 %%% thf(spec, logic, $$dhol).
% 1.56/1.33
% 1.56/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.RWmZR1h96a/DTF2DTF20686.p
% See solution above
% 1.56/1.33 ------------------------
% 1.56/1.34 ---- Cleaned THF ---
% 1.56/1.34 thf(c0_type,type,
% 1.56/1.34 c0: $i ).
% 1.56/1.34
% 1.56/1.34 thf(cS_type,type,
% 1.56/1.34 cS: $i > $i ).
% 1.56/1.34
% 1.56/1.34 thf(r_type,type,
% 1.56/1.34 r: $i > $i > $o ).
% 1.56/1.34
% 1.56/1.34 thf(cIND_type,type,
% 1.56/1.34 cIND: $o ).
% 1.56/1.34
% 1.56/1.34 thf(cIND_def,definition,
% 1.56/1.34 ( cIND
% 1.56/1.34 = ( ! [Xp: $i > $o] :
% 1.56/1.34 ( ( ( Xp @ c0 )
% 1.56/1.34 & ! [Xx: $i] :
% 1.56/1.34 ( ( Xp @ Xx )
% 1.56/1.34 => ( Xp @ ( cS @ Xx ) ) ) )
% 1.56/1.34 => ! [Xx: $i] : ( Xp @ Xx ) ) ) ) ).
% 1.56/1.34
% 1.56/1.34 thf(cTHM130,conjecture,
% 1.56/1.34 ( ( cIND
% 1.56/1.34 & ( r @ c0 @ c0 )
% 1.56/1.34 & ! [Xx: $i,Xy: $i] :
% 1.56/1.34 ( ( r @ Xx @ Xy )
% 1.56/1.34 => ( r @ ( cS @ Xx ) @ ( cS @ Xy ) ) ) )
% 1.56/1.34 => ! [Xx: $i] :
% 1.56/1.34 ? [Xy: $i] : ( r @ Xx @ Xy ) ) ).
% 1.56/1.34 ------------------------
% 1.56/1.35 % (20804)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20686 for (3000ds/183Mi)
% 1.56/1.36 % (20809)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_20686 for (3000ds/275Mi)
% 1.56/1.36 % (20808)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_20686 for (3000ds/2Mi)
% 1.56/1.36 % (20805)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_20686 for (3000ds/4Mi)
% 1.56/1.36 % (20806)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_20686 for (3000ds/27Mi)
% 1.56/1.36 % (20810)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20686 for (3000ds/18Mi)
% 1.56/1.36 % (20807)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20686 for (3000ds/2Mi)
% 1.56/1.36 % (20807)Instruction limit reached!
% 1.56/1.36 % (20807)------------------------------
% 1.56/1.36 % (20807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.36 % (20807)Termination reason: Unknown
% 1.56/1.36 % (20808)Instruction limit reached!
% 1.56/1.36 % (20808)------------------------------
% 1.56/1.36 % (20808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.36 % (20808)Termination reason: Unknown
% 1.56/1.36 % (20808)Termination phase: Saturation
% 1.56/1.36
% 1.56/1.36 % (20808)Memory used [KB]: 5500
% 1.56/1.36 % (20808)Time elapsed: 0.003 s
% 1.56/1.36 % (20808)Instructions burned: 3 (million)
% 1.56/1.36 % (20808)------------------------------
% 1.56/1.36 % (20808)------------------------------
% 1.56/1.36 % (20807)Termination phase: Saturation
% 1.56/1.36
% 1.56/1.36 % (20807)Memory used [KB]: 5373
% 1.56/1.36 % (20807)Time elapsed: 0.003 s
% 1.56/1.36 % (20807)Instructions burned: 2 (million)
% 1.56/1.36 % (20807)------------------------------
% 1.56/1.36 % (20807)------------------------------
% 1.56/1.36 % (20805)Instruction limit reached!
% 1.56/1.36 % (20805)------------------------------
% 1.56/1.36 % (20805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.36 % (20805)Termination reason: Unknown
% 1.56/1.36 % (20805)Termination phase: Saturation
% 1.56/1.36
% 1.56/1.36 % (20805)Memory used [KB]: 5500
% 1.56/1.36 % (20805)Time elapsed: 0.004 s
% 1.56/1.36 % (20805)Instructions burned: 4 (million)
% 1.56/1.36 % (20805)------------------------------
% 1.56/1.36 % (20805)------------------------------
% 1.56/1.37 % (20810)Instruction limit reached!
% 1.56/1.37 % (20810)------------------------------
% 1.56/1.37 % (20810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.37 % (20810)Termination reason: Unknown
% 1.56/1.37 % (20810)Termination phase: Saturation
% 1.56/1.37
% 1.56/1.37 % (20810)Memory used [KB]: 5628
% 1.56/1.37 % (20810)Time elapsed: 0.012 s
% 1.56/1.37 % (20810)Instructions burned: 19 (million)
% 1.56/1.37 % (20810)------------------------------
% 1.56/1.37 % (20810)------------------------------
% 1.56/1.37 % (20806)Instruction limit reached!
% 1.56/1.37 % (20806)------------------------------
% 1.56/1.37 % (20806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.37 % (20806)Termination reason: Unknown
% 1.56/1.37 % (20806)Termination phase: Saturation
% 1.56/1.37
% 1.56/1.37 % (20806)Memory used [KB]: 5628
% 1.56/1.37 % (20806)Time elapsed: 0.016 s
% 1.56/1.37 % (20806)Instructions burned: 27 (million)
% 1.56/1.37 % (20806)------------------------------
% 1.56/1.37 % (20806)------------------------------
% 1.56/1.38 % (20812)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_20686 for (2999ds/37Mi)
% 1.56/1.38 % (20811)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20686 for (2999ds/3Mi)
% 1.56/1.38 % (20813)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_20686 for (2999ds/15Mi)
% 1.56/1.38 % (20811)Instruction limit reached!
% 1.56/1.38 % (20811)------------------------------
% 1.56/1.38 % (20811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.38 % (20811)Termination reason: Unknown
% 1.56/1.38 % (20811)Termination phase: Saturation
% 1.56/1.38
% 1.56/1.38 % (20811)Memory used [KB]: 5500
% 1.56/1.38 % (20811)Time elapsed: 0.004 s
% 1.56/1.38 % (20811)Instructions burned: 4 (million)
% 1.56/1.38 % (20811)------------------------------
% 1.56/1.38 % (20811)------------------------------
% 1.56/1.39 % (20814)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_20686 for (2999ds/3Mi)
% 1.56/1.39 % (20813)Instruction limit reached!
% 1.56/1.39 % (20813)------------------------------
% 1.56/1.39 % (20813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.39 % (20813)Termination reason: Unknown
% 1.56/1.39 % (20813)Termination phase: Saturation
% 1.56/1.39
% 1.56/1.39 % (20813)Memory used [KB]: 5628
% 1.56/1.39 % (20813)Time elapsed: 0.010 s
% 1.56/1.39 % (20813)Instructions burned: 16 (million)
% 1.56/1.39 % (20813)------------------------------
% 1.56/1.39 % (20813)------------------------------
% 1.56/1.39 % (20814)Refutation not found, incomplete strategy
% 1.56/1.39 % (20814)------------------------------
% 1.56/1.39 % (20814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.39 % (20814)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.39
% 1.56/1.39
% 1.56/1.39 % (20814)Memory used [KB]: 5500
% 1.56/1.39 % (20814)Time elapsed: 0.003 s
% 1.56/1.39 % (20814)Instructions burned: 2 (million)
% 1.56/1.39 % (20814)------------------------------
% 1.56/1.39 % (20814)------------------------------
% 1.56/1.39 % (20804)First to succeed.
% 1.56/1.39 % (20815)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_20686 for (2999ds/1041Mi)
% 1.56/1.39 % (20804)Refutation found. Thanks to Tanya!
% 1.56/1.39 % SZS status Theorem for DTF2THF_20686
% 1.56/1.39 % SZS output start Proof for DTF2THF_20686
% 1.56/1.39 thf(func_def_1, type, cS: $i > $i).
% 1.56/1.39 thf(func_def_2, type, r: $i > $i > $o).
% 1.56/1.39 thf(func_def_15, type, sK2: ($i > $o) > $i).
% 1.56/1.39 thf(func_def_17, type, ph3: !>[X0: $tType]:(X0)).
% 1.56/1.39 thf(func_def_19, type, sK4: $i > $i).
% 1.56/1.39 thf(func_def_21, type, sK5: $i > $i).
% 1.56/1.39 thf(func_def_22, type, sK6: $i > $i).
% 1.56/1.39 thf(f852,plain,(
% 1.56/1.39 $false),
% 1.56/1.39 inference(avatar_sat_refutation,[status(thm)],[f143,f701,f825,f851])).
% 1.56/1.39 thf(f851,plain,(
% 1.56/1.39 ~spl1_4),
% 1.56/1.39 inference(avatar_contradiction_clause,[status(thm)],[f850])).
% 1.56/1.39 thf(f850,plain,(
% 1.56/1.39 $false | ~spl1_4),
% 1.56/1.39 inference(trivial_inequality_removal,[status(thm)],[f830])).
% 1.56/1.39 thf(f830,plain,(
% 1.56/1.39 ($true = $false) | ~spl1_4),
% 1.56/1.39 inference(superposition,[status(thm)],[f16,f134])).
% 1.56/1.39 thf(f134,plain,(
% 1.56/1.39 ((r @ c0 @ c0) = $false) | ~spl1_4),
% 1.56/1.39 inference(avatar_component_clause,[status(thm)],[f132])).
% 1.56/1.39 thf(f132,definition,(
% 1.56/1.39 spl1_4 <=> ((r @ c0 @ c0) = $false)),
% 1.56/1.39 introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition])).
% 1.56/1.39 thf(f16,plain,(
% 1.56/1.39 ((r @ c0 @ c0) = $true)),
% 1.56/1.39 inference(cnf_transformation,[status(thm)],[f13])).
% 1.56/1.39 thf(f13,plain,(
% 1.56/1.39 ! [X1 : $i] : ($true != (r @ sK0 @ X1)) & ((r @ c0 @ c0) = $true) & (cIND = $true) & ! [X2 : $i,X3 : $i] : (($true != (r @ X3 @ X2)) | ($true = (r @ (cS @ X3) @ (cS @ X2))))),
% 1.56/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f11,f12])).
% 1.56/1.39 thf(f12,plain,(
% 1.56/1.39 ? [X0 : $i] : ! [X1 : $i] : ($true != (r @ X0 @ X1)) => ! [X1 : $i] : ($true != (r @ sK0 @ X1))),
% 1.56/1.39 introduced(definition,[],[choice_axiom])).
% 1.56/1.39 thf(f11,plain,(
% 1.56/1.39 ? [X0 : $i] : ! [X1 : $i] : ($true != (r @ X0 @ X1)) & ((r @ c0 @ c0) = $true) & (cIND = $true) & ! [X2 : $i,X3 : $i] : (($true != (r @ X3 @ X2)) | ($true = (r @ (cS @ X3) @ (cS @ X2))))),
% 1.56/1.39 inference(rectify,[status(thm)],[f10])).
% 1.56/1.39 thf(f10,plain,(
% 1.56/1.39 ? [X2 : $i] : ! [X3 : $i] : ($true != (r @ X2 @ X3)) & ((r @ c0 @ c0) = $true) & (cIND = $true) & ! [X0 : $i,X1 : $i] : (($true != (r @ X1 @ X0)) | ($true = (r @ (cS @ X1) @ (cS @ X0))))),
% 1.56/1.39 inference(flattening,[status(thm)],[f9])).
% 1.56/1.39 thf(f9,plain,(
% 1.56/1.39 ? [X2 : $i] : ! [X3 : $i] : ($true != (r @ X2 @ X3)) & (! [X0 : $i,X1 : $i] : (($true != (r @ X1 @ X0)) | ($true = (r @ (cS @ X1) @ (cS @ X0)))) & ((r @ c0 @ c0) = $true) & (cIND = $true))),
% 1.56/1.39 inference(ennf_transformation,[status(thm)],[f8])).
% 1.56/1.39 thf(f8,plain,(
% 1.56/1.39 ~((! [X0 : $i,X1 : $i] : (($true = (r @ X1 @ X0)) => ($true = (r @ (cS @ X1) @ (cS @ X0)))) & ((r @ c0 @ c0) = $true) & (cIND = $true)) => ! [X2 : $i] : ? [X3 : $i] : ($true = (r @ X2 @ X3)))),
% 1.56/1.39 inference(fool_elimination,[status(thm)],[f7])).
% 1.56/1.39 thf(f7,plain,(
% 1.56/1.39 ~((! [X0 : $i,X1 : $i] : ((r @ X1 @ X0) => (r @ (cS @ X1) @ (cS @ X0))) & cIND & (r @ c0 @ c0)) => ! [X2 : $i] : ? [X3 : $i] : (r @ X2 @ X3))),
% 1.56/1.39 inference(rectify,[status(thm)],[f3])).
% 1.56/1.39 thf(f3,negated_conjecture,(
% 1.56/1.39 ~((! [X2 : $i,X1 : $i] : ((r @ X1 @ X2) => (r @ (cS @ X1) @ (cS @ X2))) & cIND & (r @ c0 @ c0)) => ! [X1 : $i] : ? [X2 : $i] : (r @ X1 @ X2))),
% 1.56/1.39 inference(negated_conjecture,[status(cth)],[f2])).
% 1.56/1.39 thf(f2,conjecture,(
% 1.56/1.39 (! [X2 : $i,X1 : $i] : ((r @ X1 @ X2) => (r @ (cS @ X1) @ (cS @ X2))) & cIND & (r @ c0 @ c0)) => ! [X1 : $i] : ? [X2 : $i] : (r @ X1 @ X2)),
% 1.56/1.39 file('/export/starexec/sandbox/tmp/tmp.RWmZR1h96a/DTF2THF_20686.p',cTHM130)).
% 1.56/1.39 thf(f825,plain,(
% 1.56/1.39 spl1_4 | spl1_5 | spl1_6),
% 1.56/1.39 inference(avatar_split_clause,[status(thm)],[f814,f139,f136,f132])).
% 1.56/1.39 thf(f136,definition,(
% 1.56/1.39 spl1_5 <=> ! [X0 : $i] : ($true = (r @ X0 @ X0))),
% 1.56/1.39 introduced(definition,[new_symbols(naming,[spl1_5])],[avatar_definition])).
% 1.56/1.39 thf(f139,definition,(
% 1.56/1.39 spl1_6 <=> ($true = (r @ (sK2 @ (^[Y0 : $i]: (r @ Y0 @ Y0))) @ (sK2 @ (^[Y0 : $i]: (r @ Y0 @ Y0)))))),
% 1.56/1.39 introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition])).
% 1.56/1.39 thf(f814,plain,(
% 1.56/1.39 ( ! [X0 : $i] : (($true = (r @ X0 @ X0)) | ((r @ c0 @ c0) = $false)) ) | spl1_6),
% 1.56/1.39 inference(beta_eta_normalization,[status(thm)],[f813])).
% 1.56/1.39 thf(f813,plain,(
% 1.56/1.39 ( ! [X0 : $i] : (($false = ((^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ c0)) | ($true = ((^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X0))) ) | spl1_6),
% 1.56/1.39 inference(trivial_inequality_removal,[status(thm)],[f812])).
% 1.56/1.39 thf(f812,plain,(
% 1.56/1.39 ( ! [X0 : $i] : (($true = ((^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X0)) | ($true != $true) | ($false = ((^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ c0))) ) | spl1_6),
% 1.56/1.39 inference(superposition,[status(thm)],[f141,f29])).
% 1.56/1.39 thf(f29,plain,(
% 1.56/1.39 ( ! [X2 : $i,X1 : $i > $o] : (($true = (X1 @ (sK2 @ X1))) | ((X1 @ c0) = $false) | ($true = (X1 @ X2))) )),
% 1.56/1.39 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.56/1.39 thf(f27,plain,(
% 1.56/1.39 ( ! [X2 : $i,X1 : $i > $o] : (($true = (X1 @ X2)) | ((X1 @ c0) = $false) | (((X1 @ (sK2 @ X1)) => (X1 @ (cS @ (sK2 @ X1)))) = $false)) )),
% 1.56/1.39 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.56/1.39 thf(f26,plain,(
% 1.56/1.39 ( ! [X2 : $i,X1 : $i > $o] : (($true = (X1 @ X2)) | (((^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ Y0)))) @ (sK2 @ X1)) = $false) | ((X1 @ c0) = $false)) )),
% 1.56/1.39 inference(sigma_clausification,[status(thm)],[f25])).
% 1.56/1.39 thf(f25,plain,(
% 1.56/1.39 ( ! [X2 : $i,X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ Y0))))) = $false) | ($true = (X1 @ X2)) | ((X1 @ c0) = $false)) )),
% 1.56/1.39 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.56/1.39 thf(f24,plain,(
% 1.56/1.39 ( ! [X2 : $i,X1 : $i > $o] : ((((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ Y0))))) & (X1 @ c0)) = $false) | ($true = (X1 @ X2))) )),
% 1.56/1.39 inference(pi_clausification,[status(thm)],[f23])).
% 1.56/1.39 thf(f23,plain,(
% 1.56/1.39 ( ! [X1 : $i > $o] : (($true = (!! @ $i @ X1)) | (((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ Y0))))) & (X1 @ c0)) = $false)) )),
% 1.56/1.39 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.56/1.39 thf(f22,plain,(
% 1.56/1.39 ( ! [X1 : $i > $o] : (($true = (((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ Y0))))) & (X1 @ c0)) => (!! @ $i @ X1)))) )),
% 1.56/1.39 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.56/1.39 thf(f21,plain,(
% 1.56/1.39 ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ Y0))) @ X1))) )),
% 1.56/1.39 inference(pi_clausification,[status(thm)],[f20])).
% 1.56/1.39 thf(f20,plain,(
% 1.56/1.39 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ Y0)))))),
% 1.56/1.39 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.56/1.39 thf(f19,plain,(
% 1.56/1.39 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 1.56/1.39 inference(definition_unfolding,[status(thm)],[f18,f15])).
% 1.56/1.39 thf(f15,plain,(
% 1.56/1.39 (cIND = $true)),
% 1.56/1.39 inference(cnf_transformation,[status(thm)],[f13])).
% 1.56/1.39 thf(f18,plain,(
% 1.56/1.39 (cIND = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 1.56/1.39 inference(cnf_transformation,[status(thm)],[f6])).
% 1.56/1.39 thf(f6,plain,(
% 1.56/1.39 (cIND = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 1.56/1.39 inference(fool_elimination,[status(thm)],[f5])).
% 1.56/1.39 thf(f5,plain,(
% 1.56/1.39 (cIND = ! [X0 : $i > $o] : (((X0 @ c0) & ! [X1 : $i] : ((X0 @ X1) => (X0 @ (cS @ X1)))) => ! [X2 : $i] : (X0 @ X2)))),
% 1.56/1.39 inference(rectify,[status(thm)],[f1])).
% 1.56/1.39 thf(f1,axiom,(
% 1.56/1.39 (cIND = ! [X0 : $i > $o] : (((X0 @ c0) & ! [X1 : $i] : ((X0 @ X1) => (X0 @ (cS @ X1)))) => ! [X1 : $i] : (X0 @ X1)))),
% 1.56/1.39 file('/export/starexec/sandbox/tmp/tmp.RWmZR1h96a/DTF2THF_20686.p',cIND_def)).
% 1.56/1.39 thf(f141,plain,(
% 1.56/1.39 ($true != (r @ (sK2 @ (^[Y0 : $i]: (r @ Y0 @ Y0))) @ (sK2 @ (^[Y0 : $i]: (r @ Y0 @ Y0))))) | spl1_6),
% 1.56/1.39 inference(avatar_component_clause,[status(thm)],[f139])).
% 1.56/1.39 thf(f701,plain,(
% 1.56/1.39 ~spl1_5),
% 1.56/1.39 inference(avatar_contradiction_clause,[status(thm)],[f700])).
% 1.56/1.39 thf(f700,plain,(
% 1.56/1.39 $false | ~spl1_5),
% 1.56/1.39 inference(trivial_inequality_removal,[status(thm)],[f683])).
% 1.56/1.39 thf(f683,plain,(
% 1.56/1.39 ($true != $true) | ~spl1_5),
% 1.56/1.39 inference(superposition,[status(thm)],[f17,f137])).
% 1.56/1.39 thf(f137,plain,(
% 1.56/1.39 ( ! [X0 : $i] : (($true = (r @ X0 @ X0))) ) | ~spl1_5),
% 1.56/1.39 inference(avatar_component_clause,[status(thm)],[f136])).
% 1.56/1.39 thf(f17,plain,(
% 1.56/1.39 ( ! [X1 : $i] : (($true != (r @ sK0 @ X1))) )),
% 1.56/1.39 inference(cnf_transformation,[status(thm)],[f13])).
% 1.56/1.39 thf(f143,plain,(
% 1.56/1.39 ~spl1_6 | spl1_5 | spl1_4),
% 1.56/1.39 inference(avatar_split_clause,[status(thm)],[f128,f132,f136,f139])).
% 1.56/1.39 thf(f128,plain,(
% 1.56/1.39 ( ! [X0 : $i] : (($true = (r @ X0 @ X0)) | ((r @ c0 @ c0) = $false) | ($true != (r @ (sK2 @ (^[Y0 : $i]: (r @ Y0 @ Y0))) @ (sK2 @ (^[Y0 : $i]: (r @ Y0 @ Y0)))))) )),
% 1.56/1.39 inference(beta_eta_normalization,[status(thm)],[f127])).
% 1.56/1.39 thf(f127,plain,(
% 1.56/1.39 ( ! [X0 : $i] : (($true != (r @ (sK2 @ (^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0)))) @ (sK2 @ (^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0)))))) | ($false = ((^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ c0)) | ($true = ((^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X0))) )),
% 1.56/1.39 inference(trivial_inequality_removal,[status(thm)],[f125])).
% 1.56/1.39 thf(f125,plain,(
% 1.56/1.39 ( ! [X0 : $i] : (($false = ((^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ c0)) | ($true = $false) | ($true = ((^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X0)) | ($true != (r @ (sK2 @ (^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0)))) @ (sK2 @ (^[Y0 : $i]: (r @ ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) )),
% 1.56/1.39 inference(superposition,[status(thm)],[f14,f28])).
% 1.56/1.39 thf(f28,plain,(
% 1.56/1.39 ( ! [X2 : $i,X1 : $i > $o] : (($false = (X1 @ (cS @ (sK2 @ X1)))) | ($true = (X1 @ X2)) | ((X1 @ c0) = $false)) )),
% 1.56/1.39 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.56/1.39 thf(f14,plain,(
% 1.56/1.39 ( ! [X2 : $i,X3 : $i] : (($true = (r @ (cS @ X3) @ (cS @ X2))) | ($true != (r @ X3 @ X2))) )),
% 1.56/1.39 inference(cnf_transformation,[status(thm)],[f13])).
% 1.56/1.39 % SZS output end Proof for DTF2THF_20686
% 1.56/1.39 % (20804)------------------------------
% 1.56/1.39 % (20804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.39 % (20804)Termination reason: Refutation
% 1.56/1.39
% 1.56/1.39 % (20804)Memory used [KB]: 6140
% 1.56/1.39 % (20804)Time elapsed: 0.038 s
% 1.56/1.39 % (20804)Instructions burned: 109 (million)
% 1.56/1.39 % (20804)------------------------------
% 1.56/1.39 % (20804)------------------------------
% 1.56/1.39 % (20803)Success in time 0.042 s
%------------------------------------------------------------------------------