%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET628^5 : 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 : n011.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 09:31:58 AM UTC 2026
% Result : Theorem 1.65s 1.45s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 4 unt; 0 typ; 3 def)
% Number of atoms : 198 ( 65 equ; 0 cnn)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 166 ( 49 ~; 40 |; 17 &; 50 @)
% ( 7 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 7 con; 0-2 aty)
% Number of variables : 54 ( 23 ^; 17 !; 14 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_5,type,
sK0: a > $o ).
thf(func_def_6,type,
sK1: a ).
thf(func_def_8,type,
sK3: a ).
thf(f51,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f25,f29,f38,f50]) ).
thf(f50,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f49]) ).
thf(f49,plain,
( $false
| ~ spl2_1
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $true = $false )
| ~ spl2_1
| ~ spl2_2 ),
inference(backward_demodulation,[status(thm)],[f19,f47]) ).
thf(f47,plain,
( ! [X1: a] :
( ( sK0 @ X1 )
= $false )
| ~ spl2_2 ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
( ! [X1: a] :
( ( sK0 @ X1 )
= ( ^ [Y0: a] : $false
@ X1 ) )
| ~ spl2_2 ),
inference(argument_congruence,[status(thm)],[f22]) ).
thf(f22,plain,
( ( sK0
= ( ^ [Y0: a] : $false ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f21,definition,
( spl2_2
<=> ( sK0
= ( ^ [Y0: a] : $false ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f19,plain,
( ( ( sK0 @ sK1 )
= $true )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f17]) ).
thf(f17,definition,
( spl2_1
<=> ( ( sK0 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f38,plain,
( spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f37]) ).
thf(f37,plain,
( $false
| spl2_2
| ~ spl2_3 ),
inference(subsumption_resolution,[status(thm)],[f36,f31]) ).
thf(f31,plain,
( ! [X1: a] :
( ( sK0 @ X1 )
= $false )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f30]) ).
thf(f30,plain,
( ! [X1: a] :
( ( ( sK0 @ X1 )
= $false )
| ( $true != $true ) )
| ~ spl2_3 ),
inference(fool_paramodulation,[status(thm)],[f28]) ).
thf(f28,plain,
( ! [X1: a] :
( $true
!= ( sK0 @ X1 ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f27,definition,
( spl2_3
<=> ! [X1: a] :
( $true
!= ( sK0 @ X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f36,plain,
( ( ( sK0 @ sK3 )
!= $false )
| spl2_2 ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( sK0 @ sK3 )
!= ( ^ [Y0: a] : $false
@ sK3 ) )
| spl2_2 ),
inference(negative_extensionality,[status(thm)],[f23]) ).
thf(f23,plain,
( ( sK0
!= ( ^ [Y0: a] : $false ) )
| spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f29,plain,
( spl2_2
| spl2_3 ),
inference(avatar_split_clause,[status(thm)],[f15,f27,f21]) ).
thf(f15,plain,
! [X1: a] :
( ( sK0
= ( ^ [Y0: a] : $false ) )
| ( $true
!= ( sK0 @ X1 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: a] :
( ( $true
!= ( sK0 @ X1 ) )
| ( sK0
= ( ^ [Y0: a] : $false ) )
| ( $true
!= ( sK0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ! [X1: a] :
( ( $true
!= ( sK0 @ X1 ) )
| ( $true
!= ( sK0 @ X1 ) ) )
| ( sK0
= ( ^ [Y0: a] : $false ) ) )
& ( ( ( ( sK0 @ sK1 )
= $true )
& ( ( sK0 @ sK1 )
= $true ) )
| ( sK0
!= ( ^ [Y0: a] : $false ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X0: a > $o] :
( ( ! [X1: a] :
( ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ X1 )
!= $true ) )
| ( ( ^ [Y0: a] : $false )
= X0 ) )
& ( ? [X2: a] :
( ( $true
= ( X0 @ X2 ) )
& ( $true
= ( X0 @ X2 ) ) )
| ( ( ^ [Y0: a] : $false )
!= X0 ) ) )
=> ( ( ! [X1: a] :
( ( $true
!= ( sK0 @ X1 ) )
| ( $true
!= ( sK0 @ X1 ) ) )
| ( sK0
= ( ^ [Y0: a] : $false ) ) )
& ( ? [X2: a] :
( ( $true
= ( sK0 @ X2 ) )
& ( $true
= ( sK0 @ X2 ) ) )
| ( sK0
!= ( ^ [Y0: a] : $false ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X2: a] :
( ( $true
= ( sK0 @ X2 ) )
& ( $true
= ( sK0 @ X2 ) ) )
=> ( ( ( sK0 @ sK1 )
= $true )
& ( ( sK0 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > $o] :
( ( ! [X1: a] :
( ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ X1 )
!= $true ) )
| ( ( ^ [Y0: a] : $false )
= X0 ) )
& ( ? [X2: a] :
( ( $true
= ( X0 @ X2 ) )
& ( $true
= ( X0 @ X2 ) ) )
| ( ( ^ [Y0: a] : $false )
!= X0 ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > $o] :
( ( ! [X1: a] :
( ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ X1 )
!= $true ) )
| ( ( ^ [Y0: a] : $false )
= X0 ) )
& ( ? [X1: a] :
( ( ( X0 @ X1 )
= $true )
& ( ( X0 @ X1 )
= $true ) )
| ( ( ^ [Y0: a] : $false )
!= X0 ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a > $o] :
( ( ( ^ [Y0: a] : $false )
!= X0 )
<~> ? [X1: a] :
( ( ( X0 @ X1 )
= $true )
& ( ( X0 @ X1 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o] :
( ( ( ^ [Y0: a] : $false )
!= X0 )
<=> ? [X1: a] :
( ( ( X0 @ X1 )
= $true )
& ( ( X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o] :
( ? [X1: a] :
( ( X0 @ X1 )
& ( X0 @ X1 ) )
<=> ( X0
!= ( ^ [X2: a] : $false ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o] :
( ? [X1: a] :
( ( X0 @ X1 )
& ( X0 @ X1 ) )
<=> ( X0
!= ( ^ [X1: a] : $false ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > $o] :
( ? [X1: a] :
( ( X0 @ X1 )
& ( X0 @ X1 ) )
<=> ( X0
!= ( ^ [X1: a] : $false ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qIYVBc25PQ/DTF2THF_22968.p',cBOOL_PROP_110_pme) ).
thf(f25,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f12,f21,f17]) ).
thf(f12,plain,
( ( ( sK0 @ sK1 )
= $true )
| ( sK0
!= ( ^ [Y0: a] : $false ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET628^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.31 % Computer : n011.cluster.edu
% 0.15/0.31 % Model : x86_64 x86_64
% 0.15/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.31 % Memory : 8042.1875MB
% 0.15/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.31 % CPULimit : 300
% 0.15/0.31 % WCLimit : 300
% 0.15/0.31 % DateTime : Tue Feb 24 12:00:32 EST 2026
% 0.15/0.31 % CPUTime :
% 0.15/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.41 ---- Original DTF file ---
% 0.16/0.41 thf(spec,logic,$$dhol).
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 % File : SET628^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.41 % Domain : Set Theory
% 0.16/0.41 % Problem : TPS problem BOOL-PROP-110
% 0.16/0.41 % Version : Especial.
% 0.16/0.41 % English : Trybulec's 110th Boolean property of sets
% 0.16/0.41
% 0.16/0.41 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.16/0.41 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.41 % Source : [Bro09]
% 0.16/0.41 % Names : tps_0376 [Bro09]
% 0.16/0.41 % : BOOL-PROP-110 [TPS]
% 0.16/0.41
% 0.16/0.41 % Status : Theorem
% 0.16/0.41 % 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, 0.14 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
% 0.16/0.41 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.16/0.41 % Number of atoms : 2 ( 1 equ; 0 cnn)
% 0.16/0.41 % Maximal formula atoms : 1 ( 2 avg)
% 0.16/0.41 % Number of connectives : 5 ( 1 ~; 0 |; 1 &; 2 @)
% 0.16/0.41 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.16/0.41 % Maximal formula depth : 6 ( 6 avg)
% 0.16/0.41 % Number of types : 2 ( 1 usr)
% 0.16/0.41 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.16/0.41 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.16/0.41 % Number of variables : 3 ( 1 ^; 1 !; 1 ?; 3 :)
% 0.16/0.41 % SPC : TH0_THM_EQU_NAR
% 0.16/0.41
% 0.16/0.41 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.41 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.41 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.41 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.41 % : Polymorphic definitions expanded.
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 thf(a_type,type,
% 0.16/0.41 a: $tType ).
% 0.16/0.41
% 0.16/0.41 thf(cBOOL_PROP_110_pme,conjecture,
% 0.16/0.41 ! [X: a > $o] :
% 0.16/0.41 ( ? [Xx: a] :
% 0.16/0.41 ( ( X @ Xx )
% 0.16/0.41 & ( X @ Xx ) )
% 0.16/0.41 <=> ( X
% 0.16/0.41 != ( ^ [Xx: a] : $false ) ) ) ).
% 0.16/0.41
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 ------------------------
% 1.65/1.42 ---- Embedded in THF ---
% 1.65/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.65/1.42 %%% Generated on Tue Feb 24 12:00:33 EST 2026
% 1.65/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.65/1.42 %%% Logic specification used:
% 1.65/1.42 %%% thf(spec, logic, $$dhol).
% 1.65/1.42
% 1.65/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.qIYVBc25PQ/DTF2DTF22968.p
% See solution above
% 1.65/1.42 ------------------------
% 1.65/1.43 ---- Cleaned THF ---
% 1.65/1.43 thf(a_type,type,
% 1.65/1.43 a: $tType ).
% 1.65/1.43
% 1.65/1.43 thf(cBOOL_PROP_110_pme,conjecture,
% 1.65/1.43 ! [X: a > $o] :
% 1.65/1.43 ( ? [Xx: a] :
% 1.65/1.43 ( ( X @ Xx )
% 1.65/1.43 & ( X @ Xx ) )
% 1.65/1.43 <=> ( X
% 1.65/1.43 != ( ^ [Xx: a] : $false ) ) ) ).
% 1.65/1.43 ------------------------
% 1.65/1.44 % (23072)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22968 for (3000ds/18Mi)
% 1.65/1.44 % (23072)Refutation not found, incomplete strategy
% 1.65/1.44 % (23072)------------------------------
% 1.65/1.44 % (23072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.44 % (23072)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.44
% 1.65/1.44
% 1.65/1.44 % (23072)Memory used [KB]: 5500
% 1.65/1.44 % (23072)Time elapsed: 0.003 s
% 1.65/1.44 % (23072)Instructions burned: 1 (million)
% 1.65/1.44 % (23072)------------------------------
% 1.65/1.44 % (23072)------------------------------
% 1.65/1.45 % (23070)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_22968 for (3000ds/2Mi)
% 1.65/1.45 % (23067)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_22968 for (3000ds/4Mi)
% 1.65/1.45 % (23069)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22968 for (3000ds/2Mi)
% 1.65/1.45 % (23068)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_22968 for (3000ds/27Mi)
% 1.65/1.45 % (23070)Instruction limit reached!
% 1.65/1.45 % (23070)------------------------------
% 1.65/1.45 % (23070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.45 % (23070)Termination reason: Unknown
% 1.65/1.45 % (23070)Termination phase: Saturation
% 1.65/1.45
% 1.65/1.45 % (23070)Memory used [KB]: 5500
% 1.65/1.45 % (23070)Time elapsed: 0.003 s
% 1.65/1.45 % (23070)Instructions burned: 2 (million)
% 1.65/1.45 % (23070)------------------------------
% 1.65/1.45 % (23070)------------------------------
% 1.65/1.45 % (23071)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_22968 for (3000ds/275Mi)
% 1.65/1.45 % (23068)Refutation not found, incomplete strategy
% 1.65/1.45 % (23068)------------------------------
% 1.65/1.45 % (23068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.45 % (23067)First to succeed.
% 1.65/1.45 % (23068)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.45
% 1.65/1.45
% 1.65/1.45 % (23068)Memory used [KB]: 5500
% 1.65/1.45 % (23068)Time elapsed: 0.002 s
% 1.65/1.45 % (23068)Instructions burned: 1 (million)
% 1.65/1.45 % (23069)Refutation not found, incomplete strategy
% 1.65/1.45 % (23069)------------------------------
% 1.65/1.45 % (23069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.45 % (23069)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.45
% 1.65/1.45
% 1.65/1.45 % (23069)Memory used [KB]: 5500
% 1.65/1.45 % (23069)Time elapsed: 0.002 s
% 1.65/1.45 % (23069)Instructions burned: 1 (million)
% 1.65/1.45 % (23069)------------------------------
% 1.65/1.45 % (23069)------------------------------
% 1.65/1.45 % (23068)------------------------------
% 1.65/1.45 % (23068)------------------------------
% 1.65/1.45 % (23071)Refutation not found, incomplete strategy
% 1.65/1.45 % (23071)------------------------------
% 1.65/1.45 % (23071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.45 % (23071)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.45
% 1.65/1.45
% 1.65/1.45 % (23071)Memory used [KB]: 5500
% 1.65/1.45 % (23071)Time elapsed: 0.004 s
% 1.65/1.45 % (23071)Instructions burned: 1 (million)
% 1.65/1.45 % (23071)------------------------------
% 1.65/1.45 % (23071)------------------------------
% 1.65/1.45 % (23067)Refutation found. Thanks to Tanya!
% 1.65/1.45 % SZS status Theorem for DTF2THF_22968
% 1.65/1.45 % SZS output start Proof for DTF2THF_22968
% 1.65/1.45 thf(type_def_5, type, a: $tType).
% 1.65/1.45 thf(func_def_0, type, a: $tType).
% 1.65/1.45 thf(func_def_5, type, sK0: a > $o).
% 1.65/1.45 thf(func_def_6, type, sK1: a).
% 1.65/1.45 thf(func_def_8, type, sK3: a).
% 1.65/1.45 thf(f51,plain,(
% 1.65/1.45 $false),
% 1.65/1.45 inference(avatar_sat_refutation,[status(thm)],[f25,f29,f38,f50])).
% 1.65/1.45 thf(f50,plain,(
% 1.65/1.45 ~spl2_1 | ~spl2_2),
% 1.65/1.45 inference(avatar_contradiction_clause,[status(thm)],[f49])).
% 1.65/1.45 thf(f49,plain,(
% 1.65/1.45 $false | (~spl2_1 | ~spl2_2)),
% 1.65/1.45 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.65/1.45 thf(f48,plain,(
% 1.65/1.45 ($true = $false) | (~spl2_1 | ~spl2_2)),
% 1.65/1.45 inference(backward_demodulation,[status(thm)],[f19,f47])).
% 1.65/1.45 thf(f47,plain,(
% 1.65/1.45 ( ! [X1 : a] : (((sK0 @ X1) = $false)) ) | ~spl2_2),
% 1.65/1.45 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.65/1.45 thf(f46,plain,(
% 1.65/1.45 ( ! [X1 : a] : (((sK0 @ X1) = ((^[Y0 : a]: ($false)) @ X1))) ) | ~spl2_2),
% 1.65/1.45 inference(argument_congruence,[status(thm)],[f22])).
% 1.65/1.45 thf(f22,plain,(
% 1.65/1.45 (sK0 = (^[Y0 : a]: ($false))) | ~spl2_2),
% 1.65/1.45 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.65/1.45 thf(f21,definition,(
% 1.65/1.45 spl2_2 <=> (sK0 = (^[Y0 : a]: ($false)))),
% 1.65/1.45 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.65/1.45 thf(f19,plain,(
% 1.65/1.45 ((sK0 @ sK1) = $true) | ~spl2_1),
% 1.65/1.45 inference(avatar_component_clause,[status(thm)],[f17])).
% 1.65/1.45 thf(f17,definition,(
% 1.65/1.45 spl2_1 <=> ((sK0 @ sK1) = $true)),
% 1.65/1.45 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.65/1.45 thf(f38,plain,(
% 1.65/1.45 spl2_2 | ~spl2_3),
% 1.65/1.45 inference(avatar_contradiction_clause,[status(thm)],[f37])).
% 1.65/1.45 thf(f37,plain,(
% 1.65/1.45 $false | (spl2_2 | ~spl2_3)),
% 1.65/1.45 inference(subsumption_resolution,[status(thm)],[f36,f31])).
% 1.65/1.45 thf(f31,plain,(
% 1.65/1.45 ( ! [X1 : a] : (((sK0 @ X1) = $false)) ) | ~spl2_3),
% 1.65/1.45 inference(trivial_inequality_removal,[status(thm)],[f30])).
% 1.65/1.45 thf(f30,plain,(
% 1.65/1.45 ( ! [X1 : a] : (((sK0 @ X1) = $false) | ($true != $true)) ) | ~spl2_3),
% 1.65/1.45 inference(fool_paramodulation,[status(thm)],[f28])).
% 1.65/1.45 thf(f28,plain,(
% 1.65/1.45 ( ! [X1 : a] : (($true != (sK0 @ X1))) ) | ~spl2_3),
% 1.65/1.45 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.65/1.45 thf(f27,definition,(
% 1.65/1.45 spl2_3 <=> ! [X1 : a] : ($true != (sK0 @ X1))),
% 1.65/1.45 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.65/1.45 thf(f36,plain,(
% 1.65/1.45 ((sK0 @ sK3) != $false) | spl2_2),
% 1.65/1.45 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.65/1.45 thf(f35,plain,(
% 1.65/1.45 ((sK0 @ sK3) != ((^[Y0 : a]: ($false)) @ sK3)) | spl2_2),
% 1.65/1.45 inference(negative_extensionality,[status(thm)],[f23])).
% 1.65/1.45 thf(f23,plain,(
% 1.65/1.45 (sK0 != (^[Y0 : a]: ($false))) | spl2_2),
% 1.65/1.45 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.65/1.45 thf(f29,plain,(
% 1.65/1.45 spl2_2 | spl2_3),
% 1.65/1.45 inference(avatar_split_clause,[status(thm)],[f15,f27,f21])).
% 1.65/1.45 thf(f15,plain,(
% 1.65/1.45 ( ! [X1 : a] : ((sK0 = (^[Y0 : a]: ($false))) | ($true != (sK0 @ X1))) )),
% 1.65/1.45 inference(duplicate_literal_removal,[status(thm)],[f14])).
% 1.65/1.45 thf(f14,plain,(
% 1.65/1.45 ( ! [X1 : a] : (($true != (sK0 @ X1)) | (sK0 = (^[Y0 : a]: ($false))) | ($true != (sK0 @ X1))) )),
% 1.65/1.45 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.45 thf(f11,plain,(
% 1.65/1.45 (! [X1 : a] : (($true != (sK0 @ X1)) | ($true != (sK0 @ X1))) | (sK0 = (^[Y0 : a]: ($false)))) & ((((sK0 @ sK1) = $true) & ((sK0 @ sK1) = $true)) | (sK0 != (^[Y0 : a]: ($false))))),
% 1.65/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9])).
% 1.65/1.45 thf(f9,plain,(
% 1.65/1.45 ? [X0 : a > $o] : ((! [X1 : a] : (((X0 @ X1) != $true) | ((X0 @ X1) != $true)) | ((^[Y0 : a]: ($false)) = X0)) & (? [X2 : a] : (($true = (X0 @ X2)) & ($true = (X0 @ X2))) | ((^[Y0 : a]: ($false)) != X0))) => ((! [X1 : a] : (($true != (sK0 @ X1)) | ($true != (sK0 @ X1))) | (sK0 = (^[Y0 : a]: ($false)))) & (? [X2 : a] : (($true = (sK0 @ X2)) & ($true = (sK0 @ X2))) | (sK0 != (^[Y0 : a]: ($false)))))),
% 1.65/1.45 introduced(definition,[],[choice_axiom])).
% 1.65/1.45 thf(f10,plain,(
% 1.65/1.45 ? [X2 : a] : (($true = (sK0 @ X2)) & ($true = (sK0 @ X2))) => (((sK0 @ sK1) = $true) & ((sK0 @ sK1) = $true))),
% 1.65/1.45 introduced(definition,[],[choice_axiom])).
% 1.65/1.45 thf(f8,plain,(
% 1.65/1.45 ? [X0 : a > $o] : ((! [X1 : a] : (((X0 @ X1) != $true) | ((X0 @ X1) != $true)) | ((^[Y0 : a]: ($false)) = X0)) & (? [X2 : a] : (($true = (X0 @ X2)) & ($true = (X0 @ X2))) | ((^[Y0 : a]: ($false)) != X0)))),
% 1.65/1.45 inference(rectify,[status(thm)],[f7])).
% 1.65/1.45 thf(f7,plain,(
% 1.65/1.45 ? [X0 : a > $o] : ((! [X1 : a] : (((X0 @ X1) != $true) | ((X0 @ X1) != $true)) | ((^[Y0 : a]: ($false)) = X0)) & (? [X1 : a] : (((X0 @ X1) = $true) & ((X0 @ X1) = $true)) | ((^[Y0 : a]: ($false)) != X0)))),
% 1.65/1.45 inference(nnf_transformation,[status(thm)],[f6])).
% 1.65/1.45 thf(f6,plain,(
% 1.65/1.45 ? [X0 : a > $o] : (((^[Y0 : a]: ($false)) != X0) <~> ? [X1 : a] : (((X0 @ X1) = $true) & ((X0 @ X1) = $true)))),
% 1.65/1.45 inference(ennf_transformation,[status(thm)],[f5])).
% 1.65/1.45 thf(f5,plain,(
% 1.65/1.45 ~! [X0 : a > $o] : (((^[Y0 : a]: ($false)) != X0) <=> ? [X1 : a] : (((X0 @ X1) = $true) & ((X0 @ X1) = $true)))),
% 1.65/1.45 inference(fool_elimination,[status(thm)],[f4])).
% 1.65/1.45 thf(f4,plain,(
% 1.65/1.45 ~! [X0 : a > $o] : (? [X1 : a] : ((X0 @ X1) & (X0 @ X1)) <=> (X0 != (^[X2 : a] : ($false))))),
% 1.65/1.45 inference(rectify,[status(thm)],[f2])).
% 1.65/1.45 thf(f2,negated_conjecture,(
% 1.65/1.45 ~! [X0 : a > $o] : (? [X1 : a] : ((X0 @ X1) & (X0 @ X1)) <=> (X0 != (^[X1 : a] : ($false))))),
% 1.65/1.45 inference(negated_conjecture,[status(cth)],[f1])).
% 1.65/1.45 thf(f1,conjecture,(
% 1.65/1.45 ! [X0 : a > $o] : (? [X1 : a] : ((X0 @ X1) & (X0 @ X1)) <=> (X0 != (^[X1 : a] : ($false))))),
% 1.65/1.45 file('/export/starexec/sandbox/tmp/tmp.qIYVBc25PQ/DTF2THF_22968.p',cBOOL_PROP_110_pme)).
% 1.65/1.45 thf(f25,plain,(
% 1.65/1.45 spl2_1 | ~spl2_2),
% 1.65/1.45 inference(avatar_split_clause,[status(thm)],[f12,f21,f17])).
% 1.65/1.45 thf(f12,plain,(
% 1.65/1.45 ((sK0 @ sK1) = $true) | (sK0 != (^[Y0 : a]: ($false)))),
% 1.65/1.45 inference(cnf_transformation,[status(thm)],[f11])).
% 1.65/1.45 % SZS output end Proof for DTF2THF_22968
% 1.65/1.45 % (23067)------------------------------
% 1.65/1.45 % (23067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.45 % (23067)Termination reason: Refutation
% 1.65/1.45
% 1.65/1.45 % (23067)Memory used [KB]: 5500
% 1.65/1.45 % (23067)Time elapsed: 0.004 s
% 1.65/1.45 % (23067)Instructions burned: 1 (million)
% 1.65/1.45 % (23067)------------------------------
% 1.65/1.45 % (23067)------------------------------
% 1.65/1.45 % (23064)Success in time 0.017 s
%------------------------------------------------------------------------------