%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN374^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n031.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 09:50:52 AM UTC 2026
% Result : Theorem 1.52s 1.23s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 70 ( 1 unt; 0 typ; 9 def)
% Number of atoms : 455 ( 108 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 375 ( 93 ~; 106 |; 9 &; 139 @)
% ( 21 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 16 con; 0-2 aty)
% Number of variables : 92 ( 0 ^; 64 !; 28 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP: $i > $o ).
thf(func_def_4,type,
sK0: $i > $i ).
thf(f130,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f38,f46,f58,f63,f78,f80,f82,f88,f98,f105,f114,f127,f129]) ).
thf(f129,plain,
( ~ spl6_1
| spl6_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f128]) ).
thf(f128,plain,
( $false
| ~ spl6_1
| spl6_9 ),
inference(subsumption_resolution,[status(thm)],[f61,f30]) ).
thf(f30,plain,
( ! [X7: $i] :
( ( cP @ X7 )
= $true )
| ~ spl6_1 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl6_1
<=> ! [X7: $i] :
( ( cP @ X7 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition]) ).
thf(f61,plain,
( ( ( cP @ sK2 )
!= $true )
| spl6_9 ),
inference(avatar_component_clause,[status(thm)],[f60]) ).
thf(f60,definition,
( spl6_9
<=> ( ( cP @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_9])],[avatar_definition]) ).
thf(f127,plain,
( spl6_4
| ~ spl6_1
| ~ spl6_8 ),
inference(avatar_split_clause,[status(thm)],[f124,f56,f29,f40]) ).
thf(f40,definition,
( spl6_4
<=> ! [X7: $i] :
( $false
= ( cP @ X7 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_4])],[avatar_definition]) ).
thf(f56,definition,
( spl6_8
<=> ! [X0: $i] :
( ( ( cP @ X0 )
= $false )
| ( $false
= ( cP @ ( sK0 @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl6_8])],[avatar_definition]) ).
thf(f124,plain,
( ! [X0: $i] :
( ( cP @ X0 )
= $false )
| ~ spl6_1
| ~ spl6_8 ),
inference(trivial_inequality_removal,[status(thm)],[f122]) ).
thf(f122,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( ( cP @ X0 )
= $false ) )
| ~ spl6_1
| ~ spl6_8 ),
inference(superposition,[status(thm)],[f57,f30]) ).
thf(f57,plain,
( ! [X0: $i] :
( ( $false
= ( cP @ ( sK0 @ X0 ) ) )
| ( ( cP @ X0 )
= $false ) )
| ~ spl6_8 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f114,plain,
( ~ spl6_1
| spl6_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f113]) ).
thf(f113,plain,
( $false
| ~ spl6_1
| spl6_7 ),
inference(trivial_inequality_removal,[status(thm)],[f107]) ).
thf(f107,plain,
( ( $true != $true )
| ~ spl6_1
| spl6_7 ),
inference(superposition,[status(thm)],[f53,f30]) ).
thf(f53,plain,
( ( ( cP @ sK1 )
!= $true )
| spl6_7 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f51,definition,
( spl6_7
<=> ( ( cP @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_7])],[avatar_definition]) ).
thf(f105,plain,
( ~ spl6_4
| ~ spl6_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f104]) ).
thf(f104,plain,
( $false
| ~ spl6_4
| ~ spl6_9 ),
inference(trivial_inequality_removal,[status(thm)],[f100]) ).
thf(f100,plain,
( ( $false = $true )
| ~ spl6_4
| ~ spl6_9 ),
inference(superposition,[status(thm)],[f62,f41]) ).
thf(f41,plain,
( ! [X7: $i] :
( $false
= ( cP @ X7 ) )
| ~ spl6_4 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f62,plain,
( ( ( cP @ sK2 )
= $true )
| ~ spl6_9 ),
inference(avatar_component_clause,[status(thm)],[f60]) ).
thf(f98,plain,
( spl6_1
| ~ spl6_4
| ~ spl6_6 ),
inference(avatar_split_clause,[status(thm)],[f95,f48,f40,f29]) ).
thf(f48,definition,
( spl6_6
<=> ! [X0: $i] :
( ( ( cP @ X0 )
= $true )
| ( ( cP @ ( sK0 @ X0 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl6_6])],[avatar_definition]) ).
thf(f95,plain,
( ! [X0: $i] :
( ( cP @ X0 )
= $true )
| ~ spl6_4
| ~ spl6_6 ),
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
thf(f93,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( ( cP @ X0 )
= $true ) )
| ~ spl6_4
| ~ spl6_6 ),
inference(superposition,[status(thm)],[f49,f41]) ).
thf(f49,plain,
( ! [X0: $i] :
( ( ( cP @ ( sK0 @ X0 ) )
= $true )
| ( ( cP @ X0 )
= $true ) )
| ~ spl6_6 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f88,plain,
( ~ spl6_3
| ~ spl6_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f87]) ).
thf(f87,plain,
( $false
| ~ spl6_3
| ~ spl6_5 ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
( ( $false = $true )
| ~ spl6_3
| ~ spl6_5 ),
inference(superposition,[status(thm)],[f45,f37]) ).
thf(f37,plain,
( ( $false
= ( cP @ sK3 ) )
| ~ spl6_3 ),
inference(avatar_component_clause,[status(thm)],[f35]) ).
thf(f35,definition,
( spl6_3
<=> ( $false
= ( cP @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_3])],[avatar_definition]) ).
thf(f45,plain,
( ( ( cP @ sK3 )
= $true )
| ~ spl6_5 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
thf(f43,definition,
( spl6_5
<=> ( ( cP @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_5])],[avatar_definition]) ).
thf(f82,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f81]) ).
thf(f81,plain,
( $false
| ~ spl6_1
| ~ spl6_2 ),
inference(subsumption_resolution,[status(thm)],[f30,f33]) ).
thf(f33,plain,
( ! [X9: $i] :
( ( cP @ X9 )
!= $true )
| ~ spl6_2 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl6_2
<=> ! [X9: $i] :
( ( cP @ X9 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition]) ).
thf(f80,plain,
( ~ spl6_2
| ~ spl6_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f79]) ).
thf(f79,plain,
( $false
| ~ spl6_2
| ~ spl6_9 ),
inference(subsumption_resolution,[status(thm)],[f62,f33]) ).
thf(f78,plain,
( ~ spl6_2
| ~ spl6_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f77]) ).
thf(f77,plain,
( $false
| ~ spl6_2
| ~ spl6_6 ),
inference(subsumption_resolution,[status(thm)],[f76,f33]) ).
thf(f76,plain,
( ! [X0: $i] :
( ( cP @ X0 )
= $true )
| ~ spl6_2
| ~ spl6_6 ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cP @ X0 )
= $true ) )
| ~ spl6_2
| ~ spl6_6 ),
inference(superposition,[status(thm)],[f33,f49]) ).
thf(f63,plain,
( spl6_6
| spl6_1
| spl6_9 ),
inference(avatar_split_clause,[status(thm)],[f22,f60,f29,f48]) ).
thf(f22,plain,
! [X0: $i,X5: $i] :
( ( ( cP @ sK2 )
= $true )
| ( ( cP @ ( sK0 @ X0 ) )
= $true )
| ( ( cP @ X5 )
= $true )
| ( ( cP @ X0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $i,X5: $i] :
( ( ( cP @ sK2 )
= $true )
| ( ( cP @ X0 )
!= ( cP @ ( sK0 @ X0 ) ) )
| ( ( cP @ X5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ! [X0: $i] :
( ( cP @ X0 )
!= ( cP @ ( sK0 @ X0 ) ) )
| ( ( ! [X2: $i] :
( ( cP @ X2 )
!= $true )
| ( ( cP @ sK1 )
!= $true ) )
& ( ( ( cP @ sK2 )
= $true )
| ! [X5: $i] :
( ( cP @ X5 )
= $true ) ) ) )
& ( ! [X7: $i] :
( ( cP @ X7 )
= ( cP @ sK3 ) )
| ( ( ! [X8: $i] :
( $true
= ( cP @ X8 ) )
| ! [X9: $i] :
( ( cP @ X9 )
!= $true ) )
& ( ( ( cP @ sK4 )
= $true )
| ( ( cP @ sK5 )
!= $true ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f14,f13,f12,f11,f10,f9]) ).
thf(f9,plain,
! [X0: $i] :
( ? [X1: $i] :
( ( cP @ X0 )
!= ( cP @ X1 ) )
=> ( ( cP @ X0 )
!= ( cP @ ( sK0 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X3: $i] :
( ( cP @ X3 )
!= $true )
=> ( ( cP @ sK1 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X4: $i] :
( ( cP @ X4 )
= $true )
=> ( ( cP @ sK2 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X6: $i] :
! [X7: $i] :
( ( cP @ X6 )
= ( cP @ X7 ) )
=> ! [X7: $i] :
( ( cP @ X7 )
= ( cP @ sK3 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X10: $i] :
( $true
= ( cP @ X10 ) )
=> ( ( cP @ sK4 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X11: $i] :
( ( cP @ X11 )
!= $true )
=> ( ( cP @ sK5 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ( ! [X0: $i] :
? [X1: $i] :
( ( cP @ X0 )
!= ( cP @ X1 ) )
| ( ( ! [X2: $i] :
( ( cP @ X2 )
!= $true )
| ? [X3: $i] :
( ( cP @ X3 )
!= $true ) )
& ( ? [X4: $i] :
( ( cP @ X4 )
= $true )
| ! [X5: $i] :
( ( cP @ X5 )
= $true ) ) ) )
& ( ? [X6: $i] :
! [X7: $i] :
( ( cP @ X6 )
= ( cP @ X7 ) )
| ( ( ! [X8: $i] :
( $true
= ( cP @ X8 ) )
| ! [X9: $i] :
( ( cP @ X9 )
!= $true ) )
& ( ? [X10: $i] :
( $true
= ( cP @ X10 ) )
| ? [X11: $i] :
( ( cP @ X11 )
!= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ! [X2: $i] :
? [X3: $i] :
( ( cP @ X3 )
!= ( cP @ X2 ) )
| ( ( ! [X0: $i] :
( ( cP @ X0 )
!= $true )
| ? [X1: $i] :
( ( cP @ X1 )
!= $true ) )
& ( ? [X0: $i] :
( ( cP @ X0 )
= $true )
| ! [X1: $i] :
( ( cP @ X1 )
= $true ) ) ) )
& ( ? [X2: $i] :
! [X3: $i] :
( ( cP @ X3 )
= ( cP @ X2 ) )
| ( ( ! [X1: $i] :
( ( cP @ X1 )
= $true )
| ! [X0: $i] :
( ( cP @ X0 )
!= $true ) )
& ( ? [X0: $i] :
( ( cP @ X0 )
= $true )
| ? [X1: $i] :
( ( cP @ X1 )
!= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ! [X1: $i] :
( ( cP @ X1 )
= $true )
<=> ? [X0: $i] :
( ( cP @ X0 )
= $true ) )
<~> ? [X2: $i] :
! [X3: $i] :
( ( cP @ X3 )
= ( cP @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ? [X2: $i] :
! [X3: $i] :
( ( cP @ X3 )
= ( cP @ X2 ) )
<=> ( ! [X1: $i] :
( ( cP @ X1 )
= $true )
<=> ? [X0: $i] :
( ( cP @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ? [X0: $i] : ( cP @ X0 )
<=> ! [X1: $i] : ( cP @ X1 ) )
<=> ? [X2: $i] :
! [X3: $i] :
( ( cP @ X2 )
<=> ( cP @ X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ? [X0: $i] : ( cP @ X0 )
<=> ! [X1: $i] : ( cP @ X1 ) )
<=> ? [X0: $i] :
! [X1: $i] :
( ( cP @ X0 )
<=> ( cP @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ? [X0: $i] : ( cP @ X0 )
<=> ! [X1: $i] : ( cP @ X1 ) )
<=> ? [X0: $i] :
! [X1: $i] :
( ( cP @ X0 )
<=> ( cP @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PXGkfGS3J0/DTF2THF_25233.p',cX2125) ).
thf(f58,plain,
( spl6_8
| spl6_2
| ~ spl6_7 ),
inference(avatar_split_clause,[status(thm)],[f25,f51,f32,f56]) ).
thf(f25,plain,
! [X2: $i,X0: $i] :
( ( ( cP @ X0 )
= $false )
| ( ( cP @ sK1 )
!= $true )
| ( ( cP @ X2 )
!= $true )
| ( $false
= ( cP @ ( sK0 @ X0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X2: $i,X0: $i] :
( ( ( cP @ X0 )
!= ( cP @ ( sK0 @ X0 ) ) )
| ( ( cP @ X2 )
!= $true )
| ( ( cP @ sK1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f46,plain,
( spl6_4
| spl6_5
| spl6_2
| spl6_1 ),
inference(avatar_split_clause,[status(thm)],[f27,f29,f32,f43,f40]) ).
thf(f27,plain,
! [X8: $i,X9: $i,X7: $i] :
( ( $false
= ( cP @ X7 ) )
| ( ( cP @ sK3 )
= $true )
| ( $true
= ( cP @ X8 ) )
| ( ( cP @ X9 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X8: $i,X9: $i,X7: $i] :
( ( ( cP @ X7 )
= ( cP @ sK3 ) )
| ( $true
= ( cP @ X8 ) )
| ( ( cP @ X9 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f38,plain,
( spl6_1
| spl6_2
| spl6_1
| spl6_3 ),
inference(avatar_split_clause,[status(thm)],[f26,f35,f29,f32,f29]) ).
thf(f26,plain,
! [X8: $i,X9: $i,X7: $i] :
( ( ( cP @ X9 )
!= $true )
| ( $false
= ( cP @ sK3 ) )
| ( $true
= ( cP @ X8 ) )
| ( ( cP @ X7 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN374^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n031.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 13:57:18 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SYN374^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.46 % Domain : Syntactic
% 0.31/0.46 % Problem : TPS problem X2125
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Bro09]
% 0.31/0.46 % Names : tps_0379 [Bro09]
% 0.31/0.46 % : THM55 [TPS]
% 0.31/0.46 % : X2125 [TPS]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % 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 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.0
% 0.31/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.31/0.46 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.31/0.46 % Number of connectives : 7 ( 0 ~; 0 |; 0 &; 4 @)
% 0.31/0.46 % ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 6 ( 6 avg)
% 0.31/0.46 % Number of types : 2 ( 0 usr)
% 0.31/0.46 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 1 ( 1 usr; 0 con; 1-1 aty)
% 0.31/0.46 % Number of variables : 4 ( 0 ^; 2 !; 2 ?; 4 :)
% 0.31/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.46 % :
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(cP,type,
% 0.31/0.46 cP: $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(cX2125,conjecture,
% 0.31/0.46 ( ? [Xx: $i] :
% 0.31/0.46 ! [Xy: $i] :
% 0.31/0.46 ( ( cP @ Xx )
% 0.31/0.46 <=> ( cP @ Xy ) )
% 0.31/0.46 <=> ( ? [Xx: $i] : ( cP @ Xx )
% 0.31/0.46 <=> ! [Xy: $i] : ( cP @ Xy ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.39/1.19 ---- Embedded in THF ---
% 1.39/1.20 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.39/1.20 %%% Generated on Tue Feb 24 13:57:19 EST 2026
% 1.39/1.20 %%% using '$$dhol' embedding, version 1.3.0.
% 1.39/1.20 %%% Logic specification used:
% 1.39/1.20 %%% thf(spec, logic, $$dhol).
% 1.39/1.20
% 1.39/1.20 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.PXGkfGS3J0/DTF2DTF25233.p
% See solution above
% 1.39/1.20 ------------------------
% 1.52/1.21 ---- Cleaned THF ---
% 1.52/1.21 thf(cP,type,
% 1.52/1.21 cP: $i > $o ).
% 1.52/1.21
% 1.52/1.21 thf(cX2125,conjecture,
% 1.52/1.21 ( ? [Xx: $i] :
% 1.52/1.21 ! [Xy: $i] :
% 1.52/1.21 ( ( cP @ Xx )
% 1.52/1.21 <=> ( cP @ Xy ) )
% 1.52/1.21 <=> ( ? [Xx: $i] : ( cP @ Xx )
% 1.52/1.21 <=> ! [Xy: $i] : ( cP @ Xy ) ) ) ).
% 1.52/1.21 ------------------------
% 1.52/1.22 % (25341)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25233 for (2999ds/183Mi)
% 1.52/1.22 % (25342)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_25233 for (2999ds/4Mi)
% 1.52/1.23 % (25341)First to succeed.
% 1.52/1.23 % (25342)Instruction limit reached!
% 1.52/1.23 % (25342)------------------------------
% 1.52/1.23 % (25342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.23 % (25342)Termination reason: Unknown
% 1.52/1.23 % (25342)Termination phase: Saturation
% 1.52/1.23
% 1.52/1.23 % (25342)Memory used [KB]: 5500
% 1.52/1.23 % (25342)Time elapsed: 0.004 s
% 1.52/1.23 % (25342)Instructions burned: 6 (million)
% 1.52/1.23 % (25342)------------------------------
% 1.52/1.23 % (25342)------------------------------
% 1.52/1.23 % (25341)Refutation found. Thanks to Tanya!
% 1.52/1.23 % SZS status Theorem for DTF2THF_25233
% 1.52/1.23 % SZS output start Proof for DTF2THF_25233
% 1.52/1.23 thf(func_def_0, type, cP: $i > $o).
% 1.52/1.23 thf(func_def_4, type, sK0: $i > $i).
% 1.52/1.23 thf(f130,plain,(
% 1.52/1.23 $false),
% 1.52/1.23 inference(avatar_sat_refutation,[status(thm)],[f38,f46,f58,f63,f78,f80,f82,f88,f98,f105,f114,f127,f129])).
% 1.52/1.23 thf(f129,plain,(
% 1.52/1.23 ~spl6_1 | spl6_9),
% 1.52/1.23 inference(avatar_contradiction_clause,[status(thm)],[f128])).
% 1.52/1.23 thf(f128,plain,(
% 1.52/1.23 $false | (~spl6_1 | spl6_9)),
% 1.52/1.23 inference(subsumption_resolution,[status(thm)],[f61,f30])).
% 1.52/1.23 thf(f30,plain,(
% 1.52/1.23 ( ! [X7 : $i] : (((cP @ X7) = $true)) ) | ~spl6_1),
% 1.52/1.23 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.52/1.23 thf(f29,definition,(
% 1.52/1.23 spl6_1 <=> ! [X7 : $i] : ((cP @ X7) = $true)),
% 1.52/1.23 introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition])).
% 1.52/1.23 thf(f61,plain,(
% 1.52/1.23 ((cP @ sK2) != $true) | spl6_9),
% 1.52/1.23 inference(avatar_component_clause,[status(thm)],[f60])).
% 1.52/1.23 thf(f60,definition,(
% 1.52/1.23 spl6_9 <=> ((cP @ sK2) = $true)),
% 1.52/1.23 introduced(definition,[new_symbols(naming,[spl6_9])],[avatar_definition])).
% 1.52/1.23 thf(f127,plain,(
% 1.52/1.23 spl6_4 | ~spl6_1 | ~spl6_8),
% 1.52/1.23 inference(avatar_split_clause,[status(thm)],[f124,f56,f29,f40])).
% 1.52/1.23 thf(f40,definition,(
% 1.52/1.23 spl6_4 <=> ! [X7 : $i] : ($false = (cP @ X7))),
% 1.52/1.23 introduced(definition,[new_symbols(naming,[spl6_4])],[avatar_definition])).
% 1.52/1.23 thf(f56,definition,(
% 1.52/1.23 spl6_8 <=> ! [X0 : $i] : (((cP @ X0) = $false) | ($false = (cP @ (sK0 @ X0))))),
% 1.52/1.23 introduced(definition,[new_symbols(naming,[spl6_8])],[avatar_definition])).
% 1.52/1.23 thf(f124,plain,(
% 1.52/1.23 ( ! [X0 : $i] : (((cP @ X0) = $false)) ) | (~spl6_1 | ~spl6_8)),
% 1.52/1.23 inference(trivial_inequality_removal,[status(thm)],[f122])).
% 1.52/1.23 thf(f122,plain,(
% 1.52/1.23 ( ! [X0 : $i] : (($false = $true) | ((cP @ X0) = $false)) ) | (~spl6_1 | ~spl6_8)),
% 1.52/1.23 inference(superposition,[status(thm)],[f57,f30])).
% 1.52/1.23 thf(f57,plain,(
% 1.52/1.23 ( ! [X0 : $i] : (($false = (cP @ (sK0 @ X0))) | ((cP @ X0) = $false)) ) | ~spl6_8),
% 1.52/1.23 inference(avatar_component_clause,[status(thm)],[f56])).
% 1.52/1.23 thf(f114,plain,(
% 1.52/1.23 ~spl6_1 | spl6_7),
% 1.52/1.23 inference(avatar_contradiction_clause,[status(thm)],[f113])).
% 1.52/1.23 thf(f113,plain,(
% 1.52/1.23 $false | (~spl6_1 | spl6_7)),
% 1.52/1.23 inference(trivial_inequality_removal,[status(thm)],[f107])).
% 1.52/1.23 thf(f107,plain,(
% 1.52/1.23 ($true != $true) | (~spl6_1 | spl6_7)),
% 1.52/1.23 inference(superposition,[status(thm)],[f53,f30])).
% 1.52/1.23 thf(f53,plain,(
% 1.52/1.23 ((cP @ sK1) != $true) | spl6_7),
% 1.52/1.23 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.52/1.23 thf(f51,definition,(
% 1.52/1.23 spl6_7 <=> ((cP @ sK1) = $true)),
% 1.52/1.23 introduced(definition,[new_symbols(naming,[spl6_7])],[avatar_definition])).
% 1.52/1.23 thf(f105,plain,(
% 1.52/1.23 ~spl6_4 | ~spl6_9),
% 1.52/1.23 inference(avatar_contradiction_clause,[status(thm)],[f104])).
% 1.52/1.23 thf(f104,plain,(
% 1.52/1.23 $false | (~spl6_4 | ~spl6_9)),
% 1.52/1.23 inference(trivial_inequality_removal,[status(thm)],[f100])).
% 1.52/1.23 thf(f100,plain,(
% 1.52/1.23 ($false = $true) | (~spl6_4 | ~spl6_9)),
% 1.52/1.23 inference(superposition,[status(thm)],[f62,f41])).
% 1.52/1.23 thf(f41,plain,(
% 1.52/1.23 ( ! [X7 : $i] : (($false = (cP @ X7))) ) | ~spl6_4),
% 1.52/1.23 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.52/1.23 thf(f62,plain,(
% 1.52/1.23 ((cP @ sK2) = $true) | ~spl6_9),
% 1.52/1.23 inference(avatar_component_clause,[status(thm)],[f60])).
% 1.52/1.23 thf(f98,plain,(
% 1.52/1.23 spl6_1 | ~spl6_4 | ~spl6_6),
% 1.52/1.23 inference(avatar_split_clause,[status(thm)],[f95,f48,f40,f29])).
% 1.52/1.23 thf(f48,definition,(
% 1.52/1.23 spl6_6 <=> ! [X0 : $i] : (((cP @ X0) = $true) | ((cP @ (sK0 @ X0)) = $true))),
% 1.52/1.23 introduced(definition,[new_symbols(naming,[spl6_6])],[avatar_definition])).
% 1.52/1.23 thf(f95,plain,(
% 1.52/1.23 ( ! [X0 : $i] : (((cP @ X0) = $true)) ) | (~spl6_4 | ~spl6_6)),
% 1.52/1.23 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.52/1.23 thf(f93,plain,(
% 1.52/1.23 ( ! [X0 : $i] : (($false = $true) | ((cP @ X0) = $true)) ) | (~spl6_4 | ~spl6_6)),
% 1.52/1.23 inference(superposition,[status(thm)],[f49,f41])).
% 1.52/1.23 thf(f49,plain,(
% 1.52/1.23 ( ! [X0 : $i] : (((cP @ (sK0 @ X0)) = $true) | ((cP @ X0) = $true)) ) | ~spl6_6),
% 1.52/1.23 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.52/1.23 thf(f88,plain,(
% 1.52/1.23 ~spl6_3 | ~spl6_5),
% 1.52/1.23 inference(avatar_contradiction_clause,[status(thm)],[f87])).
% 1.52/1.23 thf(f87,plain,(
% 1.52/1.23 $false | (~spl6_3 | ~spl6_5)),
% 1.52/1.23 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.52/1.23 thf(f83,plain,(
% 1.52/1.23 ($false = $true) | (~spl6_3 | ~spl6_5)),
% 1.52/1.23 inference(superposition,[status(thm)],[f45,f37])).
% 1.52/1.23 thf(f37,plain,(
% 1.52/1.23 ($false = (cP @ sK3)) | ~spl6_3),
% 1.52/1.23 inference(avatar_component_clause,[status(thm)],[f35])).
% 1.52/1.23 thf(f35,definition,(
% 1.52/1.23 spl6_3 <=> ($false = (cP @ sK3))),
% 1.52/1.23 introduced(definition,[new_symbols(naming,[spl6_3])],[avatar_definition])).
% 1.52/1.23 thf(f45,plain,(
% 1.52/1.23 ((cP @ sK3) = $true) | ~spl6_5),
% 1.52/1.23 inference(avatar_component_clause,[status(thm)],[f43])).
% 1.52/1.23 thf(f43,definition,(
% 1.52/1.23 spl6_5 <=> ((cP @ sK3) = $true)),
% 1.52/1.23 introduced(definition,[new_symbols(naming,[spl6_5])],[avatar_definition])).
% 1.52/1.23 thf(f82,plain,(
% 1.52/1.23 ~spl6_1 | ~spl6_2),
% 1.52/1.23 inference(avatar_contradiction_clause,[status(thm)],[f81])).
% 1.52/1.23 thf(f81,plain,(
% 1.52/1.23 $false | (~spl6_1 | ~spl6_2)),
% 1.52/1.23 inference(subsumption_resolution,[status(thm)],[f30,f33])).
% 1.52/1.23 thf(f33,plain,(
% 1.52/1.23 ( ! [X9 : $i] : (((cP @ X9) != $true)) ) | ~spl6_2),
% 1.52/1.23 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.52/1.23 thf(f32,definition,(
% 1.52/1.23 spl6_2 <=> ! [X9 : $i] : ((cP @ X9) != $true)),
% 1.52/1.23 introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition])).
% 1.52/1.23 thf(f80,plain,(
% 1.52/1.23 ~spl6_2 | ~spl6_9),
% 1.52/1.23 inference(avatar_contradiction_clause,[status(thm)],[f79])).
% 1.52/1.23 thf(f79,plain,(
% 1.52/1.23 $false | (~spl6_2 | ~spl6_9)),
% 1.52/1.23 inference(subsumption_resolution,[status(thm)],[f62,f33])).
% 1.52/1.23 thf(f78,plain,(
% 1.52/1.23 ~spl6_2 | ~spl6_6),
% 1.52/1.23 inference(avatar_contradiction_clause,[status(thm)],[f77])).
% 1.52/1.23 thf(f77,plain,(
% 1.52/1.23 $false | (~spl6_2 | ~spl6_6)),
% 1.52/1.23 inference(subsumption_resolution,[status(thm)],[f76,f33])).
% 1.52/1.23 thf(f76,plain,(
% 1.52/1.23 ( ! [X0 : $i] : (((cP @ X0) = $true)) ) | (~spl6_2 | ~spl6_6)),
% 1.52/1.23 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.52/1.23 thf(f75,plain,(
% 1.52/1.23 ( ! [X0 : $i] : (($true != $true) | ((cP @ X0) = $true)) ) | (~spl6_2 | ~spl6_6)),
% 1.52/1.23 inference(superposition,[status(thm)],[f33,f49])).
% 1.52/1.23 thf(f63,plain,(
% 1.52/1.23 spl6_6 | spl6_1 | spl6_9),
% 1.52/1.23 inference(avatar_split_clause,[status(thm)],[f22,f60,f29,f48])).
% 1.52/1.23 thf(f22,plain,(
% 1.52/1.23 ( ! [X0 : $i,X5 : $i] : (((cP @ sK2) = $true) | ((cP @ (sK0 @ X0)) = $true) | ((cP @ X5) = $true) | ((cP @ X0) = $true)) )),
% 1.52/1.23 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.52/1.23 thf(f18,plain,(
% 1.52/1.23 ( ! [X0 : $i,X5 : $i] : (((cP @ sK2) = $true) | ((cP @ X0) != (cP @ (sK0 @ X0))) | ((cP @ X5) = $true)) )),
% 1.52/1.23 inference(cnf_transformation,[status(thm)],[f15])).
% 1.52/1.23 thf(f15,plain,(
% 1.52/1.23 (! [X0 : $i] : ((cP @ X0) != (cP @ (sK0 @ X0))) | ((! [X2 : $i] : ((cP @ X2) != $true) | ((cP @ sK1) != $true)) & (((cP @ sK2) = $true) | ! [X5 : $i] : ((cP @ X5) = $true)))) & (! [X7 : $i] : ((cP @ X7) = (cP @ sK3)) | ((! [X8 : $i] : ($true = (cP @ X8)) | ! [X9 : $i] : ((cP @ X9) != $true)) & (((cP @ sK4) = $true) | ((cP @ sK5) != $true))))),
% 1.52/1.23 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f14,f13,f12,f11,f10,f9])).
% 1.52/1.23 thf(f9,plain,(
% 1.52/1.23 ! [X0 : $i] : (? [X1 : $i] : ((cP @ X0) != (cP @ X1)) => ((cP @ X0) != (cP @ (sK0 @ X0))))),
% 1.52/1.23 introduced(definition,[],[choice_axiom])).
% 1.52/1.23 thf(f10,plain,(
% 1.52/1.23 ? [X3 : $i] : ((cP @ X3) != $true) => ((cP @ sK1) != $true)),
% 1.52/1.23 introduced(definition,[],[choice_axiom])).
% 1.52/1.23 thf(f11,plain,(
% 1.52/1.23 ? [X4 : $i] : ((cP @ X4) = $true) => ((cP @ sK2) = $true)),
% 1.52/1.23 introduced(definition,[],[choice_axiom])).
% 1.52/1.23 thf(f12,plain,(
% 1.52/1.23 ? [X6 : $i] : ! [X7 : $i] : ((cP @ X6) = (cP @ X7)) => ! [X7 : $i] : ((cP @ X7) = (cP @ sK3))),
% 1.52/1.23 introduced(definition,[],[choice_axiom])).
% 1.52/1.23 thf(f13,plain,(
% 1.52/1.23 ? [X10 : $i] : ($true = (cP @ X10)) => ((cP @ sK4) = $true)),
% 1.52/1.23 introduced(definition,[],[choice_axiom])).
% 1.52/1.23 thf(f14,plain,(
% 1.52/1.23 ? [X11 : $i] : ((cP @ X11) != $true) => ((cP @ sK5) != $true)),
% 1.52/1.23 introduced(definition,[],[choice_axiom])).
% 1.52/1.23 thf(f8,plain,(
% 1.52/1.23 (! [X0 : $i] : ? [X1 : $i] : ((cP @ X0) != (cP @ X1)) | ((! [X2 : $i] : ((cP @ X2) != $true) | ? [X3 : $i] : ((cP @ X3) != $true)) & (? [X4 : $i] : ((cP @ X4) = $true) | ! [X5 : $i] : ((cP @ X5) = $true)))) & (? [X6 : $i] : ! [X7 : $i] : ((cP @ X6) = (cP @ X7)) | ((! [X8 : $i] : ($true = (cP @ X8)) | ! [X9 : $i] : ((cP @ X9) != $true)) & (? [X10 : $i] : ($true = (cP @ X10)) | ? [X11 : $i] : ((cP @ X11) != $true))))),
% 1.52/1.23 inference(rectify,[status(thm)],[f7])).
% 1.52/1.23 thf(f7,plain,(
% 1.52/1.23 (! [X2 : $i] : ? [X3 : $i] : ((cP @ X3) != (cP @ X2)) | ((! [X0 : $i] : ((cP @ X0) != $true) | ? [X1 : $i] : ((cP @ X1) != $true)) & (? [X0 : $i] : ((cP @ X0) = $true) | ! [X1 : $i] : ((cP @ X1) = $true)))) & (? [X2 : $i] : ! [X3 : $i] : ((cP @ X3) = (cP @ X2)) | ((! [X1 : $i] : ((cP @ X1) = $true) | ! [X0 : $i] : ((cP @ X0) != $true)) & (? [X0 : $i] : ((cP @ X0) = $true) | ? [X1 : $i] : ((cP @ X1) != $true))))),
% 1.52/1.23 inference(nnf_transformation,[status(thm)],[f6])).
% 1.52/1.23 thf(f6,plain,(
% 1.52/1.23 (! [X1 : $i] : ((cP @ X1) = $true) <=> ? [X0 : $i] : ((cP @ X0) = $true)) <~> ? [X2 : $i] : ! [X3 : $i] : ((cP @ X3) = (cP @ X2))),
% 1.52/1.23 inference(ennf_transformation,[status(thm)],[f5])).
% 1.52/1.23 thf(f5,plain,(
% 1.52/1.23 ~(? [X2 : $i] : ! [X3 : $i] : ((cP @ X3) = (cP @ X2)) <=> (! [X1 : $i] : ((cP @ X1) = $true) <=> ? [X0 : $i] : ((cP @ X0) = $true)))),
% 1.52/1.23 inference(fool_elimination,[status(thm)],[f4])).
% 1.52/1.23 thf(f4,plain,(
% 1.52/1.23 ~((? [X0 : $i] : (cP @ X0) <=> ! [X1 : $i] : (cP @ X1)) <=> ? [X2 : $i] : ! [X3 : $i] : ((cP @ X2) <=> (cP @ X3)))),
% 1.52/1.23 inference(rectify,[status(thm)],[f2])).
% 1.52/1.23 thf(f2,negated_conjecture,(
% 1.52/1.23 ~((? [X0 : $i] : (cP @ X0) <=> ! [X1 : $i] : (cP @ X1)) <=> ? [X0 : $i] : ! [X1 : $i] : ((cP @ X0) <=> (cP @ X1)))),
% 1.52/1.23 inference(negated_conjecture,[status(cth)],[f1])).
% 1.52/1.23 thf(f1,conjecture,(
% 1.52/1.23 (? [X0 : $i] : (cP @ X0) <=> ! [X1 : $i] : (cP @ X1)) <=> ? [X0 : $i] : ! [X1 : $i] : ((cP @ X0) <=> (cP @ X1))),
% 1.52/1.23 file('/export/starexec/sandbox/tmp/tmp.PXGkfGS3J0/DTF2THF_25233.p',cX2125)).
% 1.52/1.23 thf(f58,plain,(
% 1.52/1.23 spl6_8 | spl6_2 | ~spl6_7),
% 1.52/1.23 inference(avatar_split_clause,[status(thm)],[f25,f51,f32,f56])).
% 1.52/1.23 thf(f25,plain,(
% 1.52/1.23 ( ! [X2 : $i,X0 : $i] : (((cP @ X0) = $false) | ((cP @ sK1) != $true) | ((cP @ X2) != $true) | ($false = (cP @ (sK0 @ X0)))) )),
% 1.52/1.23 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.52/1.23 thf(f19,plain,(
% 1.52/1.23 ( ! [X2 : $i,X0 : $i] : (((cP @ X0) != (cP @ (sK0 @ X0))) | ((cP @ X2) != $true) | ((cP @ sK1) != $true)) )),
% 1.52/1.23 inference(cnf_transformation,[status(thm)],[f15])).
% 1.52/1.23 thf(f46,plain,(
% 1.52/1.23 spl6_4 | spl6_5 | spl6_2 | spl6_1),
% 1.52/1.23 inference(avatar_split_clause,[status(thm)],[f27,f29,f32,f43,f40])).
% 1.52/1.23 thf(f27,plain,(
% 1.52/1.23 ( ! [X8 : $i,X9 : $i,X7 : $i] : (($false = (cP @ X7)) | ((cP @ sK3) = $true) | ($true = (cP @ X8)) | ((cP @ X9) != $true)) )),
% 1.52/1.23 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.52/1.23 thf(f17,plain,(
% 1.52/1.23 ( ! [X8 : $i,X9 : $i,X7 : $i] : (((cP @ X7) = (cP @ sK3)) | ($true = (cP @ X8)) | ((cP @ X9) != $true)) )),
% 1.52/1.23 inference(cnf_transformation,[status(thm)],[f15])).
% 1.52/1.23 thf(f38,plain,(
% 1.52/1.23 spl6_1 | spl6_2 | spl6_1 | spl6_3),
% 1.52/1.23 inference(avatar_split_clause,[status(thm)],[f26,f35,f29,f32,f29])).
% 1.52/1.23 thf(f26,plain,(
% 1.52/1.23 ( ! [X8 : $i,X9 : $i,X7 : $i] : (((cP @ X9) != $true) | ($false = (cP @ sK3)) | ($true = (cP @ X8)) | ((cP @ X7) = $true)) )),
% 1.52/1.23 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.52/1.23 % SZS output end Proof for DTF2THF_25233
% 1.52/1.23 % (25341)------------------------------
% 1.52/1.23 % (25341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.23 % (25341)Termination reason: Refutation
% 1.52/1.23
% 1.52/1.23 % (25341)Memory used [KB]: 5500
% 1.52/1.23 % (25341)Time elapsed: 0.004 s
% 1.52/1.23 % (25341)Instructions burned: 4 (million)
% 1.52/1.23 % (25341)------------------------------
% 1.52/1.23 % (25341)------------------------------
% 1.52/1.23 % (25340)Success in time 0.014 s
%------------------------------------------------------------------------------