%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO113^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:46:38 AM UTC 2026
% Result : Theorem 0.08s 0.27s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of formulae : 105 ( 21 unt; 0 typ; 13 def)
% Number of atoms : 926 ( 214 equ; 0 cnn)
% Maximal formula atoms : 22 ( 8 avg)
% Number of connectives : 858 ( 153 ~; 155 |; 102 &; 409 @)
% ( 19 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 18 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 58 !; 10 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cNUMBER: $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(f1,conjecture,
( ( ( ( ( cNUMBER @ c0 )
& ( cNUMBER @ ( cS @ c0 ) )
& ! [X1: $i] :
( ( ( cNUMBER @ X1 )
& ( cNUMBER @ ( cS @ X1 ) ) )
=> ( ( cNUMBER @ ( cS @ X1 ) )
& ( cNUMBER @ ( cS @ ( cS @ X1 ) ) ) ) ) )
=> ! [X1: $i] :
( ( cNUMBER @ ( cS @ X1 ) )
& ( cNUMBER @ X1 ) ) )
& ( cODD @ ( cS @ c0 ) )
& ! [X0: $i] :
( ( ( cEVEN @ X0 )
| ( cODD @ X0 ) )
<=> ( cNUMBER @ X0 ) )
& ! [X0: $i] :
( ( cODD @ X0 )
=> ( cODD @ ( cS @ ( cS @ X0 ) ) ) )
& ( cEVEN @ c0 )
& ! [X0: $i] :
( ( cEVEN @ X0 )
=> ( cEVEN @ ( cS @ ( cS @ X0 ) ) ) ) )
=> ! [X0: $i] : ( cNUMBER @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM350) ).
thf(f2,negated_conjecture,
~ ( ( ( ( ( cNUMBER @ c0 )
& ( cNUMBER @ ( cS @ c0 ) )
& ! [X1: $i] :
( ( ( cNUMBER @ X1 )
& ( cNUMBER @ ( cS @ X1 ) ) )
=> ( ( cNUMBER @ ( cS @ X1 ) )
& ( cNUMBER @ ( cS @ ( cS @ X1 ) ) ) ) ) )
=> ! [X1: $i] :
( ( cNUMBER @ ( cS @ X1 ) )
& ( cNUMBER @ X1 ) ) )
& ( cODD @ ( cS @ c0 ) )
& ! [X0: $i] :
( ( ( cEVEN @ X0 )
| ( cODD @ X0 ) )
<=> ( cNUMBER @ X0 ) )
& ! [X0: $i] :
( ( cODD @ X0 )
=> ( cODD @ ( cS @ ( cS @ X0 ) ) ) )
& ( cEVEN @ c0 )
& ! [X0: $i] :
( ( cEVEN @ X0 )
=> ( cEVEN @ ( cS @ ( cS @ X0 ) ) ) ) )
=> ! [X0: $i] : ( cNUMBER @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( ( ( cNUMBER @ c0 )
& ( cNUMBER @ ( cS @ c0 ) )
& ! [X0: $i] :
( ( ( cNUMBER @ X0 )
& ( cNUMBER @ ( cS @ X0 ) ) )
=> ( ( cNUMBER @ ( cS @ X0 ) )
& ( cNUMBER @ ( cS @ ( cS @ X0 ) ) ) ) ) )
=> ! [X1: $i] :
( ( cNUMBER @ ( cS @ X1 ) )
& ( cNUMBER @ X1 ) ) )
& ( cODD @ ( cS @ c0 ) )
& ! [X2: $i] :
( ( ( cEVEN @ X2 )
| ( cODD @ X2 ) )
<=> ( cNUMBER @ X2 ) )
& ! [X3: $i] :
( ( cODD @ X3 )
=> ( cODD @ ( cS @ ( cS @ X3 ) ) ) )
& ( cEVEN @ c0 )
& ! [X4: $i] :
( ( cEVEN @ X4 )
=> ( cEVEN @ ( cS @ ( cS @ X4 ) ) ) ) )
=> ! [X5: $i] : ( cNUMBER @ X5 ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X4: $i] :
( ( ( cEVEN @ X4 )
= $true )
=> ( $true
= ( cEVEN @ ( cS @ ( cS @ X4 ) ) ) ) )
& ( ( ! [X0: $i] :
( ( ( ( cNUMBER @ X0 )
= $true )
& ( ( cNUMBER @ ( cS @ X0 ) )
= $true ) )
=> ( ( ( cNUMBER @ ( cS @ X0 ) )
= $true )
& ( ( cNUMBER @ ( cS @ ( cS @ X0 ) ) )
= $true ) ) )
& ( ( cNUMBER @ c0 )
= $true )
& ( ( cNUMBER @ ( cS @ c0 ) )
= $true ) )
=> ! [X1: $i] :
( ( ( cNUMBER @ ( cS @ X1 ) )
= $true )
& ( ( cNUMBER @ X1 )
= $true ) ) )
& ! [X2: $i] :
( ( ( ( cEVEN @ X2 )
= $true )
| ( ( cODD @ X2 )
= $true ) )
<=> ( ( cNUMBER @ X2 )
= $true ) )
& ( ( cODD @ ( cS @ c0 ) )
= $true )
& ! [X3: $i] :
( ( ( cODD @ X3 )
= $true )
=> ( ( cODD @ ( cS @ ( cS @ X3 ) ) )
= $true ) )
& ( ( cEVEN @ c0 )
= $true ) )
=> ! [X5: $i] :
( $true
= ( cNUMBER @ X5 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ? [X5: $i] :
( $true
!= ( cNUMBER @ X5 ) )
& ! [X4: $i] :
( ( ( cEVEN @ X4 )
!= $true )
| ( $true
= ( cEVEN @ ( cS @ ( cS @ X4 ) ) ) ) )
& ( ! [X1: $i] :
( ( ( cNUMBER @ ( cS @ X1 ) )
= $true )
& ( ( cNUMBER @ X1 )
= $true ) )
| ? [X0: $i] :
( ( ( ( cNUMBER @ ( cS @ X0 ) )
!= $true )
| ( ( cNUMBER @ ( cS @ ( cS @ X0 ) ) )
!= $true ) )
& ( ( cNUMBER @ X0 )
= $true )
& ( ( cNUMBER @ ( cS @ X0 ) )
= $true ) )
| ( ( cNUMBER @ c0 )
!= $true )
| ( ( cNUMBER @ ( cS @ c0 ) )
!= $true ) )
& ! [X2: $i] :
( ( ( ( cEVEN @ X2 )
= $true )
| ( ( cODD @ X2 )
= $true ) )
<=> ( ( cNUMBER @ X2 )
= $true ) )
& ( ( cODD @ ( cS @ c0 ) )
= $true )
& ! [X3: $i] :
( ( ( cODD @ ( cS @ ( cS @ X3 ) ) )
= $true )
| ( ( cODD @ X3 )
!= $true ) )
& ( ( cEVEN @ c0 )
= $true ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ! [X3: $i] :
( ( ( cODD @ ( cS @ ( cS @ X3 ) ) )
= $true )
| ( ( cODD @ X3 )
!= $true ) )
& ( ( cEVEN @ c0 )
= $true )
& ! [X4: $i] :
( ( ( cEVEN @ X4 )
!= $true )
| ( $true
= ( cEVEN @ ( cS @ ( cS @ X4 ) ) ) ) )
& ( ( ( cNUMBER @ c0 )
!= $true )
| ! [X1: $i] :
( ( ( cNUMBER @ ( cS @ X1 ) )
= $true )
& ( ( cNUMBER @ X1 )
= $true ) )
| ? [X0: $i] :
( ( ( cNUMBER @ X0 )
= $true )
& ( ( cNUMBER @ ( cS @ X0 ) )
= $true )
& ( ( ( cNUMBER @ ( cS @ X0 ) )
!= $true )
| ( ( cNUMBER @ ( cS @ ( cS @ X0 ) ) )
!= $true ) ) )
| ( ( cNUMBER @ ( cS @ c0 ) )
!= $true ) )
& ( ( cODD @ ( cS @ c0 ) )
= $true )
& ! [X2: $i] :
( ( ( ( cEVEN @ X2 )
= $true )
| ( ( cODD @ X2 )
= $true ) )
<=> ( ( cNUMBER @ X2 )
= $true ) )
& ? [X5: $i] :
( $true
!= ( cNUMBER @ X5 ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ! [X3: $i] :
( ( ( cODD @ ( cS @ ( cS @ X3 ) ) )
= $true )
| ( ( cODD @ X3 )
!= $true ) )
& ( ( cEVEN @ c0 )
= $true )
& ! [X4: $i] :
( ( ( cEVEN @ X4 )
!= $true )
| ( $true
= ( cEVEN @ ( cS @ ( cS @ X4 ) ) ) ) )
& ( ( ( cNUMBER @ c0 )
!= $true )
| ! [X1: $i] :
( ( ( cNUMBER @ ( cS @ X1 ) )
= $true )
& ( ( cNUMBER @ X1 )
= $true ) )
| ? [X0: $i] :
( ( ( cNUMBER @ X0 )
= $true )
& ( ( cNUMBER @ ( cS @ X0 ) )
= $true )
& ( ( ( cNUMBER @ ( cS @ X0 ) )
!= $true )
| ( ( cNUMBER @ ( cS @ ( cS @ X0 ) ) )
!= $true ) ) )
| ( ( cNUMBER @ ( cS @ c0 ) )
!= $true ) )
& ( ( cODD @ ( cS @ c0 ) )
= $true )
& ! [X2: $i] :
( ( ( ( cEVEN @ X2 )
= $true )
| ( ( cODD @ X2 )
= $true )
| ( ( cNUMBER @ X2 )
!= $true ) )
& ( ( ( cNUMBER @ X2 )
= $true )
| ( ( ( cEVEN @ X2 )
!= $true )
& ( ( cODD @ X2 )
!= $true ) ) ) )
& ? [X5: $i] :
( $true
!= ( cNUMBER @ X5 ) ) ),
inference(nnf_transformation,[],[f6]) ).
thf(f8,plain,
( ! [X3: $i] :
( ( ( cODD @ ( cS @ ( cS @ X3 ) ) )
= $true )
| ( ( cODD @ X3 )
!= $true ) )
& ( ( cEVEN @ c0 )
= $true )
& ! [X4: $i] :
( ( ( cEVEN @ X4 )
!= $true )
| ( $true
= ( cEVEN @ ( cS @ ( cS @ X4 ) ) ) ) )
& ( ( ( cNUMBER @ c0 )
!= $true )
| ! [X1: $i] :
( ( ( cNUMBER @ ( cS @ X1 ) )
= $true )
& ( ( cNUMBER @ X1 )
= $true ) )
| ? [X0: $i] :
( ( ( cNUMBER @ X0 )
= $true )
& ( ( cNUMBER @ ( cS @ X0 ) )
= $true )
& ( ( ( cNUMBER @ ( cS @ X0 ) )
!= $true )
| ( ( cNUMBER @ ( cS @ ( cS @ X0 ) ) )
!= $true ) ) )
| ( ( cNUMBER @ ( cS @ c0 ) )
!= $true ) )
& ( ( cODD @ ( cS @ c0 ) )
= $true )
& ! [X2: $i] :
( ( ( ( cEVEN @ X2 )
= $true )
| ( ( cODD @ X2 )
= $true )
| ( ( cNUMBER @ X2 )
!= $true ) )
& ( ( ( cNUMBER @ X2 )
= $true )
| ( ( ( cEVEN @ X2 )
!= $true )
& ( ( cODD @ X2 )
!= $true ) ) ) )
& ? [X5: $i] :
( $true
!= ( cNUMBER @ X5 ) ) ),
inference(flattening,[],[f7]) ).
thf(f9,plain,
( ! [X0: $i] :
( ( ( cODD @ ( cS @ ( cS @ X0 ) ) )
= $true )
| ( ( cODD @ X0 )
!= $true ) )
& ( ( cEVEN @ c0 )
= $true )
& ! [X1: $i] :
( ( ( cEVEN @ X1 )
!= $true )
| ( $true
= ( cEVEN @ ( cS @ ( cS @ X1 ) ) ) ) )
& ( ( ( cNUMBER @ c0 )
!= $true )
| ! [X2: $i] :
( ( $true
= ( cNUMBER @ ( cS @ X2 ) ) )
& ( ( cNUMBER @ X2 )
= $true ) )
| ? [X3: $i] :
( ( $true
= ( cNUMBER @ X3 ) )
& ( $true
= ( cNUMBER @ ( cS @ X3 ) ) )
& ( ( $true
!= ( cNUMBER @ ( cS @ X3 ) ) )
| ( ( cNUMBER @ ( cS @ ( cS @ X3 ) ) )
!= $true ) ) )
| ( ( cNUMBER @ ( cS @ c0 ) )
!= $true ) )
& ( ( cODD @ ( cS @ c0 ) )
= $true )
& ! [X4: $i] :
( ( ( ( cEVEN @ X4 )
= $true )
| ( ( cODD @ X4 )
= $true )
| ( ( cNUMBER @ X4 )
!= $true ) )
& ( ( ( cNUMBER @ X4 )
= $true )
| ( ( ( cEVEN @ X4 )
!= $true )
& ( ( cODD @ X4 )
!= $true ) ) ) )
& ? [X5: $i] :
( $true
!= ( cNUMBER @ X5 ) ) ),
inference(rectify,[],[f8]) ).
thf(f10,plain,
( ! [X0: $i] :
( ( ( cODD @ ( cS @ ( cS @ X0 ) ) )
= $true )
| ( ( cODD @ X0 )
!= $true ) )
& ( ( cEVEN @ c0 )
= $true )
& ! [X1: $i] :
( ( ( cEVEN @ X1 )
!= $true )
| ( $true
= ( cEVEN @ ( cS @ ( cS @ X1 ) ) ) ) )
& ( ( ( cNUMBER @ c0 )
!= $true )
| ! [X2: $i] :
( ( $true
= ( cNUMBER @ ( cS @ X2 ) ) )
& ( ( cNUMBER @ X2 )
= $true ) )
| ( ( ( cNUMBER @ sK0 )
= $true )
& ( $true
= ( cNUMBER @ ( cS @ sK0 ) ) )
& ( ( $true
!= ( cNUMBER @ ( cS @ sK0 ) ) )
| ( ( cNUMBER @ ( cS @ ( cS @ sK0 ) ) )
!= $true ) ) )
| ( ( cNUMBER @ ( cS @ c0 ) )
!= $true ) )
& ( ( cODD @ ( cS @ c0 ) )
= $true )
& ! [X4: $i] :
( ( ( ( cEVEN @ X4 )
= $true )
| ( ( cODD @ X4 )
= $true )
| ( ( cNUMBER @ X4 )
!= $true ) )
& ( ( ( cNUMBER @ X4 )
= $true )
| ( ( ( cEVEN @ X4 )
!= $true )
& ( ( cODD @ X4 )
!= $true ) ) ) )
& ( $true
!= ( cNUMBER @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0),skolemize(X5,sK1)],[f9]) ).
thf(f11,plain,
( $true
!= ( cNUMBER @ sK1 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f12,plain,
! [X4: $i] :
( ( ( cNUMBER @ X4 )
= $true )
| ( ( cODD @ X4 )
!= $true ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f13,plain,
! [X4: $i] :
( ( ( cNUMBER @ X4 )
= $true )
| ( ( cEVEN @ X4 )
!= $true ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f14,plain,
! [X4: $i] :
( ( ( cEVEN @ X4 )
= $true )
| ( ( cNUMBER @ X4 )
!= $true )
| ( ( cODD @ X4 )
= $true ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f15,plain,
( ( cODD @ ( cS @ c0 ) )
= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f16,plain,
! [X2: $i] :
( ( ( cNUMBER @ X2 )
= $true )
| ( ( cNUMBER @ c0 )
!= $true )
| ( ( cNUMBER @ ( cS @ c0 ) )
!= $true )
| ( ( cNUMBER @ ( cS @ ( cS @ sK0 ) ) )
!= $true )
| ( $true
!= ( cNUMBER @ ( cS @ sK0 ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f17,plain,
! [X2: $i] :
( ( ( cNUMBER @ c0 )
!= $true )
| ( ( cNUMBER @ ( cS @ c0 ) )
!= $true )
| ( $true
= ( cNUMBER @ ( cS @ sK0 ) ) )
| ( ( cNUMBER @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f18,plain,
! [X2: $i] :
( ( ( cNUMBER @ sK0 )
= $true )
| ( ( cNUMBER @ c0 )
!= $true )
| ( ( cNUMBER @ X2 )
= $true )
| ( ( cNUMBER @ ( cS @ c0 ) )
!= $true ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f22,plain,
! [X1: $i] :
( ( $true
= ( cEVEN @ ( cS @ ( cS @ X1 ) ) ) )
| ( ( cEVEN @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f23,plain,
( ( cEVEN @ c0 )
= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f24,plain,
! [X0: $i] :
( ( ( cODD @ ( cS @ ( cS @ X0 ) ) )
= $true )
| ( ( cODD @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f27,definition,
( spl2_1
<=> ( ( cNUMBER @ ( cS @ c0 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f29,plain,
( ( ( cNUMBER @ ( cS @ c0 ) )
!= $true )
| spl2_1 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f31,definition,
( spl2_2
<=> ( $true
= ( cNUMBER @ ( cS @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f38,definition,
( spl2_4
<=> ( ( cNUMBER @ c0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f40,plain,
( ( ( cNUMBER @ c0 )
!= $true )
| spl2_4 ),
inference(avatar_component_clause,[],[f38]) ).
thf(f43,definition,
( spl2_5
<=> ( ( cEVEN @ c0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
thf(f45,plain,
( ( ( cEVEN @ c0 )
= $true )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f43]) ).
thf(f46,plain,
spl2_5,
inference(avatar_split_clause,[],[f23,f43]) ).
thf(f48,definition,
( spl2_6
<=> ( ( cNUMBER @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
thf(f50,plain,
( ( ( cNUMBER @ sK0 )
= $true )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f53,definition,
( spl2_7
<=> ( ( cNUMBER @ ( cS @ ( cS @ sK0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
thf(f55,plain,
( ( ( cNUMBER @ ( cS @ ( cS @ sK0 ) ) )
!= $true )
| spl2_7 ),
inference(avatar_component_clause,[],[f53]) ).
thf(f58,definition,
( spl2_8
<=> ( ( cODD @ ( cS @ c0 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition]) ).
thf(f60,plain,
( ( ( cODD @ ( cS @ c0 ) )
= $true )
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f58]) ).
thf(f61,plain,
spl2_8,
inference(avatar_split_clause,[],[f15,f58]) ).
thf(f63,definition,
( spl2_9
<=> ! [X2: $i] :
( ( cNUMBER @ X2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
thf(f64,plain,
( ! [X2: $i] :
( ( cNUMBER @ X2 )
= $true )
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f63]) ).
thf(f65,plain,
( ~ spl2_7
| ~ spl2_1
| ~ spl2_2
| spl2_9
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f16,f38,f63,f31,f27,f53]) ).
thf(f67,definition,
( spl2_10
<=> ( $true
= ( cNUMBER @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
thf(f69,plain,
( ( $true
!= ( cNUMBER @ sK1 ) )
| spl2_10 ),
inference(avatar_component_clause,[],[f67]) ).
thf(f70,plain,
~ spl2_10,
inference(avatar_split_clause,[],[f11,f67]) ).
thf(f71,plain,
( ~ spl2_1
| spl2_2
| spl2_9
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f17,f38,f63,f31,f27]) ).
thf(f72,plain,
( ~ spl2_1
| spl2_6
| ~ spl2_4
| spl2_9 ),
inference(avatar_split_clause,[],[f18,f63,f38,f48,f27]) ).
thf(f88,plain,
( ( $true != $true )
| ( ( cODD @ ( cS @ c0 ) )
!= $true )
| spl2_1 ),
inference(superposition,[],[f29,f12]) ).
thf(f89,plain,
( ( ( cODD @ ( cS @ c0 ) )
!= $true )
| spl2_1 ),
inference(trivial_inequality_removal,[],[f88]) ).
thf(f91,plain,
( $false
| spl2_1
| ~ spl2_8 ),
inference(forward_subsumption_resolution,[],[f89,f60]) ).
thf(f92,plain,
( spl2_1
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f91]) ).
thf(f98,plain,
( ( ( cEVEN @ c0 )
!= $true )
| ( $true != $true )
| spl2_4 ),
inference(superposition,[],[f40,f13]) ).
thf(f101,plain,
( ( ( cEVEN @ c0 )
!= $true )
| spl2_4 ),
inference(trivial_inequality_removal,[],[f98]) ).
thf(f107,plain,
( $false
| spl2_4
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f101,f45]) ).
thf(f108,plain,
( spl2_4
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[],[f107]) ).
thf(f109,plain,
( ( $true != $true )
| ~ spl2_9
| spl2_10 ),
inference(superposition,[],[f69,f64]) ).
thf(f110,plain,
( $false
| ~ spl2_9
| spl2_10 ),
inference(trivial_inequality_removal,[],[f109]) ).
thf(f111,plain,
( ~ spl2_9
| spl2_10 ),
inference(avatar_contradiction_clause,[],[f110]) ).
thf(f112,plain,
( ( ( cEVEN @ ( cS @ ( cS @ sK0 ) ) )
!= $true )
| ( $true != $true )
| spl2_7 ),
inference(superposition,[],[f55,f13]) ).
thf(f113,plain,
( ( $true
!= ( cODD @ ( cS @ ( cS @ sK0 ) ) ) )
| ( $true != $true )
| spl2_7 ),
inference(superposition,[],[f55,f12]) ).
thf(f114,plain,
( ( ( cEVEN @ ( cS @ ( cS @ sK0 ) ) )
!= $true )
| spl2_7 ),
inference(trivial_inequality_removal,[],[f112]) ).
thf(f115,plain,
( ( $true
!= ( cODD @ ( cS @ ( cS @ sK0 ) ) ) )
| spl2_7 ),
inference(trivial_inequality_removal,[],[f113]) ).
thf(f117,definition,
( spl2_15
<=> ( ( cEVEN @ ( cS @ ( cS @ sK0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_15])],[avatar_definition]) ).
thf(f119,plain,
( ( ( cEVEN @ ( cS @ ( cS @ sK0 ) ) )
!= $true )
| spl2_15 ),
inference(avatar_component_clause,[],[f117]) ).
thf(f120,plain,
( ~ spl2_15
| spl2_7 ),
inference(avatar_split_clause,[],[f114,f53,f117]) ).
thf(f122,definition,
( spl2_16
<=> ( $true
= ( cODD @ ( cS @ ( cS @ sK0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_16])],[avatar_definition]) ).
thf(f124,plain,
( ( $true
!= ( cODD @ ( cS @ ( cS @ sK0 ) ) ) )
| spl2_16 ),
inference(avatar_component_clause,[],[f122]) ).
thf(f125,plain,
( ~ spl2_16
| spl2_7 ),
inference(avatar_split_clause,[],[f115,f53,f122]) ).
thf(f131,plain,
( ( $true != $true )
| ( $true
!= ( cEVEN @ sK0 ) )
| spl2_15 ),
inference(superposition,[],[f119,f22]) ).
thf(f133,plain,
( ( $true
!= ( cEVEN @ sK0 ) )
| spl2_15 ),
inference(trivial_inequality_removal,[],[f131]) ).
thf(f136,definition,
( spl2_17
<=> ( $true
= ( cEVEN @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_17])],[avatar_definition]) ).
thf(f138,plain,
( ( $true
!= ( cEVEN @ sK0 ) )
| spl2_17 ),
inference(avatar_component_clause,[],[f136]) ).
thf(f139,plain,
( ~ spl2_17
| spl2_15 ),
inference(avatar_split_clause,[],[f133,f117,f136]) ).
thf(f140,plain,
( ( $true != $true )
| ( $true
!= ( cODD @ sK0 ) )
| spl2_16 ),
inference(superposition,[],[f124,f24]) ).
thf(f141,plain,
( ( $true
!= ( cODD @ sK0 ) )
| spl2_16 ),
inference(trivial_inequality_removal,[],[f140]) ).
thf(f143,definition,
( spl2_18
<=> ( $true
= ( cODD @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_18])],[avatar_definition]) ).
thf(f146,plain,
( ~ spl2_18
| spl2_16 ),
inference(avatar_split_clause,[],[f141,f122,f143]) ).
thf(f147,plain,
( ( ( cNUMBER @ sK0 )
!= $true )
| ( $true != $true )
| ( $true
= ( cODD @ sK0 ) )
| spl2_17 ),
inference(superposition,[],[f138,f14]) ).
thf(f148,plain,
( ( ( cNUMBER @ sK0 )
!= $true )
| ( $true
= ( cODD @ sK0 ) )
| spl2_17 ),
inference(trivial_inequality_removal,[],[f147]) ).
thf(f149,plain,
( ( $true
= ( cODD @ sK0 ) )
| ~ spl2_6
| spl2_17 ),
inference(forward_subsumption_resolution,[],[f148,f50]) ).
thf(f150,plain,
( spl2_18
| ~ spl2_6
| spl2_17 ),
inference(avatar_split_clause,[],[f149,f136,f48,f143]) ).
cnf(s2,plain,
spl2_5,
inference(sat_conversion,[],[f46]) ).
cnf(s5,plain,
spl2_8,
inference(sat_conversion,[],[f61]) ).
cnf(s6,plain,
( ~ spl2_1
| ~ spl2_2
| ~ spl2_4
| ~ spl2_7
| spl2_9 ),
inference(sat_conversion,[],[f65]) ).
cnf(s7,plain,
~ spl2_10,
inference(sat_conversion,[],[f70]) ).
cnf(s8,plain,
( ~ spl2_1
| spl2_2
| ~ spl2_4
| spl2_9 ),
inference(sat_conversion,[],[f71]) ).
cnf(s9,plain,
( ~ spl2_1
| ~ spl2_4
| spl2_6
| spl2_9 ),
inference(sat_conversion,[],[f72]) ).
cnf(s12,plain,
( spl2_1
| ~ spl2_8 ),
inference(sat_conversion,[],[f92]) ).
cnf(s15,plain,
( spl2_4
| ~ spl2_5 ),
inference(sat_conversion,[],[f108]) ).
cnf(s16,plain,
( ~ spl2_9
| spl2_10 ),
inference(sat_conversion,[],[f111]) ).
cnf(s17,plain,
( spl2_7
| ~ spl2_15 ),
inference(sat_conversion,[],[f120]) ).
cnf(s18,plain,
( spl2_7
| ~ spl2_16 ),
inference(sat_conversion,[],[f125]) ).
cnf(s20,plain,
( spl2_15
| ~ spl2_17 ),
inference(sat_conversion,[],[f139]) ).
cnf(s21,plain,
( spl2_16
| ~ spl2_18 ),
inference(sat_conversion,[],[f146]) ).
cnf(s22,plain,
( ~ spl2_6
| spl2_17
| spl2_18 ),
inference(sat_conversion,[],[f150]) ).
cnf(s23,plain,
~ spl2_9,
inference(rat,[],[s16,s7]) ).
cnf(s26,plain,
( ~ spl2_1
| ~ spl2_2
| ~ spl2_4
| ~ spl2_7 ),
inference(rat,[],[s6,s23]) ).
cnf(s27,plain,
spl2_1,
inference(rat,[],[s12,s5]) ).
cnf(s30,plain,
spl2_4,
inference(rat,[],[s15,s2]) ).
cnf(s31,plain,
spl2_6,
inference(rat,[],[s9,s23,s27,s30]) ).
cnf(s32,plain,
spl2_2,
inference(rat,[],[s8,s23,s27,s30]) ).
cnf(s33,plain,
~ spl2_7,
inference(rat,[],[s26,s30,s27,s32]) ).
cnf(s35,plain,
~ spl2_16,
inference(rat,[],[s18,s33]) ).
cnf(s36,plain,
~ spl2_15,
inference(rat,[],[s17,s33]) ).
cnf(s37,plain,
~ spl2_18,
inference(rat,[],[s21,s35]) ).
cnf(s38,plain,
~ spl2_17,
inference(rat,[],[s20,s36]) ).
cnf(s39,plain,
$false,
inference(rat,[],[s22,s31,s37,s38]) ).
thf(f151,plain,
$false,
inference(avatar_sat_refutation,[],[s39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO113^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n004.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:34:07 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.27 % (1519077)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.27 % (1519085)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=718588849:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.08/0.27 % (1519085) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1519077-1519085"...
% 0.08/0.27 % (1519088)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.27 % (1519088)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.08/0.27 % (1519085)...printing done.
% 0.08/0.27 % (1519085)Refutation found. Thanks to Tanya!
% 0.08/0.27 % SZS status Theorem for theBenchmark
% 0.08/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.28 % (1519085)------------------------------
% 0.08/0.28 % (1519085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.28 % (1519085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.28 % (1519085)CaDiCaL version: 2.1.3
% 0.08/0.28 % (1519085)Termination reason: Refutation
% 0.08/0.28 % (1519085)Time elapsed: 0.004 s
% 0.08/0.28 % (1519085)Peak memory usage: 13 MB
% 0.08/0.28 % (1519085)Instructions burned: 10 (million)
% 0.08/0.28 % (1519077)Success in time 0.027 s
% 0.08/0.28 % Vampire exiting
%------------------------------------------------------------------------------