%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV397^5 : 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 : n018.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 09:41:10 AM UTC 2026
% Result : Theorem 1.64s 1.32s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 3 unt; 0 typ; 3 def)
% Number of atoms : 359 ( 109 equ; 0 cnn)
% Maximal formula atoms : 28 ( 14 avg)
% Number of connectives : 297 ( 51 ~; 67 |; 40 &; 130 @)
% ( 7 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 8 ( 0 ^; 4 !; 4 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cZ: a > $o ).
thf(func_def_2,type,
cY: a > $o ).
thf(func_def_3,type,
cX: a > $o ).
thf(func_def_5,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_8,type,
sK0: a ).
thf(f58,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f42,f54,f56,f57]) ).
thf(f57,plain,
~ spl1_3,
inference(avatar_split_clause,[status(thm)],[f23,f44]) ).
thf(f44,definition,
( spl1_3
<=> ( $true
= ( cZ @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition]) ).
thf(f23,plain,
( $true
!= ( cZ @ sK0 ) ),
inference(duplicate_literal_removal,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $true
!= ( cZ @ sK0 ) )
| ( $true
!= ( cZ @ sK0 ) )
| ( $true
!= ( cZ @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( ( ( cX @ sK0 )
!= $true )
& ( $true
!= ( cZ @ sK0 ) ) )
| ( ( $true
!= ( cY @ sK0 ) )
& ( $true
!= ( cZ @ sK0 ) ) )
| ( ( $true
!= ( cZ @ sK0 ) )
& ( ( $true
!= ( cY @ sK0 ) )
| ( ( cX @ sK0 )
!= $true ) ) ) )
& ( ( ( ( ( cX @ sK0 )
= $true )
| ( $true
= ( cZ @ sK0 ) ) )
& ( ( $true
= ( cY @ sK0 ) )
| ( $true
= ( cZ @ sK0 ) ) ) )
| ( $true
= ( cZ @ sK0 ) )
| ( ( $true
= ( cY @ sK0 ) )
& ( ( cX @ sK0 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: a] :
( ( ( ( ( cX @ X0 )
!= $true )
& ( ( cZ @ X0 )
!= $true ) )
| ( ( ( cY @ X0 )
!= $true )
& ( ( cZ @ X0 )
!= $true ) )
| ( ( ( cZ @ X0 )
!= $true )
& ( ( ( cY @ X0 )
!= $true )
| ( ( cX @ X0 )
!= $true ) ) ) )
& ( ( ( ( ( cX @ X0 )
= $true )
| ( ( cZ @ X0 )
= $true ) )
& ( ( ( cY @ X0 )
= $true )
| ( ( cZ @ X0 )
= $true ) ) )
| ( ( cZ @ X0 )
= $true )
| ( ( ( cY @ X0 )
= $true )
& ( ( cX @ X0 )
= $true ) ) ) )
=> ( ( ( ( ( cX @ sK0 )
!= $true )
& ( $true
!= ( cZ @ sK0 ) ) )
| ( ( $true
!= ( cY @ sK0 ) )
& ( $true
!= ( cZ @ sK0 ) ) )
| ( ( $true
!= ( cZ @ sK0 ) )
& ( ( $true
!= ( cY @ sK0 ) )
| ( ( cX @ sK0 )
!= $true ) ) ) )
& ( ( ( ( ( cX @ sK0 )
= $true )
| ( $true
= ( cZ @ sK0 ) ) )
& ( ( $true
= ( cY @ sK0 ) )
| ( $true
= ( cZ @ sK0 ) ) ) )
| ( $true
= ( cZ @ sK0 ) )
| ( ( $true
= ( cY @ sK0 ) )
& ( ( cX @ sK0 )
= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a] :
( ( ( ( ( cX @ X0 )
!= $true )
& ( ( cZ @ X0 )
!= $true ) )
| ( ( ( cY @ X0 )
!= $true )
& ( ( cZ @ X0 )
!= $true ) )
| ( ( ( cZ @ X0 )
!= $true )
& ( ( ( cY @ X0 )
!= $true )
| ( ( cX @ X0 )
!= $true ) ) ) )
& ( ( ( ( ( cX @ X0 )
= $true )
| ( ( cZ @ X0 )
= $true ) )
& ( ( ( cY @ X0 )
= $true )
| ( ( cZ @ X0 )
= $true ) ) )
| ( ( cZ @ X0 )
= $true )
| ( ( ( cY @ X0 )
= $true )
& ( ( cX @ X0 )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a] :
( ( ( ( ( cX @ X0 )
!= $true )
& ( ( cZ @ X0 )
!= $true ) )
| ( ( ( cY @ X0 )
!= $true )
& ( ( cZ @ X0 )
!= $true ) )
| ( ( ( cZ @ X0 )
!= $true )
& ( ( ( cY @ X0 )
!= $true )
| ( ( cX @ X0 )
!= $true ) ) ) )
& ( ( ( ( ( cX @ X0 )
= $true )
| ( ( cZ @ X0 )
= $true ) )
& ( ( ( cY @ X0 )
= $true )
| ( ( cZ @ X0 )
= $true ) ) )
| ( ( cZ @ X0 )
= $true )
| ( ( ( cY @ X0 )
= $true )
& ( ( cX @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a] :
( ( ( ( cZ @ X0 )
= $true )
| ( ( ( cY @ X0 )
= $true )
& ( ( cX @ X0 )
= $true ) ) )
<~> ( ( ( ( cX @ X0 )
= $true )
| ( ( cZ @ X0 )
= $true ) )
& ( ( ( cY @ X0 )
= $true )
| ( ( cZ @ X0 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a] :
( ( ( ( cZ @ X0 )
= $true )
| ( ( ( cY @ X0 )
= $true )
& ( ( cX @ X0 )
= $true ) ) )
<=> ( ( ( ( cX @ X0 )
= $true )
| ( ( cZ @ X0 )
= $true ) )
& ( ( ( cY @ X0 )
= $true )
| ( ( cZ @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a] :
( ( ( cZ @ X0 )
| ( ( cY @ X0 )
& ( cX @ X0 ) ) )
<=> ( ( ( cY @ X0 )
| ( cZ @ X0 ) )
& ( ( cX @ X0 )
| ( cZ @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a] :
( ( ( cZ @ X0 )
| ( ( cY @ X0 )
& ( cX @ X0 ) ) )
<=> ( ( ( cY @ X0 )
| ( cZ @ X0 ) )
& ( ( cX @ X0 )
| ( cZ @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a] :
( ( ( cZ @ X0 )
| ( ( cY @ X0 )
& ( cX @ X0 ) ) )
<=> ( ( ( cY @ X0 )
| ( cZ @ X0 ) )
& ( ( cX @ X0 )
| ( cZ @ X0 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Co1TRSM1bY/DTF2THF_13900.p',cTHM59_pme) ).
thf(f56,plain,
( spl1_1
| spl1_3 ),
inference(avatar_split_clause,[status(thm)],[f24,f44,f35]) ).
thf(f35,definition,
( spl1_1
<=> ( ( cX @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f24,plain,
( ( $true
= ( cZ @ sK0 ) )
| ( ( cX @ sK0 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $true
= ( cZ @ sK0 ) )
| ( ( cX @ sK0 )
= $true )
| ( $true
= ( cZ @ sK0 ) )
| ( ( cX @ sK0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f54,plain,
( spl1_3
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f26,f39,f44]) ).
thf(f39,definition,
( spl1_2
<=> ( $true
= ( cY @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f26,plain,
( ( $true
= ( cY @ sK0 ) )
| ( $true
= ( cZ @ sK0 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f12]) ).
thf(f12,plain,
( ( $true
= ( cZ @ sK0 ) )
| ( $true
= ( cZ @ sK0 ) )
| ( $true
= ( cY @ sK0 ) )
| ( $true
= ( cY @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f42,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f33,f39,f35]) ).
thf(f33,plain,
( ( ( cX @ sK0 )
!= $true )
| ( $true
!= ( cY @ sK0 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $true
!= ( cY @ sK0 ) )
| ( $true
!= ( cY @ sK0 ) )
| ( ( cX @ sK0 )
!= $true )
| ( ( cX @ sK0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV397^5 : 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
% 0.18/0.34 % Computer : n018.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:46:01 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 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 : SEV397^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.46 % Domain : Set Theory
% 0.28/0.46 % Problem : TPS problem THM59
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English :
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Bro09]
% 0.28/0.46 % Names : tps_0381 [Bro09]
% 0.28/0.46 % : THM58 [TPS]
% 0.28/0.46 % : THM59 [TPS]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.28/0.46 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.28/0.46 % Number of atoms : 7 ( 0 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 7 ( 7 avg)
% 0.28/0.46 % Number of connectives : 13 ( 0 ~; 3 |; 2 &; 7 @)
% 0.28/0.46 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 6 ( 6 avg)
% 0.28/0.46 % Number of types : 2 ( 1 usr)
% 0.28/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 3 ( 3 usr; 0 con; 1-1 aty)
% 0.28/0.46 % Number of variables : 1 ( 0 ^; 1 !; 0 ?; 1 :)
% 0.28/0.46 % SPC : TH0_THM_NEQ_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(cZ,type,
% 0.28/0.46 cZ: a > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cY,type,
% 0.28/0.46 cY: a > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cX,type,
% 0.28/0.46 cX: a > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cTHM59_pme,conjecture,
% 0.28/0.46 ! [Xx: a] :
% 0.28/0.46 ( ( ( ( cX @ Xx )
% 0.28/0.46 & ( cY @ Xx ) )
% 0.28/0.46 | ( cZ @ Xx ) )
% 0.28/0.46 <=> ( ( ( cX @ Xx )
% 0.28/0.46 | ( cZ @ Xx ) )
% 0.28/0.46 & ( ( cY @ Xx )
% 0.28/0.46 | ( cZ @ Xx ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.44/1.28 ---- Embedded in THF ---
% 1.44/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.44/1.28 %%% Generated on Tue Feb 24 12:46:02 EST 2026
% 1.44/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.44/1.28 %%% Logic specification used:
% 1.44/1.28 %%% thf(spec, logic, $$dhol).
% 1.44/1.28
% 1.44/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Co1TRSM1bY/DTF2DTF13900.p
% See solution above
% 1.44/1.28 ------------------------
% 1.44/1.29 ---- Cleaned THF ---
% 1.44/1.29 thf(a_type,type,
% 1.44/1.29 a: $tType ).
% 1.44/1.29
% 1.44/1.29 thf(cZ,type,
% 1.44/1.29 cZ: a > $o ).
% 1.44/1.29
% 1.44/1.29 thf(cY,type,
% 1.44/1.29 cY: a > $o ).
% 1.44/1.29
% 1.44/1.29 thf(cX,type,
% 1.44/1.29 cX: a > $o ).
% 1.44/1.29
% 1.44/1.29 thf(cTHM59_pme,conjecture,
% 1.44/1.29 ! [Xx: a] :
% 1.44/1.29 ( ( ( ( cX @ Xx )
% 1.44/1.29 & ( cY @ Xx ) )
% 1.44/1.29 | ( cZ @ Xx ) )
% 1.44/1.29 <=> ( ( ( cX @ Xx )
% 1.44/1.29 | ( cZ @ Xx ) )
% 1.44/1.29 & ( ( cY @ Xx )
% 1.44/1.29 | ( cZ @ Xx ) ) ) ) ).
% 1.44/1.29 ------------------------
% 1.64/1.31 % (14175)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_13900 for (2999ds/2Mi)
% 1.64/1.31 % (14174)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13900 for (2999ds/2Mi)
% 1.64/1.31 % (14175)Refutation not found, incomplete strategy
% 1.64/1.31 % (14175)------------------------------
% 1.64/1.31 % (14175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (14175)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.31
% 1.64/1.31
% 1.64/1.31 % (14175)Memory used [KB]: 5500
% 1.64/1.31 % (14175)Time elapsed: 0.002 s
% 1.64/1.31 % (14175)Instructions burned: 1 (million)
% 1.64/1.31 % (14175)------------------------------
% 1.64/1.31 % (14175)------------------------------
% 1.64/1.31 % (14174)Instruction limit reached!
% 1.64/1.31 % (14174)------------------------------
% 1.64/1.31 % (14174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (14174)Termination reason: Unknown
% 1.64/1.31 % (14174)Termination phase: Saturation
% 1.64/1.31
% 1.64/1.31 % (14174)Memory used [KB]: 5373
% 1.64/1.31 % (14174)Time elapsed: 0.002 s
% 1.64/1.31 % (14174)Instructions burned: 2 (million)
% 1.64/1.31 % (14174)------------------------------
% 1.64/1.31 % (14174)------------------------------
% 1.64/1.32 % (14172)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_13900 for (2999ds/4Mi)
% 1.64/1.32 % (14171)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13900 for (2999ds/183Mi)
% 1.64/1.32 % (14173)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_13900 for (2999ds/27Mi)
% 1.64/1.32 % (14177)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13900 for (2999ds/18Mi)
% 1.64/1.32 % (14176)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_13900 for (2999ds/275Mi)
% 1.64/1.32 % (14173)First to succeed.
% 1.64/1.32 % (14171)Also succeeded, but the first one will report.
% 1.64/1.32 % (14172)Instruction limit reached!
% 1.64/1.32 % (14172)------------------------------
% 1.64/1.32 % (14172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (14172)Termination reason: Unknown
% 1.64/1.32 % (14172)Termination phase: Saturation
% 1.64/1.32
% 1.64/1.32 % (14172)Memory used [KB]: 5500
% 1.64/1.32 % (14172)Time elapsed: 0.006 s
% 1.64/1.32 % (14172)Instructions burned: 5 (million)
% 1.64/1.32 % (14172)------------------------------
% 1.64/1.32 % (14172)------------------------------
% 1.64/1.32 % (14173)Refutation found. Thanks to Tanya!
% 1.64/1.32 % SZS status Theorem for DTF2THF_13900
% 1.64/1.32 % SZS output start Proof for DTF2THF_13900
% 1.64/1.32 thf(type_def_5, type, a: $tType).
% 1.64/1.32 thf(func_def_0, type, a: $tType).
% 1.64/1.32 thf(func_def_1, type, cZ: a > $o).
% 1.64/1.32 thf(func_def_2, type, cY: a > $o).
% 1.64/1.32 thf(func_def_3, type, cX: a > $o).
% 1.64/1.32 thf(func_def_5, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.64/1.32 thf(func_def_8, type, sK0: a).
% 1.64/1.32 thf(f58,plain,(
% 1.64/1.32 $false),
% 1.64/1.32 inference(avatar_sat_refutation,[status(thm)],[f42,f54,f56,f57])).
% 1.64/1.32 thf(f57,plain,(
% 1.64/1.32 ~spl1_3),
% 1.64/1.32 inference(avatar_split_clause,[status(thm)],[f23,f44])).
% 1.64/1.32 thf(f44,definition,(
% 1.64/1.32 spl1_3 <=> ($true = (cZ @ sK0))),
% 1.64/1.32 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 1.64/1.32 thf(f23,plain,(
% 1.64/1.32 ($true != (cZ @ sK0))),
% 1.64/1.32 inference(duplicate_literal_removal,[status(thm)],[f16])).
% 1.64/1.32 thf(f16,plain,(
% 1.64/1.32 ($true != (cZ @ sK0)) | ($true != (cZ @ sK0)) | ($true != (cZ @ sK0))),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f10])).
% 1.64/1.32 thf(f10,plain,(
% 1.64/1.32 ((((cX @ sK0) != $true) & ($true != (cZ @ sK0))) | (($true != (cY @ sK0)) & ($true != (cZ @ sK0))) | (($true != (cZ @ sK0)) & (($true != (cY @ sK0)) | ((cX @ sK0) != $true)))) & (((((cX @ sK0) = $true) | ($true = (cZ @ sK0))) & (($true = (cY @ sK0)) | ($true = (cZ @ sK0)))) | ($true = (cZ @ sK0)) | (($true = (cY @ sK0)) & ((cX @ sK0) = $true)))),
% 1.64/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9])).
% 1.64/1.32 thf(f9,plain,(
% 1.64/1.32 ? [X0 : a] : (((((cX @ X0) != $true) & ((cZ @ X0) != $true)) | (((cY @ X0) != $true) & ((cZ @ X0) != $true)) | (((cZ @ X0) != $true) & (((cY @ X0) != $true) | ((cX @ X0) != $true)))) & (((((cX @ X0) = $true) | ((cZ @ X0) = $true)) & (((cY @ X0) = $true) | ((cZ @ X0) = $true))) | ((cZ @ X0) = $true) | (((cY @ X0) = $true) & ((cX @ X0) = $true)))) => (((((cX @ sK0) != $true) & ($true != (cZ @ sK0))) | (($true != (cY @ sK0)) & ($true != (cZ @ sK0))) | (($true != (cZ @ sK0)) & (($true != (cY @ sK0)) | ((cX @ sK0) != $true)))) & (((((cX @ sK0) = $true) | ($true = (cZ @ sK0))) & (($true = (cY @ sK0)) | ($true = (cZ @ sK0)))) | ($true = (cZ @ sK0)) | (($true = (cY @ sK0)) & ((cX @ sK0) = $true))))),
% 1.64/1.32 introduced(definition,[],[choice_axiom])).
% 1.64/1.32 thf(f8,plain,(
% 1.64/1.32 ? [X0 : a] : (((((cX @ X0) != $true) & ((cZ @ X0) != $true)) | (((cY @ X0) != $true) & ((cZ @ X0) != $true)) | (((cZ @ X0) != $true) & (((cY @ X0) != $true) | ((cX @ X0) != $true)))) & (((((cX @ X0) = $true) | ((cZ @ X0) = $true)) & (((cY @ X0) = $true) | ((cZ @ X0) = $true))) | ((cZ @ X0) = $true) | (((cY @ X0) = $true) & ((cX @ X0) = $true))))),
% 1.64/1.32 inference(flattening,[status(thm)],[f7])).
% 1.64/1.32 thf(f7,plain,(
% 1.64/1.32 ? [X0 : a] : ((((((cX @ X0) != $true) & ((cZ @ X0) != $true)) | (((cY @ X0) != $true) & ((cZ @ X0) != $true))) | (((cZ @ X0) != $true) & (((cY @ X0) != $true) | ((cX @ X0) != $true)))) & (((((cX @ X0) = $true) | ((cZ @ X0) = $true)) & (((cY @ X0) = $true) | ((cZ @ X0) = $true))) | (((cZ @ X0) = $true) | (((cY @ X0) = $true) & ((cX @ X0) = $true)))))),
% 1.64/1.32 inference(nnf_transformation,[status(thm)],[f6])).
% 1.64/1.32 thf(f6,plain,(
% 1.64/1.32 ? [X0 : a] : ((((cZ @ X0) = $true) | (((cY @ X0) = $true) & ((cX @ X0) = $true))) <~> ((((cX @ X0) = $true) | ((cZ @ X0) = $true)) & (((cY @ X0) = $true) | ((cZ @ X0) = $true))))),
% 1.64/1.32 inference(ennf_transformation,[status(thm)],[f5])).
% 1.64/1.32 thf(f5,plain,(
% 1.64/1.32 ~! [X0 : a] : ((((cZ @ X0) = $true) | (((cY @ X0) = $true) & ((cX @ X0) = $true))) <=> ((((cX @ X0) = $true) | ((cZ @ X0) = $true)) & (((cY @ X0) = $true) | ((cZ @ X0) = $true))))),
% 1.64/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.64/1.32 thf(f4,plain,(
% 1.64/1.32 ~! [X0 : a] : (((cZ @ X0) | ((cY @ X0) & (cX @ X0))) <=> (((cY @ X0) | (cZ @ X0)) & ((cX @ X0) | (cZ @ X0))))),
% 1.64/1.32 inference(rectify,[status(thm)],[f2])).
% 1.64/1.32 thf(f2,negated_conjecture,(
% 1.64/1.32 ~! [X0 : a] : (((cZ @ X0) | ((cY @ X0) & (cX @ X0))) <=> (((cY @ X0) | (cZ @ X0)) & ((cX @ X0) | (cZ @ X0))))),
% 1.64/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.64/1.32 thf(f1,conjecture,(
% 1.64/1.32 ! [X0 : a] : (((cZ @ X0) | ((cY @ X0) & (cX @ X0))) <=> (((cY @ X0) | (cZ @ X0)) & ((cX @ X0) | (cZ @ X0))))),
% 1.64/1.32 file('/export/starexec/sandbox2/tmp/tmp.Co1TRSM1bY/DTF2THF_13900.p',cTHM59_pme)).
% 1.64/1.32 thf(f56,plain,(
% 1.64/1.32 spl1_1 | spl1_3),
% 1.64/1.32 inference(avatar_split_clause,[status(thm)],[f24,f44,f35])).
% 1.64/1.32 thf(f35,definition,(
% 1.64/1.32 spl1_1 <=> ((cX @ sK0) = $true)),
% 1.64/1.32 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.64/1.32 thf(f24,plain,(
% 1.64/1.32 ($true = (cZ @ sK0)) | ((cX @ sK0) = $true)),
% 1.64/1.32 inference(duplicate_literal_removal,[status(thm)],[f13])).
% 1.64/1.32 thf(f13,plain,(
% 1.64/1.32 ($true = (cZ @ sK0)) | ((cX @ sK0) = $true) | ($true = (cZ @ sK0)) | ((cX @ sK0) = $true)),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f10])).
% 1.64/1.32 thf(f54,plain,(
% 1.64/1.32 spl1_3 | spl1_2),
% 1.64/1.32 inference(avatar_split_clause,[status(thm)],[f26,f39,f44])).
% 1.64/1.32 thf(f39,definition,(
% 1.64/1.32 spl1_2 <=> ($true = (cY @ sK0))),
% 1.64/1.32 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.64/1.32 thf(f26,plain,(
% 1.64/1.32 ($true = (cY @ sK0)) | ($true = (cZ @ sK0))),
% 1.64/1.32 inference(duplicate_literal_removal,[status(thm)],[f12])).
% 1.64/1.32 thf(f12,plain,(
% 1.64/1.32 ($true = (cZ @ sK0)) | ($true = (cZ @ sK0)) | ($true = (cY @ sK0)) | ($true = (cY @ sK0))),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f10])).
% 1.64/1.32 thf(f42,plain,(
% 1.64/1.32 ~spl1_1 | ~spl1_2),
% 1.64/1.32 inference(avatar_split_clause,[status(thm)],[f33,f39,f35])).
% 1.64/1.32 thf(f33,plain,(
% 1.64/1.32 ((cX @ sK0) != $true) | ($true != (cY @ sK0))),
% 1.64/1.32 inference(duplicate_literal_removal,[status(thm)],[f21])).
% 1.64/1.32 thf(f21,plain,(
% 1.64/1.32 ($true != (cY @ sK0)) | ($true != (cY @ sK0)) | ((cX @ sK0) != $true) | ((cX @ sK0) != $true)),
% 1.64/1.32 inference(cnf_transformation,[status(thm)],[f10])).
% 1.64/1.32 % SZS output end Proof for DTF2THF_13900
% 1.64/1.32 % (14173)------------------------------
% 1.64/1.32 % (14173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (14173)Termination reason: Refutation
% 1.64/1.32
% 1.64/1.32 % (14173)Memory used [KB]: 5500
% 1.64/1.32 % (14173)Time elapsed: 0.005 s
% 1.64/1.32 % (14173)Instructions burned: 2 (million)
% 1.64/1.32 % (14173)------------------------------
% 1.64/1.32 % (14173)------------------------------
% 1.64/1.32 % (14170)Success in time 0.021 s
%------------------------------------------------------------------------------