%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV070^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n025.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 09:40:13 AM UTC 2026
% Result : Theorem 1.45s 1.29s
% Output : Refutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 3 unt; 0 typ; 3 def)
% Number of atoms : 443 ( 153 equ; 0 cnn)
% Maximal formula atoms : 24 ( 9 avg)
% Number of connectives : 503 ( 84 ~; 78 |; 60 &; 246 @)
% ( 3 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 93 ( 0 ^; 63 !; 30 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cS: $i > $i ).
thf(func_def_7,type,
sK3: ( $i > $o ) > $i ).
thf(func_def_8,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_9,type,
sK5: $i > $o ).
thf(func_def_12,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f155,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f138,f144,f149,f154]) ).
thf(f154,plain,
( ~ spl6_8
| spl6_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f153]) ).
thf(f153,plain,
( $false
| ~ spl6_8
| spl6_10 ),
inference(subsumption_resolution,[status(thm)],[f152,f15]) ).
thf(f15,plain,
( ( sK5 @ sK2 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X3: $i > $o] :
( ( $true
!= ( X3 @ sK1 ) )
| ( $true
= ( X3 @ sK2 ) )
| ( ( ( X3 @ ( sK3 @ X3 ) )
= $true )
& ( ( X3 @ ( cS @ ( sK3 @ X3 ) ) )
!= $true ) ) )
& ! [X5: $i > $o] :
( ( ( X5 @ sK0 )
!= $true )
| ( ( X5 @ sK1 )
= $true )
| ( ( ( X5 @ ( cS @ ( sK4 @ X5 ) ) )
!= $true )
& ( ( X5 @ ( sK4 @ X5 ) )
= $true ) ) )
& ! [X8: $i] :
( ( $true
= ( sK5 @ ( cS @ X8 ) ) )
| ( $true
!= ( sK5 @ X8 ) ) )
& ( ( sK5 @ sK2 )
!= $true )
& ( ( sK5 @ sK0 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i > $o] :
( ( ( X3 @ X1 )
!= $true )
| ( ( X3 @ X2 )
= $true )
| ? [X4: $i] :
( ( ( X3 @ X4 )
= $true )
& ( ( X3 @ ( cS @ X4 ) )
!= $true ) ) )
& ! [X5: $i > $o] :
( ( $true
!= ( X5 @ X0 ) )
| ( $true
= ( X5 @ X1 ) )
| ? [X6: $i] :
( ( ( X5 @ ( cS @ X6 ) )
!= $true )
& ( ( X5 @ X6 )
= $true ) ) )
& ? [X7: $i > $o] :
( ! [X8: $i] :
( ( ( X7 @ ( cS @ X8 ) )
= $true )
| ( ( X7 @ X8 )
!= $true ) )
& ( ( X7 @ X2 )
!= $true )
& ( ( X7 @ X0 )
= $true ) ) )
=> ( ! [X3: $i > $o] :
( ( $true
!= ( X3 @ sK1 ) )
| ( $true
= ( X3 @ sK2 ) )
| ? [X4: $i] :
( ( ( X3 @ X4 )
= $true )
& ( ( X3 @ ( cS @ X4 ) )
!= $true ) ) )
& ! [X5: $i > $o] :
( ( ( X5 @ sK0 )
!= $true )
| ( ( X5 @ sK1 )
= $true )
| ? [X6: $i] :
( ( ( X5 @ ( cS @ X6 ) )
!= $true )
& ( ( X5 @ X6 )
= $true ) ) )
& ? [X7: $i > $o] :
( ! [X8: $i] :
( ( ( X7 @ ( cS @ X8 ) )
= $true )
| ( ( X7 @ X8 )
!= $true ) )
& ( ( X7 @ sK2 )
!= $true )
& ( $true
= ( X7 @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X3: $i > $o] :
( ? [X4: $i] :
( ( ( X3 @ X4 )
= $true )
& ( ( X3 @ ( cS @ X4 ) )
!= $true ) )
=> ( ( ( X3 @ ( sK3 @ X3 ) )
= $true )
& ( ( X3 @ ( cS @ ( sK3 @ X3 ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X5: $i > $o] :
( ? [X6: $i] :
( ( ( X5 @ ( cS @ X6 ) )
!= $true )
& ( ( X5 @ X6 )
= $true ) )
=> ( ( ( X5 @ ( cS @ ( sK4 @ X5 ) ) )
!= $true )
& ( ( X5 @ ( sK4 @ X5 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X7: $i > $o] :
( ! [X8: $i] :
( ( ( X7 @ ( cS @ X8 ) )
= $true )
| ( ( X7 @ X8 )
!= $true ) )
& ( ( X7 @ sK2 )
!= $true )
& ( $true
= ( X7 @ sK0 ) ) )
=> ( ! [X8: $i] :
( ( $true
= ( sK5 @ ( cS @ X8 ) ) )
| ( $true
!= ( sK5 @ X8 ) ) )
& ( ( sK5 @ sK2 )
!= $true )
& ( ( sK5 @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i > $o] :
( ( ( X3 @ X1 )
!= $true )
| ( ( X3 @ X2 )
= $true )
| ? [X4: $i] :
( ( ( X3 @ X4 )
= $true )
& ( ( X3 @ ( cS @ X4 ) )
!= $true ) ) )
& ! [X5: $i > $o] :
( ( $true
!= ( X5 @ X0 ) )
| ( $true
= ( X5 @ X1 ) )
| ? [X6: $i] :
( ( ( X5 @ ( cS @ X6 ) )
!= $true )
& ( ( X5 @ X6 )
= $true ) ) )
& ? [X7: $i > $o] :
( ! [X8: $i] :
( ( ( X7 @ ( cS @ X8 ) )
= $true )
| ( ( X7 @ X8 )
!= $true ) )
& ( ( X7 @ X2 )
!= $true )
& ( ( X7 @ X0 )
= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X2: $i,X0: $i,X1: $i] :
( ! [X5: $i > $o] :
( ( $true
!= ( X5 @ X0 ) )
| ( $true
= ( X5 @ X1 ) )
| ? [X6: $i] :
( ( ( X5 @ X6 )
= $true )
& ( ( X5 @ ( cS @ X6 ) )
!= $true ) ) )
& ! [X3: $i > $o] :
( ( ( X3 @ X2 )
!= $true )
| ( ( X3 @ X0 )
= $true )
| ? [X4: $i] :
( ( ( X3 @ ( cS @ X4 ) )
!= $true )
& ( ( X3 @ X4 )
= $true ) ) )
& ? [X7: $i > $o] :
( ! [X8: $i] :
( ( ( X7 @ ( cS @ X8 ) )
= $true )
| ( ( X7 @ X8 )
!= $true ) )
& ( $true
!= ( X7 @ X1 ) )
& ( ( X7 @ X2 )
= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: $i,X2: $i,X1: $i] :
( ? [X7: $i > $o] :
( ( $true
!= ( X7 @ X1 ) )
& ( ( X7 @ X2 )
= $true )
& ! [X8: $i] :
( ( ( X7 @ ( cS @ X8 ) )
= $true )
| ( ( X7 @ X8 )
!= $true ) ) )
& ! [X3: $i > $o] :
( ( ( X3 @ X0 )
= $true )
| ( ( X3 @ X2 )
!= $true )
| ? [X4: $i] :
( ( ( X3 @ ( cS @ X4 ) )
!= $true )
& ( ( X3 @ X4 )
= $true ) ) )
& ! [X5: $i > $o] :
( ( $true
= ( X5 @ X1 ) )
| ( $true
!= ( X5 @ X0 ) )
| ? [X6: $i] :
( ( ( X5 @ X6 )
= $true )
& ( ( X5 @ ( cS @ X6 ) )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i,X2: $i,X1: $i] :
( ( ! [X3: $i > $o] :
( ( ( ( X3 @ X2 )
= $true )
& ! [X4: $i] :
( ( ( X3 @ X4 )
= $true )
=> ( ( X3 @ ( cS @ X4 ) )
= $true ) ) )
=> ( ( X3 @ X0 )
= $true ) )
& ! [X5: $i > $o] :
( ( ( $true
= ( X5 @ X0 ) )
& ! [X6: $i] :
( ( ( X5 @ X6 )
= $true )
=> ( ( X5 @ ( cS @ X6 ) )
= $true ) ) )
=> ( $true
= ( X5 @ X1 ) ) ) )
=> ! [X7: $i > $o] :
( ( ( ( X7 @ X2 )
= $true )
& ! [X8: $i] :
( ( ( X7 @ X8 )
= $true )
=> ( ( X7 @ ( cS @ X8 ) )
= $true ) ) )
=> ( $true
= ( X7 @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i,X2: $i] :
( ( ! [X3: $i > $o] :
( ( ( X3 @ X2 )
& ! [X4: $i] :
( ( X3 @ X4 )
=> ( X3 @ ( cS @ X4 ) ) ) )
=> ( X3 @ X0 ) )
& ! [X5: $i > $o] :
( ( ( X5 @ X0 )
& ! [X6: $i] :
( ( X5 @ X6 )
=> ( X5 @ ( cS @ X6 ) ) ) )
=> ( X5 @ X1 ) ) )
=> ! [X7: $i > $o] :
( ( ! [X8: $i] :
( ( X7 @ X8 )
=> ( X7 @ ( cS @ X8 ) ) )
& ( X7 @ X2 ) )
=> ( X7 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: $i,X2: $i,X0: $i] :
( ( ! [X3: $i > $o] :
( ( ( X3 @ X0 )
& ! [X4: $i] :
( ( X3 @ X4 )
=> ( X3 @ ( cS @ X4 ) ) ) )
=> ( X3 @ X1 ) )
& ! [X3: $i > $o] :
( ( ( X3 @ X1 )
& ! [X4: $i] :
( ( X3 @ X4 )
=> ( X3 @ ( cS @ X4 ) ) ) )
=> ( X3 @ X2 ) ) )
=> ! [X3: $i > $o] :
( ( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X3 @ ( cS @ X4 ) ) )
& ( X3 @ X0 ) )
=> ( X3 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: $i,X2: $i,X0: $i] :
( ( ! [X3: $i > $o] :
( ( ( X3 @ X0 )
& ! [X4: $i] :
( ( X3 @ X4 )
=> ( X3 @ ( cS @ X4 ) ) ) )
=> ( X3 @ X1 ) )
& ! [X3: $i > $o] :
( ( ( X3 @ X1 )
& ! [X4: $i] :
( ( X3 @ X4 )
=> ( X3 @ ( cS @ X4 ) ) ) )
=> ( X3 @ X2 ) ) )
=> ! [X3: $i > $o] :
( ( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X3 @ ( cS @ X4 ) ) )
& ( X3 @ X0 ) )
=> ( X3 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vffKf8CsP9/DTF2THF_24028.p',cTHM577_pme) ).
thf(f152,plain,
( ( ( sK5 @ sK2 )
= $true )
| ~ spl6_8
| spl6_10 ),
inference(subsumption_resolution,[status(thm)],[f151,f133]) ).
thf(f133,plain,
( ( ( sK5 @ sK1 )
= $true )
| ~ spl6_8 ),
inference(avatar_component_clause,[status(thm)],[f131]) ).
thf(f131,definition,
( spl6_8
<=> ( ( sK5 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_8])],[avatar_definition]) ).
thf(f151,plain,
( ( ( sK5 @ sK1 )
!= $true )
| ( ( sK5 @ sK2 )
= $true )
| spl6_10 ),
inference(trivial_inequality_removal,[status(thm)],[f150]) ).
thf(f150,plain,
( ( ( sK5 @ sK1 )
!= $true )
| ( $true != $true )
| ( ( sK5 @ sK2 )
= $true )
| spl6_10 ),
inference(superposition,[status(thm)],[f143,f20]) ).
thf(f20,plain,
! [X3: $i > $o] :
( ( ( X3 @ ( sK3 @ X3 ) )
= $true )
| ( $true
!= ( X3 @ sK1 ) )
| ( $true
= ( X3 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f143,plain,
( ( $true
!= ( sK5 @ ( sK3 @ sK5 ) ) )
| spl6_10 ),
inference(avatar_component_clause,[status(thm)],[f141]) ).
thf(f141,definition,
( spl6_10
<=> ( $true
= ( sK5 @ ( sK3 @ sK5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_10])],[avatar_definition]) ).
thf(f149,plain,
( spl6_8
| spl6_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f148]) ).
thf(f148,plain,
( $false
| spl6_8
| spl6_9 ),
inference(subsumption_resolution,[status(thm)],[f147,f132]) ).
thf(f132,plain,
( ( ( sK5 @ sK1 )
!= $true )
| spl6_8 ),
inference(avatar_component_clause,[status(thm)],[f131]) ).
thf(f147,plain,
( ( ( sK5 @ sK1 )
= $true )
| spl6_9 ),
inference(subsumption_resolution,[status(thm)],[f146,f14]) ).
thf(f14,plain,
( ( sK5 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f146,plain,
( ( ( sK5 @ sK0 )
!= $true )
| ( ( sK5 @ sK1 )
= $true )
| spl6_9 ),
inference(trivial_inequality_removal,[status(thm)],[f145]) ).
thf(f145,plain,
( ( ( sK5 @ sK0 )
!= $true )
| ( ( sK5 @ sK1 )
= $true )
| ( $true != $true )
| spl6_9 ),
inference(superposition,[status(thm)],[f137,f17]) ).
thf(f17,plain,
! [X5: $i > $o] :
( ( ( X5 @ ( sK4 @ X5 ) )
= $true )
| ( ( X5 @ sK0 )
!= $true )
| ( ( X5 @ sK1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f137,plain,
( ( ( sK5 @ ( sK4 @ sK5 ) )
!= $true )
| spl6_9 ),
inference(avatar_component_clause,[status(thm)],[f135]) ).
thf(f135,definition,
( spl6_9
<=> ( ( sK5 @ ( sK4 @ sK5 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_9])],[avatar_definition]) ).
thf(f144,plain,
( ~ spl6_10
| ~ spl6_8 ),
inference(avatar_split_clause,[status(thm)],[f139,f131,f141]) ).
thf(f139,plain,
( ( $true
!= ( sK5 @ ( sK3 @ sK5 ) ) )
| ( ( sK5 @ sK1 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f106,f15]) ).
thf(f106,plain,
( ( ( sK5 @ sK1 )
!= $true )
| ( $true
!= ( sK5 @ ( sK3 @ sK5 ) ) )
| ( ( sK5 @ sK2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f105]) ).
thf(f105,plain,
( ( $true
!= ( sK5 @ ( sK3 @ sK5 ) ) )
| ( $true != $true )
| ( ( sK5 @ sK2 )
= $true )
| ( ( sK5 @ sK1 )
!= $true ) ),
inference(superposition,[status(thm)],[f19,f16]) ).
thf(f16,plain,
! [X8: $i] :
( ( $true
= ( sK5 @ ( cS @ X8 ) ) )
| ( $true
!= ( sK5 @ X8 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f19,plain,
! [X3: $i > $o] :
( ( ( X3 @ ( cS @ ( sK3 @ X3 ) ) )
!= $true )
| ( $true
!= ( X3 @ sK1 ) )
| ( $true
= ( X3 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f138,plain,
( spl6_8
| ~ spl6_9 ),
inference(avatar_split_clause,[status(thm)],[f129,f135,f131]) ).
thf(f129,plain,
( ( ( sK5 @ sK1 )
= $true )
| ( ( sK5 @ ( sK4 @ sK5 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f82,f14]) ).
thf(f82,plain,
( ( ( sK5 @ ( sK4 @ sK5 ) )
!= $true )
| ( ( sK5 @ sK1 )
= $true )
| ( ( sK5 @ sK0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
( ( ( sK5 @ ( sK4 @ sK5 ) )
!= $true )
| ( ( sK5 @ sK0 )
!= $true )
| ( ( sK5 @ sK1 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f18,f16]) ).
thf(f18,plain,
! [X5: $i > $o] :
( ( ( X5 @ ( cS @ ( sK4 @ X5 ) ) )
!= $true )
| ( ( X5 @ sK0 )
!= $true )
| ( ( X5 @ sK1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV070^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n025.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:39:57 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : SEV070^5 : TPTP v9.2.1. Released v4.0.0.
% 0.27/0.47 % Domain : Set Theory (Relations)
% 0.27/0.47 % Problem : TPS problem THM577
% 0.27/0.47 % Version : Especial.
% 0.27/0.47 % English : Inductive defn of <= on naturals is transitive.
% 0.27/0.47
% 0.27/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.47 % Source : [Bro09]
% 0.27/0.47 % Names : tps_0476 [Bro09]
% 0.27/0.47 % : THM577 [TPS]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.27/0.47 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.27/0.47 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.27/0.47 % Maximal formula atoms : 0 ( 0 avg)
% 0.27/0.47 % Number of connectives : 26 ( 0 ~; 0 |; 4 &; 15 @)
% 0.27/0.47 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 13 ( 13 avg)
% 0.27/0.47 % Number of types : 2 ( 0 usr)
% 0.27/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 1 ( 1 usr; 0 con; 1-1 aty)
% 0.27/0.47 % Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 0.27/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.27/0.47
% 0.27/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.47 % : Polymorphic definitions expanded.
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 thf(cS,type,
% 0.27/0.47 cS: $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(cTHM577_pme,conjecture,
% 0.27/0.47 ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.27/0.47 ( ( ! [Xp: $i > $o] :
% 0.27/0.47 ( ( ( Xp @ Xx )
% 0.27/0.47 & ! [Xn: $i] :
% 0.27/0.47 ( ( Xp @ Xn )
% 0.27/0.47 => ( Xp @ ( cS @ Xn ) ) ) )
% 0.27/0.47 => ( Xp @ Xy ) )
% 0.27/0.47 & ! [Xp: $i > $o] :
% 0.27/0.47 ( ( ( Xp @ Xy )
% 0.27/0.47 & ! [Xn: $i] :
% 0.27/0.47 ( ( Xp @ Xn )
% 0.27/0.47 => ( Xp @ ( cS @ Xn ) ) ) )
% 0.27/0.47 => ( Xp @ Xz ) ) )
% 0.27/0.47 => ! [Xp: $i > $o] :
% 0.27/0.47 ( ( ( Xp @ Xx )
% 0.27/0.47 & ! [Xn: $i] :
% 0.27/0.47 ( ( Xp @ Xn )
% 0.27/0.47 => ( Xp @ ( cS @ Xn ) ) ) )
% 0.27/0.47 => ( Xp @ Xz ) ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 1.45/1.26 ---- Embedded in THF ---
% 1.45/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.26 %%% Generated on Tue Feb 24 12:39:58 EST 2026
% 1.45/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.26 %%% Logic specification used:
% 1.45/1.26 %%% thf(spec, logic, $$dhol).
% 1.45/1.26
% 1.45/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.vffKf8CsP9/DTF2DTF24028.p
% See solution above
% 1.45/1.26 ------------------------
% 1.45/1.27 ---- Cleaned THF ---
% 1.45/1.27 thf(cS,type,
% 1.45/1.27 cS: $i > $i ).
% 1.45/1.27
% 1.45/1.27 thf(cTHM577_pme,conjecture,
% 1.45/1.27 ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.45/1.27 ( ( ! [Xp: $i > $o] :
% 1.45/1.27 ( ( ( Xp @ Xx )
% 1.45/1.27 & ! [Xn: $i] :
% 1.45/1.27 ( ( Xp @ Xn )
% 1.45/1.27 => ( Xp @ ( cS @ Xn ) ) ) )
% 1.45/1.27 => ( Xp @ Xy ) )
% 1.45/1.27 & ! [Xp: $i > $o] :
% 1.45/1.27 ( ( ( Xp @ Xy )
% 1.45/1.27 & ! [Xn: $i] :
% 1.45/1.27 ( ( Xp @ Xn )
% 1.45/1.27 => ( Xp @ ( cS @ Xn ) ) ) )
% 1.45/1.27 => ( Xp @ Xz ) ) )
% 1.45/1.27 => ! [Xp: $i > $o] :
% 1.45/1.27 ( ( ( Xp @ Xx )
% 1.45/1.27 & ! [Xn: $i] :
% 1.45/1.27 ( ( Xp @ Xn )
% 1.45/1.27 => ( Xp @ ( cS @ Xn ) ) ) )
% 1.45/1.27 => ( Xp @ Xz ) ) ) ).
% 1.45/1.27 ------------------------
% 1.45/1.29 % (24317)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_24028 for (2999ds/275Mi)
% 1.45/1.29 % (24314)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_24028 for (2999ds/27Mi)
% 1.45/1.29 % (24317)First to succeed.
% 1.45/1.29 % (24314)Also succeeded, but the first one will report.
% 1.45/1.29 % (24317)Refutation found. Thanks to Tanya!
% 1.45/1.29 % SZS status Theorem for DTF2THF_24028
% 1.45/1.29 % SZS output start Proof for DTF2THF_24028
% 1.45/1.29 thf(func_def_0, type, cS: $i > $i).
% 1.45/1.29 thf(func_def_7, type, sK3: ($i > $o) > $i).
% 1.45/1.29 thf(func_def_8, type, sK4: ($i > $o) > $i).
% 1.45/1.29 thf(func_def_9, type, sK5: $i > $o).
% 1.45/1.29 thf(func_def_12, type, ph7: !>[X0: $tType]:(X0)).
% 1.45/1.29 thf(f155,plain,(
% 1.45/1.29 $false),
% 1.45/1.29 inference(avatar_sat_refutation,[status(thm)],[f138,f144,f149,f154])).
% 1.45/1.29 thf(f154,plain,(
% 1.45/1.29 ~spl6_8 | spl6_10),
% 1.45/1.29 inference(avatar_contradiction_clause,[status(thm)],[f153])).
% 1.45/1.29 thf(f153,plain,(
% 1.45/1.29 $false | (~spl6_8 | spl6_10)),
% 1.45/1.29 inference(subsumption_resolution,[status(thm)],[f152,f15])).
% 1.45/1.29 thf(f15,plain,(
% 1.45/1.29 ((sK5 @ sK2) != $true)),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f13])).
% 1.45/1.29 thf(f13,plain,(
% 1.45/1.29 ! [X3 : $i > $o] : (($true != (X3 @ sK1)) | ($true = (X3 @ sK2)) | (((X3 @ (sK3 @ X3)) = $true) & ((X3 @ (cS @ (sK3 @ X3))) != $true))) & ! [X5 : $i > $o] : (((X5 @ sK0) != $true) | ((X5 @ sK1) = $true) | (((X5 @ (cS @ (sK4 @ X5))) != $true) & ((X5 @ (sK4 @ X5)) = $true))) & (! [X8 : $i] : (($true = (sK5 @ (cS @ X8))) | ($true != (sK5 @ X8))) & ((sK5 @ sK2) != $true) & ((sK5 @ sK0) = $true))),
% 1.45/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f12,f11,f10,f9])).
% 1.45/1.29 thf(f9,plain,(
% 1.45/1.29 ? [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i > $o] : (((X3 @ X1) != $true) | ((X3 @ X2) = $true) | ? [X4 : $i] : (((X3 @ X4) = $true) & ((X3 @ (cS @ X4)) != $true))) & ! [X5 : $i > $o] : (($true != (X5 @ X0)) | ($true = (X5 @ X1)) | ? [X6 : $i] : (((X5 @ (cS @ X6)) != $true) & ((X5 @ X6) = $true))) & ? [X7 : $i > $o] : (! [X8 : $i] : (((X7 @ (cS @ X8)) = $true) | ((X7 @ X8) != $true)) & ((X7 @ X2) != $true) & ((X7 @ X0) = $true))) => (! [X3 : $i > $o] : (($true != (X3 @ sK1)) | ($true = (X3 @ sK2)) | ? [X4 : $i] : (((X3 @ X4) = $true) & ((X3 @ (cS @ X4)) != $true))) & ! [X5 : $i > $o] : (((X5 @ sK0) != $true) | ((X5 @ sK1) = $true) | ? [X6 : $i] : (((X5 @ (cS @ X6)) != $true) & ((X5 @ X6) = $true))) & ? [X7 : $i > $o] : (! [X8 : $i] : (((X7 @ (cS @ X8)) = $true) | ((X7 @ X8) != $true)) & ((X7 @ sK2) != $true) & ($true = (X7 @ sK0))))),
% 1.45/1.29 introduced(definition,[],[choice_axiom])).
% 1.45/1.29 thf(f10,plain,(
% 1.45/1.29 ! [X3 : $i > $o] : (? [X4 : $i] : (((X3 @ X4) = $true) & ((X3 @ (cS @ X4)) != $true)) => (((X3 @ (sK3 @ X3)) = $true) & ((X3 @ (cS @ (sK3 @ X3))) != $true)))),
% 1.45/1.29 introduced(definition,[],[choice_axiom])).
% 1.45/1.29 thf(f11,plain,(
% 1.45/1.29 ! [X5 : $i > $o] : (? [X6 : $i] : (((X5 @ (cS @ X6)) != $true) & ((X5 @ X6) = $true)) => (((X5 @ (cS @ (sK4 @ X5))) != $true) & ((X5 @ (sK4 @ X5)) = $true)))),
% 1.45/1.29 introduced(definition,[],[choice_axiom])).
% 1.45/1.29 thf(f12,plain,(
% 1.45/1.29 ? [X7 : $i > $o] : (! [X8 : $i] : (((X7 @ (cS @ X8)) = $true) | ((X7 @ X8) != $true)) & ((X7 @ sK2) != $true) & ($true = (X7 @ sK0))) => (! [X8 : $i] : (($true = (sK5 @ (cS @ X8))) | ($true != (sK5 @ X8))) & ((sK5 @ sK2) != $true) & ((sK5 @ sK0) = $true))),
% 1.45/1.29 introduced(definition,[],[choice_axiom])).
% 1.45/1.29 thf(f8,plain,(
% 1.45/1.29 ? [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i > $o] : (((X3 @ X1) != $true) | ((X3 @ X2) = $true) | ? [X4 : $i] : (((X3 @ X4) = $true) & ((X3 @ (cS @ X4)) != $true))) & ! [X5 : $i > $o] : (($true != (X5 @ X0)) | ($true = (X5 @ X1)) | ? [X6 : $i] : (((X5 @ (cS @ X6)) != $true) & ((X5 @ X6) = $true))) & ? [X7 : $i > $o] : (! [X8 : $i] : (((X7 @ (cS @ X8)) = $true) | ((X7 @ X8) != $true)) & ((X7 @ X2) != $true) & ((X7 @ X0) = $true)))),
% 1.45/1.29 inference(rectify,[status(thm)],[f7])).
% 1.45/1.29 thf(f7,plain,(
% 1.45/1.29 ? [X2 : $i,X0 : $i,X1 : $i] : (! [X5 : $i > $o] : (($true != (X5 @ X0)) | ($true = (X5 @ X1)) | ? [X6 : $i] : (((X5 @ X6) = $true) & ((X5 @ (cS @ X6)) != $true))) & ! [X3 : $i > $o] : (((X3 @ X2) != $true) | ((X3 @ X0) = $true) | ? [X4 : $i] : (((X3 @ (cS @ X4)) != $true) & ((X3 @ X4) = $true))) & ? [X7 : $i > $o] : (! [X8 : $i] : (((X7 @ (cS @ X8)) = $true) | ((X7 @ X8) != $true)) & ($true != (X7 @ X1)) & ((X7 @ X2) = $true)))),
% 1.45/1.29 inference(flattening,[status(thm)],[f6])).
% 1.45/1.29 thf(f6,plain,(
% 1.45/1.29 ? [X0 : $i,X2 : $i,X1 : $i] : (? [X7 : $i > $o] : (($true != (X7 @ X1)) & (((X7 @ X2) = $true) & ! [X8 : $i] : (((X7 @ (cS @ X8)) = $true) | ((X7 @ X8) != $true)))) & (! [X3 : $i > $o] : (((X3 @ X0) = $true) | (((X3 @ X2) != $true) | ? [X4 : $i] : (((X3 @ (cS @ X4)) != $true) & ((X3 @ X4) = $true)))) & ! [X5 : $i > $o] : (($true = (X5 @ X1)) | (($true != (X5 @ X0)) | ? [X6 : $i] : (((X5 @ X6) = $true) & ((X5 @ (cS @ X6)) != $true))))))),
% 1.45/1.29 inference(ennf_transformation,[status(thm)],[f5])).
% 1.45/1.29 thf(f5,plain,(
% 1.45/1.29 ~! [X0 : $i,X2 : $i,X1 : $i] : ((! [X3 : $i > $o] : ((((X3 @ X2) = $true) & ! [X4 : $i] : (((X3 @ X4) = $true) => ((X3 @ (cS @ X4)) = $true))) => ((X3 @ X0) = $true)) & ! [X5 : $i > $o] : ((($true = (X5 @ X0)) & ! [X6 : $i] : (((X5 @ X6) = $true) => ((X5 @ (cS @ X6)) = $true))) => ($true = (X5 @ X1)))) => ! [X7 : $i > $o] : ((((X7 @ X2) = $true) & ! [X8 : $i] : (((X7 @ X8) = $true) => ((X7 @ (cS @ X8)) = $true))) => ($true = (X7 @ X1))))),
% 1.45/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.45/1.29 thf(f4,plain,(
% 1.45/1.29 ~! [X0 : $i,X1 : $i,X2 : $i] : ((! [X3 : $i > $o] : (((X3 @ X2) & ! [X4 : $i] : ((X3 @ X4) => (X3 @ (cS @ X4)))) => (X3 @ X0)) & ! [X5 : $i > $o] : (((X5 @ X0) & ! [X6 : $i] : ((X5 @ X6) => (X5 @ (cS @ X6)))) => (X5 @ X1))) => ! [X7 : $i > $o] : ((! [X8 : $i] : ((X7 @ X8) => (X7 @ (cS @ X8))) & (X7 @ X2)) => (X7 @ X1)))),
% 1.45/1.29 inference(rectify,[status(thm)],[f2])).
% 1.45/1.29 thf(f2,negated_conjecture,(
% 1.45/1.29 ~! [X1 : $i,X2 : $i,X0 : $i] : ((! [X3 : $i > $o] : (((X3 @ X0) & ! [X4 : $i] : ((X3 @ X4) => (X3 @ (cS @ X4)))) => (X3 @ X1)) & ! [X3 : $i > $o] : (((X3 @ X1) & ! [X4 : $i] : ((X3 @ X4) => (X3 @ (cS @ X4)))) => (X3 @ X2))) => ! [X3 : $i > $o] : ((! [X4 : $i] : ((X3 @ X4) => (X3 @ (cS @ X4))) & (X3 @ X0)) => (X3 @ X2)))),
% 1.45/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.45/1.29 thf(f1,conjecture,(
% 1.45/1.29 ! [X1 : $i,X2 : $i,X0 : $i] : ((! [X3 : $i > $o] : (((X3 @ X0) & ! [X4 : $i] : ((X3 @ X4) => (X3 @ (cS @ X4)))) => (X3 @ X1)) & ! [X3 : $i > $o] : (((X3 @ X1) & ! [X4 : $i] : ((X3 @ X4) => (X3 @ (cS @ X4)))) => (X3 @ X2))) => ! [X3 : $i > $o] : ((! [X4 : $i] : ((X3 @ X4) => (X3 @ (cS @ X4))) & (X3 @ X0)) => (X3 @ X2)))),
% 1.45/1.29 file('/export/starexec/sandbox/tmp/tmp.vffKf8CsP9/DTF2THF_24028.p',cTHM577_pme)).
% 1.45/1.29 thf(f152,plain,(
% 1.45/1.29 ((sK5 @ sK2) = $true) | (~spl6_8 | spl6_10)),
% 1.45/1.29 inference(subsumption_resolution,[status(thm)],[f151,f133])).
% 1.45/1.29 thf(f133,plain,(
% 1.45/1.29 ((sK5 @ sK1) = $true) | ~spl6_8),
% 1.45/1.29 inference(avatar_component_clause,[status(thm)],[f131])).
% 1.45/1.29 thf(f131,definition,(
% 1.45/1.29 spl6_8 <=> ((sK5 @ sK1) = $true)),
% 1.45/1.29 introduced(definition,[new_symbols(naming,[spl6_8])],[avatar_definition])).
% 1.45/1.29 thf(f151,plain,(
% 1.45/1.29 ((sK5 @ sK1) != $true) | ((sK5 @ sK2) = $true) | spl6_10),
% 1.45/1.29 inference(trivial_inequality_removal,[status(thm)],[f150])).
% 1.45/1.29 thf(f150,plain,(
% 1.45/1.29 ((sK5 @ sK1) != $true) | ($true != $true) | ((sK5 @ sK2) = $true) | spl6_10),
% 1.45/1.29 inference(superposition,[status(thm)],[f143,f20])).
% 1.45/1.29 thf(f20,plain,(
% 1.45/1.29 ( ! [X3 : $i > $o] : (((X3 @ (sK3 @ X3)) = $true) | ($true != (X3 @ sK1)) | ($true = (X3 @ sK2))) )),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f13])).
% 1.45/1.29 thf(f143,plain,(
% 1.45/1.29 ($true != (sK5 @ (sK3 @ sK5))) | spl6_10),
% 1.45/1.29 inference(avatar_component_clause,[status(thm)],[f141])).
% 1.45/1.29 thf(f141,definition,(
% 1.45/1.29 spl6_10 <=> ($true = (sK5 @ (sK3 @ sK5)))),
% 1.45/1.29 introduced(definition,[new_symbols(naming,[spl6_10])],[avatar_definition])).
% 1.45/1.29 thf(f149,plain,(
% 1.45/1.29 spl6_8 | spl6_9),
% 1.45/1.29 inference(avatar_contradiction_clause,[status(thm)],[f148])).
% 1.45/1.29 thf(f148,plain,(
% 1.45/1.29 $false | (spl6_8 | spl6_9)),
% 1.45/1.29 inference(subsumption_resolution,[status(thm)],[f147,f132])).
% 1.45/1.29 thf(f132,plain,(
% 1.45/1.29 ((sK5 @ sK1) != $true) | spl6_8),
% 1.45/1.29 inference(avatar_component_clause,[status(thm)],[f131])).
% 1.45/1.29 thf(f147,plain,(
% 1.45/1.29 ((sK5 @ sK1) = $true) | spl6_9),
% 1.45/1.29 inference(subsumption_resolution,[status(thm)],[f146,f14])).
% 1.45/1.29 thf(f14,plain,(
% 1.45/1.29 ((sK5 @ sK0) = $true)),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f13])).
% 1.45/1.29 thf(f146,plain,(
% 1.45/1.29 ((sK5 @ sK0) != $true) | ((sK5 @ sK1) = $true) | spl6_9),
% 1.45/1.29 inference(trivial_inequality_removal,[status(thm)],[f145])).
% 1.45/1.29 thf(f145,plain,(
% 1.45/1.29 ((sK5 @ sK0) != $true) | ((sK5 @ sK1) = $true) | ($true != $true) | spl6_9),
% 1.45/1.29 inference(superposition,[status(thm)],[f137,f17])).
% 1.45/1.29 thf(f17,plain,(
% 1.45/1.29 ( ! [X5 : $i > $o] : (((X5 @ (sK4 @ X5)) = $true) | ((X5 @ sK0) != $true) | ((X5 @ sK1) = $true)) )),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f13])).
% 1.45/1.29 thf(f137,plain,(
% 1.45/1.29 ((sK5 @ (sK4 @ sK5)) != $true) | spl6_9),
% 1.45/1.29 inference(avatar_component_clause,[status(thm)],[f135])).
% 1.45/1.29 thf(f135,definition,(
% 1.45/1.29 spl6_9 <=> ((sK5 @ (sK4 @ sK5)) = $true)),
% 1.45/1.29 introduced(definition,[new_symbols(naming,[spl6_9])],[avatar_definition])).
% 1.45/1.29 thf(f144,plain,(
% 1.45/1.29 ~spl6_10 | ~spl6_8),
% 1.45/1.29 inference(avatar_split_clause,[status(thm)],[f139,f131,f141])).
% 1.45/1.29 thf(f139,plain,(
% 1.45/1.29 ($true != (sK5 @ (sK3 @ sK5))) | ((sK5 @ sK1) != $true)),
% 1.45/1.29 inference(subsumption_resolution,[status(thm)],[f106,f15])).
% 1.45/1.29 thf(f106,plain,(
% 1.45/1.29 ((sK5 @ sK1) != $true) | ($true != (sK5 @ (sK3 @ sK5))) | ((sK5 @ sK2) = $true)),
% 1.45/1.29 inference(trivial_inequality_removal,[status(thm)],[f105])).
% 1.45/1.29 thf(f105,plain,(
% 1.45/1.29 ($true != (sK5 @ (sK3 @ sK5))) | ($true != $true) | ((sK5 @ sK2) = $true) | ((sK5 @ sK1) != $true)),
% 1.45/1.29 inference(superposition,[status(thm)],[f19,f16])).
% 1.45/1.29 thf(f16,plain,(
% 1.45/1.29 ( ! [X8 : $i] : (($true = (sK5 @ (cS @ X8))) | ($true != (sK5 @ X8))) )),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f13])).
% 1.45/1.29 thf(f19,plain,(
% 1.45/1.29 ( ! [X3 : $i > $o] : (((X3 @ (cS @ (sK3 @ X3))) != $true) | ($true != (X3 @ sK1)) | ($true = (X3 @ sK2))) )),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f13])).
% 1.45/1.29 thf(f138,plain,(
% 1.45/1.29 spl6_8 | ~spl6_9),
% 1.45/1.29 inference(avatar_split_clause,[status(thm)],[f129,f135,f131])).
% 1.45/1.29 thf(f129,plain,(
% 1.45/1.29 ((sK5 @ sK1) = $true) | ((sK5 @ (sK4 @ sK5)) != $true)),
% 1.45/1.29 inference(subsumption_resolution,[status(thm)],[f82,f14])).
% 1.45/1.29 thf(f82,plain,(
% 1.45/1.29 ((sK5 @ (sK4 @ sK5)) != $true) | ((sK5 @ sK1) = $true) | ((sK5 @ sK0) != $true)),
% 1.45/1.29 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 1.45/1.29 thf(f72,plain,(
% 1.45/1.29 ((sK5 @ (sK4 @ sK5)) != $true) | ((sK5 @ sK0) != $true) | ((sK5 @ sK1) = $true) | ($true != $true)),
% 1.45/1.29 inference(superposition,[status(thm)],[f18,f16])).
% 1.45/1.29 thf(f18,plain,(
% 1.45/1.29 ( ! [X5 : $i > $o] : (((X5 @ (cS @ (sK4 @ X5))) != $true) | ((X5 @ sK0) != $true) | ((X5 @ sK1) = $true)) )),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f13])).
% 1.45/1.29 % SZS output end Proof for DTF2THF_24028
% 1.45/1.29 % (24317)------------------------------
% 1.45/1.29 % (24317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (24317)Termination reason: Refutation
% 1.45/1.29
% 1.45/1.29 % (24317)Memory used [KB]: 5628
% 1.45/1.29 % (24317)Time elapsed: 0.007 s
% 1.45/1.29 % (24317)Instructions burned: 9 (million)
% 1.45/1.29 % (24317)------------------------------
% 1.45/1.29 % (24317)------------------------------
% 1.45/1.29 % (24311)Success in time 0.017 s
%------------------------------------------------------------------------------