%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET011^5 : 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 : n029.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 09:30:55 AM UTC 2026
% Result : Theorem 1.47s 1.28s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 12 unt; 0 typ; 4 def)
% Number of atoms : 242 ( 65 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 285 ( 64 ~; 42 |; 49 &; 125 @)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 32 ( 20 ^; 8 !; 4 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_8,type,
sK0: a > $o ).
thf(func_def_9,type,
sK1: a > $o ).
thf(func_def_11,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
sK4: a ).
thf(f72,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f51,f52,f58,f65,f71]) ).
thf(f71,plain,
( ~ spl2_1
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f70]) ).
thf(f70,plain,
( $false
| ~ spl2_1
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ( $false = $true )
| ~ spl2_1
| ~ spl2_4 ),
inference(superposition,[status(thm)],[f41,f57]) ).
thf(f57,plain,
( ( $false
= ( sK1 @ sK4 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f55]) ).
thf(f55,definition,
( spl2_4
<=> ( $false
= ( sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f41,plain,
( ( ( sK1 @ sK4 )
= $true )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f39]) ).
thf(f39,definition,
( spl2_1
<=> ( ( sK1 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f65,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f64]) ).
thf(f64,plain,
( $false
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
( ( $false = $true )
| ~ spl2_2
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f45,f49]) ).
thf(f49,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f47]) ).
thf(f47,definition,
( spl2_3
<=> ( $false
= ( sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f45,plain,
( ( ( sK0 @ sK4 )
= $true )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
thf(f43,definition,
( spl2_2
<=> ( ( sK0 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f58,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[status(thm)],[f23,f55,f47]) ).
thf(f23,plain,
( ( $false
= ( sK1 @ sK4 ) )
| ( $false
= ( sK0 @ sK4 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f22]) ).
thf(f22,plain,
( ( $false
= ( sK1 @ sK4 ) )
| ( $false
= ( sK0 @ sK4 ) )
| ( $false
= ( sK1 @ sK4 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $false
= ( sK1 @ sK4 ) )
| ( $true
= ( ~ ( sK1 @ sK4 ) ) )
| ( $false
= ( sK0 @ sK4 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f20]) ).
thf(f20,plain,
( ( $false
= ( sK1 @ sK4 ) )
| ( $true
= ( ~ ( sK1 @ sK4 ) ) )
| ( $false
= ( sK0 @ sK4 ) )
| ( $false
= ( sK0 @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ( $false
= ( ( sK1 @ sK4 )
& ( sK0 @ sK4 ) ) )
| ( $true
= ( ~ ( sK1 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $true
= ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) )
| ( $false
= ( sK0 @ sK4 ) )
| ( $false
= ( ( sK1 @ sK4 )
& ( sK0 @ sK4 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ( ( ~ ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) )
= $false )
| ( $false
= ( ( sK1 @ sK4 )
& ( sK0 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( ( sK0 @ sK4 )
& ~ ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) )
= $false )
| ( $false
= ( ( sK1 @ sK4 )
& ( sK0 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( sK0 @ sK4 )
& ~ ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) )
!= ( ( sK1 @ sK4 )
& ( sK0 @ sK4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
@ sK4 )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
@ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) )
=> ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) )
= ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= ( ^ [X3: a] :
( ~ ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) )
& ( X0 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= ( ^ [X2: a] :
( ~ ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) )
& ( X0 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= ( ^ [X2: a] :
( ~ ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.F61EAnu1nw/DTF2THF_30388.p',cBOOL_PROP_82_pme) ).
thf(f52,plain,
spl2_2,
inference(avatar_split_clause,[status(thm)],[f28,f43]) ).
thf(f28,plain,
( ( sK0 @ sK4 )
= $true ),
inference(duplicate_literal_removal,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( sK0 @ sK4 )
= $true )
| ( ( sK0 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( sK0 @ sK4 )
= $true )
| ( $true
= ( ( sK1 @ sK4 )
& ( sK0 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( ( sK0 @ sK4 )
& ~ ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) )
= $true )
| ( $true
= ( ( sK1 @ sK4 )
& ( sK0 @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f51,plain,
( spl2_3
| spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f34,f39,f47]) ).
thf(f34,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ( ( sK1 @ sK4 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( sK1 @ sK4 )
= $true )
| ( $false
= ( sK0 @ sK4 ) )
| ( ( sK1 @ sK4 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( sK1 @ sK4 )
= $true )
| ( $false
= ( ~ ( sK1 @ sK4 ) ) )
| ( $false
= ( sK0 @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( $false
= ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) )
| ( ( sK1 @ sK4 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( ~ ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) )
= $true )
| ( ( sK1 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( $true
= ( ( sK1 @ sK4 )
& ( sK0 @ sK4 ) ) )
| ( ( ~ ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET011^5 : 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
% 0.15/0.34 % Computer : n029.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 11:48:44 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SET011^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.46 % Domain : Set Theory
% 0.29/0.46 % Problem : TPS problem BOOL-PROP-82
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : Trybulec's 82nd Boolean property of sets
% 0.29/0.46
% 0.29/0.46 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.29/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : tps_0212 [Bro09]
% 0.29/0.46 % : BOOL-PROP-82 [TPS]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 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, 0.00 v6.1.0, 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
% 0.29/0.46 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.29/0.46 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.29/0.46 % Number of connectives : 10 ( 2 ~; 0 |; 3 &; 5 @)
% 0.29/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 3 ( 3 avg)
% 0.29/0.46 % Number of types : 2 ( 1 usr)
% 0.29/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.29/0.46 % Number of variables : 4 ( 2 ^; 2 !; 0 ?; 4 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.46 % : Polymorphic definitions expanded.
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(a_type,type,
% 0.29/0.46 a: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(cBOOL_PROP_82_pme,conjecture,
% 0.29/0.46 ! [X: a > $o,Y: a > $o] :
% 0.29/0.46 ( ( ^ [Xx: a] :
% 0.29/0.46 ( ( X @ Xx )
% 0.29/0.46 & ~ ( ( X @ Xx )
% 0.29/0.46 & ~ ( Y @ Xx ) ) ) )
% 0.29/0.46 = ( ^ [Xx: a] :
% 0.29/0.46 ( ( X @ Xx )
% 0.29/0.46 & ( Y @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.47/1.25 ---- Embedded in THF ---
% 1.47/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.25 %%% Generated on Tue Feb 24 11:48:45 EST 2026
% 1.47/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.25 %%% Logic specification used:
% 1.47/1.25 %%% thf(spec, logic, $$dhol).
% 1.47/1.25
% 1.47/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.F61EAnu1nw/DTF2DTF30388.p
% See solution above
% 1.47/1.25 ------------------------
% 1.47/1.26 ---- Cleaned THF ---
% 1.47/1.26 thf(a_type,type,
% 1.47/1.26 a: $tType ).
% 1.47/1.26
% 1.47/1.26 thf(cBOOL_PROP_82_pme,conjecture,
% 1.47/1.26 ! [X: a > $o,Y: a > $o] :
% 1.47/1.26 ( ( ^ [Xx: a] :
% 1.47/1.26 ( ( X @ Xx )
% 1.47/1.26 & ~ ( ( X @ Xx )
% 1.47/1.26 & ~ ( Y @ Xx ) ) ) )
% 1.47/1.26 = ( ^ [Xx: a] :
% 1.47/1.26 ( ( X @ Xx )
% 1.47/1.26 & ( Y @ Xx ) ) ) ) ).
% 1.47/1.26 ------------------------
% 1.47/1.28 % (30692)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30388 for (2999ds/183Mi)
% 1.47/1.28 % (30692)First to succeed.
% 1.47/1.28 % (30692)Refutation found. Thanks to Tanya!
% 1.47/1.28 % SZS status Theorem for DTF2THF_30388
% 1.47/1.28 % SZS output start Proof for DTF2THF_30388
% 1.47/1.28 thf(type_def_5, type, a: $tType).
% 1.47/1.28 thf(func_def_0, type, a: $tType).
% 1.47/1.28 thf(func_def_8, type, sK0: a > $o).
% 1.47/1.28 thf(func_def_9, type, sK1: a > $o).
% 1.47/1.28 thf(func_def_11, type, ph3: !>[X0: $tType]:(X0)).
% 1.47/1.28 thf(func_def_12, type, sK4: a).
% 1.47/1.28 thf(f72,plain,(
% 1.47/1.28 $false),
% 1.47/1.28 inference(avatar_sat_refutation,[status(thm)],[f51,f52,f58,f65,f71])).
% 1.47/1.28 thf(f71,plain,(
% 1.47/1.28 ~spl2_1 | ~spl2_4),
% 1.47/1.28 inference(avatar_contradiction_clause,[status(thm)],[f70])).
% 1.47/1.28 thf(f70,plain,(
% 1.47/1.28 $false | (~spl2_1 | ~spl2_4)),
% 1.47/1.28 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.47/1.28 thf(f66,plain,(
% 1.47/1.28 ($false = $true) | (~spl2_1 | ~spl2_4)),
% 1.47/1.28 inference(superposition,[status(thm)],[f41,f57])).
% 1.47/1.28 thf(f57,plain,(
% 1.47/1.28 ($false = (sK1 @ sK4)) | ~spl2_4),
% 1.47/1.28 inference(avatar_component_clause,[status(thm)],[f55])).
% 1.47/1.28 thf(f55,definition,(
% 1.47/1.28 spl2_4 <=> ($false = (sK1 @ sK4))),
% 1.47/1.28 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.47/1.28 thf(f41,plain,(
% 1.47/1.28 ((sK1 @ sK4) = $true) | ~spl2_1),
% 1.47/1.28 inference(avatar_component_clause,[status(thm)],[f39])).
% 1.47/1.28 thf(f39,definition,(
% 1.47/1.28 spl2_1 <=> ((sK1 @ sK4) = $true)),
% 1.47/1.28 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.47/1.28 thf(f65,plain,(
% 1.47/1.28 ~spl2_2 | ~spl2_3),
% 1.47/1.28 inference(avatar_contradiction_clause,[status(thm)],[f64])).
% 1.47/1.28 thf(f64,plain,(
% 1.47/1.28 $false | (~spl2_2 | ~spl2_3)),
% 1.47/1.28 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.47/1.28 thf(f61,plain,(
% 1.47/1.28 ($false = $true) | (~spl2_2 | ~spl2_3)),
% 1.47/1.28 inference(superposition,[status(thm)],[f45,f49])).
% 1.47/1.28 thf(f49,plain,(
% 1.47/1.28 ($false = (sK0 @ sK4)) | ~spl2_3),
% 1.47/1.28 inference(avatar_component_clause,[status(thm)],[f47])).
% 1.47/1.28 thf(f47,definition,(
% 1.47/1.28 spl2_3 <=> ($false = (sK0 @ sK4))),
% 1.47/1.28 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.47/1.28 thf(f45,plain,(
% 1.47/1.28 ((sK0 @ sK4) = $true) | ~spl2_2),
% 1.47/1.28 inference(avatar_component_clause,[status(thm)],[f43])).
% 1.47/1.28 thf(f43,definition,(
% 1.47/1.28 spl2_2 <=> ((sK0 @ sK4) = $true)),
% 1.47/1.28 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.47/1.28 thf(f58,plain,(
% 1.47/1.28 spl2_3 | spl2_4),
% 1.47/1.28 inference(avatar_split_clause,[status(thm)],[f23,f55,f47])).
% 1.47/1.28 thf(f23,plain,(
% 1.47/1.28 ($false = (sK1 @ sK4)) | ($false = (sK0 @ sK4))),
% 1.47/1.28 inference(duplicate_literal_removal,[status(thm)],[f22])).
% 1.47/1.28 thf(f22,plain,(
% 1.47/1.28 ($false = (sK1 @ sK4)) | ($false = (sK0 @ sK4)) | ($false = (sK1 @ sK4))),
% 1.47/1.28 inference(not_proxy_clausification,[status(thm)],[f21])).
% 1.47/1.28 thf(f21,plain,(
% 1.47/1.28 ($false = (sK1 @ sK4)) | ($true = (~ (sK1 @ sK4))) | ($false = (sK0 @ sK4))),
% 1.47/1.28 inference(duplicate_literal_removal,[status(thm)],[f20])).
% 1.47/1.28 thf(f20,plain,(
% 1.47/1.28 ($false = (sK1 @ sK4)) | ($true = (~ (sK1 @ sK4))) | ($false = (sK0 @ sK4)) | ($false = (sK0 @ sK4))),
% 1.47/1.28 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.47/1.28 thf(f16,plain,(
% 1.47/1.28 ($false = (sK0 @ sK4)) | ($false = ((sK1 @ sK4) & (sK0 @ sK4))) | ($true = (~ (sK1 @ sK4)))),
% 1.47/1.28 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.47/1.28 thf(f15,plain,(
% 1.47/1.28 ($true = ((sK0 @ sK4) & (~ (sK1 @ sK4)))) | ($false = (sK0 @ sK4)) | ($false = ((sK1 @ sK4) & (sK0 @ sK4)))),
% 1.47/1.28 inference(not_proxy_clausification,[status(thm)],[f14])).
% 1.47/1.28 thf(f14,plain,(
% 1.47/1.28 ($false = (sK0 @ sK4)) | ((~ ((sK0 @ sK4) & (~ (sK1 @ sK4)))) = $false) | ($false = ((sK1 @ sK4) & (sK0 @ sK4)))),
% 1.47/1.28 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.47/1.28 thf(f13,plain,(
% 1.47/1.28 (((sK0 @ sK4) & (~ ((sK0 @ sK4) & (~ (sK1 @ sK4))))) = $false) | ($false = ((sK1 @ sK4) & (sK0 @ sK4)))),
% 1.47/1.28 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.47/1.28 thf(f11,plain,(
% 1.47/1.28 (((sK0 @ sK4) & (~ ((sK0 @ sK4) & (~ (sK1 @ sK4))))) != ((sK1 @ sK4) & (sK0 @ sK4)))),
% 1.47/1.28 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.47/1.28 thf(f10,plain,(
% 1.47/1.28 (((^[Y0 : a]: ((sK0 @ Y0) & (~ ((sK0 @ Y0) & (~ (sK1 @ Y0)))))) @ sK4) != ((^[Y0 : a]: ((sK1 @ Y0) & (sK0 @ Y0))) @ sK4))),
% 1.47/1.28 inference(negative_extensionality,[status(thm)],[f9])).
% 1.47/1.28 thf(f9,plain,(
% 1.47/1.28 ((^[Y0 : a]: ((sK0 @ Y0) & (~ ((sK0 @ Y0) & (~ (sK1 @ Y0)))))) != (^[Y0 : a]: ((sK1 @ Y0) & (sK0 @ Y0))))),
% 1.47/1.28 inference(cnf_transformation,[status(thm)],[f8])).
% 1.47/1.28 thf(f8,plain,(
% 1.47/1.28 ((^[Y0 : a]: ((sK0 @ Y0) & (~ ((sK0 @ Y0) & (~ (sK1 @ Y0)))))) != (^[Y0 : a]: ((sK1 @ Y0) & (sK0 @ Y0))))),
% 1.47/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7])).
% 1.47/1.28 thf(f7,plain,(
% 1.47/1.28 ? [X0 : a > $o,X1 : a > $o] : ((^[Y0 : a]: ((X0 @ Y0) & (~ ((X0 @ Y0) & (~ (X1 @ Y0)))))) != (^[Y0 : a]: ((X1 @ Y0) & (X0 @ Y0)))) => ((^[Y0 : a]: ((sK0 @ Y0) & (~ ((sK0 @ Y0) & (~ (sK1 @ Y0)))))) != (^[Y0 : a]: ((sK1 @ Y0) & (sK0 @ Y0))))),
% 1.47/1.28 introduced(definition,[],[choice_axiom])).
% 1.47/1.28 thf(f6,plain,(
% 1.47/1.28 ? [X0 : a > $o,X1 : a > $o] : ((^[Y0 : a]: ((X0 @ Y0) & (~ ((X0 @ Y0) & (~ (X1 @ Y0)))))) != (^[Y0 : a]: ((X1 @ Y0) & (X0 @ Y0))))),
% 1.47/1.28 inference(ennf_transformation,[status(thm)],[f5])).
% 1.47/1.28 thf(f5,plain,(
% 1.47/1.28 ~! [X0 : a > $o,X1 : a > $o] : ((^[Y0 : a]: ((X0 @ Y0) & (~ ((X0 @ Y0) & (~ (X1 @ Y0)))))) = (^[Y0 : a]: ((X1 @ Y0) & (X0 @ Y0))))),
% 1.47/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.47/1.28 thf(f4,plain,(
% 1.47/1.28 ~! [X0 : a > $o,X1 : a > $o] : ((^[X2 : a] : ((X0 @ X2) & (X1 @ X2))) = (^[X3 : a] : (~(~(X1 @ X3) & (X0 @ X3)) & (X0 @ X3))))),
% 1.47/1.28 inference(rectify,[status(thm)],[f2])).
% 1.47/1.28 thf(f2,negated_conjecture,(
% 1.47/1.28 ~! [X0 : a > $o,X1 : a > $o] : ((^[X2 : a] : ((X0 @ X2) & (X1 @ X2))) = (^[X2 : a] : (~(~(X1 @ X2) & (X0 @ X2)) & (X0 @ X2))))),
% 1.47/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.28 thf(f1,conjecture,(
% 1.47/1.28 ! [X0 : a > $o,X1 : a > $o] : ((^[X2 : a] : ((X0 @ X2) & (X1 @ X2))) = (^[X2 : a] : (~(~(X1 @ X2) & (X0 @ X2)) & (X0 @ X2))))),
% 1.47/1.28 file('/export/starexec/sandbox2/tmp/tmp.F61EAnu1nw/DTF2THF_30388.p',cBOOL_PROP_82_pme)).
% 1.47/1.28 thf(f52,plain,(
% 1.47/1.28 spl2_2),
% 1.47/1.28 inference(avatar_split_clause,[status(thm)],[f28,f43])).
% 1.47/1.28 thf(f28,plain,(
% 1.47/1.28 ((sK0 @ sK4) = $true)),
% 1.47/1.28 inference(duplicate_literal_removal,[status(thm)],[f26])).
% 1.47/1.28 thf(f26,plain,(
% 1.47/1.28 ((sK0 @ sK4) = $true) | ((sK0 @ sK4) = $true)),
% 1.47/1.28 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.47/1.28 thf(f25,plain,(
% 1.47/1.28 ((sK0 @ sK4) = $true) | ($true = ((sK1 @ sK4) & (sK0 @ sK4)))),
% 1.47/1.28 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.47/1.28 thf(f12,plain,(
% 1.47/1.28 (((sK0 @ sK4) & (~ ((sK0 @ sK4) & (~ (sK1 @ sK4))))) = $true) | ($true = ((sK1 @ sK4) & (sK0 @ sK4)))),
% 1.47/1.28 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.47/1.28 thf(f51,plain,(
% 1.47/1.28 spl2_3 | spl2_1),
% 1.47/1.28 inference(avatar_split_clause,[status(thm)],[f34,f39,f47])).
% 1.47/1.28 thf(f34,plain,(
% 1.47/1.28 ($false = (sK0 @ sK4)) | ((sK1 @ sK4) = $true)),
% 1.47/1.28 inference(duplicate_literal_removal,[status(thm)],[f33])).
% 1.47/1.28 thf(f33,plain,(
% 1.47/1.28 ((sK1 @ sK4) = $true) | ($false = (sK0 @ sK4)) | ((sK1 @ sK4) = $true)),
% 1.47/1.28 inference(not_proxy_clausification,[status(thm)],[f32])).
% 1.47/1.28 thf(f32,plain,(
% 1.47/1.28 ((sK1 @ sK4) = $true) | ($false = (~ (sK1 @ sK4))) | ($false = (sK0 @ sK4))),
% 1.47/1.28 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.47/1.28 thf(f31,plain,(
% 1.47/1.28 ($false = ((sK0 @ sK4) & (~ (sK1 @ sK4)))) | ((sK1 @ sK4) = $true)),
% 1.47/1.28 inference(not_proxy_clausification,[status(thm)],[f30])).
% 1.47/1.28 thf(f30,plain,(
% 1.47/1.28 ((~ ((sK0 @ sK4) & (~ (sK1 @ sK4)))) = $true) | ((sK1 @ sK4) = $true)),
% 1.47/1.28 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.47/1.28 thf(f24,plain,(
% 1.47/1.28 ($true = ((sK1 @ sK4) & (sK0 @ sK4))) | ((~ ((sK0 @ sK4) & (~ (sK1 @ sK4)))) = $true)),
% 1.47/1.28 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.47/1.28 % SZS output end Proof for DTF2THF_30388
% 1.47/1.28 % (30692)------------------------------
% 1.47/1.28 % (30692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (30692)Termination reason: Refutation
% 1.47/1.28
% 1.47/1.28 % (30692)Memory used [KB]: 5500
% 1.47/1.28 % (30692)Time elapsed: 0.003 s
% 1.47/1.28 % (30692)Instructions burned: 1 (million)
% 1.47/1.28 % (30692)------------------------------
% 1.47/1.28 % (30692)------------------------------
% 1.47/1.28 % (30691)Success in time 0.013 s
%------------------------------------------------------------------------------