%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN377^5 : 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 : n017.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 1.51s 1.24s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 47 ( 1 unt; 0 typ; 6 def)
% Number of atoms : 401 ( 101 equ; 0 cnn)
% Maximal formula atoms : 16 ( 8 avg)
% Number of connectives : 310 ( 75 ~; 77 |; 17 &; 113 @)
% ( 20 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 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 ^; 49 !; 28 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP: $i > $o ).
thf(f83,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f44,f54,f64,f68,f70,f72,f74,f76,f82]) ).
thf(f82,plain,
( ~ spl7_1
| ~ spl7_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f81]) ).
thf(f81,plain,
( $false
| ~ spl7_1
| ~ spl7_4 ),
inference(subsumption_resolution,[status(thm)],[f39,f27]) ).
thf(f27,plain,
( ! [X8: $i] :
( ( cP @ X8 )
!= $true )
| ~ spl7_1 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl7_1
<=> ! [X8: $i] :
( ( cP @ X8 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_1])],[avatar_definition]) ).
thf(f39,plain,
( ( ( cP @ sK1 )
= $true )
| ~ spl7_4 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f37,definition,
( spl7_4
<=> ( ( cP @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_4])],[avatar_definition]) ).
thf(f76,plain,
( ~ spl7_1
| ~ spl7_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f75]) ).
thf(f75,plain,
( $false
| ~ spl7_1
| ~ spl7_5 ),
inference(subsumption_resolution,[status(thm)],[f43,f27]) ).
thf(f43,plain,
( ( ( cP @ sK2 )
= $true )
| ~ spl7_5 ),
inference(avatar_component_clause,[status(thm)],[f41]) ).
thf(f41,definition,
( spl7_5
<=> ( ( cP @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_5])],[avatar_definition]) ).
thf(f74,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f73]) ).
thf(f73,plain,
( $false
| ~ spl7_1
| ~ spl7_2 ),
inference(subsumption_resolution,[status(thm)],[f27,f30]) ).
thf(f30,plain,
( ! [X7: $i] :
( ( cP @ X7 )
= $true )
| ~ spl7_2 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl7_2
<=> ! [X7: $i] :
( ( cP @ X7 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_2])],[avatar_definition]) ).
thf(f72,plain,
( ~ spl7_2
| spl7_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f71]) ).
thf(f71,plain,
( $false
| ~ spl7_2
| spl7_8 ),
inference(subsumption_resolution,[status(thm)],[f58,f30]) ).
thf(f58,plain,
( ( ( cP @ sK0 )
!= $true )
| spl7_8 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f56,definition,
( spl7_8
<=> ( ( cP @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_8])],[avatar_definition]) ).
thf(f70,plain,
( ~ spl7_2
| spl7_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f69]) ).
thf(f69,plain,
( $false
| ~ spl7_2
| spl7_9 ),
inference(subsumption_resolution,[status(thm)],[f63,f30]) ).
thf(f63,plain,
( ( ( cP @ sK3 )
!= $true )
| spl7_9 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f61,definition,
( spl7_9
<=> ( ( cP @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_9])],[avatar_definition]) ).
thf(f68,plain,
( ~ spl7_2
| spl7_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f67]) ).
thf(f67,plain,
( $false
| ~ spl7_2
| spl7_5 ),
inference(subsumption_resolution,[status(thm)],[f42,f30]) ).
thf(f42,plain,
( ( ( cP @ sK2 )
!= $true )
| spl7_5 ),
inference(avatar_component_clause,[status(thm)],[f41]) ).
thf(f64,plain,
( ~ spl7_9
| ~ spl7_5
| spl7_1
| ~ spl7_8 ),
inference(avatar_split_clause,[status(thm)],[f24,f56,f26,f41,f61]) ).
thf(f24,plain,
! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( cP @ sK2 )
!= $true )
| ( ( cP @ sK3 )
!= $true )
| ( ( cP @ sK0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( ( ! [X0: $i] :
( ( cP @ X0 )
!= $true )
| ( ( cP @ sK0 )
!= $true ) )
& ( ( ( cP @ sK1 )
= $true )
| ! [X3: $i] :
( ( cP @ X3 )
= $true ) ) )
| ( ( ( ( cP @ sK3 )
!= $true )
| ( ( cP @ sK2 )
!= $true ) )
& ( ! [X6: $i] :
( ( cP @ X6 )
= $true )
| ( ( cP @ sK2 )
= $true ) ) ) )
& ( ( ( ! [X7: $i] :
( ( cP @ X7 )
= $true )
| ! [X8: $i] :
( ( cP @ X8 )
!= $true ) )
& ( ( ( cP @ sK4 )
= $true )
| ( ( cP @ sK5 )
!= $true ) ) )
| ! [X11: $i] :
( ( ( ( cP @ X11 )
= $true )
| ( ( cP @ sK6 )
!= $true ) )
& ( ! [X13: $i] :
( ( cP @ X13 )
= $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,
( ? [X1: $i] :
( ( cP @ X1 )
!= $true )
=> ( ( cP @ sK0 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X2: $i] :
( ( cP @ X2 )
= $true )
=> ( ( cP @ sK1 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X4: $i] :
( ( ? [X5: $i] :
( ( cP @ X5 )
!= $true )
| ( ( cP @ X4 )
!= $true ) )
& ( ! [X6: $i] :
( ( cP @ X6 )
= $true )
| ( ( cP @ X4 )
= $true ) ) )
=> ( ( ? [X5: $i] :
( ( cP @ X5 )
!= $true )
| ( ( cP @ sK2 )
!= $true ) )
& ( ! [X6: $i] :
( ( cP @ X6 )
= $true )
| ( ( cP @ sK2 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X5: $i] :
( ( cP @ X5 )
!= $true )
=> ( ( cP @ sK3 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X9: $i] :
( $true
= ( cP @ X9 ) )
=> ( ( cP @ sK4 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X10: $i] :
( $true
!= ( cP @ X10 ) )
=> ( ( cP @ sK5 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ? [X12: $i] :
( $true
!= ( cP @ X12 ) )
=> ( ( 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] :
( ( cP @ X6 )
= $true )
| ( ( cP @ X4 )
= $true ) ) ) )
& ( ( ( ! [X7: $i] :
( ( cP @ X7 )
= $true )
| ! [X8: $i] :
( ( cP @ X8 )
!= $true ) )
& ( ? [X9: $i] :
( $true
= ( cP @ X9 ) )
| ? [X10: $i] :
( $true
!= ( cP @ X10 ) ) ) )
| ! [X11: $i] :
( ( ( ( cP @ X11 )
= $true )
| ? [X12: $i] :
( $true
!= ( cP @ X12 ) ) )
& ( ! [X13: $i] :
( ( cP @ X13 )
= $true )
| ( ( cP @ X11 )
!= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( ( ! [X2: $i] :
( ( cP @ X2 )
!= $true )
| ? [X3: $i] :
( ( cP @ X3 )
!= $true ) )
& ( ? [X2: $i] :
( ( cP @ X2 )
= $true )
| ! [X3: $i] :
( ( cP @ X3 )
= $true ) ) )
| ? [X0: $i] :
( ( ? [X1: $i] :
( ( cP @ X1 )
!= $true )
| ( ( cP @ X0 )
!= $true ) )
& ( ! [X1: $i] :
( ( cP @ X1 )
= $true )
| ( ( cP @ X0 )
= $true ) ) ) )
& ( ( ( ! [X3: $i] :
( ( cP @ X3 )
= $true )
| ! [X2: $i] :
( ( cP @ X2 )
!= $true ) )
& ( ? [X2: $i] :
( ( cP @ X2 )
= $true )
| ? [X3: $i] :
( ( cP @ X3 )
!= $true ) ) )
| ! [X0: $i] :
( ( ( ( cP @ X0 )
= $true )
| ? [X1: $i] :
( ( cP @ X1 )
!= $true ) )
& ( ! [X1: $i] :
( ( cP @ X1 )
= $true )
| ( ( cP @ X0 )
!= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X0: $i] :
( ( ( cP @ X0 )
= $true )
<=> ! [X1: $i] :
( ( cP @ X1 )
= $true ) )
<~> ( ! [X3: $i] :
( ( cP @ X3 )
= $true )
<=> ? [X2: $i] :
( ( cP @ X2 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i] :
( ( ( cP @ X0 )
= $true )
<=> ! [X1: $i] :
( ( cP @ X1 )
= $true ) )
<=> ( ! [X3: $i] :
( ( cP @ X3 )
= $true )
<=> ? [X2: $i] :
( ( cP @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
( ! [X1: $i] : ( cP @ X1 )
<=> ( cP @ X0 ) )
<=> ( ? [X2: $i] : ( cP @ X2 )
<=> ! [X3: $i] : ( cP @ X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] :
( ! [X1: $i] : ( cP @ X1 )
<=> ( cP @ X0 ) )
<=> ( ? [X0: $i] : ( cP @ X0 )
<=> ! [X1: $i] : ( cP @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i] :
( ! [X1: $i] : ( cP @ X1 )
<=> ( cP @ X0 ) )
<=> ( ? [X0: $i] : ( cP @ X0 )
<=> ! [X1: $i] : ( cP @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nTbHypFE5T/DTF2THF_31241.p',cX2128) ).
thf(f54,plain,
( spl7_2
| spl7_1
| spl7_2
| spl7_1 ),
inference(avatar_split_clause,[status(thm)],[f19,f26,f29,f26,f29]) ).
thf(f19,plain,
! [X11: $i,X8: $i,X7: $i,X13: $i] :
( ( ( cP @ X11 )
!= $true )
| ( ( cP @ X13 )
= $true )
| ( ( cP @ X7 )
= $true )
| ( ( cP @ X8 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f44,plain,
( spl7_4
| spl7_2
| spl7_2
| spl7_5 ),
inference(avatar_split_clause,[status(thm)],[f21,f41,f29,f29,f37]) ).
thf(f21,plain,
! [X3: $i,X6: $i] :
( ( ( cP @ X6 )
= $true )
| ( ( cP @ sK2 )
= $true )
| ( ( cP @ sK1 )
= $true )
| ( ( cP @ X3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN377^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n017.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 13:54:56 EST 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : SYN377^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.45 % Domain : Syntactic
% 0.29/0.45 % Problem : TPS problem X2128
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Bro09]
% 0.29/0.45 % Names : tps_0378 [Bro09]
% 0.29/0.45 % : THM56 [TPS]
% 0.29/0.45 % : X2128 [TPS]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % 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
% 0.29/0.45 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.29/0.45 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 4 ( 4 avg)
% 0.29/0.45 % Number of connectives : 7 ( 0 ~; 0 |; 0 &; 4 @)
% 0.29/0.45 % ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 6 ( 6 avg)
% 0.29/0.45 % Number of types : 2 ( 0 usr)
% 0.29/0.45 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 1 ( 1 usr; 0 con; 1-1 aty)
% 0.29/0.45 % Number of variables : 4 ( 0 ^; 3 !; 1 ?; 4 :)
% 0.29/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.45 % :
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(cP,type,
% 0.29/0.45 cP: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(cX2128,conjecture,
% 0.29/0.45 ( ! [Xx: $i] :
% 0.29/0.45 ( ( cP @ Xx )
% 0.29/0.45 <=> ! [Xy: $i] : ( cP @ Xy ) )
% 0.29/0.45 <=> ( ? [Xx: $i] : ( cP @ Xx )
% 0.29/0.45 <=> ! [Xy: $i] : ( cP @ Xy ) ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.51/1.21 ---- Embedded in THF ---
% 1.51/1.21 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.21 %%% Generated on Tue Feb 24 13:54:56 EST 2026
% 1.51/1.21 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.21 %%% Logic specification used:
% 1.51/1.21 %%% thf(spec, logic, $$dhol).
% 1.51/1.21
% 1.51/1.21 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.nTbHypFE5T/DTF2DTF31241.p
% See solution above
% 1.51/1.21 ------------------------
% 1.51/1.22 ---- Cleaned THF ---
% 1.51/1.22 thf(cP,type,
% 1.51/1.22 cP: $i > $o ).
% 1.51/1.22
% 1.51/1.22 thf(cX2128,conjecture,
% 1.51/1.22 ( ! [Xx: $i] :
% 1.51/1.22 ( ( cP @ Xx )
% 1.51/1.22 <=> ! [Xy: $i] : ( cP @ Xy ) )
% 1.51/1.22 <=> ( ? [Xx: $i] : ( cP @ Xx )
% 1.51/1.22 <=> ! [Xy: $i] : ( cP @ Xy ) ) ) ).
% 1.51/1.22 ------------------------
% 1.51/1.24 % (31361)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31241 for (3000ds/18Mi)
% 1.51/1.24 % (31356)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_31241 for (3000ds/4Mi)
% 1.51/1.24 % (31356)First to succeed.
% 1.51/1.24 % (31361)Also succeeded, but the first one will report.
% 1.51/1.24 % (31356)Refutation found. Thanks to Tanya!
% 1.51/1.24 % SZS status Theorem for DTF2THF_31241
% 1.51/1.24 % SZS output start Proof for DTF2THF_31241
% 1.51/1.24 thf(func_def_0, type, cP: $i > $o).
% 1.51/1.24 thf(f83,plain,(
% 1.51/1.24 $false),
% 1.51/1.24 inference(avatar_sat_refutation,[status(thm)],[f44,f54,f64,f68,f70,f72,f74,f76,f82])).
% 1.51/1.24 thf(f82,plain,(
% 1.51/1.24 ~spl7_1 | ~spl7_4),
% 1.51/1.24 inference(avatar_contradiction_clause,[status(thm)],[f81])).
% 1.51/1.24 thf(f81,plain,(
% 1.51/1.24 $false | (~spl7_1 | ~spl7_4)),
% 1.51/1.24 inference(subsumption_resolution,[status(thm)],[f39,f27])).
% 1.51/1.24 thf(f27,plain,(
% 1.51/1.24 ( ! [X8 : $i] : (((cP @ X8) != $true)) ) | ~spl7_1),
% 1.51/1.24 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.51/1.24 thf(f26,definition,(
% 1.51/1.24 spl7_1 <=> ! [X8 : $i] : ((cP @ X8) != $true)),
% 1.51/1.24 introduced(definition,[new_symbols(naming,[spl7_1])],[avatar_definition])).
% 1.51/1.24 thf(f39,plain,(
% 1.51/1.24 ((cP @ sK1) = $true) | ~spl7_4),
% 1.51/1.24 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.51/1.24 thf(f37,definition,(
% 1.51/1.24 spl7_4 <=> ((cP @ sK1) = $true)),
% 1.51/1.24 introduced(definition,[new_symbols(naming,[spl7_4])],[avatar_definition])).
% 1.51/1.24 thf(f76,plain,(
% 1.51/1.24 ~spl7_1 | ~spl7_5),
% 1.51/1.24 inference(avatar_contradiction_clause,[status(thm)],[f75])).
% 1.51/1.24 thf(f75,plain,(
% 1.51/1.24 $false | (~spl7_1 | ~spl7_5)),
% 1.51/1.24 inference(subsumption_resolution,[status(thm)],[f43,f27])).
% 1.51/1.24 thf(f43,plain,(
% 1.51/1.24 ((cP @ sK2) = $true) | ~spl7_5),
% 1.51/1.24 inference(avatar_component_clause,[status(thm)],[f41])).
% 1.51/1.24 thf(f41,definition,(
% 1.51/1.24 spl7_5 <=> ((cP @ sK2) = $true)),
% 1.51/1.24 introduced(definition,[new_symbols(naming,[spl7_5])],[avatar_definition])).
% 1.51/1.24 thf(f74,plain,(
% 1.51/1.24 ~spl7_1 | ~spl7_2),
% 1.51/1.24 inference(avatar_contradiction_clause,[status(thm)],[f73])).
% 1.51/1.24 thf(f73,plain,(
% 1.51/1.24 $false | (~spl7_1 | ~spl7_2)),
% 1.51/1.24 inference(subsumption_resolution,[status(thm)],[f27,f30])).
% 1.51/1.24 thf(f30,plain,(
% 1.51/1.24 ( ! [X7 : $i] : (((cP @ X7) = $true)) ) | ~spl7_2),
% 1.51/1.24 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.51/1.24 thf(f29,definition,(
% 1.51/1.24 spl7_2 <=> ! [X7 : $i] : ((cP @ X7) = $true)),
% 1.51/1.24 introduced(definition,[new_symbols(naming,[spl7_2])],[avatar_definition])).
% 1.51/1.24 thf(f72,plain,(
% 1.51/1.24 ~spl7_2 | spl7_8),
% 1.51/1.24 inference(avatar_contradiction_clause,[status(thm)],[f71])).
% 1.51/1.24 thf(f71,plain,(
% 1.51/1.24 $false | (~spl7_2 | spl7_8)),
% 1.51/1.24 inference(subsumption_resolution,[status(thm)],[f58,f30])).
% 1.51/1.24 thf(f58,plain,(
% 1.51/1.24 ((cP @ sK0) != $true) | spl7_8),
% 1.51/1.24 inference(avatar_component_clause,[status(thm)],[f56])).
% 1.51/1.24 thf(f56,definition,(
% 1.51/1.24 spl7_8 <=> ((cP @ sK0) = $true)),
% 1.51/1.24 introduced(definition,[new_symbols(naming,[spl7_8])],[avatar_definition])).
% 1.51/1.24 thf(f70,plain,(
% 1.51/1.24 ~spl7_2 | spl7_9),
% 1.51/1.24 inference(avatar_contradiction_clause,[status(thm)],[f69])).
% 1.51/1.24 thf(f69,plain,(
% 1.51/1.24 $false | (~spl7_2 | spl7_9)),
% 1.51/1.24 inference(subsumption_resolution,[status(thm)],[f63,f30])).
% 1.51/1.24 thf(f63,plain,(
% 1.51/1.24 ((cP @ sK3) != $true) | spl7_9),
% 1.51/1.24 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.51/1.24 thf(f61,definition,(
% 1.51/1.24 spl7_9 <=> ((cP @ sK3) = $true)),
% 1.51/1.24 introduced(definition,[new_symbols(naming,[spl7_9])],[avatar_definition])).
% 1.51/1.24 thf(f68,plain,(
% 1.51/1.24 ~spl7_2 | spl7_5),
% 1.51/1.24 inference(avatar_contradiction_clause,[status(thm)],[f67])).
% 1.51/1.24 thf(f67,plain,(
% 1.51/1.24 $false | (~spl7_2 | spl7_5)),
% 1.51/1.24 inference(subsumption_resolution,[status(thm)],[f42,f30])).
% 1.51/1.24 thf(f42,plain,(
% 1.51/1.24 ((cP @ sK2) != $true) | spl7_5),
% 1.51/1.24 inference(avatar_component_clause,[status(thm)],[f41])).
% 1.51/1.24 thf(f64,plain,(
% 1.51/1.24 ~spl7_9 | ~spl7_5 | spl7_1 | ~spl7_8),
% 1.51/1.24 inference(avatar_split_clause,[status(thm)],[f24,f56,f26,f41,f61])).
% 1.51/1.24 thf(f24,plain,(
% 1.51/1.24 ( ! [X0 : $i] : (((cP @ X0) != $true) | ((cP @ sK2) != $true) | ((cP @ sK3) != $true) | ((cP @ sK0) != $true)) )),
% 1.51/1.24 inference(cnf_transformation,[status(thm)],[f16])).
% 1.51/1.24 thf(f16,plain,(
% 1.51/1.24 (((! [X0 : $i] : ((cP @ X0) != $true) | ((cP @ sK0) != $true)) & (((cP @ sK1) = $true) | ! [X3 : $i] : ((cP @ X3) = $true))) | ((((cP @ sK3) != $true) | ((cP @ sK2) != $true)) & (! [X6 : $i] : ((cP @ X6) = $true) | ((cP @ sK2) = $true)))) & (((! [X7 : $i] : ((cP @ X7) = $true) | ! [X8 : $i] : ((cP @ X8) != $true)) & (((cP @ sK4) = $true) | ((cP @ sK5) != $true))) | ! [X11 : $i] : ((((cP @ X11) = $true) | ((cP @ sK6) != $true)) & (! [X13 : $i] : ((cP @ X13) = $true) | ((cP @ X11) != $true))))),
% 1.51/1.24 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f8,f15,f14,f13,f12,f11,f10,f9])).
% 1.51/1.24 thf(f9,plain,(
% 1.51/1.24 ? [X1 : $i] : ((cP @ X1) != $true) => ((cP @ sK0) != $true)),
% 1.51/1.24 introduced(definition,[],[choice_axiom])).
% 1.51/1.24 thf(f10,plain,(
% 1.51/1.24 ? [X2 : $i] : ((cP @ X2) = $true) => ((cP @ sK1) = $true)),
% 1.51/1.24 introduced(definition,[],[choice_axiom])).
% 1.51/1.24 thf(f11,plain,(
% 1.51/1.24 ? [X4 : $i] : ((? [X5 : $i] : ((cP @ X5) != $true) | ((cP @ X4) != $true)) & (! [X6 : $i] : ((cP @ X6) = $true) | ((cP @ X4) = $true))) => ((? [X5 : $i] : ((cP @ X5) != $true) | ((cP @ sK2) != $true)) & (! [X6 : $i] : ((cP @ X6) = $true) | ((cP @ sK2) = $true)))),
% 1.51/1.24 introduced(definition,[],[choice_axiom])).
% 1.51/1.24 thf(f12,plain,(
% 1.51/1.24 ? [X5 : $i] : ((cP @ X5) != $true) => ((cP @ sK3) != $true)),
% 1.51/1.24 introduced(definition,[],[choice_axiom])).
% 1.51/1.24 thf(f13,plain,(
% 1.51/1.24 ? [X9 : $i] : ($true = (cP @ X9)) => ((cP @ sK4) = $true)),
% 1.51/1.24 introduced(definition,[],[choice_axiom])).
% 1.51/1.24 thf(f14,plain,(
% 1.51/1.24 ? [X10 : $i] : ($true != (cP @ X10)) => ((cP @ sK5) != $true)),
% 1.51/1.24 introduced(definition,[],[choice_axiom])).
% 1.51/1.24 thf(f15,plain,(
% 1.51/1.24 ? [X12 : $i] : ($true != (cP @ X12)) => ((cP @ sK6) != $true)),
% 1.51/1.24 introduced(definition,[],[choice_axiom])).
% 1.51/1.24 thf(f8,plain,(
% 1.51/1.24 (((! [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] : ((cP @ X6) = $true) | ((cP @ X4) = $true)))) & (((! [X7 : $i] : ((cP @ X7) = $true) | ! [X8 : $i] : ((cP @ X8) != $true)) & (? [X9 : $i] : ($true = (cP @ X9)) | ? [X10 : $i] : ($true != (cP @ X10)))) | ! [X11 : $i] : ((((cP @ X11) = $true) | ? [X12 : $i] : ($true != (cP @ X12))) & (! [X13 : $i] : ((cP @ X13) = $true) | ((cP @ X11) != $true))))),
% 1.51/1.24 inference(rectify,[status(thm)],[f7])).
% 1.51/1.24 thf(f7,plain,(
% 1.51/1.24 (((! [X2 : $i] : ((cP @ X2) != $true) | ? [X3 : $i] : ((cP @ X3) != $true)) & (? [X2 : $i] : ((cP @ X2) = $true) | ! [X3 : $i] : ((cP @ X3) = $true))) | ? [X0 : $i] : ((? [X1 : $i] : ((cP @ X1) != $true) | ((cP @ X0) != $true)) & (! [X1 : $i] : ((cP @ X1) = $true) | ((cP @ X0) = $true)))) & (((! [X3 : $i] : ((cP @ X3) = $true) | ! [X2 : $i] : ((cP @ X2) != $true)) & (? [X2 : $i] : ((cP @ X2) = $true) | ? [X3 : $i] : ((cP @ X3) != $true))) | ! [X0 : $i] : ((((cP @ X0) = $true) | ? [X1 : $i] : ((cP @ X1) != $true)) & (! [X1 : $i] : ((cP @ X1) = $true) | ((cP @ X0) != $true))))),
% 1.51/1.24 inference(nnf_transformation,[status(thm)],[f6])).
% 1.51/1.24 thf(f6,plain,(
% 1.51/1.24 ! [X0 : $i] : (((cP @ X0) = $true) <=> ! [X1 : $i] : ((cP @ X1) = $true)) <~> (! [X3 : $i] : ((cP @ X3) = $true) <=> ? [X2 : $i] : ((cP @ X2) = $true))),
% 1.51/1.24 inference(ennf_transformation,[status(thm)],[f5])).
% 1.51/1.24 thf(f5,plain,(
% 1.51/1.24 ~(! [X0 : $i] : (((cP @ X0) = $true) <=> ! [X1 : $i] : ((cP @ X1) = $true)) <=> (! [X3 : $i] : ((cP @ X3) = $true) <=> ? [X2 : $i] : ((cP @ X2) = $true)))),
% 1.51/1.24 inference(fool_elimination,[status(thm)],[f4])).
% 1.51/1.24 thf(f4,plain,(
% 1.51/1.24 ~(! [X0 : $i] : (! [X1 : $i] : (cP @ X1) <=> (cP @ X0)) <=> (? [X2 : $i] : (cP @ X2) <=> ! [X3 : $i] : (cP @ X3)))),
% 1.51/1.24 inference(rectify,[status(thm)],[f2])).
% 1.51/1.24 thf(f2,negated_conjecture,(
% 1.51/1.24 ~(! [X0 : $i] : (! [X1 : $i] : (cP @ X1) <=> (cP @ X0)) <=> (? [X0 : $i] : (cP @ X0) <=> ! [X1 : $i] : (cP @ X1)))),
% 1.51/1.24 inference(negated_conjecture,[status(cth)],[f1])).
% 1.51/1.24 thf(f1,conjecture,(
% 1.51/1.24 ! [X0 : $i] : (! [X1 : $i] : (cP @ X1) <=> (cP @ X0)) <=> (? [X0 : $i] : (cP @ X0) <=> ! [X1 : $i] : (cP @ X1))),
% 1.51/1.24 file('/export/starexec/sandbox2/tmp/tmp.nTbHypFE5T/DTF2THF_31241.p',cX2128)).
% 1.51/1.24 thf(f54,plain,(
% 1.51/1.24 spl7_2 | spl7_1 | spl7_2 | spl7_1),
% 1.51/1.24 inference(avatar_split_clause,[status(thm)],[f19,f26,f29,f26,f29])).
% 1.51/1.24 thf(f19,plain,(
% 1.51/1.24 ( ! [X11 : $i,X8 : $i,X7 : $i,X13 : $i] : (((cP @ X11) != $true) | ((cP @ X13) = $true) | ((cP @ X7) = $true) | ((cP @ X8) != $true)) )),
% 1.51/1.24 inference(cnf_transformation,[status(thm)],[f16])).
% 1.51/1.24 thf(f44,plain,(
% 1.51/1.24 spl7_4 | spl7_2 | spl7_2 | spl7_5),
% 1.51/1.24 inference(avatar_split_clause,[status(thm)],[f21,f41,f29,f29,f37])).
% 1.51/1.24 thf(f21,plain,(
% 1.51/1.24 ( ! [X3 : $i,X6 : $i] : (((cP @ X6) = $true) | ((cP @ sK2) = $true) | ((cP @ sK1) = $true) | ((cP @ X3) = $true)) )),
% 1.51/1.24 inference(cnf_transformation,[status(thm)],[f16])).
% 1.51/1.24 % SZS output end Proof for DTF2THF_31241
% 1.51/1.24 % (31356)------------------------------
% 1.51/1.24 % (31356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.24 % (31356)Termination reason: Refutation
% 1.51/1.24
% 1.51/1.24 % (31356)Memory used [KB]: 5500
% 1.51/1.24 % (31356)Time elapsed: 0.003 s
% 1.51/1.24 % (31356)Instructions burned: 2 (million)
% 1.51/1.24 % (31356)------------------------------
% 1.51/1.24 % (31356)------------------------------
% 1.51/1.24 % (31354)Success in time 0.004 s
%------------------------------------------------------------------------------