%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM824^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 09:24:51 AM UTC 2026
% Result : Theorem 1.56s 1.31s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 103 ( 3 unt; 0 typ; 9 def)
% Number of atoms : 1187 ( 331 equ; 0 cnn)
% Maximal formula atoms : 15 ( 11 avg)
% Number of connectives : 1211 ( 238 ~; 274 |; 54 &; 601 @)
% ( 9 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 58 ( 58 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 13 con; 0-2 aty)
% Number of variables : 153 ( 0 ^; 141 !; 12 ?; 153 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cN: $i > $o ).
thf(func_def_1,type,
cODD: $i > $o ).
thf(func_def_2,type,
cEVEN: $i > $o ).
thf(func_def_3,type,
cS: $i > $i ).
thf(func_def_9,type,
sK1: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_10,type,
sK2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_13,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f437,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f33,f98,f166,f181,f201,f256,f262,f286,f326,f351,f376,f379,f429,f430]) ).
thf(f430,plain,
( ~ spl3_7
| spl3_6
| spl3_8 ),
inference(avatar_split_clause,[status(thm)],[f422,f137,f96,f133]) ).
thf(f133,definition,
( spl3_7
<=> ( $true
= ( cN @ ( sK1 @ cN @ cN ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_7])],[avatar_definition]) ).
thf(f96,definition,
( spl3_6
<=> ! [X1: $i] :
( ( ( cN @ X1 )
= $true )
| ( $true
!= ( cODD @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f137,definition,
( spl3_8
<=> ( $true
= ( cN @ ( sK2 @ cN @ cN ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition]) ).
thf(f422,plain,
( ! [X0: $i] :
( ( $true
= ( cN @ X0 ) )
| ( $true
!= ( cN @ ( sK1 @ cN @ cN ) ) )
| ( $true
!= ( cODD @ X0 ) ) )
| spl3_8 ),
inference(trivial_inequality_removal,[status(thm)],[f418]) ).
thf(f418,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( cN @ ( sK1 @ cN @ cN ) ) )
| ( $true
= ( cN @ X0 ) )
| ( $true
!= ( cODD @ X0 ) ) )
| spl3_8 ),
inference(superposition,[status(thm)],[f138,f129]) ).
thf(f129,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( cN @ ( sK2 @ cN @ X0 ) ) )
| ( $true
!= ( cODD @ X1 ) )
| ( $true
!= ( cN @ ( sK1 @ cN @ X0 ) ) )
| ( $true
= ( X0 @ X1 ) ) ),
inference(subsumption_resolution,[status(thm)],[f124,f24]) ).
thf(f24,plain,
( ( cN @ c0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( cN @ c0 )
= $true )
& ( $true
!= ( cN @ sK0 ) )
& ( ( $true
= ( cEVEN @ sK0 ) )
| ( $true
= ( cODD @ sK0 ) ) )
& ! [X1: $i] :
( ( ( cN @ X1 )
!= $true )
| ( $true
= ( cN @ ( cS @ X1 ) ) ) )
& ! [X2: $i > $o,X3: $i > $o] :
( ( ( $true
!= ( X3 @ ( cS @ ( sK1 @ X3 @ X2 ) ) ) )
& ( $true
= ( X2 @ ( sK1 @ X3 @ X2 ) ) ) )
| ( ! [X5: $i] :
( ( ( X3 @ X5 )
= $true )
| ( ( cEVEN @ X5 )
!= $true ) )
& ! [X6: $i] :
( ( $true
= ( X2 @ X6 ) )
| ( ( cODD @ X6 )
!= $true ) ) )
| ( ( ( X2 @ ( cS @ ( sK2 @ X3 @ X2 ) ) )
!= $true )
& ( $true
= ( X3 @ ( sK2 @ X3 @ X2 ) ) ) )
| ( $true
!= ( X3 @ c0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: $i] :
( ( $true
!= ( cN @ X0 ) )
& ( ( ( cEVEN @ X0 )
= $true )
| ( $true
= ( cODD @ X0 ) ) ) )
=> ( ( $true
!= ( cN @ sK0 ) )
& ( ( $true
= ( cEVEN @ sK0 ) )
| ( $true
= ( cODD @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X2: $i > $o,X3: $i > $o] :
( ? [X4: $i] :
( ( $true
!= ( X3 @ ( cS @ X4 ) ) )
& ( $true
= ( X2 @ X4 ) ) )
=> ( ( $true
!= ( X3 @ ( cS @ ( sK1 @ X3 @ X2 ) ) ) )
& ( $true
= ( X2 @ ( sK1 @ X3 @ X2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X2: $i > $o,X3: $i > $o] :
( ? [X7: $i] :
( ( ( X2 @ ( cS @ X7 ) )
!= $true )
& ( ( X3 @ X7 )
= $true ) )
=> ( ( ( X2 @ ( cS @ ( sK2 @ X3 @ X2 ) ) )
!= $true )
& ( $true
= ( X3 @ ( sK2 @ X3 @ X2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ( ( cN @ c0 )
= $true )
& ? [X0: $i] :
( ( $true
!= ( cN @ X0 ) )
& ( ( ( cEVEN @ X0 )
= $true )
| ( $true
= ( cODD @ X0 ) ) ) )
& ! [X1: $i] :
( ( ( cN @ X1 )
!= $true )
| ( $true
= ( cN @ ( cS @ X1 ) ) ) )
& ! [X2: $i > $o,X3: $i > $o] :
( ? [X4: $i] :
( ( $true
!= ( X3 @ ( cS @ X4 ) ) )
& ( $true
= ( X2 @ X4 ) ) )
| ( ! [X5: $i] :
( ( ( X3 @ X5 )
= $true )
| ( ( cEVEN @ X5 )
!= $true ) )
& ! [X6: $i] :
( ( $true
= ( X2 @ X6 ) )
| ( ( cODD @ X6 )
!= $true ) ) )
| ? [X7: $i] :
( ( ( X2 @ ( cS @ X7 ) )
!= $true )
& ( ( X3 @ X7 )
= $true ) )
| ( $true
!= ( X3 @ c0 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( cN @ c0 )
= $true )
& ? [X7: $i] :
( ( ( cN @ X7 )
!= $true )
& ( ( $true
= ( cEVEN @ X7 ) )
| ( $true
= ( cODD @ X7 ) ) ) )
& ! [X0: $i] :
( ( $true
!= ( cN @ X0 ) )
| ( $true
= ( cN @ ( cS @ X0 ) ) ) )
& ! [X2: $i > $o,X1: $i > $o] :
( ? [X4: $i] :
( ( $true
!= ( X1 @ ( cS @ X4 ) ) )
& ( $true
= ( X2 @ X4 ) ) )
| ( ! [X5: $i] :
( ( $true
= ( X1 @ X5 ) )
| ( ( cEVEN @ X5 )
!= $true ) )
& ! [X6: $i] :
( ( $true
= ( X2 @ X6 ) )
| ( ( cODD @ X6 )
!= $true ) ) )
| ? [X3: $i] :
( ( $true
!= ( X2 @ ( cS @ X3 ) ) )
& ( ( X1 @ X3 )
= $true ) )
| ( $true
!= ( X1 @ c0 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X7: $i] :
( ( ( cN @ X7 )
!= $true )
& ( ( $true
= ( cEVEN @ X7 ) )
| ( $true
= ( cODD @ X7 ) ) ) )
& ! [X0: $i] :
( ( $true
!= ( cN @ X0 ) )
| ( $true
= ( cN @ ( cS @ X0 ) ) ) )
& ( ( cN @ c0 )
= $true )
& ! [X2: $i > $o,X1: $i > $o] :
( ( ! [X5: $i] :
( ( $true
= ( X1 @ X5 ) )
| ( ( cEVEN @ X5 )
!= $true ) )
& ! [X6: $i] :
( ( $true
= ( X2 @ X6 ) )
| ( ( cODD @ X6 )
!= $true ) ) )
| ? [X4: $i] :
( ( $true
!= ( X1 @ ( cS @ X4 ) ) )
& ( $true
= ( X2 @ X4 ) ) )
| ? [X3: $i] :
( ( $true
!= ( X2 @ ( cS @ X3 ) ) )
& ( ( X1 @ X3 )
= $true ) )
| ( $true
!= ( X1 @ c0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: $i] :
( ( $true
= ( cN @ X0 ) )
=> ( $true
= ( cN @ ( cS @ X0 ) ) ) )
& ( ( cN @ c0 )
= $true )
& ! [X2: $i > $o,X1: $i > $o] :
( ( ! [X4: $i] :
( ( $true
= ( X2 @ X4 ) )
=> ( $true
= ( X1 @ ( cS @ X4 ) ) ) )
& ! [X3: $i] :
( ( ( X1 @ X3 )
= $true )
=> ( $true
= ( X2 @ ( cS @ X3 ) ) ) )
& ( $true
= ( X1 @ c0 ) ) )
=> ( ! [X5: $i] :
( ( ( cEVEN @ X5 )
= $true )
=> ( $true
= ( X1 @ X5 ) ) )
& ! [X6: $i] :
( ( ( cODD @ X6 )
= $true )
=> ( $true
= ( X2 @ X6 ) ) ) ) ) )
=> ! [X7: $i] :
( ( ( $true
= ( cEVEN @ X7 ) )
| ( $true
= ( cODD @ X7 ) ) )
=> ( ( cN @ X7 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] :
( ( cN @ X0 )
=> ( cN @ ( cS @ X0 ) ) )
& ( cN @ c0 )
& ! [X1: $i > $o,X2: $i > $o] :
( ( ( X1 @ c0 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ ( cS @ X3 ) ) )
& ! [X4: $i] :
( ( X2 @ X4 )
=> ( X1 @ ( cS @ X4 ) ) ) )
=> ( ! [X5: $i] :
( ( cEVEN @ X5 )
=> ( X1 @ X5 ) )
& ! [X6: $i] :
( ( cODD @ X6 )
=> ( X2 @ X6 ) ) ) ) )
=> ! [X7: $i] :
( ( ( cEVEN @ X7 )
| ( cODD @ X7 ) )
=> ( cN @ X7 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X5: $i] :
( ( cN @ X5 )
=> ( cN @ ( cS @ X5 ) ) )
& ( cN @ c0 )
& ! [X0: $i > $o,X1: $i > $o] :
( ( ( X0 @ c0 )
& ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ ( cS @ X2 ) ) )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X0 @ ( cS @ X3 ) ) ) )
=> ( ! [X4: $i] :
( ( cEVEN @ X4 )
=> ( X0 @ X4 ) )
& ! [X4: $i] :
( ( cODD @ X4 )
=> ( X1 @ X4 ) ) ) ) )
=> ! [X6: $i] :
( ( ( cEVEN @ X6 )
| ( cODD @ X6 ) )
=> ( cN @ X6 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X5: $i] :
( ( cN @ X5 )
=> ( cN @ ( cS @ X5 ) ) )
& ( cN @ c0 )
& ! [X0: $i > $o,X1: $i > $o] :
( ( ( X0 @ c0 )
& ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ ( cS @ X2 ) ) )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X0 @ ( cS @ X3 ) ) ) )
=> ( ! [X4: $i] :
( ( cEVEN @ X4 )
=> ( X0 @ X4 ) )
& ! [X4: $i] :
( ( cODD @ X4 )
=> ( X1 @ X4 ) ) ) ) )
=> ! [X6: $i] :
( ( ( cEVEN @ X6 )
| ( cODD @ X6 ) )
=> ( cN @ X6 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8aGlDTHdDd/DTF2THF_15126.p',cTHM623_pme) ).
thf(f124,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( cN @ ( sK2 @ cN @ X0 ) ) )
| ( $true
!= ( cODD @ X1 ) )
| ( $true
= ( X0 @ X1 ) )
| ( ( cN @ c0 )
!= $true )
| ( $true
!= ( cN @ ( sK1 @ cN @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f119]) ).
thf(f119,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( X0 @ X1 ) )
| ( $true != $true )
| ( ( cN @ c0 )
!= $true )
| ( $true
!= ( cODD @ X1 ) )
| ( $true
!= ( cN @ ( sK1 @ cN @ X0 ) ) )
| ( $true
= ( cN @ ( sK2 @ cN @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f17,f21]) ).
thf(f21,plain,
! [X1: $i] :
( ( $true
= ( cN @ ( cS @ X1 ) ) )
| ( ( cN @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f17,plain,
! [X2: $i > $o,X3: $i > $o,X6: $i] :
( ( $true
!= ( X3 @ ( cS @ ( sK1 @ X3 @ X2 ) ) ) )
| ( ( cODD @ X6 )
!= $true )
| ( $true
= ( X3 @ ( sK2 @ X3 @ X2 ) ) )
| ( $true
!= ( X3 @ c0 ) )
| ( $true
= ( X2 @ X6 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f138,plain,
( ( $true
!= ( cN @ ( sK2 @ cN @ cN ) ) )
| spl3_8 ),
inference(avatar_component_clause,[status(thm)],[f137]) ).
thf(f429,plain,
( spl3_6
| spl3_7
| spl3_8 ),
inference(avatar_split_clause,[status(thm)],[f428,f137,f133,f96]) ).
thf(f428,plain,
( ! [X0: $i] :
( ( $true
= ( cN @ X0 ) )
| ( $true
!= ( cODD @ X0 ) ) )
| spl3_7
| spl3_8 ),
inference(subsumption_resolution,[status(thm)],[f427,f24]) ).
thf(f427,plain,
( ! [X0: $i] :
( ( $true
!= ( cODD @ X0 ) )
| ( ( cN @ c0 )
!= $true )
| ( $true
= ( cN @ X0 ) ) )
| spl3_7
| spl3_8 ),
inference(subsumption_resolution,[status(thm)],[f426,f135]) ).
thf(f135,plain,
( ( $true
!= ( cN @ ( sK1 @ cN @ cN ) ) )
| spl3_7 ),
inference(avatar_component_clause,[status(thm)],[f133]) ).
thf(f426,plain,
( ! [X0: $i] :
( ( $true
!= ( cODD @ X0 ) )
| ( $true
= ( cN @ ( sK1 @ cN @ cN ) ) )
| ( $true
= ( cN @ X0 ) )
| ( ( cN @ c0 )
!= $true ) )
| spl3_8 ),
inference(trivial_inequality_removal,[status(thm)],[f421]) ).
thf(f421,plain,
( ! [X0: $i] :
( ( $true
!= ( cODD @ X0 ) )
| ( ( cN @ c0 )
!= $true )
| ( $true
= ( cN @ X0 ) )
| ( $true != $true )
| ( $true
= ( cN @ ( sK1 @ cN @ cN ) ) ) )
| spl3_8 ),
inference(superposition,[status(thm)],[f138,f13]) ).
thf(f13,plain,
! [X2: $i > $o,X3: $i > $o,X6: $i] :
( ( $true
= ( X3 @ ( sK2 @ X3 @ X2 ) ) )
| ( $true
!= ( X3 @ c0 ) )
| ( $true
= ( X2 @ ( sK1 @ X3 @ X2 ) ) )
| ( ( cODD @ X6 )
!= $true )
| ( $true
= ( X2 @ X6 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f379,plain,
( spl3_6
| ~ spl3_7
| ~ spl3_8 ),
inference(avatar_split_clause,[status(thm)],[f378,f137,f133,f96]) ).
thf(f378,plain,
( ! [X0: $i] :
( ( $true
= ( cN @ X0 ) )
| ( $true
!= ( cODD @ X0 ) ) )
| ~ spl3_7
| ~ spl3_8 ),
inference(subsumption_resolution,[status(thm)],[f377,f134]) ).
thf(f134,plain,
( ( $true
= ( cN @ ( sK1 @ cN @ cN ) ) )
| ~ spl3_7 ),
inference(avatar_component_clause,[status(thm)],[f133]) ).
thf(f377,plain,
( ! [X0: $i] :
( ( $true
!= ( cODD @ X0 ) )
| ( $true
!= ( cN @ ( sK1 @ cN @ cN ) ) )
| ( $true
= ( cN @ X0 ) ) )
| ~ spl3_8 ),
inference(subsumption_resolution,[status(thm)],[f306,f139]) ).
thf(f139,plain,
( ( $true
= ( cN @ ( sK2 @ cN @ cN ) ) )
| ~ spl3_8 ),
inference(avatar_component_clause,[status(thm)],[f137]) ).
thf(f306,plain,
! [X0: $i] :
( ( $true
= ( cN @ X0 ) )
| ( $true
!= ( cN @ ( sK2 @ cN @ cN ) ) )
| ( $true
!= ( cODD @ X0 ) )
| ( $true
!= ( cN @ ( sK1 @ cN @ cN ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f304]) ).
thf(f304,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( cODD @ X0 ) )
| ( $true
= ( cN @ X0 ) )
| ( $true
!= ( cN @ ( sK1 @ cN @ cN ) ) )
| ( $true
!= ( cN @ ( sK2 @ cN @ cN ) ) ) ),
inference(superposition,[status(thm)],[f226,f21]) ).
thf(f226,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
!= ( X0 @ ( cS @ ( sK2 @ cN @ X0 ) ) ) )
| ( $true
!= ( cODD @ X1 ) )
| ( $true
= ( X0 @ X1 ) )
| ( $true
!= ( cN @ ( sK1 @ cN @ X0 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f215,f24]) ).
thf(f215,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
!= ( cN @ ( sK1 @ cN @ X0 ) ) )
| ( $true
!= ( X0 @ ( cS @ ( sK2 @ cN @ X0 ) ) ) )
| ( ( cN @ c0 )
!= $true )
| ( $true
= ( X0 @ X1 ) )
| ( $true
!= ( cODD @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f206]) ).
thf(f206,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
!= ( cN @ ( sK1 @ cN @ X0 ) ) )
| ( $true
!= ( cODD @ X1 ) )
| ( ( cN @ c0 )
!= $true )
| ( $true
= ( X0 @ X1 ) )
| ( $true != $true )
| ( $true
!= ( X0 @ ( cS @ ( sK2 @ cN @ X0 ) ) ) ) ),
inference(superposition,[status(thm)],[f18,f21]) ).
thf(f18,plain,
! [X2: $i > $o,X3: $i > $o,X6: $i] :
( ( $true
!= ( X3 @ ( cS @ ( sK1 @ X3 @ X2 ) ) ) )
| ( $true
!= ( X3 @ c0 ) )
| ( ( cODD @ X6 )
!= $true )
| ( $true
= ( X2 @ X6 ) )
| ( ( X2 @ ( cS @ ( sK2 @ X3 @ X2 ) ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f376,plain,
( ~ spl3_7
| spl3_8
| ~ spl3_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f375]) ).
thf(f375,plain,
( $false
| ~ spl3_7
| spl3_8
| ~ spl3_11 ),
inference(subsumption_resolution,[status(thm)],[f370,f134]) ).
thf(f370,plain,
( ( $true
!= ( cN @ ( sK1 @ cN @ cN ) ) )
| spl3_8
| ~ spl3_11 ),
inference(trivial_inequality_removal,[status(thm)],[f365]) ).
thf(f365,plain,
( ( $true != $true )
| ( $true
!= ( cN @ ( sK1 @ cN @ cN ) ) )
| spl3_8
| ~ spl3_11 ),
inference(superposition,[status(thm)],[f138,f165]) ).
thf(f165,plain,
( ! [X0: $i > $o] :
( ( $true
= ( cN @ ( sK2 @ cN @ X0 ) ) )
| ( $true
!= ( cN @ ( sK1 @ cN @ X0 ) ) ) )
| ~ spl3_11 ),
inference(avatar_component_clause,[status(thm)],[f164]) ).
thf(f164,definition,
( spl3_11
<=> ! [X0: $i > $o] :
( ( $true
!= ( cN @ ( sK1 @ cN @ X0 ) ) )
| ( $true
= ( cN @ ( sK2 @ cN @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_11])],[avatar_definition]) ).
thf(f351,plain,
( ~ spl3_8
| ~ spl3_7
| ~ spl3_17 ),
inference(avatar_split_clause,[status(thm)],[f348,f254,f133,f137]) ).
thf(f254,definition,
( spl3_17
<=> ! [X0: $i > $o] :
( ( $true
!= ( X0 @ ( cS @ ( sK2 @ cN @ X0 ) ) ) )
| ( $true
!= ( cN @ ( sK1 @ cN @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_17])],[avatar_definition]) ).
thf(f348,plain,
( ( $true
!= ( cN @ ( sK2 @ cN @ cN ) ) )
| ~ spl3_7
| ~ spl3_17 ),
inference(subsumption_resolution,[status(thm)],[f294,f134]) ).
thf(f294,plain,
( ( $true
!= ( cN @ ( sK1 @ cN @ cN ) ) )
| ( $true
!= ( cN @ ( sK2 @ cN @ cN ) ) )
| ~ spl3_17 ),
inference(trivial_inequality_removal,[status(thm)],[f291]) ).
thf(f291,plain,
( ( $true != $true )
| ( $true
!= ( cN @ ( sK1 @ cN @ cN ) ) )
| ( $true
!= ( cN @ ( sK2 @ cN @ cN ) ) )
| ~ spl3_17 ),
inference(superposition,[status(thm)],[f255,f21]) ).
thf(f255,plain,
( ! [X0: $i > $o] :
( ( $true
!= ( X0 @ ( cS @ ( sK2 @ cN @ X0 ) ) ) )
| ( $true
!= ( cN @ ( sK1 @ cN @ X0 ) ) ) )
| ~ spl3_17 ),
inference(avatar_component_clause,[status(thm)],[f254]) ).
thf(f326,plain,
( spl3_10
| spl3_7
| ~ spl3_8 ),
inference(avatar_split_clause,[status(thm)],[f325,f137,f133,f161]) ).
thf(f161,definition,
( spl3_10
<=> ! [X1: $i] :
( ( $true
!= ( cEVEN @ X1 ) )
| ( ( cN @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl3_10])],[avatar_definition]) ).
thf(f325,plain,
( ! [X0: $i] :
( ( ( cEVEN @ X0 )
!= $true )
| ( $true
= ( cN @ X0 ) ) )
| spl3_7
| ~ spl3_8 ),
inference(subsumption_resolution,[status(thm)],[f324,f24]) ).
thf(f324,plain,
( ! [X0: $i] :
( ( $true
= ( cN @ X0 ) )
| ( ( cN @ c0 )
!= $true )
| ( ( cEVEN @ X0 )
!= $true ) )
| spl3_7
| ~ spl3_8 ),
inference(subsumption_resolution,[status(thm)],[f319,f139]) ).
thf(f319,plain,
( ! [X0: $i] :
( ( ( cEVEN @ X0 )
!= $true )
| ( $true
= ( cN @ X0 ) )
| ( $true
!= ( cN @ ( sK2 @ cN @ cN ) ) )
| ( ( cN @ c0 )
!= $true ) )
| spl3_7 ),
inference(trivial_inequality_removal,[status(thm)],[f317]) ).
thf(f317,plain,
( ! [X0: $i] :
( ( $true
= ( cN @ X0 ) )
| ( $true != $true )
| ( ( cEVEN @ X0 )
!= $true )
| ( $true
!= ( cN @ ( sK2 @ cN @ cN ) ) )
| ( ( cN @ c0 )
!= $true ) )
| spl3_7 ),
inference(superposition,[status(thm)],[f135,f112]) ).
thf(f112,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( cN @ ( sK1 @ X0 @ cN ) ) )
| ( ( X0 @ c0 )
!= $true )
| ( $true
= ( X0 @ X1 ) )
| ( $true
!= ( cN @ ( sK2 @ X0 @ cN ) ) )
| ( $true
!= ( cEVEN @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f108]) ).
thf(f108,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
!= ( cN @ ( sK2 @ X0 @ cN ) ) )
| ( $true
!= ( cEVEN @ X1 ) )
| ( $true != $true )
| ( $true
= ( cN @ ( sK1 @ X0 @ cN ) ) )
| ( ( X0 @ c0 )
!= $true )
| ( $true
= ( X0 @ X1 ) ) ),
inference(superposition,[status(thm)],[f16,f21]) ).
thf(f16,plain,
! [X2: $i > $o,X3: $i > $o,X5: $i] :
( ( ( X2 @ ( cS @ ( sK2 @ X3 @ X2 ) ) )
!= $true )
| ( $true
= ( X2 @ ( sK1 @ X3 @ X2 ) ) )
| ( ( X3 @ X5 )
= $true )
| ( $true
!= ( X3 @ c0 ) )
| ( ( cEVEN @ X5 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f286,plain,
( spl3_10
| spl3_7
| spl3_8 ),
inference(avatar_split_clause,[status(thm)],[f285,f137,f133,f161]) ).
thf(f285,plain,
( ! [X0: $i] :
( ( $true
= ( cN @ X0 ) )
| ( ( cEVEN @ X0 )
!= $true ) )
| spl3_7
| spl3_8 ),
inference(subsumption_resolution,[status(thm)],[f284,f135]) ).
thf(f284,plain,
( ! [X0: $i] :
( ( $true
= ( cN @ ( sK1 @ cN @ cN ) ) )
| ( $true
= ( cN @ X0 ) )
| ( ( cEVEN @ X0 )
!= $true ) )
| spl3_8 ),
inference(subsumption_resolution,[status(thm)],[f282,f24]) ).
thf(f282,plain,
( ! [X0: $i] :
( ( ( cN @ c0 )
!= $true )
| ( $true
= ( cN @ ( sK1 @ cN @ cN ) ) )
| ( $true
= ( cN @ X0 ) )
| ( ( cEVEN @ X0 )
!= $true ) )
| spl3_8 ),
inference(trivial_inequality_removal,[status(thm)],[f278]) ).
thf(f278,plain,
( ! [X0: $i] :
( ( $true
= ( cN @ ( sK1 @ cN @ cN ) ) )
| ( ( cEVEN @ X0 )
!= $true )
| ( $true != $true )
| ( ( cN @ c0 )
!= $true )
| ( $true
= ( cN @ X0 ) ) )
| spl3_8 ),
inference(superposition,[status(thm)],[f138,f15]) ).
thf(f15,plain,
! [X2: $i > $o,X3: $i > $o,X5: $i] :
( ( $true
= ( X3 @ ( sK2 @ X3 @ X2 ) ) )
| ( ( X3 @ X5 )
= $true )
| ( $true
= ( X2 @ ( sK1 @ X3 @ X2 ) ) )
| ( ( cEVEN @ X5 )
!= $true )
| ( $true
!= ( X3 @ c0 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f262,plain,
( ~ spl3_8
| ~ spl3_5
| spl3_7 ),
inference(avatar_split_clause,[status(thm)],[f261,f133,f93,f137]) ).
thf(f93,definition,
( spl3_5
<=> ! [X0: $i > $o] :
( ( $true
= ( cN @ ( sK1 @ X0 @ cN ) ) )
| ( $true
!= ( cN @ ( sK2 @ X0 @ cN ) ) )
| ( ( X0 @ c0 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f261,plain,
( ( $true
!= ( cN @ ( sK2 @ cN @ cN ) ) )
| ~ spl3_5
| spl3_7 ),
inference(subsumption_resolution,[status(thm)],[f259,f24]) ).
thf(f259,plain,
( ( $true
!= ( cN @ ( sK2 @ cN @ cN ) ) )
| ( ( cN @ c0 )
!= $true )
| ~ spl3_5
| spl3_7 ),
inference(trivial_inequality_removal,[status(thm)],[f257]) ).
thf(f257,plain,
( ( $true != $true )
| ( ( cN @ c0 )
!= $true )
| ( $true
!= ( cN @ ( sK2 @ cN @ cN ) ) )
| ~ spl3_5
| spl3_7 ),
inference(superposition,[status(thm)],[f135,f94]) ).
thf(f94,plain,
( ! [X0: $i > $o] :
( ( $true
= ( cN @ ( sK1 @ X0 @ cN ) ) )
| ( $true
!= ( cN @ ( sK2 @ X0 @ cN ) ) )
| ( ( X0 @ c0 )
!= $true ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f93]) ).
thf(f256,plain,
( spl3_17
| spl3_10 ),
inference(avatar_split_clause,[status(thm)],[f252,f161,f254]) ).
thf(f252,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
!= ( cEVEN @ X1 ) )
| ( ( cN @ X1 )
= $true )
| ( $true
!= ( X0 @ ( cS @ ( sK2 @ cN @ X0 ) ) ) )
| ( $true
!= ( cN @ ( sK1 @ cN @ X0 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f234,f24]) ).
thf(f234,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
!= ( X0 @ ( cS @ ( sK2 @ cN @ X0 ) ) ) )
| ( ( cN @ c0 )
!= $true )
| ( $true
!= ( cN @ ( sK1 @ cN @ X0 ) ) )
| ( ( cN @ X1 )
= $true )
| ( $true
!= ( cEVEN @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f232]) ).
thf(f232,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
!= ( cEVEN @ X1 ) )
| ( $true != $true )
| ( ( cN @ c0 )
!= $true )
| ( ( cN @ X1 )
= $true )
| ( $true
!= ( X0 @ ( cS @ ( sK2 @ cN @ X0 ) ) ) )
| ( $true
!= ( cN @ ( sK1 @ cN @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f20,f21]) ).
thf(f20,plain,
! [X2: $i > $o,X3: $i > $o,X5: $i] :
( ( $true
!= ( X3 @ ( cS @ ( sK1 @ X3 @ X2 ) ) ) )
| ( ( X2 @ ( cS @ ( sK2 @ X3 @ X2 ) ) )
!= $true )
| ( ( X3 @ X5 )
= $true )
| ( $true
!= ( X3 @ c0 ) )
| ( ( cEVEN @ X5 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f201,plain,
( ~ spl3_2
| ~ spl3_6 ),
inference(avatar_split_clause,[status(thm)],[f188,f96,f30]) ).
thf(f30,definition,
( spl3_2
<=> ( $true
= ( cODD @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f188,plain,
( ( $true
!= ( cODD @ sK0 ) )
| ~ spl3_6 ),
inference(trivial_inequality_removal,[status(thm)],[f183]) ).
thf(f183,plain,
( ( $true
!= ( cODD @ sK0 ) )
| ( $true != $true )
| ~ spl3_6 ),
inference(superposition,[status(thm)],[f23,f97]) ).
thf(f97,plain,
( ! [X1: $i] :
( ( ( cN @ X1 )
= $true )
| ( $true
!= ( cODD @ X1 ) ) )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f96]) ).
thf(f23,plain,
( $true
!= ( cN @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f181,plain,
( ~ spl3_1
| ~ spl3_10 ),
inference(avatar_split_clause,[status(thm)],[f174,f161,f26]) ).
thf(f26,definition,
( spl3_1
<=> ( $true
= ( cEVEN @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f174,plain,
( ( $true
!= ( cEVEN @ sK0 ) )
| ~ spl3_10 ),
inference(trivial_inequality_removal,[status(thm)],[f167]) ).
thf(f167,plain,
( ( $true
!= ( cEVEN @ sK0 ) )
| ( $true != $true )
| ~ spl3_10 ),
inference(superposition,[status(thm)],[f23,f162]) ).
thf(f162,plain,
( ! [X1: $i] :
( ( ( cN @ X1 )
= $true )
| ( $true
!= ( cEVEN @ X1 ) ) )
| ~ spl3_10 ),
inference(avatar_component_clause,[status(thm)],[f161]) ).
thf(f166,plain,
( spl3_10
| spl3_11 ),
inference(avatar_split_clause,[status(thm)],[f159,f164,f161]) ).
thf(f159,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
!= ( cN @ ( sK1 @ cN @ X0 ) ) )
| ( $true
!= ( cEVEN @ X1 ) )
| ( ( cN @ X1 )
= $true )
| ( $true
= ( cN @ ( sK2 @ cN @ X0 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f156,f24]) ).
thf(f156,plain,
! [X0: $i > $o,X1: $i] :
( ( ( cN @ X1 )
= $true )
| ( $true
!= ( cN @ ( sK1 @ cN @ X0 ) ) )
| ( $true
= ( cN @ ( sK2 @ cN @ X0 ) ) )
| ( ( cN @ c0 )
!= $true )
| ( $true
!= ( cEVEN @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f148]) ).
thf(f148,plain,
! [X0: $i > $o,X1: $i] :
( ( $true != $true )
| ( $true
!= ( cN @ ( sK1 @ cN @ X0 ) ) )
| ( ( cN @ X1 )
= $true )
| ( ( cN @ c0 )
!= $true )
| ( $true
= ( cN @ ( sK2 @ cN @ X0 ) ) )
| ( $true
!= ( cEVEN @ X1 ) ) ),
inference(superposition,[status(thm)],[f19,f21]) ).
thf(f19,plain,
! [X2: $i > $o,X3: $i > $o,X5: $i] :
( ( $true
!= ( X3 @ ( cS @ ( sK1 @ X3 @ X2 ) ) ) )
| ( $true
= ( X3 @ ( sK2 @ X3 @ X2 ) ) )
| ( $true
!= ( X3 @ c0 ) )
| ( ( cEVEN @ X5 )
!= $true )
| ( ( X3 @ X5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f98,plain,
( spl3_5
| spl3_6 ),
inference(avatar_split_clause,[status(thm)],[f87,f96,f93]) ).
thf(f87,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( cN @ ( sK1 @ X0 @ cN ) ) )
| ( ( X0 @ c0 )
!= $true )
| ( ( cN @ X1 )
= $true )
| ( $true
!= ( cODD @ X1 ) )
| ( $true
!= ( cN @ ( sK2 @ X0 @ cN ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( cN @ ( sK1 @ X0 @ cN ) ) )
| ( $true
!= ( cN @ ( sK2 @ X0 @ cN ) ) )
| ( ( X0 @ c0 )
!= $true )
| ( $true
!= ( cODD @ X1 ) )
| ( ( cN @ X1 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f14,f21]) ).
thf(f14,plain,
! [X2: $i > $o,X3: $i > $o,X6: $i] :
( ( ( X2 @ ( cS @ ( sK2 @ X3 @ X2 ) ) )
!= $true )
| ( ( cODD @ X6 )
!= $true )
| ( $true
!= ( X3 @ c0 ) )
| ( $true
= ( X2 @ X6 ) )
| ( $true
= ( X2 @ ( sK1 @ X3 @ X2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f33,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f22,f30,f26]) ).
thf(f22,plain,
( ( $true
= ( cEVEN @ sK0 ) )
| ( $true
= ( cODD @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM824^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.32 % Computer : n006.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue Feb 24 11:14:45 EST 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.44 ---- Original DTF file ---
% 0.17/0.44 thf(spec,logic,$$dhol).
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 % File : NUM824^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.44 % Domain : Number Theory (Induction on naturals)
% 0.17/0.44 % Problem : TPS problem from IND-THMS
% 0.17/0.44 % Version : Especial.
% 0.17/0.44 % English :
% 0.17/0.44
% 0.17/0.44 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.44 % Source : [Bro09]
% 0.17/0.44 % Names : tps_1001 [Bro09]
% 0.17/0.44
% 0.17/0.44 % Status : Theorem
% 0.17/0.44 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.0
% 0.17/0.44 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.17/0.44 % Number of atoms : 8 ( 0 equ; 0 cnn)
% 0.17/0.44 % Maximal formula atoms : 8 ( 8 avg)
% 0.17/0.44 % Number of connectives : 32 ( 0 ~; 1 |; 5 &; 18 @)
% 0.17/0.44 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.17/0.44 % Maximal formula depth : 12 ( 12 avg)
% 0.17/0.44 % Number of types : 2 ( 0 usr)
% 0.17/0.44 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.17/0.44 % Number of symbols : 5 ( 5 usr; 1 con; 0-1 aty)
% 0.17/0.44 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.17/0.44 % SPC : TH0_THM_NEQ_NAR
% 0.17/0.44
% 0.17/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.44 % :
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 thf(cN,type,
% 0.17/0.44 cN: $i > $o ).
% 0.17/0.44
% 0.17/0.44 thf(cODD,type,
% 0.17/0.44 cODD: $i > $o ).
% 0.17/0.44
% 0.17/0.44 thf(cEVEN,type,
% 0.17/0.44 cEVEN: $i > $o ).
% 0.17/0.44
% 0.17/0.44 thf(cS,type,
% 0.17/0.44 cS: $i > $i ).
% 0.17/0.44
% 0.17/0.44 thf(c0,type,
% 0.17/0.44 c0: $i ).
% 0.17/0.44
% 0.17/0.44 thf(cTHM623_pme,conjecture,
% 0.17/0.44 ( ( ! [Xp: $i > $o,Xq: $i > $o] :
% 0.17/0.44 ( ( ( Xp @ c0 )
% 0.17/0.44 & ! [Xu: $i] :
% 0.17/0.45 ( ( Xp @ Xu )
% 0.17/0.45 => ( Xq @ ( cS @ Xu ) ) )
% 0.17/0.45 & ! [Xv: $i] :
% 0.17/0.45 ( ( Xq @ Xv )
% 0.17/0.45 => ( Xp @ ( cS @ Xv ) ) ) )
% 0.17/0.45 => ( ! [Xx: $i] :
% 0.17/0.45 ( ( cEVEN @ Xx )
% 0.17/0.45 => ( Xp @ Xx ) )
% 0.17/0.45 & ! [Xx: $i] :
% 0.17/0.45 ( ( cODD @ Xx )
% 0.17/0.45 => ( Xq @ Xx ) ) ) )
% 0.17/0.45 & ( cN @ c0 )
% 0.17/0.45 & ! [Xn: $i] :
% 0.17/0.45 ( ( cN @ Xn )
% 0.17/0.45 => ( cN @ ( cS @ Xn ) ) ) )
% 0.17/0.45 => ! [Xm: $i] :
% 0.17/0.45 ( ( ( cEVEN @ Xm )
% 0.17/0.45 | ( cODD @ Xm ) )
% 0.17/0.45 => ( cN @ Xm ) ) ) ).
% 0.17/0.45
% 0.17/0.45 %------------------------------------------------------------------------------
% 0.17/0.45 ------------------------
% 1.51/1.23 ---- Embedded in THF ---
% 1.51/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.23 %%% Generated on Tue Feb 24 11:14:46 EST 2026
% 1.51/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.23 %%% Logic specification used:
% 1.51/1.23 %%% thf(spec, logic, $$dhol).
% 1.51/1.23
% 1.51/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.8aGlDTHdDd/DTF2DTF15126.p
% See solution above
% 1.51/1.23 ------------------------
% 1.51/1.24 ---- Cleaned THF ---
% 1.51/1.24 thf(cN,type,
% 1.51/1.24 cN: $i > $o ).
% 1.51/1.24
% 1.51/1.24 thf(cODD,type,
% 1.51/1.24 cODD: $i > $o ).
% 1.51/1.24
% 1.51/1.24 thf(cEVEN,type,
% 1.51/1.24 cEVEN: $i > $o ).
% 1.51/1.24
% 1.51/1.24 thf(cS,type,
% 1.51/1.24 cS: $i > $i ).
% 1.51/1.24
% 1.51/1.24 thf(c0,type,
% 1.51/1.24 c0: $i ).
% 1.51/1.24
% 1.51/1.24 thf(cTHM623_pme,conjecture,
% 1.51/1.24 ( ( ! [Xp: $i > $o,Xq: $i > $o] :
% 1.51/1.24 ( ( ( Xp @ c0 )
% 1.51/1.24 & ! [Xu: $i] :
% 1.51/1.24 ( ( Xp @ Xu )
% 1.51/1.24 => ( Xq @ ( cS @ Xu ) ) )
% 1.51/1.24 & ! [Xv: $i] :
% 1.51/1.24 ( ( Xq @ Xv )
% 1.51/1.24 => ( Xp @ ( cS @ Xv ) ) ) )
% 1.51/1.24 => ( ! [Xx: $i] :
% 1.51/1.24 ( ( cEVEN @ Xx )
% 1.51/1.24 => ( Xp @ Xx ) )
% 1.51/1.24 & ! [Xx: $i] :
% 1.51/1.24 ( ( cODD @ Xx )
% 1.51/1.24 => ( Xq @ Xx ) ) ) )
% 1.51/1.24 & ( cN @ c0 )
% 1.51/1.24 & ! [Xn: $i] :
% 1.51/1.24 ( ( cN @ Xn )
% 1.51/1.24 => ( cN @ ( cS @ Xn ) ) ) )
% 1.51/1.24 => ! [Xm: $i] :
% 1.51/1.24 ( ( ( cEVEN @ Xm )
% 1.51/1.24 | ( cODD @ Xm ) )
% 1.51/1.24 => ( cN @ Xm ) ) ) ).
% 1.51/1.24 ------------------------
% 1.51/1.26 % (15361)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15126 for (3000ds/2Mi)
% 1.51/1.26 % (15361)Instruction limit reached!
% 1.51/1.26 % (15361)------------------------------
% 1.51/1.26 % (15361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.26 % (15361)Termination reason: Unknown
% 1.51/1.26 % (15361)Termination phase: Saturation
% 1.51/1.26
% 1.51/1.26 % (15361)Memory used [KB]: 5500
% 1.51/1.26 % (15361)Time elapsed: 0.003 s
% 1.51/1.26 % (15361)Instructions burned: 3 (million)
% 1.51/1.26 % (15361)------------------------------
% 1.51/1.26 % (15361)------------------------------
% 1.51/1.26 % (15358)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15126 for (3000ds/183Mi)
% 1.51/1.26 % (15359)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_15126 for (3000ds/4Mi)
% 1.51/1.26 % (15360)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_15126 for (3000ds/27Mi)
% 1.51/1.26 % (15362)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_15126 for (3000ds/2Mi)
% 1.51/1.26 % (15363)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_15126 for (3000ds/275Mi)
% 1.51/1.26 % (15364)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15126 for (3000ds/18Mi)
% 1.51/1.26 % (15362)Instruction limit reached!
% 1.51/1.26 % (15362)------------------------------
% 1.51/1.26 % (15362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.26 % (15362)Termination reason: Unknown
% 1.51/1.26 % (15362)Termination phase: Property scanning
% 1.51/1.26
% 1.51/1.26 % (15362)Memory used [KB]: 895
% 1.51/1.26 % (15362)Time elapsed: 0.003 s
% 1.51/1.26 % (15362)Instructions burned: 2 (million)
% 1.51/1.26 % (15362)------------------------------
% 1.51/1.26 % (15362)------------------------------
% 1.51/1.27 % (15359)Instruction limit reached!
% 1.51/1.27 % (15359)------------------------------
% 1.51/1.27 % (15359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.27 % (15359)Termination reason: Unknown
% 1.51/1.27 % (15359)Termination phase: Saturation
% 1.51/1.27
% 1.51/1.27 % (15359)Memory used [KB]: 5500
% 1.51/1.27 % (15359)Time elapsed: 0.005 s
% 1.51/1.27 % (15359)Instructions burned: 4 (million)
% 1.51/1.27 % (15359)------------------------------
% 1.51/1.27 % (15359)------------------------------
% 1.51/1.27 % (15365)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15126 for (2999ds/3Mi)
% 1.51/1.27 % (15365)Instruction limit reached!
% 1.51/1.27 % (15365)------------------------------
% 1.51/1.27 % (15365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.27 % (15365)Termination reason: Unknown
% 1.51/1.27 % (15365)Termination phase: Saturation
% 1.51/1.27
% 1.51/1.27 % (15365)Memory used [KB]: 5500
% 1.51/1.27 % (15365)Time elapsed: 0.003 s
% 1.51/1.27 % (15365)Instructions burned: 4 (million)
% 1.51/1.27 % (15365)------------------------------
% 1.51/1.27 % (15365)------------------------------
% 1.51/1.27 % (15364)Instruction limit reached!
% 1.51/1.27 % (15364)------------------------------
% 1.51/1.27 % (15364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.27 % (15364)Termination reason: Unknown
% 1.51/1.27 % (15364)Termination phase: Saturation
% 1.51/1.27
% 1.51/1.27 % (15364)Memory used [KB]: 5628
% 1.51/1.27 % (15364)Time elapsed: 0.013 s
% 1.51/1.27 % (15364)Instructions burned: 18 (million)
% 1.51/1.27 % (15364)------------------------------
% 1.51/1.27 % (15364)------------------------------
% 1.51/1.28 % (15368)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_15126 for (2999ds/3Mi)
% 1.51/1.28 % (15360)Instruction limit reached!
% 1.51/1.28 % (15360)------------------------------
% 1.51/1.28 % (15360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.28 % (15360)Termination reason: Unknown
% 1.51/1.28 % (15360)Termination phase: Saturation
% 1.51/1.28
% 1.51/1.28 % (15360)Memory used [KB]: 5628
% 1.51/1.28 % (15360)Time elapsed: 0.019 s
% 1.51/1.28 % (15360)Instructions burned: 27 (million)
% 1.51/1.28 % (15360)------------------------------
% 1.51/1.28 % (15360)------------------------------
% 1.51/1.28 % (15368)Instruction limit reached!
% 1.51/1.28 % (15368)------------------------------
% 1.51/1.28 % (15368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.28 % (15368)Termination reason: Unknown
% 1.51/1.28 % (15368)Termination phase: Saturation
% 1.51/1.28
% 1.51/1.28 % (15368)Memory used [KB]: 5500
% 1.51/1.28 % (15368)Time elapsed: 0.003 s
% 1.51/1.28 % (15368)Instructions burned: 3 (million)
% 1.51/1.28 % (15368)------------------------------
% 1.51/1.28 % (15368)------------------------------
% 1.51/1.28 % (15366)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_15126 for (2999ds/37Mi)
% 1.51/1.28 % (15367)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_15126 for (2999ds/15Mi)
% 1.51/1.29 % (15367)Instruction limit reached!
% 1.51/1.29 % (15367)------------------------------
% 1.51/1.29 % (15367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.29 % (15367)Termination reason: Unknown
% 1.51/1.29 % (15367)Termination phase: Saturation
% 1.51/1.29
% 1.51/1.29 % (15367)Memory used [KB]: 5628
% 1.51/1.29 % (15367)Time elapsed: 0.010 s
% 1.51/1.29 % (15367)Instructions burned: 17 (million)
% 1.51/1.29 % (15367)------------------------------
% 1.51/1.29 % (15367)------------------------------
% 1.51/1.29 % (15371)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_15126 for (2999ds/16Mi)
% 1.51/1.29 % (15369)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_15126 for (2999ds/1041Mi)
% 1.51/1.30 % (15371)Instruction limit reached!
% 1.51/1.30 % (15371)------------------------------
% 1.51/1.30 % (15371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.30 % (15371)Termination reason: Unknown
% 1.51/1.30 % (15371)Termination phase: Saturation
% 1.51/1.30
% 1.51/1.30 % (15371)Memory used [KB]: 5628
% 1.51/1.30 % (15371)Time elapsed: 0.007 s
% 1.51/1.30 % (15371)Instructions burned: 16 (million)
% 1.51/1.30 % (15371)------------------------------
% 1.51/1.30 % (15371)------------------------------
% 1.56/1.30 % (15370)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_15126 for (2999ds/7Mi)
% 1.56/1.30 % (15372)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_15126 for (2999ds/3Mi)
% 1.56/1.30 % (15372)Instruction limit reached!
% 1.56/1.30 % (15372)------------------------------
% 1.56/1.30 % (15372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.30 % (15372)Termination reason: Unknown
% 1.56/1.30 % (15372)Termination phase: Twee Goal Transformation
% 1.56/1.30
% 1.56/1.30 % (15372)Memory used [KB]: 1023
% 1.56/1.30 % (15372)Time elapsed: 0.002 s
% 1.56/1.30 % (15372)Instructions burned: 3 (million)
% 1.56/1.30 % (15372)------------------------------
% 1.56/1.30 % (15372)------------------------------
% 1.56/1.30 % (15370)Instruction limit reached!
% 1.56/1.30 % (15370)------------------------------
% 1.56/1.30 % (15370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.30 % (15370)Termination reason: Unknown
% 1.56/1.30 % (15370)Termination phase: Saturation
% 1.56/1.30
% 1.56/1.30 % (15370)Memory used [KB]: 1023
% 1.56/1.30 % (15370)Time elapsed: 0.007 s
% 1.56/1.30 % (15370)Instructions burned: 8 (million)
% 1.56/1.30 % (15370)------------------------------
% 1.56/1.30 % (15370)------------------------------
% 1.56/1.30 % (15366)Instruction limit reached!
% 1.56/1.30 % (15366)------------------------------
% 1.56/1.30 % (15366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.30 % (15366)Termination reason: Unknown
% 1.56/1.30 % (15366)Termination phase: Saturation
% 1.56/1.30
% 1.56/1.30 % (15366)Memory used [KB]: 5628
% 1.56/1.30 % (15366)Time elapsed: 0.024 s
% 1.56/1.30 % (15366)Instructions burned: 38 (million)
% 1.56/1.30 % (15366)------------------------------
% 1.56/1.30 % (15366)------------------------------
% 1.56/1.31 % (15373)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_15126 for (2999ds/3Mi)
% 1.56/1.31 % (15363)First to succeed.
% 1.56/1.31 % (15373)Instruction limit reached!
% 1.56/1.31 % (15373)------------------------------
% 1.56/1.31 % (15373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.31 % (15373)Termination reason: Unknown
% 1.56/1.31 % (15373)Termination phase: Saturation
% 1.56/1.31
% 1.56/1.31 % (15373)Memory used [KB]: 1023
% 1.56/1.31 % (15373)Time elapsed: 0.003 s
% 1.56/1.31 % (15373)Instructions burned: 4 (million)
% 1.56/1.31 % (15373)------------------------------
% 1.56/1.31 % (15373)------------------------------
% 1.56/1.31 % (15363)Refutation found. Thanks to Tanya!
% 1.56/1.31 % SZS status Theorem for DTF2THF_15126
% 1.56/1.31 % SZS output start Proof for DTF2THF_15126
% 1.56/1.31 thf(func_def_0, type, cN: $i > $o).
% 1.56/1.31 thf(func_def_1, type, cODD: $i > $o).
% 1.56/1.31 thf(func_def_2, type, cEVEN: $i > $o).
% 1.56/1.31 thf(func_def_3, type, cS: $i > $i).
% 1.56/1.31 thf(func_def_9, type, sK1: ($i > $o) > ($i > $o) > $i).
% 1.56/1.31 thf(func_def_10, type, sK2: ($i > $o) > ($i > $o) > $i).
% 1.56/1.31 thf(func_def_13, type, ph4: !>[X0: $tType]:(X0)).
% 1.56/1.31 thf(f437,plain,(
% 1.56/1.31 $false),
% 1.56/1.31 inference(avatar_sat_refutation,[status(thm)],[f33,f98,f166,f181,f201,f256,f262,f286,f326,f351,f376,f379,f429,f430])).
% 1.56/1.31 thf(f430,plain,(
% 1.56/1.31 ~spl3_7 | spl3_6 | spl3_8),
% 1.56/1.31 inference(avatar_split_clause,[status(thm)],[f422,f137,f96,f133])).
% 1.56/1.31 thf(f133,definition,(
% 1.56/1.31 spl3_7 <=> ($true = (cN @ (sK1 @ cN @ cN)))),
% 1.56/1.31 introduced(definition,[new_symbols(naming,[spl3_7])],[avatar_definition])).
% 1.56/1.31 thf(f96,definition,(
% 1.56/1.31 spl3_6 <=> ! [X1 : $i] : (((cN @ X1) = $true) | ($true != (cODD @ X1)))),
% 1.56/1.31 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.56/1.31 thf(f137,definition,(
% 1.56/1.31 spl3_8 <=> ($true = (cN @ (sK2 @ cN @ cN)))),
% 1.56/1.31 introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition])).
% 1.56/1.31 thf(f422,plain,(
% 1.56/1.31 ( ! [X0 : $i] : (($true = (cN @ X0)) | ($true != (cN @ (sK1 @ cN @ cN))) | ($true != (cODD @ X0))) ) | spl3_8),
% 1.56/1.31 inference(trivial_inequality_removal,[status(thm)],[f418])).
% 1.56/1.31 thf(f418,plain,(
% 1.56/1.31 ( ! [X0 : $i] : (($true != $true) | ($true != (cN @ (sK1 @ cN @ cN))) | ($true = (cN @ X0)) | ($true != (cODD @ X0))) ) | spl3_8),
% 1.56/1.31 inference(superposition,[status(thm)],[f138,f129])).
% 1.56/1.31 thf(f129,plain,(
% 1.56/1.31 ( ! [X0 : $i > $o,X1 : $i] : (($true = (cN @ (sK2 @ cN @ X0))) | ($true != (cODD @ X1)) | ($true != (cN @ (sK1 @ cN @ X0))) | ($true = (X0 @ X1))) )),
% 1.56/1.31 inference(subsumption_resolution,[status(thm)],[f124,f24])).
% 1.56/1.31 thf(f24,plain,(
% 1.56/1.31 ((cN @ c0) = $true)),
% 1.56/1.31 inference(cnf_transformation,[status(thm)],[f12])).
% 1.56/1.31 thf(f12,plain,(
% 1.56/1.31 ((cN @ c0) = $true) & (($true != (cN @ sK0)) & (($true = (cEVEN @ sK0)) | ($true = (cODD @ sK0)))) & ! [X1 : $i] : (((cN @ X1) != $true) | ($true = (cN @ (cS @ X1)))) & ! [X2 : $i > $o,X3 : $i > $o] : ((($true != (X3 @ (cS @ (sK1 @ X3 @ X2)))) & ($true = (X2 @ (sK1 @ X3 @ X2)))) | (! [X5 : $i] : (((X3 @ X5) = $true) | ((cEVEN @ X5) != $true)) & ! [X6 : $i] : (($true = (X2 @ X6)) | ((cODD @ X6) != $true))) | (((X2 @ (cS @ (sK2 @ X3 @ X2))) != $true) & ($true = (X3 @ (sK2 @ X3 @ X2)))) | ($true != (X3 @ c0)))),
% 1.56/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9])).
% 1.56/1.31 thf(f9,plain,(
% 1.56/1.31 ? [X0 : $i] : (($true != (cN @ X0)) & (((cEVEN @ X0) = $true) | ($true = (cODD @ X0)))) => (($true != (cN @ sK0)) & (($true = (cEVEN @ sK0)) | ($true = (cODD @ sK0))))),
% 1.56/1.31 introduced(definition,[],[choice_axiom])).
% 1.56/1.31 thf(f10,plain,(
% 1.56/1.31 ! [X2 : $i > $o,X3 : $i > $o] : (? [X4 : $i] : (($true != (X3 @ (cS @ X4))) & ($true = (X2 @ X4))) => (($true != (X3 @ (cS @ (sK1 @ X3 @ X2)))) & ($true = (X2 @ (sK1 @ X3 @ X2)))))),
% 1.56/1.31 introduced(definition,[],[choice_axiom])).
% 1.56/1.31 thf(f11,plain,(
% 1.56/1.31 ! [X2 : $i > $o,X3 : $i > $o] : (? [X7 : $i] : (((X2 @ (cS @ X7)) != $true) & ((X3 @ X7) = $true)) => (((X2 @ (cS @ (sK2 @ X3 @ X2))) != $true) & ($true = (X3 @ (sK2 @ X3 @ X2)))))),
% 1.56/1.31 introduced(definition,[],[choice_axiom])).
% 1.56/1.31 thf(f8,plain,(
% 1.56/1.31 ((cN @ c0) = $true) & ? [X0 : $i] : (($true != (cN @ X0)) & (((cEVEN @ X0) = $true) | ($true = (cODD @ X0)))) & ! [X1 : $i] : (((cN @ X1) != $true) | ($true = (cN @ (cS @ X1)))) & ! [X2 : $i > $o,X3 : $i > $o] : (? [X4 : $i] : (($true != (X3 @ (cS @ X4))) & ($true = (X2 @ X4))) | (! [X5 : $i] : (((X3 @ X5) = $true) | ((cEVEN @ X5) != $true)) & ! [X6 : $i] : (($true = (X2 @ X6)) | ((cODD @ X6) != $true))) | ? [X7 : $i] : (((X2 @ (cS @ X7)) != $true) & ((X3 @ X7) = $true)) | ($true != (X3 @ c0)))),
% 1.56/1.31 inference(rectify,[status(thm)],[f7])).
% 1.56/1.31 thf(f7,plain,(
% 1.56/1.31 ((cN @ c0) = $true) & ? [X7 : $i] : (((cN @ X7) != $true) & (($true = (cEVEN @ X7)) | ($true = (cODD @ X7)))) & ! [X0 : $i] : (($true != (cN @ X0)) | ($true = (cN @ (cS @ X0)))) & ! [X2 : $i > $o,X1 : $i > $o] : (? [X4 : $i] : (($true != (X1 @ (cS @ X4))) & ($true = (X2 @ X4))) | (! [X5 : $i] : (($true = (X1 @ X5)) | ((cEVEN @ X5) != $true)) & ! [X6 : $i] : (($true = (X2 @ X6)) | ((cODD @ X6) != $true))) | ? [X3 : $i] : (($true != (X2 @ (cS @ X3))) & ((X1 @ X3) = $true)) | ($true != (X1 @ c0)))),
% 1.56/1.31 inference(flattening,[status(thm)],[f6])).
% 1.56/1.31 thf(f6,plain,(
% 1.56/1.31 ? [X7 : $i] : (((cN @ X7) != $true) & (($true = (cEVEN @ X7)) | ($true = (cODD @ X7)))) & (! [X0 : $i] : (($true != (cN @ X0)) | ($true = (cN @ (cS @ X0)))) & ((cN @ c0) = $true) & ! [X2 : $i > $o,X1 : $i > $o] : ((! [X5 : $i] : (($true = (X1 @ X5)) | ((cEVEN @ X5) != $true)) & ! [X6 : $i] : (($true = (X2 @ X6)) | ((cODD @ X6) != $true))) | (? [X4 : $i] : (($true != (X1 @ (cS @ X4))) & ($true = (X2 @ X4))) | ? [X3 : $i] : (($true != (X2 @ (cS @ X3))) & ((X1 @ X3) = $true)) | ($true != (X1 @ c0)))))),
% 1.56/1.31 inference(ennf_transformation,[status(thm)],[f5])).
% 1.56/1.31 thf(f5,plain,(
% 1.56/1.31 ~((! [X0 : $i] : (($true = (cN @ X0)) => ($true = (cN @ (cS @ X0)))) & ((cN @ c0) = $true) & ! [X2 : $i > $o,X1 : $i > $o] : ((! [X4 : $i] : (($true = (X2 @ X4)) => ($true = (X1 @ (cS @ X4)))) & ! [X3 : $i] : (((X1 @ X3) = $true) => ($true = (X2 @ (cS @ X3)))) & ($true = (X1 @ c0))) => (! [X5 : $i] : (((cEVEN @ X5) = $true) => ($true = (X1 @ X5))) & ! [X6 : $i] : (((cODD @ X6) = $true) => ($true = (X2 @ X6)))))) => ! [X7 : $i] : ((($true = (cEVEN @ X7)) | ($true = (cODD @ X7))) => ((cN @ X7) = $true)))),
% 1.56/1.31 inference(fool_elimination,[status(thm)],[f4])).
% 1.56/1.31 thf(f4,plain,(
% 1.56/1.31 ~((! [X0 : $i] : ((cN @ X0) => (cN @ (cS @ X0))) & (cN @ c0) & ! [X1 : $i > $o,X2 : $i > $o] : (((X1 @ c0) & ! [X3 : $i] : ((X1 @ X3) => (X2 @ (cS @ X3))) & ! [X4 : $i] : ((X2 @ X4) => (X1 @ (cS @ X4)))) => (! [X5 : $i] : ((cEVEN @ X5) => (X1 @ X5)) & ! [X6 : $i] : ((cODD @ X6) => (X2 @ X6))))) => ! [X7 : $i] : (((cEVEN @ X7) | (cODD @ X7)) => (cN @ X7)))),
% 1.56/1.31 inference(rectify,[status(thm)],[f2])).
% 1.56/1.31 thf(f2,negated_conjecture,(
% 1.56/1.31 ~((! [X5 : $i] : ((cN @ X5) => (cN @ (cS @ X5))) & (cN @ c0) & ! [X0 : $i > $o,X1 : $i > $o] : (((X0 @ c0) & ! [X2 : $i] : ((X0 @ X2) => (X1 @ (cS @ X2))) & ! [X3 : $i] : ((X1 @ X3) => (X0 @ (cS @ X3)))) => (! [X4 : $i] : ((cEVEN @ X4) => (X0 @ X4)) & ! [X4 : $i] : ((cODD @ X4) => (X1 @ X4))))) => ! [X6 : $i] : (((cEVEN @ X6) | (cODD @ X6)) => (cN @ X6)))),
% 1.56/1.31 inference(negated_conjecture,[status(cth)],[f1])).
% 1.56/1.31 thf(f1,conjecture,(
% 1.56/1.31 (! [X5 : $i] : ((cN @ X5) => (cN @ (cS @ X5))) & (cN @ c0) & ! [X0 : $i > $o,X1 : $i > $o] : (((X0 @ c0) & ! [X2 : $i] : ((X0 @ X2) => (X1 @ (cS @ X2))) & ! [X3 : $i] : ((X1 @ X3) => (X0 @ (cS @ X3)))) => (! [X4 : $i] : ((cEVEN @ X4) => (X0 @ X4)) & ! [X4 : $i] : ((cODD @ X4) => (X1 @ X4))))) => ! [X6 : $i] : (((cEVEN @ X6) | (cODD @ X6)) => (cN @ X6))),
% 1.56/1.31 file('/export/starexec/sandbox2/tmp/tmp.8aGlDTHdDd/DTF2THF_15126.p',cTHM623_pme)).
% 1.56/1.31 thf(f124,plain,(
% 1.56/1.31 ( ! [X0 : $i > $o,X1 : $i] : (($true = (cN @ (sK2 @ cN @ X0))) | ($true != (cODD @ X1)) | ($true = (X0 @ X1)) | ((cN @ c0) != $true) | ($true != (cN @ (sK1 @ cN @ X0)))) )),
% 1.56/1.31 inference(trivial_inequality_removal,[status(thm)],[f119])).
% 1.56/1.31 thf(f119,plain,(
% 1.56/1.31 ( ! [X0 : $i > $o,X1 : $i] : (($true = (X0 @ X1)) | ($true != $true) | ((cN @ c0) != $true) | ($true != (cODD @ X1)) | ($true != (cN @ (sK1 @ cN @ X0))) | ($true = (cN @ (sK2 @ cN @ X0)))) )),
% 1.56/1.31 inference(superposition,[status(thm)],[f17,f21])).
% 1.56/1.31 thf(f21,plain,(
% 1.56/1.31 ( ! [X1 : $i] : (($true = (cN @ (cS @ X1))) | ((cN @ X1) != $true)) )),
% 1.56/1.31 inference(cnf_transformation,[status(thm)],[f12])).
% 1.56/1.31 thf(f17,plain,(
% 1.56/1.31 ( ! [X2 : $i > $o,X3 : $i > $o,X6 : $i] : (($true != (X3 @ (cS @ (sK1 @ X3 @ X2)))) | ((cODD @ X6) != $true) | ($true = (X3 @ (sK2 @ X3 @ X2))) | ($true != (X3 @ c0)) | ($true = (X2 @ X6))) )),
% 1.56/1.31 inference(cnf_transformation,[status(thm)],[f12])).
% 1.56/1.31 thf(f138,plain,(
% 1.56/1.31 ($true != (cN @ (sK2 @ cN @ cN))) | spl3_8),
% 1.56/1.31 inference(avatar_component_clause,[status(thm)],[f137])).
% 1.56/1.31 thf(f429,plain,(
% 1.56/1.31 spl3_6 | spl3_7 | spl3_8),
% 1.56/1.31 inference(avatar_split_clause,[status(thm)],[f428,f137,f133,f96])).
% 1.56/1.31 thf(f428,plain,(
% 1.56/1.31 ( ! [X0 : $i] : (($true = (cN @ X0)) | ($true != (cODD @ X0))) ) | (spl3_7 | spl3_8)),
% 1.56/1.31 inference(subsumption_resolution,[status(thm)],[f427,f24])).
% 1.56/1.31 thf(f427,plain,(
% 1.56/1.31 ( ! [X0 : $i] : (($true != (cODD @ X0)) | ((cN @ c0) != $true) | ($true = (cN @ X0))) ) | (spl3_7 | spl3_8)),
% 1.56/1.31 inference(subsumption_resolution,[status(thm)],[f426,f135])).
% 1.56/1.31 thf(f135,plain,(
% 1.56/1.31 ($true != (cN @ (sK1 @ cN @ cN))) | spl3_7),
% 1.56/1.31 inference(avatar_component_clause,[status(thm)],[f133])).
% 1.56/1.31 thf(f426,plain,(
% 1.56/1.31 ( ! [X0 : $i] : (($true != (cODD @ X0)) | ($true = (cN @ (sK1 @ cN @ cN))) | ($true = (cN @ X0)) | ((cN @ c0) != $true)) ) | spl3_8),
% 1.56/1.31 inference(trivial_inequality_removal,[status(thm)],[f421])).
% 1.56/1.31 thf(f421,plain,(
% 1.56/1.31 ( ! [X0 : $i] : (($true != (cODD @ X0)) | ((cN @ c0) != $true) | ($true = (cN @ X0)) | ($true != $true) | ($true = (cN @ (sK1 @ cN @ cN)))) ) | spl3_8),
% 1.56/1.31 inference(superposition,[status(thm)],[f138,f13])).
% 1.56/1.31 thf(f13,plain,(
% 1.56/1.31 ( ! [X2 : $i > $o,X3 : $i > $o,X6 : $i] : (($true = (X3 @ (sK2 @ X3 @ X2))) | ($true != (X3 @ c0)) | ($true = (X2 @ (sK1 @ X3 @ X2))) | ((cODD @ X6) != $true) | ($true = (X2 @ X6))) )),
% 1.56/1.31 inference(cnf_transformation,[status(thm)],[f12])).
% 1.56/1.31 thf(f379,plain,(
% 1.56/1.31 spl3_6 | ~spl3_7 | ~spl3_8),
% 1.56/1.31 inference(avatar_split_clause,[status(thm)],[f378,f137,f133,f96])).
% 1.56/1.31 thf(f378,plain,(
% 1.56/1.31 ( ! [X0 : $i] : (($true = (cN @ X0)) | ($true != (cODD @ X0))) ) | (~spl3_7 | ~spl3_8)),
% 1.56/1.31 inference(subsumption_resolution,[status(thm)],[f377,f134])).
% 1.56/1.31 thf(f134,plain,(
% 1.56/1.31 ($true = (cN @ (sK1 @ cN @ cN))) | ~spl3_7),
% 1.56/1.31 inference(avatar_component_clause,[status(thm)],[f133])).
% 1.56/1.31 thf(f377,plain,(
% 1.56/1.31 ( ! [X0 : $i] : (($true != (cODD @ X0)) | ($true != (cN @ (sK1 @ cN @ cN))) | ($true = (cN @ X0))) ) | ~spl3_8),
% 1.56/1.31 inference(subsumption_resolution,[status(thm)],[f306,f139])).
% 1.56/1.31 thf(f139,plain,(
% 1.56/1.31 ($true = (cN @ (sK2 @ cN @ cN))) | ~spl3_8),
% 1.56/1.31 inference(avatar_component_clause,[status(thm)],[f137])).
% 1.56/1.31 thf(f306,plain,(
% 1.56/1.31 ( ! [X0 : $i] : (($true = (cN @ X0)) | ($true != (cN @ (sK2 @ cN @ cN))) | ($true != (cODD @ X0)) | ($true != (cN @ (sK1 @ cN @ cN)))) )),
% 1.56/1.31 inference(trivial_inequality_removal,[status(thm)],[f304])).
% 1.56/1.31 thf(f304,plain,(
% 1.56/1.31 ( ! [X0 : $i] : (($true != $true) | ($true != (cODD @ X0)) | ($true = (cN @ X0)) | ($true != (cN @ (sK1 @ cN @ cN))) | ($true != (cN @ (sK2 @ cN @ cN)))) )),
% 1.56/1.31 inference(superposition,[status(thm)],[f226,f21])).
% 1.56/1.31 thf(f226,plain,(
% 1.56/1.31 ( ! [X0 : $i > $o,X1 : $i] : (($true != (X0 @ (cS @ (sK2 @ cN @ X0)))) | ($true != (cODD @ X1)) | ($true = (X0 @ X1)) | ($true != (cN @ (sK1 @ cN @ X0)))) )),
% 1.56/1.31 inference(subsumption_resolution,[status(thm)],[f215,f24])).
% 1.56/1.31 thf(f215,plain,(
% 1.56/1.31 ( ! [X0 : $i > $o,X1 : $i] : (($true != (cN @ (sK1 @ cN @ X0))) | ($true != (X0 @ (cS @ (sK2 @ cN @ X0)))) | ((cN @ c0) != $true) | ($true = (X0 @ X1)) | ($true != (cODD @ X1))) )),
% 1.56/1.31 inference(trivial_inequality_removal,[status(thm)],[f206])).
% 1.56/1.31 thf(f206,plain,(
% 1.56/1.31 ( ! [X0 : $i > $o,X1 : $i] : (($true != (cN @ (sK1 @ cN @ X0))) | ($true != (cODD @ X1)) | ((cN @ c0) != $true) | ($true = (X0 @ X1)) | ($true != $true) | ($true != (X0 @ (cS @ (sK2 @ cN @ X0))))) )),
% 1.56/1.31 inference(superposition,[status(thm)],[f18,f21])).
% 1.56/1.31 thf(f18,plain,(
% 1.56/1.31 ( ! [X2 : $i > $o,X3 : $i > $o,X6 : $i] : (($true != (X3 @ (cS @ (sK1 @ X3 @ X2)))) | ($true != (X3 @ c0)) | ((cODD @ X6) != $true) | ($true = (X2 @ X6)) | ((X2 @ (cS @ (sK2 @ X3 @ X2))) != $true)) )),
% 1.56/1.31 inference(cnf_transformation,[status(thm)],[f12])).
% 1.56/1.31 thf(f376,plain,(
% 1.56/1.31 ~spl3_7 | spl3_8 | ~spl3_11),
% 1.56/1.31 inference(avatar_contradiction_clause,[status(thm)],[f375])).
% 1.56/1.31 thf(f375,plain,(
% 1.56/1.31 $false | (~spl3_7 | spl3_8 | ~spl3_11)),
% 1.56/1.31 inference(subsumption_resolution,[status(thm)],[f370,f134])).
% 1.56/1.31 thf(f370,plain,(
% 1.56/1.31 ($true != (cN @ (sK1 @ cN @ cN))) | (spl3_8 | ~spl3_11)),
% 1.56/1.31 inference(trivial_inequality_removal,[status(thm)],[f365])).
% 1.56/1.31 thf(f365,plain,(
% 1.56/1.31 ($true != $true) | ($true != (cN @ (sK1 @ cN @ cN))) | (spl3_8 | ~spl3_11)),
% 1.56/1.31 inference(superposition,[status(thm)],[f138,f165])).
% 1.56/1.31 thf(f165,plain,(
% 1.56/1.31 ( ! [X0 : $i > $o] : (($true = (cN @ (sK2 @ cN @ X0))) | ($true != (cN @ (sK1 @ cN @ X0)))) ) | ~spl3_11),
% 1.56/1.31 inference(avatar_component_clause,[status(thm)],[f164])).
% 1.56/1.31 thf(f164,definition,(
% 1.56/1.31 spl3_11 <=> ! [X0 : $i > $o] : (($true != (cN @ (sK1 @ cN @ X0))) | ($true = (cN @ (sK2 @ cN @ X0))))),
% 1.56/1.31 introduced(definition,[new_symbols(naming,[spl3_11])],[avatar_definition])).
% 1.56/1.31 thf(f351,plain,(
% 1.56/1.31 ~spl3_8 | ~spl3_7 | ~spl3_17),
% 1.56/1.31 inference(avatar_split_clause,[status(thm)],[f348,f254,f133,f137])).
% 1.56/1.31 thf(f254,definition,(
% 1.56/1.31 spl3_17 <=> ! [X0 : $i > $o] : (($true != (X0 @ (cS @ (sK2 @ cN @ X0)))) | ($true != (cN @ (sK1 @ cN @ X0))))),
% 1.56/1.31 introduced(definition,[new_symbols(naming,[spl3_17])],[avatar_definition])).
% 1.56/1.31 thf(f348,plain,(
% 1.56/1.31 ($true != (cN @ (sK2 @ cN @ cN))) | (~spl3_7 | ~spl3_17)),
% 1.56/1.31 inference(subsumption_resolution,[status(thm)],[f294,f134])).
% 1.56/1.31 thf(f294,plain,(
% 1.56/1.31 ($true != (cN @ (sK1 @ cN @ cN))) | ($true != (cN @ (sK2 @ cN @ cN))) | ~spl3_17),
% 1.56/1.31 inference(trivial_inequality_removal,[status(thm)],[f291])).
% 1.56/1.31 thf(f291,plain,(
% 1.56/1.31 ($true != $true) | ($true != (cN @ (sK1 @ cN @ cN))) | ($true != (cN @ (sK2 @ cN @ cN))) | ~spl3_17),
% 1.56/1.31 inference(superposition,[status(thm)],[f255,f21])).
% 1.56/1.31 thf(f255,plain,(
% 1.56/1.31 ( ! [X0 : $i > $o] : (($true != (X0 @ (cS @ (sK2 @ cN @ X0)))) | ($true != (cN @ (sK1 @ cN @ X0)))) ) | ~spl3_17),
% 1.56/1.31 inference(avatar_component_clause,[status(thm)],[f254])).
% 1.56/1.31 thf(f326,plain,(
% 1.56/1.31 spl3_10 | spl3_7 | ~spl3_8),
% 1.56/1.31 inference(avatar_split_clause,[status(thm)],[f325,f137,f133,f161])).
% 1.56/1.31 thf(f161,definition,(
% 1.56/1.31 spl3_10 <=> ! [X1 : $i] : (($true != (cEVEN @ X1)) | ((cN @ X1) = $true))),
% 1.56/1.31 introduced(definition,[new_symbols(naming,[spl3_10])],[avatar_definition])).
% 1.56/1.31 thf(f325,plain,(
% 1.56/1.31 ( ! [X0 : $i] : (((cEVEN @ X0) != $true) | ($true = (cN @ X0))) ) | (spl3_7 | ~spl3_8)),
% 1.56/1.31 inference(subsumption_resolution,[status(thm)],[f324,f24])).
% 1.56/1.31 thf(f324,plain,(
% 1.56/1.31 ( ! [X0 : $i] : (($true = (cN @ X0)) | ((cN @ c0) != $true) | ((cEVEN @ X0) != $true)) ) | (spl3_7 | ~spl3_8)),
% 1.56/1.31 inference(subsumption_resolution,[status(thm)],[f319,f139])).
% 1.56/1.31 thf(f319,plain,(
% 1.56/1.31 ( ! [X0 : $i] : (((cEVEN @ X0) != $true) | ($true = (cN @ X0)) | ($true != (cN @ (sK2 @ cN @ cN))) | ((cN @ c0) != $true)) ) | spl3_7),
% 1.56/1.31 inference(trivial_inequality_removal,[status(thm)],[f317])).
% 1.56/1.31 thf(f317,plain,(
% 1.56/1.31 ( ! [X0 : $i] : (($true = (cN @ X0)) | ($true != $true) | ((cEVEN @ X0) != $true) | ($true != (cN @ (sK2 @ cN @ cN))) | ((cN @ c0) != $true)) ) | spl3_7),
% 1.56/1.31 inference(superposition,[status(thm)],[f135,f112])).
% 1.56/1.31 thf(f112,plain,(
% 1.56/1.31 ( ! [X0 : $i > $o,X1 : $i] : (($true = (cN @ (sK1 @ X0 @ cN))) | ((X0 @ c0) != $true) | ($true = (X0 @ X1)) | ($true != (cN @ (sK2 @ X0 @ cN))) | ($true != (cEVEN @ X1))) )),
% 1.56/1.31 inference(trivial_inequality_removal,[status(thm)],[f108])).
% 1.56/1.31 thf(f108,plain,(
% 1.56/1.31 ( ! [X0 : $i > $o,X1 : $i] : (($true != (cN @ (sK2 @ X0 @ cN))) | ($true != (cEVEN @ X1)) | ($true != $true) | ($true = (cN @ (sK1 @ X0 @ cN))) | ((X0 @ c0) != $true) | ($true = (X0 @ X1))) )),
% 1.56/1.31 inference(superposition,[status(thm)],[f16,f21])).
% 1.56/1.31 thf(f16,plain,(
% 1.56/1.31 ( ! [X2 : $i > $o,X3 : $i > $o,X5 : $i] : (((X2 @ (cS @ (sK2 @ X3 @ X2))) != $true) | ($true = (X2 @ (sK1 @ X3 @ X2))) | ((X3 @ X5) = $true) | ($true != (X3 @ c0)) | ((cEVEN @ X5) != $true)) )),
% 1.56/1.31 inference(cnf_transformation,[status(thm)],[f12])).
% 1.56/1.31 thf(f286,plain,(
% 1.56/1.31 spl3_10 | spl3_7 | spl3_8),
% 1.56/1.31 inference(avatar_split_clause,[status(thm)],[f285,f137,f133,f161])).
% 1.56/1.31 thf(f285,plain,(
% 1.56/1.31 ( ! [X0 : $i] : (($true = (cN @ X0)) | ((cEVEN @ X0) != $true)) ) | (spl3_7 | spl3_8)),
% 1.56/1.31 inference(subsumption_resolution,[status(thm)],[f284,f135])).
% 1.56/1.31 thf(f284,plain,(
% 1.56/1.31 ( ! [X0 : $i] : (($true = (cN @ (sK1 @ cN @ cN))) | ($true = (cN @ X0)) | ((cEVEN @ X0) != $true)) ) | spl3_8),
% 1.56/1.31 inference(subsumption_resolution,[status(thm)],[f282,f24])).
% 1.56/1.31 thf(f282,plain,(
% 1.56/1.31 ( ! [X0 : $i] : (((cN @ c0) != $true) | ($true = (cN @ (sK1 @ cN @ cN))) | ($true = (cN @ X0)) | ((cEVEN @ X0) != $true)) ) | spl3_8),
% 1.56/1.31 inference(trivial_inequality_removal,[status(thm)],[f278])).
% 1.56/1.31 thf(f278,plain,(
% 1.56/1.31 ( ! [X0 : $i] : (($true = (cN @ (sK1 @ cN @ cN))) | ((cEVEN @ X0) != $true) | ($true != $true) | ((cN @ c0) != $true) | ($true = (cN @ X0))) ) | spl3_8),
% 1.56/1.31 inference(superposition,[status(thm)],[f138,f15])).
% 1.56/1.31 thf(f15,plain,(
% 1.56/1.31 ( ! [X2 : $i > $o,X3 : $i > $o,X5 : $i] : (($true = (X3 @ (sK2 @ X3 @ X2))) | ((X3 @ X5) = $true) | ($true = (X2 @ (sK1 @ X3 @ X2))) | ((cEVEN @ X5) != $true) | ($true != (X3 @ c0))) )),
% 1.56/1.31 inference(cnf_transformation,[status(thm)],[f12])).
% 1.56/1.31 thf(f262,plain,(
% 1.56/1.31 ~spl3_8 | ~spl3_5 | spl3_7),
% 1.56/1.31 inference(avatar_split_clause,[status(thm)],[f261,f133,f93,f137])).
% 1.56/1.31 thf(f93,definition,(
% 1.56/1.31 spl3_5 <=> ! [X0 : $i > $o] : (($true = (cN @ (sK1 @ X0 @ cN))) | ($true != (cN @ (sK2 @ X0 @ cN))) | ((X0 @ c0) != $true))),
% 1.56/1.31 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.56/1.31 thf(f261,plain,(
% 1.56/1.31 ($true != (cN @ (sK2 @ cN @ cN))) | (~spl3_5 | spl3_7)),
% 1.56/1.31 inference(subsumption_resolution,[status(thm)],[f259,f24])).
% 1.56/1.31 thf(f259,plain,(
% 1.56/1.31 ($true != (cN @ (sK2 @ cN @ cN))) | ((cN @ c0) != $true) | (~spl3_5 | spl3_7)),
% 1.56/1.31 inference(trivial_inequality_removal,[status(thm)],[f257])).
% 1.56/1.31 thf(f257,plain,(
% 1.56/1.31 ($true != $true) | ((cN @ c0) != $true) | ($true != (cN @ (sK2 @ cN @ cN))) | (~spl3_5 | spl3_7)),
% 1.56/1.31 inference(superposition,[status(thm)],[f135,f94])).
% 1.56/1.31 thf(f94,plain,(
% 1.56/1.31 ( ! [X0 : $i > $o] : (($true = (cN @ (sK1 @ X0 @ cN))) | ($true != (cN @ (sK2 @ X0 @ cN))) | ((X0 @ c0) != $true)) ) | ~spl3_5),
% 1.56/1.31 inference(avatar_component_clause,[status(thm)],[f93])).
% 1.56/1.31 thf(f256,plain,(
% 1.56/1.31 spl3_17 | spl3_10),
% 1.56/1.31 inference(avatar_split_clause,[status(thm)],[f252,f161,f254])).
% 1.56/1.31 thf(f252,plain,(
% 1.56/1.31 ( ! [X0 : $i > $o,X1 : $i] : (($true != (cEVEN @ X1)) | ((cN @ X1) = $true) | ($true != (X0 @ (cS @ (sK2 @ cN @ X0)))) | ($true != (cN @ (sK1 @ cN @ X0)))) )),
% 1.56/1.31 inference(subsumption_resolution,[status(thm)],[f234,f24])).
% 1.56/1.31 thf(f234,plain,(
% 1.56/1.31 ( ! [X0 : $i > $o,X1 : $i] : (($true != (X0 @ (cS @ (sK2 @ cN @ X0)))) | ((cN @ c0) != $true) | ($true != (cN @ (sK1 @ cN @ X0))) | ((cN @ X1) = $true) | ($true != (cEVEN @ X1))) )),
% 1.56/1.31 inference(trivial_inequality_removal,[status(thm)],[f232])).
% 1.56/1.31 thf(f232,plain,(
% 1.56/1.31 ( ! [X0 : $i > $o,X1 : $i] : (($true != (cEVEN @ X1)) | ($true != $true) | ((cN @ c0) != $true) | ((cN @ X1) = $true) | ($true != (X0 @ (cS @ (sK2 @ cN @ X0)))) | ($true != (cN @ (sK1 @ cN @ X0)))) )),
% 1.56/1.31 inference(superposition,[status(thm)],[f20,f21])).
% 1.56/1.31 thf(f20,plain,(
% 1.56/1.31 ( ! [X2 : $i > $o,X3 : $i > $o,X5 : $i] : (($true != (X3 @ (cS @ (sK1 @ X3 @ X2)))) | ((X2 @ (cS @ (sK2 @ X3 @ X2))) != $true) | ((X3 @ X5) = $true) | ($true != (X3 @ c0)) | ((cEVEN @ X5) != $true)) )),
% 1.56/1.31 inference(cnf_transformation,[status(thm)],[f12])).
% 1.56/1.31 thf(f201,plain,(
% 1.56/1.31 ~spl3_2 | ~spl3_6),
% 1.56/1.31 inference(avatar_split_clause,[status(thm)],[f188,f96,f30])).
% 1.56/1.31 thf(f30,definition,(
% 1.56/1.31 spl3_2 <=> ($true = (cODD @ sK0))),
% 1.56/1.31 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.56/1.31 thf(f188,plain,(
% 1.56/1.31 ($true != (cODD @ sK0)) | ~spl3_6),
% 1.56/1.31 inference(trivial_inequality_removal,[status(thm)],[f183])).
% 1.56/1.31 thf(f183,plain,(
% 1.56/1.31 ($true != (cODD @ sK0)) | ($true != $true) | ~spl3_6),
% 1.56/1.31 inference(superposition,[status(thm)],[f23,f97])).
% 1.56/1.31 thf(f97,plain,(
% 1.56/1.31 ( ! [X1 : $i] : (((cN @ X1) = $true) | ($true != (cODD @ X1))) ) | ~spl3_6),
% 1.56/1.31 inference(avatar_component_clause,[status(thm)],[f96])).
% 1.56/1.31 thf(f23,plain,(
% 1.56/1.31 ($true != (cN @ sK0))),
% 1.56/1.31 inference(cnf_transformation,[status(thm)],[f12])).
% 1.56/1.31 thf(f181,plain,(
% 1.56/1.31 ~spl3_1 | ~spl3_10),
% 1.56/1.31 inference(avatar_split_clause,[status(thm)],[f174,f161,f26])).
% 1.56/1.31 thf(f26,definition,(
% 1.56/1.31 spl3_1 <=> ($true = (cEVEN @ sK0))),
% 1.56/1.31 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.56/1.31 thf(f174,plain,(
% 1.56/1.31 ($true != (cEVEN @ sK0)) | ~spl3_10),
% 1.56/1.31 inference(trivial_inequality_removal,[status(thm)],[f167])).
% 1.56/1.31 thf(f167,plain,(
% 1.56/1.31 ($true != (cEVEN @ sK0)) | ($true != $true) | ~spl3_10),
% 1.56/1.31 inference(superposition,[status(thm)],[f23,f162])).
% 1.56/1.31 thf(f162,plain,(
% 1.56/1.31 ( ! [X1 : $i] : (((cN @ X1) = $true) | ($true != (cEVEN @ X1))) ) | ~spl3_10),
% 1.56/1.31 inference(avatar_component_clause,[status(thm)],[f161])).
% 1.56/1.31 thf(f166,plain,(
% 1.56/1.31 spl3_10 | spl3_11),
% 1.56/1.31 inference(avatar_split_clause,[status(thm)],[f159,f164,f161])).
% 1.56/1.31 thf(f159,plain,(
% 1.56/1.31 ( ! [X0 : $i > $o,X1 : $i] : (($true != (cN @ (sK1 @ cN @ X0))) | ($true != (cEVEN @ X1)) | ((cN @ X1) = $true) | ($true = (cN @ (sK2 @ cN @ X0)))) )),
% 1.56/1.31 inference(subsumption_resolution,[status(thm)],[f156,f24])).
% 1.56/1.31 thf(f156,plain,(
% 1.56/1.31 ( ! [X0 : $i > $o,X1 : $i] : (((cN @ X1) = $true) | ($true != (cN @ (sK1 @ cN @ X0))) | ($true = (cN @ (sK2 @ cN @ X0))) | ((cN @ c0) != $true) | ($true != (cEVEN @ X1))) )),
% 1.56/1.31 inference(trivial_inequality_removal,[status(thm)],[f148])).
% 1.56/1.31 thf(f148,plain,(
% 1.56/1.31 ( ! [X0 : $i > $o,X1 : $i] : (($true != $true) | ($true != (cN @ (sK1 @ cN @ X0))) | ((cN @ X1) = $true) | ((cN @ c0) != $true) | ($true = (cN @ (sK2 @ cN @ X0))) | ($true != (cEVEN @ X1))) )),
% 1.56/1.31 inference(superposition,[status(thm)],[f19,f21])).
% 1.56/1.31 thf(f19,plain,(
% 1.56/1.31 ( ! [X2 : $i > $o,X3 : $i > $o,X5 : $i] : (($true != (X3 @ (cS @ (sK1 @ X3 @ X2)))) | ($true = (X3 @ (sK2 @ X3 @ X2))) | ($true != (X3 @ c0)) | ((cEVEN @ X5) != $true) | ((X3 @ X5) = $true)) )),
% 1.56/1.31 inference(cnf_transformation,[status(thm)],[f12])).
% 1.56/1.31 thf(f98,plain,(
% 1.56/1.31 spl3_5 | spl3_6),
% 1.56/1.31 inference(avatar_split_clause,[status(thm)],[f87,f96,f93])).
% 1.56/1.31 thf(f87,plain,(
% 1.56/1.31 ( ! [X0 : $i > $o,X1 : $i] : (($true = (cN @ (sK1 @ X0 @ cN))) | ((X0 @ c0) != $true) | ((cN @ X1) = $true) | ($true != (cODD @ X1)) | ($true != (cN @ (sK2 @ X0 @ cN)))) )),
% 1.56/1.31 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.56/1.31 thf(f79,plain,(
% 1.56/1.31 ( ! [X0 : $i > $o,X1 : $i] : (($true = (cN @ (sK1 @ X0 @ cN))) | ($true != (cN @ (sK2 @ X0 @ cN))) | ((X0 @ c0) != $true) | ($true != (cODD @ X1)) | ((cN @ X1) = $true) | ($true != $true)) )),
% 1.56/1.31 inference(superposition,[status(thm)],[f14,f21])).
% 1.56/1.31 thf(f14,plain,(
% 1.56/1.31 ( ! [X2 : $i > $o,X3 : $i > $o,X6 : $i] : (((X2 @ (cS @ (sK2 @ X3 @ X2))) != $true) | ((cODD @ X6) != $true) | ($true != (X3 @ c0)) | ($true = (X2 @ X6)) | ($true = (X2 @ (sK1 @ X3 @ X2)))) )),
% 1.56/1.31 inference(cnf_transformation,[status(thm)],[f12])).
% 1.56/1.31 thf(f33,plain,(
% 1.56/1.31 spl3_1 | spl3_2),
% 1.56/1.31 inference(avatar_split_clause,[status(thm)],[f22,f30,f26])).
% 1.56/1.31 thf(f22,plain,(
% 1.56/1.31 ($true = (cEVEN @ sK0)) | ($true = (cODD @ sK0))),
% 1.56/1.31 inference(cnf_transformation,[status(thm)],[f12])).
% 1.56/1.31 % SZS output end Proof for DTF2THF_15126
% 1.56/1.31 % (15363)------------------------------
% 1.56/1.31 % (15363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.31 % (15363)Termination reason: Refutation
% 1.56/1.31
% 1.56/1.31 % (15363)Memory used [KB]: 5756
% 1.56/1.31 % (15363)Time elapsed: 0.049 s
% 1.56/1.31 % (15363)Instructions burned: 68 (million)
% 1.56/1.31 % (15363)------------------------------
% 1.56/1.31 % (15363)------------------------------
% 1.56/1.31 % (15357)Success in time 0.057 s
%------------------------------------------------------------------------------