%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET636^5 : 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 : n008.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 09:32:00 AM UTC 2026
% Result : Theorem 1.47s 1.26s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 4 unt; 0 typ; 4 def)
% Number of atoms : 267 ( 79 equ; 0 cnn)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 292 ( 66 ~; 59 |; 43 &; 112 @)
% ( 9 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 88 ( 48 ^; 22 !; 18 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_7,type,
sK0: a > $o ).
thf(func_def_8,type,
sK1: a > $o ).
thf(func_def_9,type,
sK2: a ).
thf(func_def_11,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
sK5: a ).
thf(f66,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f24,f29,f33,f46,f65]) ).
thf(f65,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f64]) ).
thf(f64,plain,
( $false
| ~ spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(backward_demodulation,[status(thm)],[f23,f62]) ).
thf(f62,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ~ spl3_1
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK2 ) )
| ~ spl3_1
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f28,f56]) ).
thf(f56,plain,
( ! [X1: a] :
( ( ( sK1 @ X1 )
= $false )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl3_1 ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ! [X1: a] :
( $false
= ( ( sK0 @ X1 )
& ( sK1 @ X1 ) ) )
| ~ spl3_1 ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
( ! [X1: a] :
( ( ^ [Y0: a] : $false
@ X1 )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 ) )
| ~ spl3_1 ),
inference(argument_congruence,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f17]) ).
thf(f17,definition,
( spl3_1
<=> ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f28,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl3_3
<=> ( $true
= ( sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f23,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f21,definition,
( spl3_2
<=> ( $true
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f46,plain,
( spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f45]) ).
thf(f45,plain,
( $false
| spl3_1
| ~ spl3_4 ),
inference(subsumption_resolution,[status(thm)],[f44,f41]) ).
thf(f41,plain,
( ( $true
= ( sK0 @ sK5 ) )
| spl3_1 ),
inference(binary_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( ( sK0 @ sK5 )
& ( sK1 @ sK5 ) )
!= $false )
| spl3_1 ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK5 )
!= ( ^ [Y0: a] : $false
@ sK5 ) )
| spl3_1 ),
inference(negative_extensionality,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f17]) ).
thf(f44,plain,
( ( $true
!= ( sK0 @ sK5 ) )
| spl3_1
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
( ( $true != $true )
| ( $true
!= ( sK0 @ sK5 ) )
| spl3_1
| ~ spl3_4 ),
inference(superposition,[status(thm)],[f32,f40]) ).
thf(f40,plain,
( ( $true
= ( sK1 @ sK5 ) )
| spl3_1 ),
inference(binary_proxy_clausification,[status(thm)],[f39]) ).
thf(f32,plain,
( ! [X3: a] :
( ( ( sK1 @ X3 )
!= $true )
| ( ( sK0 @ X3 )
!= $true ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f31,definition,
( spl3_4
<=> ! [X3: a] :
( ( ( sK1 @ X3 )
!= $true )
| ( ( sK0 @ X3 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f33,plain,
( spl3_4
| spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f13,f17,f31]) ).
thf(f13,plain,
! [X3: a] :
( ( ( sK1 @ X3 )
!= $true )
| ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( ( sK0 @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( ( $true
= ( sK1 @ sK2 ) )
& ( $true
= ( sK0 @ sK2 ) ) ) )
& ( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ! [X3: a] :
( ( ( sK1 @ X3 )
!= $true )
| ( ( sK0 @ X3 )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f11,f10]) ).
thf(f10,plain,
( ? [X0: a > $o,X1: a > $o] :
( ( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
| ? [X2: a] :
( ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
= $true ) ) )
& ( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
| ! [X3: a] :
( ( $true
!= ( X1 @ X3 ) )
| ( $true
!= ( X0 @ X3 ) ) ) ) )
=> ( ( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ? [X2: a] :
( ( $true
= ( sK1 @ X2 ) )
& ( $true
= ( sK0 @ X2 ) ) ) )
& ( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ! [X3: a] :
( ( ( sK1 @ X3 )
!= $true )
| ( ( sK0 @ X3 )
!= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X2: a] :
( ( $true
= ( sK1 @ X2 ) )
& ( $true
= ( sK0 @ X2 ) ) )
=> ( ( $true
= ( sK1 @ sK2 ) )
& ( $true
= ( sK0 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: a > $o,X1: a > $o] :
( ( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
| ? [X2: a] :
( ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
= $true ) ) )
& ( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
| ! [X3: a] :
( ( $true
!= ( X1 @ X3 ) )
| ( $true
!= ( X0 @ X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o] :
( ( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
| ? [X2: a] :
( ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
= $true ) ) )
& ( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
| ! [X2: a] :
( ( ( X1 @ X2 )
!= $true )
| ( ( X0 @ X2 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( ( X1 @ X2 )
!= $true )
| ( ( X0 @ X2 )
!= $true ) )
<~> ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
<=> ~ ? [X2: a] :
( ( ( X0 @ X2 )
= $true )
& ( ( X1 @ X2 )
= $true ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
<=> ~ ? [X4: a] :
( ( $true
= ( X0 @ X4 ) )
& ( ( X1 @ X4 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] : $false )
= ( ^ [X3: a] :
( ( X1 @ X3 )
& ( X0 @ X3 ) ) ) )
<=> ~ ? [X4: a] :
( ( X0 @ X4 )
& ( X1 @ X4 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] : $false )
= ( ^ [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) )
<=> ~ ? [X2: a] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] : $false )
= ( ^ [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) )
<=> ~ ? [X2: a] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OgMg93J4ZX/DTF2THF_2554.p',cBOOL_PROP_118_pme) ).
thf(f29,plain,
( ~ spl3_1
| spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f15,f26,f17]) ).
thf(f15,plain,
( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( $true
= ( sK1 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f24,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f14,f21,f17]) ).
thf(f14,plain,
( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET636^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n008.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 12:01:09 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SET636^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.46 % Domain : Set Theory
% 0.28/0.46 % Problem : TPS problem BOOL-PROP-118
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English : Trybulec's 118th Boolean property of sets
% 0.28/0.46
% 0.28/0.46 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.28/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Bro09]
% 0.28/0.46 % Names : tps_0428 [Bro09]
% 0.28/0.46 % : BOOL-PROP-118 [TPS]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.28/0.46 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.28/0.46 % Number of atoms : 2 ( 1 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 1 ( 2 avg)
% 0.28/0.46 % Number of connectives : 8 ( 1 ~; 0 |; 2 &; 4 @)
% 0.28/0.46 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 8 ( 8 avg)
% 0.28/0.46 % Number of types : 2 ( 1 usr)
% 0.28/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.28/0.46 % Number of variables : 5 ( 2 ^; 2 !; 1 ?; 5 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.46 % : Polymorphic definitions expanded.
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(a_type,type,
% 0.28/0.46 a: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(cBOOL_PROP_118_pme,conjecture,
% 0.28/0.46 ! [X: a > $o,Y: a > $o] :
% 0.28/0.46 ( ~ ? [Xx: a] :
% 0.28/0.46 ( ( X @ Xx )
% 0.28/0.46 & ( Y @ Xx ) )
% 0.28/0.46 <=> ( ( ^ [Xx: a] :
% 0.28/0.46 ( ( X @ Xx )
% 0.28/0.46 & ( Y @ Xx ) ) )
% 0.28/0.46 = ( ^ [Xx: a] : $false ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.47/1.24 ---- Embedded in THF ---
% 1.47/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.24 %%% Generated on Tue Feb 24 12:01:10 EST 2026
% 1.47/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.24 %%% Logic specification used:
% 1.47/1.24 %%% thf(spec, logic, $$dhol).
% 1.47/1.24
% 1.47/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.OgMg93J4ZX/DTF2DTF2554.p
% See solution above
% 1.47/1.24 ------------------------
% 1.47/1.24 ---- Cleaned THF ---
% 1.47/1.25 thf(a_type,type,
% 1.47/1.25 a: $tType ).
% 1.47/1.25
% 1.47/1.25 thf(cBOOL_PROP_118_pme,conjecture,
% 1.47/1.25 ! [X: a > $o,Y: a > $o] :
% 1.47/1.25 ( ~ ? [Xx: a] :
% 1.47/1.25 ( ( X @ Xx )
% 1.47/1.25 & ( Y @ Xx ) )
% 1.47/1.25 <=> ( ( ^ [Xx: a] :
% 1.47/1.25 ( ( X @ Xx )
% 1.47/1.25 & ( Y @ Xx ) ) )
% 1.47/1.25 = ( ^ [Xx: a] : $false ) ) ) ).
% 1.47/1.25 ------------------------
% 1.47/1.26 % (2829)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_2554 for (2999ds/4Mi)
% 1.47/1.26 % (2829)First to succeed.
% 1.47/1.26 % (2829)Refutation found. Thanks to Tanya!
% 1.47/1.26 % SZS status Theorem for DTF2THF_2554
% 1.47/1.26 % SZS output start Proof for DTF2THF_2554
% 1.47/1.26 thf(type_def_5, type, a: $tType).
% 1.47/1.26 thf(func_def_0, type, a: $tType).
% 1.47/1.26 thf(func_def_7, type, sK0: a > $o).
% 1.47/1.26 thf(func_def_8, type, sK1: a > $o).
% 1.47/1.26 thf(func_def_9, type, sK2: a).
% 1.47/1.26 thf(func_def_11, type, ph4: !>[X0: $tType]:(X0)).
% 1.47/1.26 thf(func_def_12, type, sK5: a).
% 1.47/1.26 thf(f66,plain,(
% 1.47/1.26 $false),
% 1.47/1.26 inference(avatar_sat_refutation,[status(thm)],[f24,f29,f33,f46,f65])).
% 1.47/1.26 thf(f65,plain,(
% 1.47/1.26 ~spl3_1 | ~spl3_2 | ~spl3_3),
% 1.47/1.26 inference(avatar_contradiction_clause,[status(thm)],[f64])).
% 1.47/1.26 thf(f64,plain,(
% 1.47/1.26 $false | (~spl3_1 | ~spl3_2 | ~spl3_3)),
% 1.47/1.26 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.47/1.26 thf(f63,plain,(
% 1.47/1.26 ($true = $false) | (~spl3_1 | ~spl3_2 | ~spl3_3)),
% 1.47/1.26 inference(backward_demodulation,[status(thm)],[f23,f62])).
% 1.47/1.26 thf(f62,plain,(
% 1.47/1.26 ($false = (sK0 @ sK2)) | (~spl3_1 | ~spl3_3)),
% 1.47/1.26 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.47/1.26 thf(f59,plain,(
% 1.47/1.26 ($true = $false) | ($false = (sK0 @ sK2)) | (~spl3_1 | ~spl3_3)),
% 1.47/1.26 inference(superposition,[status(thm)],[f28,f56])).
% 1.47/1.26 thf(f56,plain,(
% 1.47/1.26 ( ! [X1 : a] : (((sK1 @ X1) = $false) | ($false = (sK0 @ X1))) ) | ~spl3_1),
% 1.47/1.26 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.47/1.26 thf(f55,plain,(
% 1.47/1.26 ( ! [X1 : a] : (($false = ((sK0 @ X1) & (sK1 @ X1)))) ) | ~spl3_1),
% 1.47/1.26 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.47/1.26 thf(f54,plain,(
% 1.47/1.26 ( ! [X1 : a] : ((((^[Y0 : a]: ($false)) @ X1) = ((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) @ X1))) ) | ~spl3_1),
% 1.47/1.26 inference(argument_congruence,[status(thm)],[f18])).
% 1.47/1.26 thf(f18,plain,(
% 1.47/1.26 ((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0)))) | ~spl3_1),
% 1.47/1.26 inference(avatar_component_clause,[status(thm)],[f17])).
% 1.47/1.26 thf(f17,definition,(
% 1.47/1.26 spl3_1 <=> ((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))))),
% 1.47/1.26 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.47/1.26 thf(f28,plain,(
% 1.47/1.26 ($true = (sK1 @ sK2)) | ~spl3_3),
% 1.47/1.26 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.47/1.26 thf(f26,definition,(
% 1.47/1.26 spl3_3 <=> ($true = (sK1 @ sK2))),
% 1.47/1.26 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.47/1.26 thf(f23,plain,(
% 1.47/1.26 ($true = (sK0 @ sK2)) | ~spl3_2),
% 1.47/1.26 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.47/1.26 thf(f21,definition,(
% 1.47/1.26 spl3_2 <=> ($true = (sK0 @ sK2))),
% 1.47/1.26 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.47/1.26 thf(f46,plain,(
% 1.47/1.26 spl3_1 | ~spl3_4),
% 1.47/1.26 inference(avatar_contradiction_clause,[status(thm)],[f45])).
% 1.47/1.26 thf(f45,plain,(
% 1.47/1.26 $false | (spl3_1 | ~spl3_4)),
% 1.47/1.26 inference(subsumption_resolution,[status(thm)],[f44,f41])).
% 1.47/1.26 thf(f41,plain,(
% 1.47/1.26 ($true = (sK0 @ sK5)) | spl3_1),
% 1.47/1.26 inference(binary_proxy_clausification,[status(thm)],[f39])).
% 1.47/1.26 thf(f39,plain,(
% 1.47/1.26 (((sK0 @ sK5) & (sK1 @ sK5)) != $false) | spl3_1),
% 1.47/1.26 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.47/1.26 thf(f38,plain,(
% 1.47/1.26 (((^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0))) @ sK5) != ((^[Y0 : a]: ($false)) @ sK5)) | spl3_1),
% 1.47/1.26 inference(negative_extensionality,[status(thm)],[f19])).
% 1.47/1.26 thf(f19,plain,(
% 1.47/1.26 ((^[Y0 : a]: ($false)) != (^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0)))) | spl3_1),
% 1.47/1.26 inference(avatar_component_clause,[status(thm)],[f17])).
% 1.47/1.26 thf(f44,plain,(
% 1.47/1.26 ($true != (sK0 @ sK5)) | (spl3_1 | ~spl3_4)),
% 1.47/1.26 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.47/1.26 thf(f43,plain,(
% 1.47/1.26 ($true != $true) | ($true != (sK0 @ sK5)) | (spl3_1 | ~spl3_4)),
% 1.47/1.26 inference(superposition,[status(thm)],[f32,f40])).
% 1.47/1.26 thf(f40,plain,(
% 1.47/1.26 ($true = (sK1 @ sK5)) | spl3_1),
% 1.47/1.26 inference(binary_proxy_clausification,[status(thm)],[f39])).
% 1.47/1.26 thf(f32,plain,(
% 1.47/1.26 ( ! [X3 : a] : (((sK1 @ X3) != $true) | ((sK0 @ X3) != $true)) ) | ~spl3_4),
% 1.47/1.26 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.47/1.26 thf(f31,definition,(
% 1.47/1.26 spl3_4 <=> ! [X3 : a] : (((sK1 @ X3) != $true) | ((sK0 @ X3) != $true))),
% 1.47/1.26 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.47/1.26 thf(f33,plain,(
% 1.47/1.26 spl3_4 | spl3_1),
% 1.47/1.26 inference(avatar_split_clause,[status(thm)],[f13,f17,f31])).
% 1.47/1.26 thf(f13,plain,(
% 1.47/1.26 ( ! [X3 : a] : (((sK1 @ X3) != $true) | ((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0)))) | ((sK0 @ X3) != $true)) )),
% 1.47/1.26 inference(cnf_transformation,[status(thm)],[f12])).
% 1.47/1.26 thf(f12,plain,(
% 1.47/1.26 (((^[Y0 : a]: ($false)) != (^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0)))) | (($true = (sK1 @ sK2)) & ($true = (sK0 @ sK2)))) & (((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0)))) | ! [X3 : a] : (((sK1 @ X3) != $true) | ((sK0 @ X3) != $true)))),
% 1.47/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f11,f10])).
% 1.47/1.26 thf(f10,plain,(
% 1.47/1.26 ? [X0 : a > $o,X1 : a > $o] : ((((^[Y0 : a]: ($false)) != (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0)))) | ? [X2 : a] : (((X1 @ X2) = $true) & ((X0 @ X2) = $true))) & (((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0)))) | ! [X3 : a] : (($true != (X1 @ X3)) | ($true != (X0 @ X3))))) => ((((^[Y0 : a]: ($false)) != (^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0)))) | ? [X2 : a] : (($true = (sK1 @ X2)) & ($true = (sK0 @ X2)))) & (((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0)))) | ! [X3 : a] : (((sK1 @ X3) != $true) | ((sK0 @ X3) != $true))))),
% 1.47/1.26 introduced(definition,[],[choice_axiom])).
% 1.47/1.26 thf(f11,plain,(
% 1.47/1.26 ? [X2 : a] : (($true = (sK1 @ X2)) & ($true = (sK0 @ X2))) => (($true = (sK1 @ sK2)) & ($true = (sK0 @ sK2)))),
% 1.47/1.26 introduced(definition,[],[choice_axiom])).
% 1.47/1.26 thf(f9,plain,(
% 1.47/1.26 ? [X0 : a > $o,X1 : a > $o] : ((((^[Y0 : a]: ($false)) != (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0)))) | ? [X2 : a] : (((X1 @ X2) = $true) & ((X0 @ X2) = $true))) & (((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0)))) | ! [X3 : a] : (($true != (X1 @ X3)) | ($true != (X0 @ X3)))))),
% 1.47/1.26 inference(rectify,[status(thm)],[f8])).
% 1.47/1.26 thf(f8,plain,(
% 1.47/1.26 ? [X0 : a > $o,X1 : a > $o] : ((((^[Y0 : a]: ($false)) != (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0)))) | ? [X2 : a] : (((X1 @ X2) = $true) & ((X0 @ X2) = $true))) & (((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0)))) | ! [X2 : a] : (((X1 @ X2) != $true) | ((X0 @ X2) != $true))))),
% 1.47/1.26 inference(nnf_transformation,[status(thm)],[f7])).
% 1.47/1.26 thf(f7,plain,(
% 1.47/1.26 ? [X0 : a > $o,X1 : a > $o] : (! [X2 : a] : (((X1 @ X2) != $true) | ((X0 @ X2) != $true)) <~> ((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0)))))),
% 1.47/1.26 inference(ennf_transformation,[status(thm)],[f6])).
% 1.47/1.26 thf(f6,plain,(
% 1.47/1.26 ~! [X0 : a > $o,X1 : a > $o] : (((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0)))) <=> ~? [X2 : a] : (((X0 @ X2) = $true) & ((X1 @ X2) = $true)))),
% 1.47/1.26 inference(rectify,[status(thm)],[f5])).
% 1.47/1.26 thf(f5,plain,(
% 1.47/1.26 ~! [X0 : a > $o,X1 : a > $o] : (((^[Y0 : a]: ($false)) = (^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0)))) <=> ~? [X4 : a] : (($true = (X0 @ X4)) & ((X1 @ X4) = $true)))),
% 1.47/1.26 inference(fool_elimination,[status(thm)],[f4])).
% 1.47/1.26 thf(f4,plain,(
% 1.47/1.26 ~! [X0 : a > $o,X1 : a > $o] : (((^[X2 : a] : ($false)) = (^[X3 : a] : ((X1 @ X3) & (X0 @ X3)))) <=> ~? [X4 : a] : ((X0 @ X4) & (X1 @ X4)))),
% 1.47/1.26 inference(rectify,[status(thm)],[f2])).
% 1.47/1.26 thf(f2,negated_conjecture,(
% 1.47/1.26 ~! [X0 : a > $o,X1 : a > $o] : (((^[X2 : a] : ($false)) = (^[X2 : a] : ((X1 @ X2) & (X0 @ X2)))) <=> ~? [X2 : a] : ((X0 @ X2) & (X1 @ X2)))),
% 1.47/1.26 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.26 thf(f1,conjecture,(
% 1.47/1.26 ! [X0 : a > $o,X1 : a > $o] : (((^[X2 : a] : ($false)) = (^[X2 : a] : ((X1 @ X2) & (X0 @ X2)))) <=> ~? [X2 : a] : ((X0 @ X2) & (X1 @ X2)))),
% 1.47/1.26 file('/export/starexec/sandbox2/tmp/tmp.OgMg93J4ZX/DTF2THF_2554.p',cBOOL_PROP_118_pme)).
% 1.47/1.26 thf(f29,plain,(
% 1.47/1.26 ~spl3_1 | spl3_3),
% 1.47/1.26 inference(avatar_split_clause,[status(thm)],[f15,f26,f17])).
% 1.47/1.26 thf(f15,plain,(
% 1.47/1.26 ((^[Y0 : a]: ($false)) != (^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0)))) | ($true = (sK1 @ sK2))),
% 1.47/1.26 inference(cnf_transformation,[status(thm)],[f12])).
% 1.47/1.26 thf(f24,plain,(
% 1.47/1.26 ~spl3_1 | spl3_2),
% 1.47/1.26 inference(avatar_split_clause,[status(thm)],[f14,f21,f17])).
% 1.47/1.26 thf(f14,plain,(
% 1.47/1.26 ((^[Y0 : a]: ($false)) != (^[Y0 : a]: ((sK0 @ Y0) & (sK1 @ Y0)))) | ($true = (sK0 @ sK2))),
% 1.47/1.26 inference(cnf_transformation,[status(thm)],[f12])).
% 1.47/1.26 % SZS output end Proof for DTF2THF_2554
% 1.47/1.26 % (2829)------------------------------
% 1.47/1.26 % (2829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.26 % (2829)Termination reason: Refutation
% 1.47/1.26
% 1.47/1.26 % (2829)Memory used [KB]: 5500
% 1.47/1.26 % (2829)Time elapsed: 0.004 s
% 1.47/1.26 % (2829)Instructions burned: 3 (million)
% 1.47/1.26 % (2829)------------------------------
% 1.47/1.26 % (2829)------------------------------
% 1.47/1.26 % (2827)Success in time 0.013 s
%------------------------------------------------------------------------------