%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN056^5 : 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 : n019.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 09:50:26 AM UTC 2026
% Result : Theorem 1.48s 1.28s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 85 ( 1 unt; 0 typ; 13 def)
% Number of atoms : 790 ( 200 equ; 0 cnn)
% Maximal formula atoms : 18 ( 9 avg)
% Number of connectives : 668 ( 161 ~; 140 |; 66 &; 236 @)
% ( 13 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 20 con; 0-2 aty)
% Number of variables : 114 ( 0 ^; 77 !; 37 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cR: $i > $o ).
thf(func_def_1,type,
cP: $i > $o ).
thf(func_def_2,type,
cS: $i > $o ).
thf(func_def_3,type,
cQ: $i > $o ).
thf(f107,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f36,f45,f49,f54,f59,f63,f68,f72,f80,f84,f86,f88,f91,f97,f99,f101,f103,f106]) ).
thf(f106,plain,
( ~ spl5_1
| ~ spl5_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f105]) ).
thf(f105,plain,
( $false
| ~ spl5_1
| ~ spl5_12 ),
inference(trivial_inequality_removal,[status(thm)],[f104]) ).
thf(f104,plain,
( ( $true != $true )
| ~ spl5_1
| ~ spl5_12 ),
inference(superposition,[status(thm)],[f79,f32]) ).
thf(f32,plain,
( ( ( cQ @ sK2 )
= $true )
| ~ spl5_1 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f30,definition,
( spl5_1
<=> ( ( cQ @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition]) ).
thf(f79,plain,
( ! [X7: $i] :
( ( cQ @ X7 )
!= $true )
| ~ spl5_12 ),
inference(avatar_component_clause,[status(thm)],[f78]) ).
thf(f78,definition,
( spl5_12
<=> ! [X7: $i] :
( ( cQ @ X7 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_12])],[avatar_definition]) ).
thf(f103,plain,
( spl5_12
| ~ spl5_5
| ~ spl5_10 ),
inference(avatar_split_clause,[status(thm)],[f102,f70,f47,f78]) ).
thf(f47,definition,
( spl5_5
<=> ! [X0: $i] :
( ( ( cQ @ X0 )
!= $true )
| ( ( cS @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition]) ).
thf(f70,definition,
( spl5_10
<=> ! [X1: $i] :
( ( ( cQ @ X1 )
!= $true )
| ( ( cS @ X1 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl5_10])],[avatar_definition]) ).
thf(f102,plain,
( ! [X1: $i] :
( ( cQ @ X1 )
!= $true )
| ~ spl5_5
| ~ spl5_10 ),
inference(subsumption_resolution,[status(thm)],[f71,f48]) ).
thf(f48,plain,
( ! [X0: $i] :
( ( ( cS @ X0 )
= $true )
| ( ( cQ @ X0 )
!= $true ) )
| ~ spl5_5 ),
inference(avatar_component_clause,[status(thm)],[f47]) ).
thf(f71,plain,
( ! [X1: $i] :
( ( ( cS @ X1 )
!= $true )
| ( ( cQ @ X1 )
!= $true ) )
| ~ spl5_10 ),
inference(avatar_component_clause,[status(thm)],[f70]) ).
thf(f101,plain,
( ~ spl5_4
| spl5_7
| ~ spl5_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f100]) ).
thf(f100,plain,
( $false
| ~ spl5_4
| spl5_7
| ~ spl5_8 ),
inference(subsumption_resolution,[status(thm)],[f93,f44]) ).
thf(f44,plain,
( ( $true
= ( cP @ sK1 ) )
| ~ spl5_4 ),
inference(avatar_component_clause,[status(thm)],[f42]) ).
thf(f42,definition,
( spl5_4
<=> ( $true
= ( cP @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition]) ).
thf(f93,plain,
( ( $true
!= ( cP @ sK1 ) )
| spl5_7
| ~ spl5_8 ),
inference(trivial_inequality_removal,[status(thm)],[f92]) ).
thf(f92,plain,
( ( $true
!= ( cP @ sK1 ) )
| ( $true != $true )
| spl5_7
| ~ spl5_8 ),
inference(superposition,[status(thm)],[f58,f62]) ).
thf(f62,plain,
( ! [X4: $i] :
( ( $true
= ( cR @ X4 ) )
| ( ( cP @ X4 )
!= $true ) )
| ~ spl5_8 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f61,definition,
( spl5_8
<=> ! [X4: $i] :
( ( ( cP @ X4 )
!= $true )
| ( $true
= ( cR @ X4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_8])],[avatar_definition]) ).
thf(f58,plain,
( ( ( cR @ sK1 )
!= $true )
| spl5_7 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f56,definition,
( spl5_7
<=> ( ( cR @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_7])],[avatar_definition]) ).
thf(f99,plain,
( spl5_2
| ~ spl5_8
| ~ spl5_13 ),
inference(avatar_split_clause,[status(thm)],[f98,f82,f61,f34]) ).
thf(f34,definition,
( spl5_2
<=> ! [X2: $i] :
( ( cP @ X2 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition]) ).
thf(f82,definition,
( spl5_13
<=> ! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( cR @ X0 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl5_13])],[avatar_definition]) ).
thf(f98,plain,
( ! [X0: $i] :
( ( cP @ X0 )
!= $true )
| ~ spl5_8
| ~ spl5_13 ),
inference(subsumption_resolution,[status(thm)],[f83,f62]) ).
thf(f83,plain,
( ! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( cR @ X0 )
!= $true ) )
| ~ spl5_13 ),
inference(avatar_component_clause,[status(thm)],[f82]) ).
thf(f97,plain,
( ~ spl5_5
| spl5_6
| ~ spl5_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f96]) ).
thf(f96,plain,
( $false
| ~ spl5_5
| spl5_6
| ~ spl5_9 ),
inference(subsumption_resolution,[status(thm)],[f95,f67]) ).
thf(f67,plain,
( ( $true
= ( cQ @ sK3 ) )
| ~ spl5_9 ),
inference(avatar_component_clause,[status(thm)],[f65]) ).
thf(f65,definition,
( spl5_9
<=> ( $true
= ( cQ @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_9])],[avatar_definition]) ).
thf(f95,plain,
( ( $true
!= ( cQ @ sK3 ) )
| ~ spl5_5
| spl5_6 ),
inference(trivial_inequality_removal,[status(thm)],[f94]) ).
thf(f94,plain,
( ( $true
!= ( cQ @ sK3 ) )
| ( $true != $true )
| ~ spl5_5
| spl5_6 ),
inference(superposition,[status(thm)],[f53,f48]) ).
thf(f53,plain,
( ( $true
!= ( cS @ sK3 ) )
| spl5_6 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f51,definition,
( spl5_6
<=> ( $true
= ( cS @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_6])],[avatar_definition]) ).
thf(f91,plain,
( ~ spl5_9
| ~ spl5_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f90]) ).
thf(f90,plain,
( $false
| ~ spl5_9
| ~ spl5_12 ),
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
( ( $true != $true )
| ~ spl5_9
| ~ spl5_12 ),
inference(superposition,[status(thm)],[f79,f67]) ).
thf(f88,plain,
( ~ spl5_2
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f87]) ).
thf(f87,plain,
( $false
| ~ spl5_2
| ~ spl5_4 ),
inference(subsumption_resolution,[status(thm)],[f44,f35]) ).
thf(f35,plain,
( ! [X2: $i] :
( ( cP @ X2 )
!= $true )
| ~ spl5_2 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f86,plain,
( ~ spl5_2
| ~ spl5_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f85]) ).
thf(f85,plain,
( $false
| ~ spl5_2
| ~ spl5_11 ),
inference(subsumption_resolution,[status(thm)],[f76,f35]) ).
thf(f76,plain,
( ( ( cP @ sK4 )
= $true )
| ~ spl5_11 ),
inference(avatar_component_clause,[status(thm)],[f74]) ).
thf(f74,definition,
( spl5_11
<=> ( ( cP @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_11])],[avatar_definition]) ).
thf(f84,plain,
( spl5_5
| spl5_13 ),
inference(avatar_split_clause,[status(thm)],[f27,f82,f47]) ).
thf(f27,plain,
! [X0: $i,X1: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( cR @ X0 )
!= $true )
| ( ( cQ @ X1 )
!= $true )
| ( ( cS @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X0: $i,X1: $i] :
( ( ( ( ( cR @ X0 )
= $true )
| ( ( cS @ X1 )
!= $true ) )
& ( ( ( cR @ X0 )
!= $true )
| ( ( cS @ X1 )
= $true ) ) )
| ( ( cQ @ X1 )
!= $true )
| ( ( cP @ X0 )
!= $true ) )
& ( ! [X2: $i] :
( ( cP @ X2 )
!= $true )
| ( ( cQ @ sK2 )
= $true ) )
& ( ( ! [X4: $i] :
( ( ( cP @ X4 )
!= $true )
| ( $true
= ( cR @ X4 ) ) )
& ( $true
= ( cQ @ sK3 ) )
& ( $true
!= ( cS @ sK3 ) ) )
| ( sP0 = $true ) )
& ( ( ( cP @ sK4 )
= $true )
| ! [X7: $i] :
( ( cQ @ X7 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f14,f17,f16,f15]) ).
thf(f15,plain,
( ? [X3: $i] :
( ( cQ @ X3 )
= $true )
=> ( ( cQ @ sK2 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X5: $i] :
( ( ( cQ @ X5 )
= $true )
& ( ( cS @ X5 )
!= $true ) )
=> ( ( $true
= ( cQ @ sK3 ) )
& ( $true
!= ( cS @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X6: $i] :
( ( cP @ X6 )
= $true )
=> ( ( cP @ sK4 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ! [X0: $i,X1: $i] :
( ( ( ( ( cR @ X0 )
= $true )
| ( ( cS @ X1 )
!= $true ) )
& ( ( ( cR @ X0 )
!= $true )
| ( ( cS @ X1 )
= $true ) ) )
| ( ( cQ @ X1 )
!= $true )
| ( ( cP @ X0 )
!= $true ) )
& ( ! [X2: $i] :
( ( cP @ X2 )
!= $true )
| ? [X3: $i] :
( ( cQ @ X3 )
= $true ) )
& ( ( ! [X4: $i] :
( ( ( cP @ X4 )
!= $true )
| ( $true
= ( cR @ X4 ) ) )
& ? [X5: $i] :
( ( ( cQ @ X5 )
= $true )
& ( ( cS @ X5 )
!= $true ) ) )
| ( sP0 = $true ) )
& ( ? [X6: $i] :
( ( cP @ X6 )
= $true )
| ! [X7: $i] :
( ( cQ @ X7 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X3: $i,X2: $i] :
( ( ( ( ( cR @ X3 )
= $true )
| ( $true
!= ( cS @ X2 ) ) )
& ( ( ( cR @ X3 )
!= $true )
| ( $true
= ( cS @ X2 ) ) ) )
| ( $true
!= ( cQ @ X2 ) )
| ( ( cP @ X3 )
!= $true ) )
& ( ! [X4: $i] :
( ( cP @ X4 )
!= $true )
| ? [X5: $i] :
( ( cQ @ X5 )
= $true ) )
& ( ( ! [X8: $i] :
( ( ( cP @ X8 )
!= $true )
| ( ( cR @ X8 )
= $true ) )
& ? [X9: $i] :
( ( $true
= ( cQ @ X9 ) )
& ( ( cS @ X9 )
!= $true ) ) )
| ( sP0 = $true ) )
& ( ? [X1: $i] :
( ( cP @ X1 )
= $true )
| ! [X0: $i] :
( ( cQ @ X0 )
!= $true ) ) ),
inference(definition_folding,[status(thm)],[f7,f8]) ).
thf(f8,plain,
( ( ! [X6: $i] :
( ( $true
!= ( cQ @ X6 ) )
| ( ( cS @ X6 )
= $true ) )
& ? [X7: $i] :
( ( $true
= ( cP @ X7 ) )
& ( $true
!= ( cR @ X7 ) ) ) )
| ( sP0 != $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f7,plain,
( ! [X3: $i,X2: $i] :
( ( ( ( ( cR @ X3 )
= $true )
| ( $true
!= ( cS @ X2 ) ) )
& ( ( ( cR @ X3 )
!= $true )
| ( $true
= ( cS @ X2 ) ) ) )
| ( $true
!= ( cQ @ X2 ) )
| ( ( cP @ X3 )
!= $true ) )
& ( ! [X4: $i] :
( ( cP @ X4 )
!= $true )
| ? [X5: $i] :
( ( cQ @ X5 )
= $true ) )
& ( ( ! [X8: $i] :
( ( ( cP @ X8 )
!= $true )
| ( ( cR @ X8 )
= $true ) )
& ? [X9: $i] :
( ( $true
= ( cQ @ X9 ) )
& ( ( cS @ X9 )
!= $true ) ) )
| ( ! [X6: $i] :
( ( $true
!= ( cQ @ X6 ) )
| ( ( cS @ X6 )
= $true ) )
& ? [X7: $i] :
( ( $true
= ( cP @ X7 ) )
& ( $true
!= ( cR @ X7 ) ) ) ) )
& ( ? [X1: $i] :
( ( cP @ X1 )
= $true )
| ! [X0: $i] :
( ( cQ @ X0 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( ! [X8: $i] :
( ( ( cP @ X8 )
!= $true )
| ( ( cR @ X8 )
= $true ) )
& ? [X9: $i] :
( ( $true
= ( cQ @ X9 ) )
& ( ( cS @ X9 )
!= $true ) ) )
| ( ! [X6: $i] :
( ( $true
!= ( cQ @ X6 ) )
| ( ( cS @ X6 )
= $true ) )
& ? [X7: $i] :
( ( $true
= ( cP @ X7 ) )
& ( $true
!= ( cR @ X7 ) ) ) ) )
& ( ? [X1: $i] :
( ( cP @ X1 )
= $true )
| ! [X0: $i] :
( ( cQ @ X0 )
!= $true ) )
& ! [X2: $i,X3: $i] :
( ( ( ( ( cR @ X3 )
= $true )
| ( $true
!= ( cS @ X2 ) ) )
& ( ( ( cR @ X3 )
!= $true )
| ( $true
= ( cS @ X2 ) ) ) )
| ( $true
!= ( cQ @ X2 ) )
| ( ( cP @ X3 )
!= $true ) )
& ( ! [X4: $i] :
( ( cP @ X4 )
!= $true )
| ? [X5: $i] :
( ( cQ @ X5 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ? [X0: $i] :
( ( cQ @ X0 )
= $true )
=> ? [X1: $i] :
( ( cP @ X1 )
= $true ) )
& ! [X2: $i,X3: $i] :
( ( ( $true
= ( cQ @ X2 ) )
& ( ( cP @ X3 )
= $true ) )
=> ( ( ( $true
= ( cS @ X2 ) )
=> ( ( cR @ X3 )
= $true ) )
& ( ( ( cR @ X3 )
= $true )
=> ( $true
= ( cS @ X2 ) ) ) ) )
& ( ? [X4: $i] :
( ( cP @ X4 )
= $true )
=> ? [X5: $i] :
( ( cQ @ X5 )
= $true ) ) )
=> ( ( ! [X6: $i] :
( ( $true
= ( cQ @ X6 ) )
=> ( ( cS @ X6 )
= $true ) )
=> ! [X7: $i] :
( ( $true
= ( cP @ X7 ) )
=> ( $true
= ( cR @ X7 ) ) ) )
& ( ! [X8: $i] :
( ( ( cP @ X8 )
= $true )
=> ( ( cR @ X8 )
= $true ) )
=> ! [X9: $i] :
( ( $true
= ( cQ @ X9 ) )
=> ( ( cS @ X9 )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( ? [X0: $i] : ( cQ @ X0 )
=> ? [X1: $i] : ( cP @ X1 ) )
& ! [X2: $i,X3: $i] :
( ( ( cP @ X3 )
& ( cQ @ X2 ) )
=> ( ( ( cS @ X2 )
=> ( cR @ X3 ) )
& ( ( cR @ X3 )
=> ( cS @ X2 ) ) ) )
& ( ? [X4: $i] : ( cP @ X4 )
=> ? [X5: $i] : ( cQ @ X5 ) ) )
=> ( ( ! [X6: $i] :
( ( cQ @ X6 )
=> ( cS @ X6 ) )
=> ! [X7: $i] :
( ( cP @ X7 )
=> ( cR @ X7 ) ) )
& ( ! [X8: $i] :
( ( cP @ X8 )
=> ( cR @ X8 ) )
=> ! [X9: $i] :
( ( cQ @ X9 )
=> ( cS @ X9 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( ? [X0: $i] : ( cQ @ X0 )
=> ? [X0: $i] : ( cP @ X0 ) )
& ! [X1: $i,X0: $i] :
( ( ( cP @ X0 )
& ( cQ @ X1 ) )
=> ( ( ( cS @ X1 )
=> ( cR @ X0 ) )
& ( ( cR @ X0 )
=> ( cS @ X1 ) ) ) )
& ( ? [X0: $i] : ( cP @ X0 )
=> ? [X0: $i] : ( cQ @ X0 ) ) )
=> ( ( ! [X0: $i] :
( ( cQ @ X0 )
=> ( cS @ X0 ) )
=> ! [X0: $i] :
( ( cP @ X0 )
=> ( cR @ X0 ) ) )
& ( ! [X0: $i] :
( ( cP @ X0 )
=> ( cR @ X0 ) )
=> ! [X0: $i] :
( ( cQ @ X0 )
=> ( cS @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( ? [X0: $i] : ( cQ @ X0 )
=> ? [X0: $i] : ( cP @ X0 ) )
& ! [X1: $i,X0: $i] :
( ( ( cP @ X0 )
& ( cQ @ X1 ) )
=> ( ( ( cS @ X1 )
=> ( cR @ X0 ) )
& ( ( cR @ X0 )
=> ( cS @ X1 ) ) ) )
& ( ? [X0: $i] : ( cP @ X0 )
=> ? [X0: $i] : ( cQ @ X0 ) ) )
=> ( ( ! [X0: $i] :
( ( cQ @ X0 )
=> ( cS @ X0 ) )
=> ! [X0: $i] :
( ( cP @ X0 )
=> ( cR @ X0 ) ) )
& ( ! [X0: $i] :
( ( cP @ X0 )
=> ( cR @ X0 ) )
=> ! [X0: $i] :
( ( cQ @ X0 )
=> ( cS @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.O7ObP4OA8I/DTF2THF_4421.p',cPELL26) ).
thf(f80,plain,
( spl5_11
| spl5_12 ),
inference(avatar_split_clause,[status(thm)],[f22,f78,f74]) ).
thf(f22,plain,
! [X7: $i] :
( ( ( cP @ sK4 )
= $true )
| ( ( cQ @ X7 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f72,plain,
( spl5_8
| spl5_10 ),
inference(avatar_split_clause,[status(thm)],[f28,f70,f61]) ).
thf(f28,plain,
! [X0: $i,X1: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( cQ @ X1 )
!= $true )
| ( ( cR @ X0 )
= $true )
| ( ( cS @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f68,plain,
( spl5_3
| spl5_9 ),
inference(avatar_split_clause,[status(thm)],[f24,f65,f38]) ).
thf(f38,definition,
( spl5_3
<=> ( sP0 = $true ) ),
introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition]) ).
thf(f24,plain,
( ( sP0 = $true )
| ( $true
= ( cQ @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f63,plain,
( spl5_8
| spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f25,f38,f61]) ).
thf(f25,plain,
! [X4: $i] :
( ( sP0 = $true )
| ( ( cP @ X4 )
!= $true )
| ( $true
= ( cR @ X4 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f59,plain,
( ~ spl5_7
| ~ spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f19,f38,f56]) ).
thf(f19,plain,
( ( sP0 != $true )
| ( ( cR @ sK1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ! [X0: $i] :
( ( ( cQ @ X0 )
!= $true )
| ( ( cS @ X0 )
= $true ) )
& ( $true
= ( cP @ sK1 ) )
& ( ( cR @ sK1 )
!= $true ) )
| ( sP0 != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f11,f12]) ).
thf(f12,plain,
( ? [X1: $i] :
( ( ( cP @ X1 )
= $true )
& ( $true
!= ( cR @ X1 ) ) )
=> ( ( $true
= ( cP @ sK1 ) )
& ( ( cR @ sK1 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ( ! [X0: $i] :
( ( ( cQ @ X0 )
!= $true )
| ( ( cS @ X0 )
= $true ) )
& ? [X1: $i] :
( ( ( cP @ X1 )
= $true )
& ( $true
!= ( cR @ X1 ) ) ) )
| ( sP0 != $true ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ! [X6: $i] :
( ( $true
!= ( cQ @ X6 ) )
| ( ( cS @ X6 )
= $true ) )
& ? [X7: $i] :
( ( $true
= ( cP @ X7 ) )
& ( $true
!= ( cR @ X7 ) ) ) )
| ( sP0 != $true ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f54,plain,
( ~ spl5_6
| spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f23,f38,f51]) ).
thf(f23,plain,
( ( sP0 = $true )
| ( $true
!= ( cS @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f49,plain,
( spl5_5
| ~ spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f21,f38,f47]) ).
thf(f21,plain,
! [X0: $i] :
( ( ( cQ @ X0 )
!= $true )
| ( sP0 != $true )
| ( ( cS @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f45,plain,
( ~ spl5_3
| spl5_4 ),
inference(avatar_split_clause,[status(thm)],[f20,f42,f38]) ).
thf(f20,plain,
( ( $true
= ( cP @ sK1 ) )
| ( sP0 != $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f36,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f26,f34,f30]) ).
thf(f26,plain,
! [X2: $i] :
( ( ( cP @ X2 )
!= $true )
| ( ( cQ @ sK2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN056^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n019.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 13:50:09 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.46 thf(spec,logic,$$dhol).
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % File : SYN056^5 : TPTP v9.2.1. Released v4.0.0.
% 0.27/0.46 % Domain : Syntactic
% 0.27/0.46 % Problem : TPS problem PELL26
% 0.27/0.46 % Version : Especial.
% 0.27/0.46 % English :
% 0.27/0.46
% 0.27/0.46 % Refs : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
% 0.27/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.46 % Source : [Bro09]
% 0.27/0.46 % Names : tps_0368 [Bro09]
% 0.27/0.46 % : PELL26 [TPS]
% 0.27/0.46 % : Pelletier 26 [Pel86]
% 0.27/0.46
% 0.27/0.46 % Status : Theorem
% 0.27/0.46 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.27/0.46 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.27/0.46 % Number of atoms : 18 ( 0 equ; 0 cnn)
% 0.27/0.46 % Maximal formula atoms : 18 ( 18 avg)
% 0.27/0.46 % Number of connectives : 35 ( 0 ~; 0 |; 5 &; 18 @)
% 0.27/0.46 % ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% 0.27/0.46 % Maximal formula depth : 10 ( 10 avg)
% 0.27/0.46 % Number of types : 2 ( 0 usr)
% 0.27/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.27/0.46 % Number of symbols : 4 ( 4 usr; 0 con; 1-1 aty)
% 0.27/0.46 % Number of variables : 10 ( 0 ^; 6 !; 4 ?; 10 :)
% 0.27/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.27/0.46
% 0.27/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.46 % :
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 thf(cR,type,
% 0.27/0.46 cR: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(cP,type,
% 0.27/0.46 cP: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(cS,type,
% 0.27/0.46 cS: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(cQ,type,
% 0.27/0.46 cQ: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(cPELL26,conjecture,
% 0.27/0.46 ( ( ( ? [Xx: $i] : ( cP @ Xx )
% 0.27/0.46 => ? [Xx: $i] : ( cQ @ Xx ) )
% 0.27/0.46 & ( ? [Xx: $i] : ( cQ @ Xx )
% 0.27/0.46 => ? [Xx: $i] : ( cP @ Xx ) )
% 0.27/0.46 & ! [Xx: $i,Xy: $i] :
% 0.27/0.46 ( ( ( cP @ Xx )
% 0.27/0.46 & ( cQ @ Xy ) )
% 0.27/0.46 => ( ( ( cR @ Xx )
% 0.27/0.46 => ( cS @ Xy ) )
% 0.27/0.46 & ( ( cS @ Xy )
% 0.27/0.46 => ( cR @ Xx ) ) ) ) )
% 0.27/0.46 => ( ( ! [Xx: $i] :
% 0.27/0.46 ( ( cP @ Xx )
% 0.27/0.46 => ( cR @ Xx ) )
% 0.27/0.46 => ! [Xx: $i] :
% 0.27/0.46 ( ( cQ @ Xx )
% 0.27/0.46 => ( cS @ Xx ) ) )
% 0.27/0.46 & ( ! [Xx: $i] :
% 0.27/0.46 ( ( cQ @ Xx )
% 0.27/0.46 => ( cS @ Xx ) )
% 0.27/0.46 => ! [Xx: $i] :
% 0.27/0.46 ( ( cP @ Xx )
% 0.27/0.46 => ( cR @ Xx ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 ------------------------
% 1.48/1.24 ---- Embedded in THF ---
% 1.48/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.24 %%% Generated on Tue Feb 24 13:50:10 EST 2026
% 1.48/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.24 %%% Logic specification used:
% 1.48/1.24 %%% thf(spec, logic, $$dhol).
% 1.48/1.24
% 1.48/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.O7ObP4OA8I/DTF2DTF4421.p
% See solution above
% 1.48/1.24 ------------------------
% 1.48/1.25 ---- Cleaned THF ---
% 1.48/1.25 thf(cR,type,
% 1.48/1.25 cR: $i > $o ).
% 1.48/1.25
% 1.48/1.25 thf(cP,type,
% 1.48/1.25 cP: $i > $o ).
% 1.48/1.25
% 1.48/1.25 thf(cS,type,
% 1.48/1.25 cS: $i > $o ).
% 1.48/1.25
% 1.48/1.25 thf(cQ,type,
% 1.48/1.25 cQ: $i > $o ).
% 1.48/1.25
% 1.48/1.25 thf(cPELL26,conjecture,
% 1.48/1.25 ( ( ( ? [Xx: $i] : ( cP @ Xx )
% 1.48/1.25 => ? [Xx: $i] : ( cQ @ Xx ) )
% 1.48/1.25 & ( ? [Xx: $i] : ( cQ @ Xx )
% 1.48/1.25 => ? [Xx: $i] : ( cP @ Xx ) )
% 1.48/1.25 & ! [Xx: $i,Xy: $i] :
% 1.48/1.25 ( ( ( cP @ Xx )
% 1.48/1.25 & ( cQ @ Xy ) )
% 1.48/1.25 => ( ( ( cR @ Xx )
% 1.48/1.25 => ( cS @ Xy ) )
% 1.48/1.25 & ( ( cS @ Xy )
% 1.48/1.25 => ( cR @ Xx ) ) ) ) )
% 1.48/1.25 => ( ( ! [Xx: $i] :
% 1.48/1.25 ( ( cP @ Xx )
% 1.48/1.25 => ( cR @ Xx ) )
% 1.48/1.25 => ! [Xx: $i] :
% 1.48/1.25 ( ( cQ @ Xx )
% 1.48/1.25 => ( cS @ Xx ) ) )
% 1.48/1.25 & ( ! [Xx: $i] :
% 1.48/1.25 ( ( cQ @ Xx )
% 1.48/1.25 => ( cS @ Xx ) )
% 1.48/1.25 => ! [Xx: $i] :
% 1.48/1.25 ( ( cP @ Xx )
% 1.48/1.25 => ( cR @ Xx ) ) ) ) ) ).
% 1.48/1.25 ------------------------
% 1.48/1.27 % (4695)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4421 for (2999ds/2Mi)
% 1.48/1.27 % (4695)Instruction limit reached!
% 1.48/1.27 % (4695)------------------------------
% 1.48/1.27 % (4695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (4695)Termination reason: Unknown
% 1.48/1.27 % (4695)Termination phase: Saturation
% 1.48/1.27
% 1.48/1.27 % (4695)Memory used [KB]: 5500
% 1.48/1.27 % (4695)Time elapsed: 0.003 s
% 1.48/1.27 % (4695)Instructions burned: 3 (million)
% 1.48/1.27 % (4695)------------------------------
% 1.48/1.27 % (4695)------------------------------
% 1.48/1.28 % (4692)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4421 for (2999ds/183Mi)
% 1.48/1.28 % (4693)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_4421 for (2999ds/4Mi)
% 1.48/1.28 % (4694)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_4421 for (2999ds/27Mi)
% 1.48/1.28 % (4696)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_4421 for (2999ds/2Mi)
% 1.48/1.28 % (4697)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_4421 for (2999ds/275Mi)
% 1.48/1.28 % (4698)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4421 for (2999ds/18Mi)
% 1.48/1.28 % (4696)Instruction limit reached!
% 1.48/1.28 % (4696)------------------------------
% 1.48/1.28 % (4696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (4696)Termination reason: Unknown
% 1.48/1.28 % (4696)Termination phase: Property scanning
% 1.48/1.28
% 1.48/1.28 % (4696)Memory used [KB]: 895
% 1.48/1.28 % (4696)Time elapsed: 0.003 s
% 1.48/1.28 % (4696)Instructions burned: 2 (million)
% 1.48/1.28 % (4696)------------------------------
% 1.48/1.28 % (4696)------------------------------
% 1.48/1.28 % (4693)Instruction limit reached!
% 1.48/1.28 % (4693)------------------------------
% 1.48/1.28 % (4693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (4693)Termination reason: Unknown
% 1.48/1.28 % (4693)Termination phase: Saturation
% 1.48/1.28
% 1.48/1.28 % (4693)Memory used [KB]: 5500
% 1.48/1.28 % (4693)Time elapsed: 0.005 s
% 1.48/1.28 % (4693)Instructions burned: 4 (million)
% 1.48/1.28 % (4693)------------------------------
% 1.48/1.28 % (4693)------------------------------
% 1.48/1.28 % (4699)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4421 for (2999ds/3Mi)
% 1.48/1.28 % (4692)First to succeed.
% 1.48/1.28 % (4699)Instruction limit reached!
% 1.48/1.28 % (4699)------------------------------
% 1.48/1.28 % (4699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (4699)Termination reason: Unknown
% 1.48/1.28 % (4699)Termination phase: Saturation
% 1.48/1.28
% 1.48/1.28 % (4699)Memory used [KB]: 5500
% 1.48/1.28 % (4699)Time elapsed: 0.002 s
% 1.48/1.28 % (4699)Instructions burned: 3 (million)
% 1.48/1.28 % (4699)------------------------------
% 1.48/1.28 % (4699)------------------------------
% 1.48/1.28 % (4694)Also succeeded, but the first one will report.
% 1.48/1.28 % (4698)Also succeeded, but the first one will report.
% 1.48/1.28 % (4692)Refutation found. Thanks to Tanya!
% 1.48/1.28 % SZS status Theorem for DTF2THF_4421
% 1.48/1.28 % SZS output start Proof for DTF2THF_4421
% 1.48/1.28 thf(func_def_0, type, cR: $i > $o).
% 1.48/1.28 thf(func_def_1, type, cP: $i > $o).
% 1.48/1.28 thf(func_def_2, type, cS: $i > $o).
% 1.48/1.28 thf(func_def_3, type, cQ: $i > $o).
% 1.48/1.28 thf(f107,plain,(
% 1.48/1.28 $false),
% 1.48/1.28 inference(avatar_sat_refutation,[status(thm)],[f36,f45,f49,f54,f59,f63,f68,f72,f80,f84,f86,f88,f91,f97,f99,f101,f103,f106])).
% 1.48/1.28 thf(f106,plain,(
% 1.48/1.28 ~spl5_1 | ~spl5_12),
% 1.48/1.28 inference(avatar_contradiction_clause,[status(thm)],[f105])).
% 1.48/1.28 thf(f105,plain,(
% 1.48/1.28 $false | (~spl5_1 | ~spl5_12)),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f104])).
% 1.48/1.28 thf(f104,plain,(
% 1.48/1.28 ($true != $true) | (~spl5_1 | ~spl5_12)),
% 1.48/1.28 inference(superposition,[status(thm)],[f79,f32])).
% 1.48/1.28 thf(f32,plain,(
% 1.48/1.28 ((cQ @ sK2) = $true) | ~spl5_1),
% 1.48/1.28 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.48/1.28 thf(f30,definition,(
% 1.48/1.28 spl5_1 <=> ((cQ @ sK2) = $true)),
% 1.48/1.28 introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition])).
% 1.48/1.28 thf(f79,plain,(
% 1.48/1.28 ( ! [X7 : $i] : (((cQ @ X7) != $true)) ) | ~spl5_12),
% 1.48/1.28 inference(avatar_component_clause,[status(thm)],[f78])).
% 1.48/1.28 thf(f78,definition,(
% 1.48/1.28 spl5_12 <=> ! [X7 : $i] : ((cQ @ X7) != $true)),
% 1.48/1.28 introduced(definition,[new_symbols(naming,[spl5_12])],[avatar_definition])).
% 1.48/1.28 thf(f103,plain,(
% 1.48/1.28 spl5_12 | ~spl5_5 | ~spl5_10),
% 1.48/1.28 inference(avatar_split_clause,[status(thm)],[f102,f70,f47,f78])).
% 1.48/1.28 thf(f47,definition,(
% 1.48/1.28 spl5_5 <=> ! [X0 : $i] : (((cQ @ X0) != $true) | ((cS @ X0) = $true))),
% 1.48/1.28 introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition])).
% 1.48/1.28 thf(f70,definition,(
% 1.48/1.28 spl5_10 <=> ! [X1 : $i] : (((cQ @ X1) != $true) | ((cS @ X1) != $true))),
% 1.48/1.28 introduced(definition,[new_symbols(naming,[spl5_10])],[avatar_definition])).
% 1.48/1.28 thf(f102,plain,(
% 1.48/1.28 ( ! [X1 : $i] : (((cQ @ X1) != $true)) ) | (~spl5_5 | ~spl5_10)),
% 1.48/1.28 inference(subsumption_resolution,[status(thm)],[f71,f48])).
% 1.48/1.28 thf(f48,plain,(
% 1.48/1.28 ( ! [X0 : $i] : (((cS @ X0) = $true) | ((cQ @ X0) != $true)) ) | ~spl5_5),
% 1.48/1.28 inference(avatar_component_clause,[status(thm)],[f47])).
% 1.48/1.28 thf(f71,plain,(
% 1.48/1.28 ( ! [X1 : $i] : (((cS @ X1) != $true) | ((cQ @ X1) != $true)) ) | ~spl5_10),
% 1.48/1.28 inference(avatar_component_clause,[status(thm)],[f70])).
% 1.48/1.28 thf(f101,plain,(
% 1.48/1.28 ~spl5_4 | spl5_7 | ~spl5_8),
% 1.48/1.28 inference(avatar_contradiction_clause,[status(thm)],[f100])).
% 1.48/1.28 thf(f100,plain,(
% 1.48/1.28 $false | (~spl5_4 | spl5_7 | ~spl5_8)),
% 1.48/1.28 inference(subsumption_resolution,[status(thm)],[f93,f44])).
% 1.48/1.28 thf(f44,plain,(
% 1.48/1.28 ($true = (cP @ sK1)) | ~spl5_4),
% 1.48/1.28 inference(avatar_component_clause,[status(thm)],[f42])).
% 1.48/1.28 thf(f42,definition,(
% 1.48/1.28 spl5_4 <=> ($true = (cP @ sK1))),
% 1.48/1.28 introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition])).
% 1.48/1.28 thf(f93,plain,(
% 1.48/1.28 ($true != (cP @ sK1)) | (spl5_7 | ~spl5_8)),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f92])).
% 1.48/1.28 thf(f92,plain,(
% 1.48/1.28 ($true != (cP @ sK1)) | ($true != $true) | (spl5_7 | ~spl5_8)),
% 1.48/1.28 inference(superposition,[status(thm)],[f58,f62])).
% 1.48/1.28 thf(f62,plain,(
% 1.48/1.28 ( ! [X4 : $i] : (($true = (cR @ X4)) | ((cP @ X4) != $true)) ) | ~spl5_8),
% 1.48/1.28 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.48/1.28 thf(f61,definition,(
% 1.48/1.28 spl5_8 <=> ! [X4 : $i] : (((cP @ X4) != $true) | ($true = (cR @ X4)))),
% 1.48/1.28 introduced(definition,[new_symbols(naming,[spl5_8])],[avatar_definition])).
% 1.48/1.28 thf(f58,plain,(
% 1.48/1.28 ((cR @ sK1) != $true) | spl5_7),
% 1.48/1.28 inference(avatar_component_clause,[status(thm)],[f56])).
% 1.48/1.28 thf(f56,definition,(
% 1.48/1.28 spl5_7 <=> ((cR @ sK1) = $true)),
% 1.48/1.28 introduced(definition,[new_symbols(naming,[spl5_7])],[avatar_definition])).
% 1.48/1.28 thf(f99,plain,(
% 1.48/1.28 spl5_2 | ~spl5_8 | ~spl5_13),
% 1.48/1.28 inference(avatar_split_clause,[status(thm)],[f98,f82,f61,f34])).
% 1.48/1.28 thf(f34,definition,(
% 1.48/1.28 spl5_2 <=> ! [X2 : $i] : ((cP @ X2) != $true)),
% 1.48/1.28 introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition])).
% 1.48/1.28 thf(f82,definition,(
% 1.48/1.28 spl5_13 <=> ! [X0 : $i] : (((cP @ X0) != $true) | ((cR @ X0) != $true))),
% 1.48/1.28 introduced(definition,[new_symbols(naming,[spl5_13])],[avatar_definition])).
% 1.48/1.28 thf(f98,plain,(
% 1.48/1.28 ( ! [X0 : $i] : (((cP @ X0) != $true)) ) | (~spl5_8 | ~spl5_13)),
% 1.48/1.28 inference(subsumption_resolution,[status(thm)],[f83,f62])).
% 1.48/1.28 thf(f83,plain,(
% 1.48/1.28 ( ! [X0 : $i] : (((cP @ X0) != $true) | ((cR @ X0) != $true)) ) | ~spl5_13),
% 1.48/1.28 inference(avatar_component_clause,[status(thm)],[f82])).
% 1.48/1.28 thf(f97,plain,(
% 1.48/1.28 ~spl5_5 | spl5_6 | ~spl5_9),
% 1.48/1.28 inference(avatar_contradiction_clause,[status(thm)],[f96])).
% 1.48/1.28 thf(f96,plain,(
% 1.48/1.28 $false | (~spl5_5 | spl5_6 | ~spl5_9)),
% 1.48/1.28 inference(subsumption_resolution,[status(thm)],[f95,f67])).
% 1.48/1.28 thf(f67,plain,(
% 1.48/1.28 ($true = (cQ @ sK3)) | ~spl5_9),
% 1.48/1.28 inference(avatar_component_clause,[status(thm)],[f65])).
% 1.48/1.28 thf(f65,definition,(
% 1.48/1.28 spl5_9 <=> ($true = (cQ @ sK3))),
% 1.48/1.28 introduced(definition,[new_symbols(naming,[spl5_9])],[avatar_definition])).
% 1.48/1.28 thf(f95,plain,(
% 1.48/1.28 ($true != (cQ @ sK3)) | (~spl5_5 | spl5_6)),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f94])).
% 1.48/1.28 thf(f94,plain,(
% 1.48/1.28 ($true != (cQ @ sK3)) | ($true != $true) | (~spl5_5 | spl5_6)),
% 1.48/1.28 inference(superposition,[status(thm)],[f53,f48])).
% 1.48/1.28 thf(f53,plain,(
% 1.48/1.28 ($true != (cS @ sK3)) | spl5_6),
% 1.48/1.28 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.48/1.28 thf(f51,definition,(
% 1.48/1.28 spl5_6 <=> ($true = (cS @ sK3))),
% 1.48/1.28 introduced(definition,[new_symbols(naming,[spl5_6])],[avatar_definition])).
% 1.48/1.28 thf(f91,plain,(
% 1.48/1.28 ~spl5_9 | ~spl5_12),
% 1.48/1.28 inference(avatar_contradiction_clause,[status(thm)],[f90])).
% 1.48/1.28 thf(f90,plain,(
% 1.48/1.28 $false | (~spl5_9 | ~spl5_12)),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 1.48/1.28 thf(f89,plain,(
% 1.48/1.28 ($true != $true) | (~spl5_9 | ~spl5_12)),
% 1.48/1.28 inference(superposition,[status(thm)],[f79,f67])).
% 1.48/1.28 thf(f88,plain,(
% 1.48/1.28 ~spl5_2 | ~spl5_4),
% 1.48/1.28 inference(avatar_contradiction_clause,[status(thm)],[f87])).
% 1.48/1.28 thf(f87,plain,(
% 1.48/1.28 $false | (~spl5_2 | ~spl5_4)),
% 1.48/1.28 inference(subsumption_resolution,[status(thm)],[f44,f35])).
% 1.48/1.28 thf(f35,plain,(
% 1.48/1.28 ( ! [X2 : $i] : (((cP @ X2) != $true)) ) | ~spl5_2),
% 1.48/1.28 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.48/1.28 thf(f86,plain,(
% 1.48/1.28 ~spl5_2 | ~spl5_11),
% 1.48/1.28 inference(avatar_contradiction_clause,[status(thm)],[f85])).
% 1.48/1.28 thf(f85,plain,(
% 1.48/1.28 $false | (~spl5_2 | ~spl5_11)),
% 1.48/1.28 inference(subsumption_resolution,[status(thm)],[f76,f35])).
% 1.48/1.28 thf(f76,plain,(
% 1.48/1.28 ((cP @ sK4) = $true) | ~spl5_11),
% 1.48/1.28 inference(avatar_component_clause,[status(thm)],[f74])).
% 1.48/1.28 thf(f74,definition,(
% 1.48/1.28 spl5_11 <=> ((cP @ sK4) = $true)),
% 1.48/1.28 introduced(definition,[new_symbols(naming,[spl5_11])],[avatar_definition])).
% 1.48/1.28 thf(f84,plain,(
% 1.48/1.28 spl5_5 | spl5_13),
% 1.48/1.28 inference(avatar_split_clause,[status(thm)],[f27,f82,f47])).
% 1.48/1.28 thf(f27,plain,(
% 1.48/1.28 ( ! [X0 : $i,X1 : $i] : (((cP @ X0) != $true) | ((cR @ X0) != $true) | ((cQ @ X1) != $true) | ((cS @ X1) = $true)) )),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f18])).
% 1.48/1.28 thf(f18,plain,(
% 1.48/1.28 ! [X0 : $i,X1 : $i] : (((((cR @ X0) = $true) | ((cS @ X1) != $true)) & (((cR @ X0) != $true) | ((cS @ X1) = $true))) | ((cQ @ X1) != $true) | ((cP @ X0) != $true)) & (! [X2 : $i] : ((cP @ X2) != $true) | ((cQ @ sK2) = $true)) & ((! [X4 : $i] : (((cP @ X4) != $true) | ($true = (cR @ X4))) & (($true = (cQ @ sK3)) & ($true != (cS @ sK3)))) | (sP0 = $true)) & (((cP @ sK4) = $true) | ! [X7 : $i] : ((cQ @ X7) != $true))),
% 1.48/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f14,f17,f16,f15])).
% 1.48/1.28 thf(f15,plain,(
% 1.48/1.28 ? [X3 : $i] : ((cQ @ X3) = $true) => ((cQ @ sK2) = $true)),
% 1.48/1.28 introduced(definition,[],[choice_axiom])).
% 1.48/1.28 thf(f16,plain,(
% 1.48/1.28 ? [X5 : $i] : (((cQ @ X5) = $true) & ((cS @ X5) != $true)) => (($true = (cQ @ sK3)) & ($true != (cS @ sK3)))),
% 1.48/1.28 introduced(definition,[],[choice_axiom])).
% 1.48/1.28 thf(f17,plain,(
% 1.48/1.28 ? [X6 : $i] : ((cP @ X6) = $true) => ((cP @ sK4) = $true)),
% 1.48/1.28 introduced(definition,[],[choice_axiom])).
% 1.48/1.28 thf(f14,plain,(
% 1.48/1.28 ! [X0 : $i,X1 : $i] : (((((cR @ X0) = $true) | ((cS @ X1) != $true)) & (((cR @ X0) != $true) | ((cS @ X1) = $true))) | ((cQ @ X1) != $true) | ((cP @ X0) != $true)) & (! [X2 : $i] : ((cP @ X2) != $true) | ? [X3 : $i] : ((cQ @ X3) = $true)) & ((! [X4 : $i] : (((cP @ X4) != $true) | ($true = (cR @ X4))) & ? [X5 : $i] : (((cQ @ X5) = $true) & ((cS @ X5) != $true))) | (sP0 = $true)) & (? [X6 : $i] : ((cP @ X6) = $true) | ! [X7 : $i] : ((cQ @ X7) != $true))),
% 1.48/1.28 inference(rectify,[status(thm)],[f9])).
% 1.48/1.28 thf(f9,plain,(
% 1.48/1.28 ! [X3 : $i,X2 : $i] : (((((cR @ X3) = $true) | ($true != (cS @ X2))) & (((cR @ X3) != $true) | ($true = (cS @ X2)))) | ($true != (cQ @ X2)) | ((cP @ X3) != $true)) & (! [X4 : $i] : ((cP @ X4) != $true) | ? [X5 : $i] : ((cQ @ X5) = $true)) & ((! [X8 : $i] : (((cP @ X8) != $true) | ((cR @ X8) = $true)) & ? [X9 : $i] : (($true = (cQ @ X9)) & ((cS @ X9) != $true))) | (sP0 = $true)) & (? [X1 : $i] : ((cP @ X1) = $true) | ! [X0 : $i] : ((cQ @ X0) != $true))),
% 1.48/1.28 inference(definition_folding,[status(thm)],[f7,f8])).
% 1.48/1.28 thf(f8,plain,(
% 1.48/1.28 (! [X6 : $i] : (($true != (cQ @ X6)) | ((cS @ X6) = $true)) & ? [X7 : $i] : (($true = (cP @ X7)) & ($true != (cR @ X7)))) | ~(sP0 = $true)),
% 1.48/1.28 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.48/1.28 thf(f7,plain,(
% 1.48/1.28 ! [X3 : $i,X2 : $i] : (((((cR @ X3) = $true) | ($true != (cS @ X2))) & (((cR @ X3) != $true) | ($true = (cS @ X2)))) | ($true != (cQ @ X2)) | ((cP @ X3) != $true)) & (! [X4 : $i] : ((cP @ X4) != $true) | ? [X5 : $i] : ((cQ @ X5) = $true)) & ((! [X8 : $i] : (((cP @ X8) != $true) | ((cR @ X8) = $true)) & ? [X9 : $i] : (($true = (cQ @ X9)) & ((cS @ X9) != $true))) | (! [X6 : $i] : (($true != (cQ @ X6)) | ((cS @ X6) = $true)) & ? [X7 : $i] : (($true = (cP @ X7)) & ($true != (cR @ X7))))) & (? [X1 : $i] : ((cP @ X1) = $true) | ! [X0 : $i] : ((cQ @ X0) != $true))),
% 1.48/1.28 inference(flattening,[status(thm)],[f6])).
% 1.48/1.28 thf(f6,plain,(
% 1.48/1.28 ((! [X8 : $i] : (((cP @ X8) != $true) | ((cR @ X8) = $true)) & ? [X9 : $i] : (($true = (cQ @ X9)) & ((cS @ X9) != $true))) | (! [X6 : $i] : (($true != (cQ @ X6)) | ((cS @ X6) = $true)) & ? [X7 : $i] : (($true = (cP @ X7)) & ($true != (cR @ X7))))) & ((? [X1 : $i] : ((cP @ X1) = $true) | ! [X0 : $i] : ((cQ @ X0) != $true)) & ! [X2 : $i,X3 : $i] : (((((cR @ X3) = $true) | ($true != (cS @ X2))) & (((cR @ X3) != $true) | ($true = (cS @ X2)))) | (($true != (cQ @ X2)) | ((cP @ X3) != $true))) & (! [X4 : $i] : ((cP @ X4) != $true) | ? [X5 : $i] : ((cQ @ X5) = $true)))),
% 1.48/1.28 inference(ennf_transformation,[status(thm)],[f5])).
% 1.48/1.28 thf(f5,plain,(
% 1.48/1.28 ~(((? [X0 : $i] : ((cQ @ X0) = $true) => ? [X1 : $i] : ((cP @ X1) = $true)) & ! [X2 : $i,X3 : $i] : ((($true = (cQ @ X2)) & ((cP @ X3) = $true)) => ((($true = (cS @ X2)) => ((cR @ X3) = $true)) & (((cR @ X3) = $true) => ($true = (cS @ X2))))) & (? [X4 : $i] : ((cP @ X4) = $true) => ? [X5 : $i] : ((cQ @ X5) = $true))) => ((! [X6 : $i] : (($true = (cQ @ X6)) => ((cS @ X6) = $true)) => ! [X7 : $i] : (($true = (cP @ X7)) => ($true = (cR @ X7)))) & (! [X8 : $i] : (((cP @ X8) = $true) => ((cR @ X8) = $true)) => ! [X9 : $i] : (($true = (cQ @ X9)) => ((cS @ X9) = $true)))))),
% 1.48/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.28 thf(f4,plain,(
% 1.48/1.28 ~(((? [X0 : $i] : (cQ @ X0) => ? [X1 : $i] : (cP @ X1)) & ! [X2 : $i,X3 : $i] : (((cP @ X3) & (cQ @ X2)) => (((cS @ X2) => (cR @ X3)) & ((cR @ X3) => (cS @ X2)))) & (? [X4 : $i] : (cP @ X4) => ? [X5 : $i] : (cQ @ X5))) => ((! [X6 : $i] : ((cQ @ X6) => (cS @ X6)) => ! [X7 : $i] : ((cP @ X7) => (cR @ X7))) & (! [X8 : $i] : ((cP @ X8) => (cR @ X8)) => ! [X9 : $i] : ((cQ @ X9) => (cS @ X9)))))),
% 1.48/1.28 inference(rectify,[status(thm)],[f2])).
% 1.48/1.28 thf(f2,negated_conjecture,(
% 1.48/1.28 ~(((? [X0 : $i] : (cQ @ X0) => ? [X0 : $i] : (cP @ X0)) & ! [X1 : $i,X0 : $i] : (((cP @ X0) & (cQ @ X1)) => (((cS @ X1) => (cR @ X0)) & ((cR @ X0) => (cS @ X1)))) & (? [X0 : $i] : (cP @ X0) => ? [X0 : $i] : (cQ @ X0))) => ((! [X0 : $i] : ((cQ @ X0) => (cS @ X0)) => ! [X0 : $i] : ((cP @ X0) => (cR @ X0))) & (! [X0 : $i] : ((cP @ X0) => (cR @ X0)) => ! [X0 : $i] : ((cQ @ X0) => (cS @ X0)))))),
% 1.48/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.28 thf(f1,conjecture,(
% 1.48/1.28 ((? [X0 : $i] : (cQ @ X0) => ? [X0 : $i] : (cP @ X0)) & ! [X1 : $i,X0 : $i] : (((cP @ X0) & (cQ @ X1)) => (((cS @ X1) => (cR @ X0)) & ((cR @ X0) => (cS @ X1)))) & (? [X0 : $i] : (cP @ X0) => ? [X0 : $i] : (cQ @ X0))) => ((! [X0 : $i] : ((cQ @ X0) => (cS @ X0)) => ! [X0 : $i] : ((cP @ X0) => (cR @ X0))) & (! [X0 : $i] : ((cP @ X0) => (cR @ X0)) => ! [X0 : $i] : ((cQ @ X0) => (cS @ X0))))),
% 1.48/1.28 file('/export/starexec/sandbox2/tmp/tmp.O7ObP4OA8I/DTF2THF_4421.p',cPELL26)).
% 1.48/1.28 thf(f80,plain,(
% 1.48/1.28 spl5_11 | spl5_12),
% 1.48/1.28 inference(avatar_split_clause,[status(thm)],[f22,f78,f74])).
% 1.48/1.28 thf(f22,plain,(
% 1.48/1.28 ( ! [X7 : $i] : (((cP @ sK4) = $true) | ((cQ @ X7) != $true)) )),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f18])).
% 1.48/1.28 thf(f72,plain,(
% 1.48/1.28 spl5_8 | spl5_10),
% 1.48/1.28 inference(avatar_split_clause,[status(thm)],[f28,f70,f61])).
% 1.48/1.28 thf(f28,plain,(
% 1.48/1.28 ( ! [X0 : $i,X1 : $i] : (((cP @ X0) != $true) | ((cQ @ X1) != $true) | ((cR @ X0) = $true) | ((cS @ X1) != $true)) )),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f18])).
% 1.48/1.28 thf(f68,plain,(
% 1.48/1.28 spl5_3 | spl5_9),
% 1.48/1.28 inference(avatar_split_clause,[status(thm)],[f24,f65,f38])).
% 1.48/1.28 thf(f38,definition,(
% 1.48/1.28 spl5_3 <=> (sP0 = $true)),
% 1.48/1.28 introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition])).
% 1.48/1.28 thf(f24,plain,(
% 1.48/1.28 (sP0 = $true) | ($true = (cQ @ sK3))),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f18])).
% 1.48/1.28 thf(f63,plain,(
% 1.48/1.28 spl5_8 | spl5_3),
% 1.48/1.28 inference(avatar_split_clause,[status(thm)],[f25,f38,f61])).
% 1.48/1.28 thf(f25,plain,(
% 1.48/1.28 ( ! [X4 : $i] : ((sP0 = $true) | ((cP @ X4) != $true) | ($true = (cR @ X4))) )),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f18])).
% 1.48/1.28 thf(f59,plain,(
% 1.48/1.28 ~spl5_7 | ~spl5_3),
% 1.48/1.28 inference(avatar_split_clause,[status(thm)],[f19,f38,f56])).
% 1.48/1.28 thf(f19,plain,(
% 1.48/1.28 (sP0 != $true) | ((cR @ sK1) != $true)),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f13])).
% 1.48/1.28 thf(f13,plain,(
% 1.48/1.28 (! [X0 : $i] : (((cQ @ X0) != $true) | ((cS @ X0) = $true)) & (($true = (cP @ sK1)) & ((cR @ sK1) != $true))) | (sP0 != $true)),
% 1.48/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f11,f12])).
% 1.48/1.28 thf(f12,plain,(
% 1.48/1.28 ? [X1 : $i] : (((cP @ X1) = $true) & ($true != (cR @ X1))) => (($true = (cP @ sK1)) & ((cR @ sK1) != $true))),
% 1.48/1.28 introduced(definition,[],[choice_axiom])).
% 1.48/1.28 thf(f11,plain,(
% 1.48/1.28 (! [X0 : $i] : (((cQ @ X0) != $true) | ((cS @ X0) = $true)) & ? [X1 : $i] : (((cP @ X1) = $true) & ($true != (cR @ X1)))) | (sP0 != $true)),
% 1.48/1.28 inference(rectify,[status(thm)],[f10])).
% 1.48/1.28 thf(f10,plain,(
% 1.48/1.28 (! [X6 : $i] : (($true != (cQ @ X6)) | ((cS @ X6) = $true)) & ? [X7 : $i] : (($true = (cP @ X7)) & ($true != (cR @ X7)))) | (sP0 != $true)),
% 1.48/1.28 inference(nnf_transformation,[status(thm)],[f8])).
% 1.48/1.28 thf(f54,plain,(
% 1.48/1.28 ~spl5_6 | spl5_3),
% 1.48/1.28 inference(avatar_split_clause,[status(thm)],[f23,f38,f51])).
% 1.48/1.28 thf(f23,plain,(
% 1.48/1.28 (sP0 = $true) | ($true != (cS @ sK3))),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f18])).
% 1.48/1.28 thf(f49,plain,(
% 1.48/1.28 spl5_5 | ~spl5_3),
% 1.48/1.28 inference(avatar_split_clause,[status(thm)],[f21,f38,f47])).
% 1.48/1.28 thf(f21,plain,(
% 1.48/1.28 ( ! [X0 : $i] : (((cQ @ X0) != $true) | (sP0 != $true) | ((cS @ X0) = $true)) )),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f13])).
% 1.48/1.28 thf(f45,plain,(
% 1.48/1.28 ~spl5_3 | spl5_4),
% 1.48/1.28 inference(avatar_split_clause,[status(thm)],[f20,f42,f38])).
% 1.48/1.28 thf(f20,plain,(
% 1.48/1.28 ($true = (cP @ sK1)) | (sP0 != $true)),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f13])).
% 1.48/1.28 thf(f36,plain,(
% 1.48/1.28 spl5_1 | spl5_2),
% 1.48/1.28 inference(avatar_split_clause,[status(thm)],[f26,f34,f30])).
% 1.48/1.28 thf(f26,plain,(
% 1.48/1.28 ( ! [X2 : $i] : (((cP @ X2) != $true) | ((cQ @ sK2) = $true)) )),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f18])).
% 1.48/1.28 % SZS output end Proof for DTF2THF_4421
% 1.48/1.28 % (4692)------------------------------
% 1.48/1.28 % (4692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (4692)Termination reason: Refutation
% 1.48/1.28
% 1.48/1.28 % (4692)Memory used [KB]: 5628
% 1.48/1.28 % (4692)Time elapsed: 0.008 s
% 1.48/1.28 % (4692)Instructions burned: 5 (million)
% 1.48/1.28 % (4692)------------------------------
% 1.48/1.28 % (4692)------------------------------
% 1.48/1.28 % (4691)Success in time 0.023 s
%------------------------------------------------------------------------------