%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET589^5 : 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 : n028.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 09:31:49 AM UTC 2026
% Result : Theorem 1.53s 1.39s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 231 ( 89 equ; 0 cnn)
% Maximal formula atoms : 16 ( 8 avg)
% Number of connectives : 263 ( 55 ~; 30 |; 43 &; 111 @)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 71 ( 0 ^; 49 !; 22 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a > $o ).
thf(func_def_5,type,
sK1: a > $o ).
thf(func_def_6,type,
sK2: a > $o ).
thf(func_def_7,type,
sK3: a > $o ).
thf(func_def_8,type,
sK4: a ).
thf(f34,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f26,f29,f33]) ).
thf(f33,plain,
spl5_1,
inference(avatar_contradiction_clause,[status(thm)],[f32]) ).
thf(f32,plain,
( $false
| spl5_1 ),
inference(subsumption_resolution,[status(thm)],[f31,f13]) ).
thf(f13,plain,
( ( sK2 @ sK4 )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X4: a] :
( ( ( sK2 @ X4 )
!= $true )
| ( $true
= ( sK3 @ X4 ) ) )
& ! [X5: a] :
( ( $true
!= ( sK1 @ X5 ) )
| ( ( sK0 @ X5 )
= $true ) )
& ( ( ( sK1 @ sK4 )
= $true )
| ( $true
!= ( sK3 @ sK4 ) ) )
& ( $true
!= ( sK0 @ sK4 ) )
& ( ( sK2 @ sK4 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f9,f11,f10]) ).
thf(f10,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o,X3: a > $o] :
( ! [X4: a] :
( ( ( X2 @ X4 )
!= $true )
| ( ( X3 @ X4 )
= $true ) )
& ! [X5: a] :
( ( ( X1 @ X5 )
!= $true )
| ( ( X0 @ X5 )
= $true ) )
& ? [X6: a] :
( ( ( $true
= ( X1 @ X6 ) )
| ( ( X3 @ X6 )
!= $true ) )
& ( $true
!= ( X0 @ X6 ) )
& ( $true
= ( X2 @ X6 ) ) ) )
=> ( ! [X4: a] :
( ( ( sK2 @ X4 )
!= $true )
| ( $true
= ( sK3 @ X4 ) ) )
& ! [X5: a] :
( ( $true
!= ( sK1 @ X5 ) )
| ( ( sK0 @ X5 )
= $true ) )
& ? [X6: a] :
( ( ( ( sK1 @ X6 )
= $true )
| ( ( sK3 @ X6 )
!= $true ) )
& ( ( sK0 @ X6 )
!= $true )
& ( $true
= ( sK2 @ X6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X6: a] :
( ( ( ( sK1 @ X6 )
= $true )
| ( ( sK3 @ X6 )
!= $true ) )
& ( ( sK0 @ X6 )
!= $true )
& ( $true
= ( sK2 @ X6 ) ) )
=> ( ( ( ( sK1 @ sK4 )
= $true )
| ( $true
!= ( sK3 @ sK4 ) ) )
& ( $true
!= ( sK0 @ sK4 ) )
& ( ( sK2 @ sK4 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o,X3: a > $o] :
( ! [X4: a] :
( ( ( X2 @ X4 )
!= $true )
| ( ( X3 @ X4 )
= $true ) )
& ! [X5: a] :
( ( ( X1 @ X5 )
!= $true )
| ( ( X0 @ X5 )
= $true ) )
& ? [X6: a] :
( ( ( $true
= ( X1 @ X6 ) )
| ( ( X3 @ X6 )
!= $true ) )
& ( $true
!= ( X0 @ X6 ) )
& ( $true
= ( X2 @ X6 ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
? [X0: a > $o,X3: a > $o,X2: a > $o,X1: a > $o] :
( ! [X4: a] :
( ( ( X2 @ X4 )
!= $true )
| ( ( X1 @ X4 )
= $true ) )
& ! [X5: a] :
( ( $true
!= ( X3 @ X5 ) )
| ( ( X0 @ X5 )
= $true ) )
& ? [X6: a] :
( ( ( ( X3 @ X6 )
= $true )
| ( $true
!= ( X1 @ X6 ) ) )
& ( $true
!= ( X0 @ X6 ) )
& ( $true
= ( X2 @ X6 ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > $o,X3: a > $o,X1: a > $o,X2: a > $o] :
( ? [X6: a] :
( ( ( ( X3 @ X6 )
= $true )
| ( $true
!= ( X1 @ X6 ) ) )
& ( $true
= ( X2 @ X6 ) )
& ( $true
!= ( X0 @ X6 ) ) )
& ! [X4: a] :
( ( ( X2 @ X4 )
!= $true )
| ( ( X1 @ X4 )
= $true ) )
& ! [X5: a] :
( ( $true
!= ( X3 @ X5 ) )
| ( ( X0 @ X5 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a > $o,X3: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X4: a] :
( ( ( X2 @ X4 )
= $true )
=> ( ( X1 @ X4 )
= $true ) )
& ! [X5: a] :
( ( $true
= ( X3 @ X5 ) )
=> ( ( X0 @ X5 )
= $true ) ) )
=> ! [X6: a] :
( ( ( $true
= ( X2 @ X6 ) )
& ( $true
!= ( X0 @ X6 ) ) )
=> ( ( ( X3 @ X6 )
!= $true )
& ( $true
= ( X1 @ X6 ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o,X3: a > $o] :
( ( ! [X4: a] :
( ( ( X2 @ X4 )
= $true )
=> ( ( X1 @ X4 )
= $true ) )
& ! [X5: a] :
( ( $true
= ( X3 @ X5 ) )
=> ( ( X0 @ X5 )
= $true ) ) )
=> ! [X6: a] :
( ( ( $true
= ( X2 @ X6 ) )
& ( $true
!= ( X0 @ X6 ) ) )
=> ( ( $true
= ( X1 @ X6 ) )
& ( ( X3 @ X6 )
!= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o,X3: a > $o] :
( ( ! [X4: a] :
( ( X2 @ X4 )
=> ( X1 @ X4 ) )
& ! [X5: a] :
( ( X3 @ X5 )
=> ( X0 @ X5 ) ) )
=> ! [X6: a] :
( ( ( X2 @ X6 )
& ~ ( X0 @ X6 ) )
=> ( ( X1 @ X6 )
& ~ ( X3 @ X6 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X3: a > $o,X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ! [X4: a] :
( ( X0 @ X4 )
=> ( X1 @ X4 ) )
& ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ! [X4: a] :
( ( ( X0 @ X4 )
& ~ ( X3 @ X4 ) )
=> ( ( X1 @ X4 )
& ~ ( X2 @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X3: a > $o,X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ! [X4: a] :
( ( X0 @ X4 )
=> ( X1 @ X4 ) )
& ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ! [X4: a] :
( ( ( X0 @ X4 )
& ~ ( X3 @ X4 ) )
=> ( ( X1 @ X4 )
& ~ ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6vGnEiRn0Z/DTF2THF_17912.p',cBOOL_PROP_48_pme) ).
thf(f31,plain,
( ( ( sK2 @ sK4 )
!= $true )
| spl5_1 ),
inference(trivial_inequality_removal,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $true != $true )
| ( ( sK2 @ sK4 )
!= $true )
| spl5_1 ),
inference(superposition,[status(thm)],[f21,f17]) ).
thf(f17,plain,
! [X4: a] :
( ( $true
= ( sK3 @ X4 ) )
| ( ( sK2 @ X4 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f21,plain,
( ( $true
!= ( sK3 @ sK4 ) )
| spl5_1 ),
inference(avatar_component_clause,[status(thm)],[f19]) ).
thf(f19,definition,
( spl5_1
<=> ( $true
= ( sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition]) ).
thf(f29,plain,
~ spl5_2,
inference(avatar_split_clause,[status(thm)],[f28,f23]) ).
thf(f23,definition,
( spl5_2
<=> ( ( sK1 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition]) ).
thf(f28,plain,
( ( sK1 @ sK4 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( sK1 @ sK4 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f14,f16]) ).
thf(f16,plain,
! [X5: a] :
( ( ( sK0 @ X5 )
= $true )
| ( $true
!= ( sK1 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f14,plain,
( $true
!= ( sK0 @ sK4 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f26,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f15,f23,f19]) ).
thf(f15,plain,
( ( $true
!= ( sK3 @ sK4 ) )
| ( ( sK1 @ sK4 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET589^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.30 % Computer : n028.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 11:59:42 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.40 ---- Original DTF file ---
% 0.17/0.40 thf(spec,logic,$$dhol).
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 % File : SET589^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.40 % Domain : Set Theory
% 0.17/0.40 % Problem : TPS problem BOOL-PROP-48
% 0.17/0.40 % Version : Especial.
% 0.17/0.40 % English : Trybulec's 48th Boolean property of sets
% 0.17/0.40
% 0.17/0.40 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.17/0.40 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.40 % Source : [Bro09]
% 0.17/0.40 % Names : tps_0261 [Bro09]
% 0.17/0.40 % : BOOL-PROP-48 [TPS]
% 0.17/0.40
% 0.17/0.40 % Status : Theorem
% 0.17/0.40 % Rating : 0.00 v4.0.0
% 0.17/0.40 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.17/0.40 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.17/0.40 % Maximal formula atoms : 0 ( 0 avg)
% 0.17/0.40 % Number of connectives : 17 ( 2 ~; 0 |; 3 &; 8 @)
% 0.17/0.40 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.17/0.40 % Maximal formula depth : 11 ( 11 avg)
% 0.17/0.40 % Number of types : 2 ( 1 usr)
% 0.17/0.40 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.17/0.40 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.17/0.40 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.17/0.40 % SPC : TH0_THM_NEQ_NAR
% 0.17/0.40
% 0.17/0.40 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.40 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.40 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.40 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.40 % : Polymorphic definitions expanded.
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 thf(a_type,type,
% 0.17/0.40 a: $tType ).
% 0.17/0.40
% 0.17/0.40 thf(cBOOL_PROP_48_pme,conjecture,
% 0.17/0.40 ! [X: a > $o,Y: a > $o,Z: a > $o,V: a > $o] :
% 0.17/0.40 ( ( ! [Xx: a] :
% 0.17/0.40 ( ( X @ Xx )
% 0.17/0.40 => ( Y @ Xx ) )
% 0.17/0.40 & ! [Xx: a] :
% 0.17/0.40 ( ( Z @ Xx )
% 0.17/0.40 => ( V @ Xx ) ) )
% 0.17/0.40 => ! [Xx: a] :
% 0.17/0.40 ( ( ( X @ Xx )
% 0.17/0.40 & ~ ( V @ Xx ) )
% 0.17/0.40 => ( ( Y @ Xx )
% 0.17/0.40 & ~ ( Z @ Xx ) ) ) ) ).
% 0.17/0.40
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 ------------------------
% 1.53/1.36 ---- Embedded in THF ---
% 1.53/1.36 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.36 %%% Generated on Tue Feb 24 11:59:43 EST 2026
% 1.53/1.36 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.36 %%% Logic specification used:
% 1.53/1.36 %%% thf(spec, logic, $$dhol).
% 1.53/1.36
% 1.53/1.36 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.6vGnEiRn0Z/DTF2DTF17912.p
% See solution above
% 1.53/1.36 ------------------------
% 1.53/1.37 ---- Cleaned THF ---
% 1.53/1.37 thf(a_type,type,
% 1.53/1.37 a: $tType ).
% 1.53/1.37
% 1.53/1.37 thf(cBOOL_PROP_48_pme,conjecture,
% 1.53/1.37 ! [X: a > $o,Y: a > $o,Z: a > $o,V: a > $o] :
% 1.53/1.37 ( ( ! [Xx: a] :
% 1.53/1.37 ( ( X @ Xx )
% 1.53/1.37 => ( Y @ Xx ) )
% 1.53/1.37 & ! [Xx: a] :
% 1.53/1.37 ( ( Z @ Xx )
% 1.53/1.37 => ( V @ Xx ) ) )
% 1.53/1.37 => ! [Xx: a] :
% 1.53/1.37 ( ( ( X @ Xx )
% 1.53/1.37 & ~ ( V @ Xx ) )
% 1.53/1.37 => ( ( Y @ Xx )
% 1.53/1.37 & ~ ( Z @ Xx ) ) ) ) ).
% 1.53/1.37 ------------------------
% 1.53/1.39 % (18016)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17912 for (3000ds/18Mi)
% 1.53/1.39 % (18011)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_17912 for (3000ds/4Mi)
% 1.53/1.39 % (18010)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17912 for (3000ds/183Mi)
% 1.53/1.39 % (18015)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_17912 for (3000ds/275Mi)
% 1.53/1.39 % (18014)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_17912 for (3000ds/2Mi)
% 1.53/1.39 % (18013)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17912 for (3000ds/2Mi)
% 1.53/1.39 % (18012)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_17912 for (3000ds/27Mi)
% 1.53/1.39 % (18013)Instruction limit reached!
% 1.53/1.39 % (18013)------------------------------
% 1.53/1.39 % (18013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.39 % (18013)Termination reason: Unknown
% 1.53/1.39 % (18013)Termination phase: Saturation
% 1.53/1.39
% 1.53/1.39 % (18014)Instruction limit reached!
% 1.53/1.39 % (18014)------------------------------
% 1.53/1.39 % (18014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.39 % (18014)Termination reason: Unknown
% 1.53/1.39 % (18014)Termination phase: Saturation
% 1.53/1.39
% 1.53/1.39 % (18014)Memory used [KB]: 895
% 1.53/1.39 % (18014)Time elapsed: 0.003 s
% 1.53/1.39 % (18014)Instructions burned: 2 (million)
% 1.53/1.39 % (18014)------------------------------
% 1.53/1.39 % (18014)------------------------------
% 1.53/1.39 % (18013)Memory used [KB]: 5373
% 1.53/1.39 % (18013)Time elapsed: 0.003 s
% 1.53/1.39 % (18013)Instructions burned: 2 (million)
% 1.53/1.39 % (18013)------------------------------
% 1.53/1.39 % (18013)------------------------------
% 1.53/1.39 % (18010)First to succeed.
% 1.53/1.39 % (18011)Also succeeded, but the first one will report.
% 1.53/1.39 % (18010)Refutation found. Thanks to Tanya!
% 1.53/1.39 % SZS status Theorem for DTF2THF_17912
% 1.53/1.39 % SZS output start Proof for DTF2THF_17912
% 1.53/1.39 thf(type_def_5, type, a: $tType).
% 1.53/1.39 thf(func_def_0, type, a: $tType).
% 1.53/1.39 thf(func_def_4, type, sK0: a > $o).
% 1.53/1.39 thf(func_def_5, type, sK1: a > $o).
% 1.53/1.39 thf(func_def_6, type, sK2: a > $o).
% 1.53/1.39 thf(func_def_7, type, sK3: a > $o).
% 1.53/1.39 thf(func_def_8, type, sK4: a).
% 1.53/1.39 thf(f34,plain,(
% 1.53/1.39 $false),
% 1.53/1.39 inference(avatar_sat_refutation,[status(thm)],[f26,f29,f33])).
% 1.53/1.39 thf(f33,plain,(
% 1.53/1.39 spl5_1),
% 1.53/1.39 inference(avatar_contradiction_clause,[status(thm)],[f32])).
% 1.53/1.39 thf(f32,plain,(
% 1.53/1.39 $false | spl5_1),
% 1.53/1.39 inference(subsumption_resolution,[status(thm)],[f31,f13])).
% 1.53/1.39 thf(f13,plain,(
% 1.53/1.39 ((sK2 @ sK4) = $true)),
% 1.53/1.39 inference(cnf_transformation,[status(thm)],[f12])).
% 1.53/1.39 thf(f12,plain,(
% 1.53/1.39 ! [X4 : a] : (((sK2 @ X4) != $true) | ($true = (sK3 @ X4))) & ! [X5 : a] : (($true != (sK1 @ X5)) | ((sK0 @ X5) = $true)) & ((((sK1 @ sK4) = $true) | ($true != (sK3 @ sK4))) & ($true != (sK0 @ sK4)) & ((sK2 @ sK4) = $true))),
% 1.53/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f9,f11,f10])).
% 1.53/1.39 thf(f10,plain,(
% 1.53/1.39 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o,X3 : a > $o] : (! [X4 : a] : (((X2 @ X4) != $true) | ((X3 @ X4) = $true)) & ! [X5 : a] : (((X1 @ X5) != $true) | ((X0 @ X5) = $true)) & ? [X6 : a] : ((($true = (X1 @ X6)) | ((X3 @ X6) != $true)) & ($true != (X0 @ X6)) & ($true = (X2 @ X6)))) => (! [X4 : a] : (((sK2 @ X4) != $true) | ($true = (sK3 @ X4))) & ! [X5 : a] : (($true != (sK1 @ X5)) | ((sK0 @ X5) = $true)) & ? [X6 : a] : ((((sK1 @ X6) = $true) | ((sK3 @ X6) != $true)) & ((sK0 @ X6) != $true) & ($true = (sK2 @ X6))))),
% 1.53/1.39 introduced(definition,[],[choice_axiom])).
% 1.53/1.39 thf(f11,plain,(
% 1.53/1.39 ? [X6 : a] : ((((sK1 @ X6) = $true) | ((sK3 @ X6) != $true)) & ((sK0 @ X6) != $true) & ($true = (sK2 @ X6))) => ((((sK1 @ sK4) = $true) | ($true != (sK3 @ sK4))) & ($true != (sK0 @ sK4)) & ((sK2 @ sK4) = $true))),
% 1.53/1.39 introduced(definition,[],[choice_axiom])).
% 1.53/1.39 thf(f9,plain,(
% 1.53/1.39 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o,X3 : a > $o] : (! [X4 : a] : (((X2 @ X4) != $true) | ((X3 @ X4) = $true)) & ! [X5 : a] : (((X1 @ X5) != $true) | ((X0 @ X5) = $true)) & ? [X6 : a] : ((($true = (X1 @ X6)) | ((X3 @ X6) != $true)) & ($true != (X0 @ X6)) & ($true = (X2 @ X6))))),
% 1.53/1.39 inference(rectify,[status(thm)],[f8])).
% 1.53/1.39 thf(f8,plain,(
% 1.53/1.39 ? [X0 : a > $o,X3 : a > $o,X2 : a > $o,X1 : a > $o] : (! [X4 : a] : (((X2 @ X4) != $true) | ((X1 @ X4) = $true)) & ! [X5 : a] : (($true != (X3 @ X5)) | ((X0 @ X5) = $true)) & ? [X6 : a] : ((((X3 @ X6) = $true) | ($true != (X1 @ X6))) & ($true != (X0 @ X6)) & ($true = (X2 @ X6))))),
% 1.53/1.39 inference(flattening,[status(thm)],[f7])).
% 1.53/1.39 thf(f7,plain,(
% 1.53/1.39 ? [X0 : a > $o,X3 : a > $o,X1 : a > $o,X2 : a > $o] : (? [X6 : a] : ((((X3 @ X6) = $true) | ($true != (X1 @ X6))) & (($true = (X2 @ X6)) & ($true != (X0 @ X6)))) & (! [X4 : a] : (((X2 @ X4) != $true) | ((X1 @ X4) = $true)) & ! [X5 : a] : (($true != (X3 @ X5)) | ((X0 @ X5) = $true))))),
% 1.53/1.39 inference(ennf_transformation,[status(thm)],[f6])).
% 1.53/1.39 thf(f6,plain,(
% 1.53/1.39 ~! [X0 : a > $o,X3 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X4 : a] : (((X2 @ X4) = $true) => ((X1 @ X4) = $true)) & ! [X5 : a] : (($true = (X3 @ X5)) => ((X0 @ X5) = $true))) => ! [X6 : a] : ((($true = (X2 @ X6)) & ($true != (X0 @ X6))) => (((X3 @ X6) != $true) & ($true = (X1 @ X6)))))),
% 1.53/1.39 inference(flattening,[status(thm)],[f5])).
% 1.53/1.39 thf(f5,plain,(
% 1.53/1.39 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o,X3 : a > $o] : ((! [X4 : a] : (((X2 @ X4) = $true) => ((X1 @ X4) = $true)) & ! [X5 : a] : (($true = (X3 @ X5)) => ((X0 @ X5) = $true))) => ! [X6 : a] : ((($true = (X2 @ X6)) & ~($true = (X0 @ X6))) => (($true = (X1 @ X6)) & ~((X3 @ X6) = $true))))),
% 1.53/1.39 inference(fool_elimination,[status(thm)],[f4])).
% 1.53/1.39 thf(f4,plain,(
% 1.53/1.39 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o,X3 : a > $o] : ((! [X4 : a] : ((X2 @ X4) => (X1 @ X4)) & ! [X5 : a] : ((X3 @ X5) => (X0 @ X5))) => ! [X6 : a] : (((X2 @ X6) & ~(X0 @ X6)) => ((X1 @ X6) & ~(X3 @ X6))))),
% 1.53/1.39 inference(rectify,[status(thm)],[f2])).
% 1.53/1.39 thf(f2,negated_conjecture,(
% 1.53/1.39 ~! [X3 : a > $o,X1 : a > $o,X0 : a > $o,X2 : a > $o] : ((! [X4 : a] : ((X0 @ X4) => (X1 @ X4)) & ! [X4 : a] : ((X2 @ X4) => (X3 @ X4))) => ! [X4 : a] : (((X0 @ X4) & ~(X3 @ X4)) => ((X1 @ X4) & ~(X2 @ X4))))),
% 1.53/1.39 inference(negated_conjecture,[status(cth)],[f1])).
% 1.53/1.39 thf(f1,conjecture,(
% 1.53/1.39 ! [X3 : a > $o,X1 : a > $o,X0 : a > $o,X2 : a > $o] : ((! [X4 : a] : ((X0 @ X4) => (X1 @ X4)) & ! [X4 : a] : ((X2 @ X4) => (X3 @ X4))) => ! [X4 : a] : (((X0 @ X4) & ~(X3 @ X4)) => ((X1 @ X4) & ~(X2 @ X4))))),
% 1.53/1.39 file('/export/starexec/sandbox/tmp/tmp.6vGnEiRn0Z/DTF2THF_17912.p',cBOOL_PROP_48_pme)).
% 1.53/1.39 thf(f31,plain,(
% 1.53/1.39 ((sK2 @ sK4) != $true) | spl5_1),
% 1.53/1.39 inference(trivial_inequality_removal,[status(thm)],[f30])).
% 1.53/1.39 thf(f30,plain,(
% 1.53/1.39 ($true != $true) | ((sK2 @ sK4) != $true) | spl5_1),
% 1.53/1.39 inference(superposition,[status(thm)],[f21,f17])).
% 1.53/1.39 thf(f17,plain,(
% 1.53/1.39 ( ! [X4 : a] : (($true = (sK3 @ X4)) | ((sK2 @ X4) != $true)) )),
% 1.53/1.39 inference(cnf_transformation,[status(thm)],[f12])).
% 1.53/1.39 thf(f21,plain,(
% 1.53/1.39 ($true != (sK3 @ sK4)) | spl5_1),
% 1.53/1.39 inference(avatar_component_clause,[status(thm)],[f19])).
% 1.53/1.39 thf(f19,definition,(
% 1.53/1.39 spl5_1 <=> ($true = (sK3 @ sK4))),
% 1.53/1.39 introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition])).
% 1.53/1.39 thf(f29,plain,(
% 1.53/1.39 ~spl5_2),
% 1.53/1.39 inference(avatar_split_clause,[status(thm)],[f28,f23])).
% 1.53/1.39 thf(f23,definition,(
% 1.53/1.39 spl5_2 <=> ((sK1 @ sK4) = $true)),
% 1.53/1.39 introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition])).
% 1.53/1.39 thf(f28,plain,(
% 1.53/1.39 ((sK1 @ sK4) != $true)),
% 1.53/1.39 inference(trivial_inequality_removal,[status(thm)],[f27])).
% 1.53/1.39 thf(f27,plain,(
% 1.53/1.39 ((sK1 @ sK4) != $true) | ($true != $true)),
% 1.53/1.39 inference(superposition,[status(thm)],[f14,f16])).
% 1.53/1.39 thf(f16,plain,(
% 1.53/1.39 ( ! [X5 : a] : (((sK0 @ X5) = $true) | ($true != (sK1 @ X5))) )),
% 1.53/1.39 inference(cnf_transformation,[status(thm)],[f12])).
% 1.53/1.39 thf(f14,plain,(
% 1.53/1.39 ($true != (sK0 @ sK4))),
% 1.53/1.39 inference(cnf_transformation,[status(thm)],[f12])).
% 1.53/1.39 thf(f26,plain,(
% 1.53/1.39 ~spl5_1 | spl5_2),
% 1.53/1.39 inference(avatar_split_clause,[status(thm)],[f15,f23,f19])).
% 1.53/1.39 thf(f15,plain,(
% 1.53/1.39 ($true != (sK3 @ sK4)) | ((sK1 @ sK4) = $true)),
% 1.53/1.39 inference(cnf_transformation,[status(thm)],[f12])).
% 1.53/1.39 % SZS output end Proof for DTF2THF_17912
% 1.53/1.39 % (18010)------------------------------
% 1.53/1.39 % (18010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.39 % (18010)Termination reason: Refutation
% 1.53/1.39
% 1.53/1.39 % (18010)Memory used [KB]: 5500
% 1.53/1.39 % (18010)Time elapsed: 0.005 s
% 1.53/1.39 % (18010)Instructions burned: 2 (million)
% 1.53/1.39 % (18010)------------------------------
% 1.53/1.39 % (18010)------------------------------
% 1.53/1.39 % (18009)Success in time 0.019 s
%------------------------------------------------------------------------------