%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV241^5 : 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 : n024.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 09:40:38 AM UTC 2026
% Result : Theorem 0.98s 0.90s
% Output : Refutation 0.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 200 ( 65 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 137 ( 29 ~; 31 |; 21 &; 44 @)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 20 ( 0 ^; 12 !; 8 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cW: a > $o ).
thf(func_def_2,type,
cU: a > $o ).
thf(func_def_6,type,
sK0: a ).
thf(func_def_7,type,
sK1: a > $o ).
thf(func_def_9,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
sK4: a ).
thf(f68,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f23,f31,f67]) ).
thf(f67,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f66]) ).
thf(f66,plain,
( $false
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
( ( $false = $true )
| ~ spl2_1 ),
inference(backward_demodulation,[status(thm)],[f11,f64]) ).
thf(f64,plain,
( ( $false
= ( cW @ sK0 ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( $true != $true )
| ( $false
= ( cW @ sK0 ) )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f13,f34]) ).
thf(f34,plain,
( ! [X1: a] :
( ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( cW @ X1 ) ) )
| ~ spl2_1 ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ! [X1: a] :
( ( cW @ X1 )
= ( sK1 @ X1 ) )
| ~ spl2_1 ),
inference(argument_congruence,[status(thm)],[f18]) ).
thf(f18,plain,
( ( cW = sK1 )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f16]) ).
thf(f16,definition,
( spl2_1
<=> ( cW = sK1 ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f13,plain,
( ( sK1 @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( cW = sK1 )
| ( cU = sK1 ) )
& ( ( sK1 @ sK0 )
!= $true )
& ( ( cU @ sK0 )
= $true )
& ( $true
= ( cW @ sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8]) ).
thf(f8,plain,
( ? [X0: a] :
( ? [X1: a > $o] :
( ( ( cW = X1 )
| ( cU = X1 ) )
& ( ( X1 @ X0 )
!= $true ) )
& ( ( cU @ X0 )
= $true )
& ( ( cW @ X0 )
= $true ) )
=> ( ? [X1: a > $o] :
( ( ( cW = X1 )
| ( cU = X1 ) )
& ( $true
!= ( X1 @ sK0 ) ) )
& ( ( cU @ sK0 )
= $true )
& ( $true
= ( cW @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X1: a > $o] :
( ( ( cW = X1 )
| ( cU = X1 ) )
& ( $true
!= ( X1 @ sK0 ) ) )
=> ( ( ( cW = sK1 )
| ( cU = sK1 ) )
& ( ( sK1 @ sK0 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: a] :
( ? [X1: a > $o] :
( ( ( cW = X1 )
| ( cU = X1 ) )
& ( ( X1 @ X0 )
!= $true ) )
& ( ( cU @ X0 )
= $true )
& ( ( cW @ X0 )
= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a] :
( ? [X1: a > $o] :
( ( ( cW = X1 )
| ( cU = X1 ) )
& ( ( X1 @ X0 )
!= $true ) )
& ( ( cU @ X0 )
= $true )
& ( ( cW @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a] :
( ( ( ( cU @ X0 )
= $true )
& ( ( cW @ X0 )
= $true ) )
=> ! [X1: a > $o] :
( ( ( cW = X1 )
| ( cU = X1 ) )
=> ( ( X1 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a] :
( ( ( cU @ X0 )
& ( cW @ X0 ) )
=> ! [X1: a > $o] :
( ( ( cU = X1 )
| ( cW = X1 ) )
=> ( X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a] :
( ( ( cU @ X0 )
& ( cW @ X0 ) )
=> ! [X1: a > $o] :
( ( ( cU = X1 )
| ( cW = X1 ) )
=> ( X1 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a] :
( ( ( cU @ X0 )
& ( cW @ X0 ) )
=> ! [X1: a > $o] :
( ( ( cU = X1 )
| ( cW = X1 ) )
=> ( X1 @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.D2SSJ5S8Oa/DTF2THF_8470.p',cX5201A_pme) ).
thf(f11,plain,
( $true
= ( cW @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f31,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f30]) ).
thf(f30,plain,
( $false
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ( $false = $true )
| ~ spl2_2 ),
inference(backward_demodulation,[status(thm)],[f12,f28]) ).
thf(f28,plain,
( ( ( cU @ sK0 )
= $false )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( cU @ sK0 )
= $false )
| ( $true != $true )
| ~ spl2_2 ),
inference(superposition,[status(thm)],[f13,f25]) ).
thf(f25,plain,
( ! [X1: a] :
( ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( cU @ X1 ) ) )
| ~ spl2_2 ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ! [X1: a] :
( ( sK1 @ X1 )
= ( cU @ X1 ) )
| ~ spl2_2 ),
inference(argument_congruence,[status(thm)],[f22]) ).
thf(f22,plain,
( ( cU = sK1 )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f20,definition,
( spl2_2
<=> ( cU = sK1 ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f12,plain,
( ( cU @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f23,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f14,f20,f16]) ).
thf(f14,plain,
( ( cU = sK1 )
| ( cW = sK1 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEV241^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n024.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 07:42:25 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.31 ---- Original DTF file ---
% 0.07/0.31 thf(spec,logic,$$dhol).
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 % File : SEV241^5 : TPTP v9.2.1. Released v4.0.0.
% 0.07/0.31 % Domain : Set Theory (Sets of sets)
% 0.07/0.31 % Problem : TPS problem from SETS-OF-SETS-THMS
% 0.07/0.31 % Version : Especial.
% 0.07/0.31 % English :
% 0.07/0.31
% 0.07/0.31 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.07/0.31 % Source : [Bro09]
% 0.07/0.31 % Names : tps_0779 [Bro09]
% 0.07/0.31
% 0.07/0.31 % Status : Theorem
% 0.07/0.31 % Rating : 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 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.07/0.31 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.07/0.31 % Number of atoms : 6 ( 2 equ; 0 cnn)
% 0.07/0.31 % Maximal formula atoms : 4 ( 6 avg)
% 0.07/0.31 % Number of connectives : 7 ( 0 ~; 1 |; 1 &; 3 @)
% 0.07/0.31 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.07/0.31 % Maximal formula depth : 6 ( 6 avg)
% 0.07/0.31 % Number of types : 2 ( 1 usr)
% 0.07/0.31 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.07/0.31 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.07/0.31 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.07/0.31 % SPC : TH0_THM_EQU_NAR
% 0.07/0.31
% 0.07/0.31 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.07/0.31 % project in the Department of Mathematical Sciences at Carnegie
% 0.07/0.31 % Mellon University. Distributed under the Creative Commons copyleft
% 0.07/0.31 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 thf(a_type,type,
% 0.07/0.31 a: $tType ).
% 0.07/0.31
% 0.07/0.31 thf(cW,type,
% 0.07/0.31 cW: a > $o ).
% 0.07/0.31
% 0.07/0.31 thf(cU,type,
% 0.07/0.31 cU: a > $o ).
% 0.07/0.31
% 0.07/0.31 thf(cX5201A_pme,conjecture,
% 0.07/0.31 ! [Xx: a] :
% 0.07/0.31 ( ( ( cU @ Xx )
% 0.07/0.31 & ( cW @ Xx ) )
% 0.07/0.31 => ! [S: a > $o] :
% 0.07/0.31 ( ( ( S = cU )
% 0.07/0.31 | ( S = cW ) )
% 0.07/0.31 => ( S @ Xx ) ) ) ).
% 0.07/0.31
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 ------------------------
% 0.82/0.88 ---- Embedded in THF ---
% 0.82/0.88 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.82/0.88 %%% Generated on Tue Feb 24 07:42:26 EST 2026
% 0.82/0.88 %%% using '$$dhol' embedding, version 1.3.0.
% 0.82/0.88 %%% Logic specification used:
% 0.82/0.88 %%% thf(spec, logic, $$dhol).
% 0.82/0.88
% 0.82/0.88 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.D2SSJ5S8Oa/DTF2DTF8470.p
% See solution above
% 0.82/0.88 ------------------------
% 0.82/0.88 ---- Cleaned THF ---
% 0.82/0.88 thf(a_type,type,
% 0.82/0.88 a: $tType ).
% 0.82/0.88
% 0.82/0.88 thf(cW,type,
% 0.82/0.88 cW: a > $o ).
% 0.82/0.88
% 0.82/0.88 thf(cU,type,
% 0.82/0.88 cU: a > $o ).
% 0.82/0.88
% 0.82/0.88 thf(cX5201A_pme,conjecture,
% 0.82/0.88 ! [Xx: a] :
% 0.82/0.88 ( ( ( cU @ Xx )
% 0.82/0.88 & ( cW @ Xx ) )
% 0.82/0.88 => ! [S: a > $o] :
% 0.82/0.88 ( ( ( S = cU )
% 0.82/0.88 | ( S = cW ) )
% 0.82/0.88 => ( S @ Xx ) ) ) ).
% 0.82/0.88 ------------------------
% 0.82/0.90 % (8736)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_8470 for (3000ds/275Mi)
% 0.82/0.90 % (8733)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_8470 for (3000ds/27Mi)
% 0.82/0.90 % (8735)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_8470 for (3000ds/2Mi)
% 0.82/0.90 % (8734)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8470 for (3000ds/2Mi)
% 0.82/0.90 % (8732)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_8470 for (3000ds/4Mi)
% 0.82/0.90 % (8731)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8470 for (3000ds/183Mi)
% 0.82/0.90 % (8737)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8470 for (3000ds/18Mi)
% 0.98/0.90 % (8735)Instruction limit reached!
% 0.98/0.90 % (8735)------------------------------
% 0.98/0.90 % (8735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/0.90 % (8735)Termination reason: Unknown
% 0.98/0.90 % (8735)Termination phase: Saturation
% 0.98/0.90
% 0.98/0.90 % (8735)Memory used [KB]: 5373
% 0.98/0.90 % (8735)Time elapsed: 0.002 s
% 0.98/0.90 % (8735)Instructions burned: 2 (million)
% 0.98/0.90 % (8735)------------------------------
% 0.98/0.90 % (8735)------------------------------
% 0.98/0.90 % (8734)Instruction limit reached!
% 0.98/0.90 % (8734)------------------------------
% 0.98/0.90 % (8734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/0.90 % (8734)Termination reason: Unknown
% 0.98/0.90 % (8734)Termination phase: Saturation
% 0.98/0.90
% 0.98/0.90 % (8734)Memory used [KB]: 5500
% 0.98/0.90 % (8734)Time elapsed: 0.003 s
% 0.98/0.90 % (8734)Instructions burned: 3 (million)
% 0.98/0.90 % (8734)------------------------------
% 0.98/0.90 % (8734)------------------------------
% 0.98/0.90 % (8737)First to succeed.
% 0.98/0.90 % (8732)Instruction limit reached!
% 0.98/0.90 % (8732)------------------------------
% 0.98/0.90 % (8732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/0.90 % (8732)Termination reason: Unknown
% 0.98/0.90 % (8732)Termination phase: Saturation
% 0.98/0.90
% 0.98/0.90 % (8732)Memory used [KB]: 5500
% 0.98/0.90 % (8732)Time elapsed: 0.004 s
% 0.98/0.90 % (8732)Instructions burned: 5 (million)
% 0.98/0.90 % (8732)------------------------------
% 0.98/0.90 % (8732)------------------------------
% 0.98/0.90 % (8736)Also succeeded, but the first one will report.
% 0.98/0.90 % (8731)Also succeeded, but the first one will report.
% 0.98/0.90 % (8737)Refutation found. Thanks to Tanya!
% 0.98/0.90 % SZS status Theorem for DTF2THF_8470
% 0.98/0.90 % SZS output start Proof for DTF2THF_8470
% 0.98/0.90 thf(type_def_5, type, a: $tType).
% 0.98/0.90 thf(func_def_0, type, a: $tType).
% 0.98/0.90 thf(func_def_1, type, cW: a > $o).
% 0.98/0.90 thf(func_def_2, type, cU: a > $o).
% 0.98/0.90 thf(func_def_6, type, sK0: a).
% 0.98/0.90 thf(func_def_7, type, sK1: a > $o).
% 0.98/0.90 thf(func_def_9, type, ph3: !>[X0: $tType]:(X0)).
% 0.98/0.90 thf(func_def_10, type, sK4: a).
% 0.98/0.90 thf(f68,plain,(
% 0.98/0.90 $false),
% 0.98/0.90 inference(avatar_sat_refutation,[status(thm)],[f23,f31,f67])).
% 0.98/0.90 thf(f67,plain,(
% 0.98/0.90 ~spl2_1),
% 0.98/0.90 inference(avatar_contradiction_clause,[status(thm)],[f66])).
% 0.98/0.90 thf(f66,plain,(
% 0.98/0.90 $false | ~spl2_1),
% 0.98/0.90 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 0.98/0.90 thf(f65,plain,(
% 0.98/0.90 ($false = $true) | ~spl2_1),
% 0.98/0.90 inference(backward_demodulation,[status(thm)],[f11,f64])).
% 0.98/0.90 thf(f64,plain,(
% 0.98/0.90 ($false = (cW @ sK0)) | ~spl2_1),
% 0.98/0.90 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 0.98/0.90 thf(f63,plain,(
% 0.98/0.90 ($true != $true) | ($false = (cW @ sK0)) | ~spl2_1),
% 0.98/0.90 inference(superposition,[status(thm)],[f13,f34])).
% 0.98/0.90 thf(f34,plain,(
% 0.98/0.90 ( ! [X1 : a] : (($true = (sK1 @ X1)) | ($false = (cW @ X1))) ) | ~spl2_1),
% 0.98/0.90 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 0.98/0.90 thf(f32,plain,(
% 0.98/0.90 ( ! [X1 : a] : (((cW @ X1) = (sK1 @ X1))) ) | ~spl2_1),
% 0.98/0.90 inference(argument_congruence,[status(thm)],[f18])).
% 0.98/0.90 thf(f18,plain,(
% 0.98/0.90 (cW = sK1) | ~spl2_1),
% 0.98/0.90 inference(avatar_component_clause,[status(thm)],[f16])).
% 0.98/0.90 thf(f16,definition,(
% 0.98/0.90 spl2_1 <=> (cW = sK1)),
% 0.98/0.90 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 0.98/0.90 thf(f13,plain,(
% 0.98/0.90 ((sK1 @ sK0) != $true)),
% 0.98/0.90 inference(cnf_transformation,[status(thm)],[f10])).
% 0.98/0.90 thf(f10,plain,(
% 0.98/0.90 (((cW = sK1) | (cU = sK1)) & ((sK1 @ sK0) != $true)) & ((cU @ sK0) = $true) & ($true = (cW @ sK0))),
% 0.98/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8])).
% 0.98/0.90 thf(f8,plain,(
% 0.98/0.90 ? [X0 : a] : (? [X1 : a > $o] : (((cW = X1) | (cU = X1)) & ((X1 @ X0) != $true)) & ((cU @ X0) = $true) & ((cW @ X0) = $true)) => (? [X1 : a > $o] : (((cW = X1) | (cU = X1)) & ($true != (X1 @ sK0))) & ((cU @ sK0) = $true) & ($true = (cW @ sK0)))),
% 0.98/0.90 introduced(definition,[],[choice_axiom])).
% 0.98/0.90 thf(f9,plain,(
% 0.98/0.90 ? [X1 : a > $o] : (((cW = X1) | (cU = X1)) & ($true != (X1 @ sK0))) => (((cW = sK1) | (cU = sK1)) & ((sK1 @ sK0) != $true))),
% 0.98/0.90 introduced(definition,[],[choice_axiom])).
% 0.98/0.90 thf(f7,plain,(
% 0.98/0.90 ? [X0 : a] : (? [X1 : a > $o] : (((cW = X1) | (cU = X1)) & ((X1 @ X0) != $true)) & ((cU @ X0) = $true) & ((cW @ X0) = $true))),
% 0.98/0.90 inference(flattening,[status(thm)],[f6])).
% 0.98/0.90 thf(f6,plain,(
% 0.98/0.90 ? [X0 : a] : (? [X1 : a > $o] : (((cW = X1) | (cU = X1)) & ((X1 @ X0) != $true)) & (((cU @ X0) = $true) & ((cW @ X0) = $true)))),
% 0.98/0.90 inference(ennf_transformation,[status(thm)],[f5])).
% 0.98/0.90 thf(f5,plain,(
% 0.98/0.90 ~! [X0 : a] : ((((cU @ X0) = $true) & ((cW @ X0) = $true)) => ! [X1 : a > $o] : (((cW = X1) | (cU = X1)) => ((X1 @ X0) = $true)))),
% 0.98/0.90 inference(fool_elimination,[status(thm)],[f4])).
% 0.98/0.90 thf(f4,plain,(
% 0.98/0.90 ~! [X0 : a] : (((cU @ X0) & (cW @ X0)) => ! [X1 : a > $o] : (((cU = X1) | (cW = X1)) => (X1 @ X0)))),
% 0.98/0.90 inference(rectify,[status(thm)],[f2])).
% 0.98/0.90 thf(f2,negated_conjecture,(
% 0.98/0.90 ~! [X0 : a] : (((cU @ X0) & (cW @ X0)) => ! [X1 : a > $o] : (((cU = X1) | (cW = X1)) => (X1 @ X0)))),
% 0.98/0.90 inference(negated_conjecture,[status(cth)],[f1])).
% 0.98/0.90 thf(f1,conjecture,(
% 0.98/0.90 ! [X0 : a] : (((cU @ X0) & (cW @ X0)) => ! [X1 : a > $o] : (((cU = X1) | (cW = X1)) => (X1 @ X0)))),
% 0.98/0.90 file('/export/starexec/sandbox/tmp/tmp.D2SSJ5S8Oa/DTF2THF_8470.p',cX5201A_pme)).
% 0.98/0.90 thf(f11,plain,(
% 0.98/0.90 ($true = (cW @ sK0))),
% 0.98/0.90 inference(cnf_transformation,[status(thm)],[f10])).
% 0.98/0.90 thf(f31,plain,(
% 0.98/0.90 ~spl2_2),
% 0.98/0.90 inference(avatar_contradiction_clause,[status(thm)],[f30])).
% 0.98/0.90 thf(f30,plain,(
% 0.98/0.90 $false | ~spl2_2),
% 0.98/0.90 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 0.98/0.90 thf(f29,plain,(
% 0.98/0.90 ($false = $true) | ~spl2_2),
% 0.98/0.90 inference(backward_demodulation,[status(thm)],[f12,f28])).
% 0.98/0.90 thf(f28,plain,(
% 0.98/0.90 ((cU @ sK0) = $false) | ~spl2_2),
% 0.98/0.90 inference(trivial_inequality_removal,[status(thm)],[f27])).
% 0.98/0.90 thf(f27,plain,(
% 0.98/0.90 ((cU @ sK0) = $false) | ($true != $true) | ~spl2_2),
% 0.98/0.90 inference(superposition,[status(thm)],[f13,f25])).
% 0.98/0.90 thf(f25,plain,(
% 0.98/0.90 ( ! [X1 : a] : (($true = (sK1 @ X1)) | ($false = (cU @ X1))) ) | ~spl2_2),
% 0.98/0.90 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 0.98/0.90 thf(f24,plain,(
% 0.98/0.90 ( ! [X1 : a] : (((sK1 @ X1) = (cU @ X1))) ) | ~spl2_2),
% 0.98/0.90 inference(argument_congruence,[status(thm)],[f22])).
% 0.98/0.90 thf(f22,plain,(
% 0.98/0.90 (cU = sK1) | ~spl2_2),
% 0.98/0.90 inference(avatar_component_clause,[status(thm)],[f20])).
% 0.98/0.90 thf(f20,definition,(
% 0.98/0.90 spl2_2 <=> (cU = sK1)),
% 0.98/0.90 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 0.98/0.90 thf(f12,plain,(
% 0.98/0.90 ((cU @ sK0) = $true)),
% 0.98/0.90 inference(cnf_transformation,[status(thm)],[f10])).
% 0.98/0.90 thf(f23,plain,(
% 0.98/0.90 spl2_1 | spl2_2),
% 0.98/0.90 inference(avatar_split_clause,[status(thm)],[f14,f20,f16])).
% 0.98/0.90 thf(f14,plain,(
% 0.98/0.90 (cU = sK1) | (cW = sK1)),
% 0.98/0.90 inference(cnf_transformation,[status(thm)],[f10])).
% 0.98/0.90 % SZS output end Proof for DTF2THF_8470
% 0.98/0.90 % (8737)------------------------------
% 0.98/0.90 % (8737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.98/0.90 % (8737)Termination reason: Refutation
% 0.98/0.90
% 0.98/0.90 % (8737)Memory used [KB]: 5500
% 0.98/0.90 % (8737)Time elapsed: 0.003 s
% 0.98/0.90 % (8737)Instructions burned: 3 (million)
% 0.98/0.90 % (8737)------------------------------
% 0.98/0.90 % (8737)------------------------------
% 0.98/0.90 % (8730)Success in time 0.01 s
%------------------------------------------------------------------------------