%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO112^5 : 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 : n005.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 09:53:24 AM UTC 2026
% Result : Theorem 1.52s 1.28s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 48 ( 1 unt; 0 typ; 6 def)
% Number of atoms : 406 ( 102 equ; 0 cnn)
% Maximal formula atoms : 16 ( 8 avg)
% Number of connectives : 311 ( 74 ~; 79 |; 17 &; 113 @)
% ( 20 <=>; 7 =>; 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 : 17 ( 14 usr; 15 con; 0-2 aty)
% Number of variables : 77 ( 0 ^; 44 !; 33 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP: $i > $o ).
thf(f85,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f49,f61,f66,f72,f74,f76,f78,f82,f84]) ).
thf(f84,plain,
( ~ spl7_1
| ~ spl7_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f83]) ).
thf(f83,plain,
( $false
| ~ spl7_1
| ~ spl7_7 ),
inference(subsumption_resolution,[status(thm)],[f53,f27]) ).
thf(f27,plain,
( ! [X11: $i] :
( ( cP @ X11 )
!= $true )
| ~ spl7_1 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl7_1
<=> ! [X11: $i] :
( ( cP @ X11 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_1])],[avatar_definition]) ).
thf(f53,plain,
( ( ( cP @ sK1 )
= $true )
| ~ spl7_7 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f51,definition,
( spl7_7
<=> ( ( cP @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_7])],[avatar_definition]) ).
thf(f82,plain,
( ~ spl7_1
| ~ spl7_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f81]) ).
thf(f81,plain,
( $false
| ~ spl7_1
| ~ spl7_6 ),
inference(subsumption_resolution,[status(thm)],[f47,f27]) ).
thf(f47,plain,
( ( ( cP @ sK2 )
= $true )
| ~ spl7_6 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f46,definition,
( spl7_6
<=> ( ( cP @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_6])],[avatar_definition]) ).
thf(f78,plain,
( ~ spl7_1
| ~ spl7_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f77]) ).
thf(f77,plain,
( $false
| ~ spl7_1
| ~ spl7_9 ),
inference(subsumption_resolution,[status(thm)],[f60,f27]) ).
thf(f60,plain,
( ( ( cP @ sK3 )
= $true )
| ~ spl7_9 ),
inference(avatar_component_clause,[status(thm)],[f58]) ).
thf(f58,definition,
( spl7_9
<=> ( ( cP @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_9])],[avatar_definition]) ).
thf(f76,plain,
( ~ spl7_1
| ~ spl7_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f75]) ).
thf(f75,plain,
( $false
| ~ spl7_1
| ~ spl7_8 ),
inference(subsumption_resolution,[status(thm)],[f27,f56]) ).
thf(f56,plain,
( ! [X2: $i] :
( ( cP @ X2 )
= $true )
| ~ spl7_8 ),
inference(avatar_component_clause,[status(thm)],[f55]) ).
thf(f55,definition,
( spl7_8
<=> ! [X2: $i] :
( ( cP @ X2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_8])],[avatar_definition]) ).
thf(f74,plain,
( spl7_6
| ~ spl7_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f73]) ).
thf(f73,plain,
( $false
| spl7_6
| ~ spl7_8 ),
inference(subsumption_resolution,[status(thm)],[f48,f56]) ).
thf(f48,plain,
( ( ( cP @ sK2 )
!= $true )
| spl7_6 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f72,plain,
( spl7_5
| ~ spl7_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f71]) ).
thf(f71,plain,
( $false
| spl7_5
| ~ spl7_8 ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
( ( $true != $true )
| spl7_5
| ~ spl7_8 ),
inference(superposition,[status(thm)],[f44,f56]) ).
thf(f44,plain,
( ( ( cP @ sK0 )
!= $true )
| spl7_5 ),
inference(avatar_component_clause,[status(thm)],[f42]) ).
thf(f42,definition,
( spl7_5
<=> ( ( cP @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_5])],[avatar_definition]) ).
thf(f66,plain,
( spl7_1
| spl7_8
| spl7_8
| spl7_1 ),
inference(avatar_split_clause,[status(thm)],[f18,f26,f55,f55,f26]) ).
thf(f18,plain,
! [X10: $i,X11: $i,X9: $i,X12: $i] :
( ( ( cP @ X12 )
!= $true )
| ( ( cP @ X10 )
!= $true )
| ( ( cP @ X11 )
= $true )
| ( ( cP @ X9 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( ( ( ( cP @ sK0 )
!= $true )
| ! [X1: $i] :
( ( cP @ X1 )
!= $true ) )
& ( ! [X2: $i] :
( ( cP @ X2 )
= $true )
| ( ( cP @ sK1 )
= $true ) ) )
| ( ( ! [X5: $i] :
( ( cP @ X5 )
!= $true )
| ( ( cP @ sK2 )
!= $true ) )
& ( ( ( cP @ sK3 )
= $true )
| ( ( cP @ sK2 )
= $true ) ) ) )
& ( ( ( ( ( cP @ sK4 )
= $true )
| ( ( cP @ sK5 )
!= $true ) )
& ( ! [X9: $i] :
( ( cP @ X9 )
= $true )
| ! [X10: $i] :
( ( cP @ X10 )
!= $true ) ) )
| ! [X11: $i] :
( ( ( ( cP @ X11 )
= $true )
| ! [X12: $i] :
( ( cP @ X12 )
!= $true ) )
& ( ( ( cP @ sK6 )
= $true )
| ( ( cP @ X11 )
!= $true ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f8,f15,f14,f13,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: $i] :
( ( cP @ X0 )
!= $true )
=> ( ( cP @ sK0 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X3: $i] :
( ( cP @ X3 )
= $true )
=> ( ( cP @ sK1 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X4: $i] :
( ( ! [X5: $i] :
( ( cP @ X5 )
!= $true )
| ( ( cP @ X4 )
!= $true ) )
& ( ? [X6: $i] :
( $true
= ( cP @ X6 ) )
| ( ( cP @ X4 )
= $true ) ) )
=> ( ( ! [X5: $i] :
( ( cP @ X5 )
!= $true )
| ( ( cP @ sK2 )
!= $true ) )
& ( ? [X6: $i] :
( $true
= ( cP @ X6 ) )
| ( ( cP @ sK2 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X6: $i] :
( $true
= ( cP @ X6 ) )
=> ( ( cP @ sK3 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X7: $i] :
( ( cP @ X7 )
= $true )
=> ( ( cP @ sK4 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X8: $i] :
( ( cP @ X8 )
!= $true )
=> ( ( cP @ sK5 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ? [X13: $i] :
( ( cP @ X13 )
= $true )
=> ( ( cP @ sK6 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ( ( ( ? [X0: $i] :
( ( cP @ X0 )
!= $true )
| ! [X1: $i] :
( ( cP @ X1 )
!= $true ) )
& ( ! [X2: $i] :
( ( cP @ X2 )
= $true )
| ? [X3: $i] :
( ( cP @ X3 )
= $true ) ) )
| ? [X4: $i] :
( ( ! [X5: $i] :
( ( cP @ X5 )
!= $true )
| ( ( cP @ X4 )
!= $true ) )
& ( ? [X6: $i] :
( $true
= ( cP @ X6 ) )
| ( ( cP @ X4 )
= $true ) ) ) )
& ( ( ( ? [X7: $i] :
( ( cP @ X7 )
= $true )
| ? [X8: $i] :
( ( cP @ X8 )
!= $true ) )
& ( ! [X9: $i] :
( ( cP @ X9 )
= $true )
| ! [X10: $i] :
( ( cP @ X10 )
!= $true ) ) )
| ! [X11: $i] :
( ( ( ( cP @ X11 )
= $true )
| ! [X12: $i] :
( ( cP @ X12 )
!= $true ) )
& ( ? [X13: $i] :
( ( cP @ X13 )
= $true )
| ( ( cP @ X11 )
!= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( ( ? [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 )
!= $true )
| ( ( cP @ X2 )
!= $true ) )
& ( ? [X3: $i] :
( ( cP @ X3 )
= $true )
| ( ( cP @ X2 )
= $true ) ) ) )
& ( ( ( ? [X1: $i] :
( ( cP @ X1 )
= $true )
| ? [X0: $i] :
( ( cP @ X0 )
!= $true ) )
& ( ! [X0: $i] :
( ( cP @ X0 )
= $true )
| ! [X1: $i] :
( ( cP @ X1 )
!= $true ) ) )
| ! [X2: $i] :
( ( ( ( cP @ X2 )
= $true )
| ! [X3: $i] :
( ( cP @ X3 )
!= $true ) )
& ( ? [X3: $i] :
( ( cP @ X3 )
= $true )
| ( ( cP @ X2 )
!= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X2: $i] :
( ( ( cP @ X2 )
= $true )
<=> ? [X3: $i] :
( ( cP @ X3 )
= $true ) )
<~> ( ? [X1: $i] :
( ( cP @ X1 )
= $true )
<=> ! [X0: $i] :
( ( cP @ X0 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ? [X1: $i] :
( ( cP @ X1 )
= $true )
<=> ! [X0: $i] :
( ( cP @ X0 )
= $true ) )
<=> ! [X2: $i] :
( ( ( cP @ X2 )
= $true )
<=> ? [X3: $i] :
( ( cP @ X3 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] : ( cP @ X0 )
<=> ? [X1: $i] : ( cP @ X1 ) )
<=> ! [X2: $i] :
( ? [X3: $i] : ( cP @ X3 )
<=> ( cP @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i] : ( cP @ X0 )
<=> ? [X1: $i] : ( cP @ X1 ) )
<=> ! [X0: $i] :
( ? [X1: $i] : ( cP @ X1 )
<=> ( cP @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: $i] : ( cP @ X0 )
<=> ? [X1: $i] : ( cP @ X1 ) )
<=> ! [X0: $i] :
( ? [X1: $i] : ( cP @ X1 )
<=> ( cP @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.azw7MPOaOs/DTF2THF_19116.p',cTHM53) ).
thf(f61,plain,
( spl7_7
| spl7_8
| spl7_9
| spl7_6 ),
inference(avatar_split_clause,[status(thm)],[f21,f46,f58,f55,f51]) ).
thf(f21,plain,
! [X2: $i] :
( ( ( cP @ X2 )
= $true )
| ( ( cP @ sK2 )
= $true )
| ( ( cP @ sK3 )
= $true )
| ( ( cP @ sK1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f49,plain,
( ~ spl7_5
| ~ spl7_6
| spl7_1
| spl7_1 ),
inference(avatar_split_clause,[status(thm)],[f24,f26,f26,f46,f42]) ).
thf(f24,plain,
! [X1: $i,X5: $i] :
( ( ( cP @ X5 )
!= $true )
| ( ( cP @ sK0 )
!= $true )
| ( ( cP @ sK2 )
!= $true )
| ( ( cP @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO112^5 : 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
% 0.16/0.34 % Computer : n005.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:24:29 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : SYO112^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.47 % Domain : Syntactic
% 0.20/0.47 % Problem : TPS problem THM53
% 0.20/0.47 % Version : Especial.
% 0.20/0.47 % English :
% 0.20/0.47
% 0.20/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.47 % Source : [Bro09]
% 0.20/0.47 % Names : tps_0481 [Bro09]
% 0.20/0.47 % : THM53 [TPS]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % 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 v4.0.0
% 0.20/0.47 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.20/0.47 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 4 ( 4 avg)
% 0.20/0.47 % Number of connectives : 7 ( 0 ~; 0 |; 0 &; 4 @)
% 0.20/0.47 % ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 6 ( 6 avg)
% 0.20/0.47 % Number of types : 2 ( 0 usr)
% 0.20/0.47 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 1 ( 1 usr; 0 con; 1-1 aty)
% 0.20/0.47 % Number of variables : 4 ( 0 ^; 2 !; 2 ?; 4 :)
% 0.20/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.47
% 0.20/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 thf(cP,type,
% 0.20/0.47 cP: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(cTHM53,conjecture,
% 0.20/0.47 ( ! [X: $i] :
% 0.20/0.47 ( ( cP @ X )
% 0.20/0.47 <=> ? [Y: $i] : ( cP @ Y ) )
% 0.20/0.47 <=> ( ! [X: $i] : ( cP @ X )
% 0.20/0.47 <=> ? [Y: $i] : ( cP @ Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 1.52/1.26 ---- Embedded in THF ---
% 1.52/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.26 %%% Generated on Tue Feb 24 14:24:30 EST 2026
% 1.52/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.26 %%% Logic specification used:
% 1.52/1.26 %%% thf(spec, logic, $$dhol).
% 1.52/1.26
% 1.52/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.azw7MPOaOs/DTF2DTF19116.p
% See solution above
% 1.52/1.26 ------------------------
% 1.52/1.27 ---- Cleaned THF ---
% 1.52/1.27 thf(cP,type,
% 1.52/1.27 cP: $i > $o ).
% 1.52/1.27
% 1.52/1.27 thf(cTHM53,conjecture,
% 1.52/1.27 ( ! [X: $i] :
% 1.52/1.27 ( ( cP @ X )
% 1.52/1.27 <=> ? [Y: $i] : ( cP @ Y ) )
% 1.52/1.27 <=> ( ! [X: $i] : ( cP @ X )
% 1.52/1.27 <=> ? [Y: $i] : ( cP @ Y ) ) ) ).
% 1.52/1.27 ------------------------
% 1.52/1.28 % (19304)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19116 for (2999ds/183Mi)
% 1.52/1.28 % (19307)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19116 for (2999ds/2Mi)
% 1.52/1.28 % (19304)First to succeed.
% 1.52/1.28 % (19307)Instruction limit reached!
% 1.52/1.28 % (19307)------------------------------
% 1.52/1.28 % (19307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.28 % (19307)Termination reason: Unknown
% 1.52/1.28 % (19307)Termination phase: Saturation
% 1.52/1.28
% 1.52/1.28 % (19307)Memory used [KB]: 5500
% 1.52/1.28 % (19307)Time elapsed: 0.002 s
% 1.52/1.28 % (19307)Instructions burned: 3 (million)
% 1.52/1.28 % (19307)------------------------------
% 1.52/1.28 % (19307)------------------------------
% 1.52/1.28 % (19304)Refutation found. Thanks to Tanya!
% 1.52/1.28 % SZS status Theorem for DTF2THF_19116
% 1.52/1.28 % SZS output start Proof for DTF2THF_19116
% 1.52/1.28 thf(func_def_0, type, cP: $i > $o).
% 1.52/1.28 thf(f85,plain,(
% 1.52/1.28 $false),
% 1.52/1.28 inference(avatar_sat_refutation,[status(thm)],[f49,f61,f66,f72,f74,f76,f78,f82,f84])).
% 1.52/1.28 thf(f84,plain,(
% 1.52/1.28 ~spl7_1 | ~spl7_7),
% 1.52/1.28 inference(avatar_contradiction_clause,[status(thm)],[f83])).
% 1.52/1.28 thf(f83,plain,(
% 1.52/1.28 $false | (~spl7_1 | ~spl7_7)),
% 1.52/1.28 inference(subsumption_resolution,[status(thm)],[f53,f27])).
% 1.52/1.28 thf(f27,plain,(
% 1.52/1.28 ( ! [X11 : $i] : (((cP @ X11) != $true)) ) | ~spl7_1),
% 1.52/1.28 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.52/1.28 thf(f26,definition,(
% 1.52/1.28 spl7_1 <=> ! [X11 : $i] : ((cP @ X11) != $true)),
% 1.52/1.28 introduced(definition,[new_symbols(naming,[spl7_1])],[avatar_definition])).
% 1.52/1.28 thf(f53,plain,(
% 1.52/1.28 ((cP @ sK1) = $true) | ~spl7_7),
% 1.52/1.28 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.52/1.28 thf(f51,definition,(
% 1.52/1.28 spl7_7 <=> ((cP @ sK1) = $true)),
% 1.52/1.28 introduced(definition,[new_symbols(naming,[spl7_7])],[avatar_definition])).
% 1.52/1.28 thf(f82,plain,(
% 1.52/1.28 ~spl7_1 | ~spl7_6),
% 1.52/1.28 inference(avatar_contradiction_clause,[status(thm)],[f81])).
% 1.52/1.28 thf(f81,plain,(
% 1.52/1.28 $false | (~spl7_1 | ~spl7_6)),
% 1.52/1.28 inference(subsumption_resolution,[status(thm)],[f47,f27])).
% 1.52/1.28 thf(f47,plain,(
% 1.52/1.28 ((cP @ sK2) = $true) | ~spl7_6),
% 1.52/1.28 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.52/1.28 thf(f46,definition,(
% 1.52/1.28 spl7_6 <=> ((cP @ sK2) = $true)),
% 1.52/1.28 introduced(definition,[new_symbols(naming,[spl7_6])],[avatar_definition])).
% 1.52/1.28 thf(f78,plain,(
% 1.52/1.28 ~spl7_1 | ~spl7_9),
% 1.52/1.28 inference(avatar_contradiction_clause,[status(thm)],[f77])).
% 1.52/1.28 thf(f77,plain,(
% 1.52/1.28 $false | (~spl7_1 | ~spl7_9)),
% 1.52/1.28 inference(subsumption_resolution,[status(thm)],[f60,f27])).
% 1.52/1.28 thf(f60,plain,(
% 1.52/1.28 ((cP @ sK3) = $true) | ~spl7_9),
% 1.52/1.28 inference(avatar_component_clause,[status(thm)],[f58])).
% 1.52/1.28 thf(f58,definition,(
% 1.52/1.28 spl7_9 <=> ((cP @ sK3) = $true)),
% 1.52/1.28 introduced(definition,[new_symbols(naming,[spl7_9])],[avatar_definition])).
% 1.52/1.28 thf(f76,plain,(
% 1.52/1.28 ~spl7_1 | ~spl7_8),
% 1.52/1.28 inference(avatar_contradiction_clause,[status(thm)],[f75])).
% 1.52/1.28 thf(f75,plain,(
% 1.52/1.28 $false | (~spl7_1 | ~spl7_8)),
% 1.52/1.28 inference(subsumption_resolution,[status(thm)],[f27,f56])).
% 1.52/1.28 thf(f56,plain,(
% 1.52/1.28 ( ! [X2 : $i] : (((cP @ X2) = $true)) ) | ~spl7_8),
% 1.52/1.28 inference(avatar_component_clause,[status(thm)],[f55])).
% 1.52/1.28 thf(f55,definition,(
% 1.52/1.28 spl7_8 <=> ! [X2 : $i] : ((cP @ X2) = $true)),
% 1.52/1.28 introduced(definition,[new_symbols(naming,[spl7_8])],[avatar_definition])).
% 1.52/1.28 thf(f74,plain,(
% 1.52/1.28 spl7_6 | ~spl7_8),
% 1.52/1.28 inference(avatar_contradiction_clause,[status(thm)],[f73])).
% 1.52/1.28 thf(f73,plain,(
% 1.52/1.28 $false | (spl7_6 | ~spl7_8)),
% 1.52/1.28 inference(subsumption_resolution,[status(thm)],[f48,f56])).
% 1.52/1.28 thf(f48,plain,(
% 1.52/1.28 ((cP @ sK2) != $true) | spl7_6),
% 1.52/1.28 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.52/1.28 thf(f72,plain,(
% 1.52/1.28 spl7_5 | ~spl7_8),
% 1.52/1.28 inference(avatar_contradiction_clause,[status(thm)],[f71])).
% 1.52/1.28 thf(f71,plain,(
% 1.52/1.28 $false | (spl7_5 | ~spl7_8)),
% 1.52/1.28 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.52/1.28 thf(f68,plain,(
% 1.52/1.28 ($true != $true) | (spl7_5 | ~spl7_8)),
% 1.52/1.28 inference(superposition,[status(thm)],[f44,f56])).
% 1.52/1.28 thf(f44,plain,(
% 1.52/1.28 ((cP @ sK0) != $true) | spl7_5),
% 1.52/1.28 inference(avatar_component_clause,[status(thm)],[f42])).
% 1.52/1.28 thf(f42,definition,(
% 1.52/1.28 spl7_5 <=> ((cP @ sK0) = $true)),
% 1.52/1.28 introduced(definition,[new_symbols(naming,[spl7_5])],[avatar_definition])).
% 1.52/1.28 thf(f66,plain,(
% 1.52/1.28 spl7_1 | spl7_8 | spl7_8 | spl7_1),
% 1.52/1.28 inference(avatar_split_clause,[status(thm)],[f18,f26,f55,f55,f26])).
% 1.52/1.28 thf(f18,plain,(
% 1.52/1.28 ( ! [X10 : $i,X11 : $i,X9 : $i,X12 : $i] : (((cP @ X12) != $true) | ((cP @ X10) != $true) | ((cP @ X11) = $true) | ((cP @ X9) = $true)) )),
% 1.52/1.28 inference(cnf_transformation,[status(thm)],[f16])).
% 1.52/1.28 thf(f16,plain,(
% 1.52/1.28 (((((cP @ sK0) != $true) | ! [X1 : $i] : ((cP @ X1) != $true)) & (! [X2 : $i] : ((cP @ X2) = $true) | ((cP @ sK1) = $true))) | ((! [X5 : $i] : ((cP @ X5) != $true) | ((cP @ sK2) != $true)) & (((cP @ sK3) = $true) | ((cP @ sK2) = $true)))) & (((((cP @ sK4) = $true) | ((cP @ sK5) != $true)) & (! [X9 : $i] : ((cP @ X9) = $true) | ! [X10 : $i] : ((cP @ X10) != $true))) | ! [X11 : $i] : ((((cP @ X11) = $true) | ! [X12 : $i] : ((cP @ X12) != $true)) & (((cP @ sK6) = $true) | ((cP @ X11) != $true))))),
% 1.52/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f8,f15,f14,f13,f12,f11,f10,f9])).
% 1.52/1.28 thf(f9,plain,(
% 1.52/1.28 ? [X0 : $i] : ((cP @ X0) != $true) => ((cP @ sK0) != $true)),
% 1.52/1.28 introduced(definition,[],[choice_axiom])).
% 1.52/1.28 thf(f10,plain,(
% 1.52/1.28 ? [X3 : $i] : ((cP @ X3) = $true) => ((cP @ sK1) = $true)),
% 1.52/1.28 introduced(definition,[],[choice_axiom])).
% 1.52/1.28 thf(f11,plain,(
% 1.52/1.28 ? [X4 : $i] : ((! [X5 : $i] : ((cP @ X5) != $true) | ((cP @ X4) != $true)) & (? [X6 : $i] : ($true = (cP @ X6)) | ((cP @ X4) = $true))) => ((! [X5 : $i] : ((cP @ X5) != $true) | ((cP @ sK2) != $true)) & (? [X6 : $i] : ($true = (cP @ X6)) | ((cP @ sK2) = $true)))),
% 1.52/1.28 introduced(definition,[],[choice_axiom])).
% 1.52/1.28 thf(f12,plain,(
% 1.52/1.28 ? [X6 : $i] : ($true = (cP @ X6)) => ((cP @ sK3) = $true)),
% 1.52/1.28 introduced(definition,[],[choice_axiom])).
% 1.52/1.28 thf(f13,plain,(
% 1.52/1.28 ? [X7 : $i] : ((cP @ X7) = $true) => ((cP @ sK4) = $true)),
% 1.52/1.28 introduced(definition,[],[choice_axiom])).
% 1.52/1.28 thf(f14,plain,(
% 1.52/1.28 ? [X8 : $i] : ((cP @ X8) != $true) => ((cP @ sK5) != $true)),
% 1.52/1.28 introduced(definition,[],[choice_axiom])).
% 1.52/1.28 thf(f15,plain,(
% 1.52/1.28 ? [X13 : $i] : ((cP @ X13) = $true) => ((cP @ sK6) = $true)),
% 1.52/1.28 introduced(definition,[],[choice_axiom])).
% 1.52/1.28 thf(f8,plain,(
% 1.52/1.28 (((? [X0 : $i] : ((cP @ X0) != $true) | ! [X1 : $i] : ((cP @ X1) != $true)) & (! [X2 : $i] : ((cP @ X2) = $true) | ? [X3 : $i] : ((cP @ X3) = $true))) | ? [X4 : $i] : ((! [X5 : $i] : ((cP @ X5) != $true) | ((cP @ X4) != $true)) & (? [X6 : $i] : ($true = (cP @ X6)) | ((cP @ X4) = $true)))) & (((? [X7 : $i] : ((cP @ X7) = $true) | ? [X8 : $i] : ((cP @ X8) != $true)) & (! [X9 : $i] : ((cP @ X9) = $true) | ! [X10 : $i] : ((cP @ X10) != $true))) | ! [X11 : $i] : ((((cP @ X11) = $true) | ! [X12 : $i] : ((cP @ X12) != $true)) & (? [X13 : $i] : ((cP @ X13) = $true) | ((cP @ X11) != $true))))),
% 1.52/1.28 inference(rectify,[status(thm)],[f7])).
% 1.52/1.28 thf(f7,plain,(
% 1.52/1.28 (((? [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) != $true) | ((cP @ X2) != $true)) & (? [X3 : $i] : ((cP @ X3) = $true) | ((cP @ X2) = $true)))) & (((? [X1 : $i] : ((cP @ X1) = $true) | ? [X0 : $i] : ((cP @ X0) != $true)) & (! [X0 : $i] : ((cP @ X0) = $true) | ! [X1 : $i] : ((cP @ X1) != $true))) | ! [X2 : $i] : ((((cP @ X2) = $true) | ! [X3 : $i] : ((cP @ X3) != $true)) & (? [X3 : $i] : ((cP @ X3) = $true) | ((cP @ X2) != $true))))),
% 1.52/1.28 inference(nnf_transformation,[status(thm)],[f6])).
% 1.52/1.28 thf(f6,plain,(
% 1.52/1.28 ! [X2 : $i] : (((cP @ X2) = $true) <=> ? [X3 : $i] : ((cP @ X3) = $true)) <~> (? [X1 : $i] : ((cP @ X1) = $true) <=> ! [X0 : $i] : ((cP @ X0) = $true))),
% 1.52/1.28 inference(ennf_transformation,[status(thm)],[f5])).
% 1.52/1.28 thf(f5,plain,(
% 1.52/1.28 ~((? [X1 : $i] : ((cP @ X1) = $true) <=> ! [X0 : $i] : ((cP @ X0) = $true)) <=> ! [X2 : $i] : (((cP @ X2) = $true) <=> ? [X3 : $i] : ((cP @ X3) = $true)))),
% 1.52/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.52/1.28 thf(f4,plain,(
% 1.52/1.28 ~((! [X0 : $i] : (cP @ X0) <=> ? [X1 : $i] : (cP @ X1)) <=> ! [X2 : $i] : (? [X3 : $i] : (cP @ X3) <=> (cP @ X2)))),
% 1.52/1.28 inference(rectify,[status(thm)],[f2])).
% 1.52/1.28 thf(f2,negated_conjecture,(
% 1.52/1.28 ~((! [X0 : $i] : (cP @ X0) <=> ? [X1 : $i] : (cP @ X1)) <=> ! [X0 : $i] : (? [X1 : $i] : (cP @ X1) <=> (cP @ X0)))),
% 1.52/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.52/1.28 thf(f1,conjecture,(
% 1.52/1.28 (! [X0 : $i] : (cP @ X0) <=> ? [X1 : $i] : (cP @ X1)) <=> ! [X0 : $i] : (? [X1 : $i] : (cP @ X1) <=> (cP @ X0))),
% 1.52/1.28 file('/export/starexec/sandbox/tmp/tmp.azw7MPOaOs/DTF2THF_19116.p',cTHM53)).
% 1.52/1.28 thf(f61,plain,(
% 1.52/1.28 spl7_7 | spl7_8 | spl7_9 | spl7_6),
% 1.52/1.28 inference(avatar_split_clause,[status(thm)],[f21,f46,f58,f55,f51])).
% 1.52/1.28 thf(f21,plain,(
% 1.52/1.28 ( ! [X2 : $i] : (((cP @ X2) = $true) | ((cP @ sK2) = $true) | ((cP @ sK3) = $true) | ((cP @ sK1) = $true)) )),
% 1.52/1.28 inference(cnf_transformation,[status(thm)],[f16])).
% 1.52/1.28 thf(f49,plain,(
% 1.52/1.28 ~spl7_5 | ~spl7_6 | spl7_1 | spl7_1),
% 1.52/1.28 inference(avatar_split_clause,[status(thm)],[f24,f26,f26,f46,f42])).
% 1.52/1.28 thf(f24,plain,(
% 1.52/1.28 ( ! [X1 : $i,X5 : $i] : (((cP @ X5) != $true) | ((cP @ sK0) != $true) | ((cP @ sK2) != $true) | ((cP @ X1) != $true)) )),
% 1.52/1.28 inference(cnf_transformation,[status(thm)],[f16])).
% 1.52/1.28 % SZS output end Proof for DTF2THF_19116
% 1.52/1.28 % (19304)------------------------------
% 1.52/1.28 % (19304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.28 % (19304)Termination reason: Refutation
% 1.52/1.28
% 1.52/1.28 % (19304)Memory used [KB]: 5500
% 1.52/1.28 % (19304)Time elapsed: 0.003 s
% 1.52/1.28 % (19304)Instructions burned: 2 (million)
% 1.52/1.28 % (19304)------------------------------
% 1.52/1.28 % (19304)------------------------------
% 1.52/1.28 % (19303)Success in time 0.002 s
%------------------------------------------------------------------------------