%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET014^5 : 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 : n023.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 09:30:56 AM UTC 2026
% Result : Theorem 1.68s 1.44s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 188 ( 71 equ; 0 cnn)
% Maximal formula atoms : 14 ( 7 avg)
% Number of connectives : 202 ( 36 ~; 32 |; 24 &; 90 @)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 56 ( 0 ^; 38 !; 18 ?; 56 :)
% 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 ).
thf(f32,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f24,f27,f31]) ).
thf(f31,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[status(thm)],[f30]) ).
thf(f30,plain,
( $false
| ~ spl4_2 ),
inference(subsumption_resolution,[status(thm)],[f29,f23]) ).
thf(f23,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f21,definition,
( spl4_2
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f29,plain,
( $true
!= ( sK0 @ sK3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
( ( $true != $true )
| ( $true
!= ( sK0 @ sK3 ) ) ),
inference(superposition,[status(thm)],[f12,f15]) ).
thf(f15,plain,
! [X3: a] :
( ( $true
= ( sK2 @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X3: a] :
( ( $true
= ( sK2 @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) ) )
& ! [X4: a] :
( ( ( sK2 @ X4 )
= $true )
| ( $true
!= ( sK1 @ X4 ) ) )
& ( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) )
& ( $true
!= ( sK2 @ sK3 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( $true
= ( X2 @ X4 ) )
| ( $true
!= ( X1 @ X4 ) ) )
& ? [X5: a] :
( ( ( $true
= ( X1 @ X5 ) )
| ( $true
= ( X0 @ X5 ) ) )
& ( $true
!= ( X2 @ X5 ) ) ) )
=> ( ! [X3: a] :
( ( $true
= ( sK2 @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) ) )
& ! [X4: a] :
( ( ( sK2 @ X4 )
= $true )
| ( $true
!= ( sK1 @ X4 ) ) )
& ? [X5: a] :
( ( ( $true
= ( sK1 @ X5 ) )
| ( $true
= ( sK0 @ X5 ) ) )
& ( $true
!= ( sK2 @ X5 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X5: a] :
( ( ( $true
= ( sK1 @ X5 ) )
| ( $true
= ( sK0 @ X5 ) ) )
& ( $true
!= ( sK2 @ X5 ) ) )
=> ( ( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) )
& ( $true
!= ( sK2 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( $true
= ( X2 @ X4 ) )
| ( $true
!= ( X1 @ X4 ) ) )
& ? [X5: a] :
( ( ( $true
= ( X1 @ X5 ) )
| ( $true
= ( X0 @ X5 ) ) )
& ( $true
!= ( X2 @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X2: a > $o,X0: a > $o,X1: a > $o] :
( ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
| ( ( X2 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( $true
= ( X1 @ X4 ) )
| ( $true
!= ( X0 @ X4 ) ) )
& ? [X5: a] :
( ( ( $true
= ( X0 @ X5 ) )
| ( $true
= ( X2 @ X5 ) ) )
& ( $true
!= ( X1 @ X5 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X1: a > $o,X2: a > $o,X0: a > $o] :
( ? [X5: a] :
( ( ( $true
= ( X0 @ X5 ) )
| ( $true
= ( X2 @ X5 ) ) )
& ( $true
!= ( X1 @ X5 ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
| ( ( X2 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( $true
= ( X1 @ X4 ) )
| ( $true
!= ( X0 @ X4 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
=> ( ( X1 @ X3 )
= $true ) )
& ! [X4: a] :
( ( $true
= ( X0 @ X4 ) )
=> ( $true
= ( X1 @ X4 ) ) ) )
=> ! [X5: a] :
( ( ( $true
= ( X0 @ X5 ) )
| ( $true
= ( X2 @ X5 ) ) )
=> ( $true
= ( X1 @ X5 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) )
& ! [X4: a] :
( ( X0 @ X4 )
=> ( X1 @ X4 ) ) )
=> ! [X5: a] :
( ( ( X2 @ X5 )
| ( X0 @ X5 ) )
=> ( X1 @ X5 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] :
( ( ( X0 @ X3 )
| ( X1 @ X3 ) )
=> ( X2 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] :
( ( ( X0 @ X3 )
| ( X1 @ X3 ) )
=> ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Vi6xzMhfdl/DTF2THF_31689.p',cBOOL_PROP_32_pme) ).
thf(f12,plain,
( $true
!= ( sK2 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f27,plain,
~ spl4_1,
inference(avatar_split_clause,[status(thm)],[f26,f17]) ).
thf(f17,definition,
( spl4_1
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f26,plain,
( $true
!= ( sK1 @ sK3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
( ( $true != $true )
| ( $true
!= ( sK1 @ sK3 ) ) ),
inference(superposition,[status(thm)],[f12,f14]) ).
thf(f14,plain,
! [X4: a] :
( ( ( sK2 @ X4 )
= $true )
| ( $true
!= ( sK1 @ X4 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f24,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f13,f21,f17]) ).
thf(f13,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET014^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n023.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 11:49:49 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.49 ---- Original DTF file ---
% 0.32/0.49 thf(spec,logic,$$dhol).
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 % File : SET014^5 : TPTP v9.2.1. Released v4.0.0.
% 0.32/0.49 % Domain : Set Theory
% 0.32/0.49 % Problem : TPS problem BOOL-PROP-32
% 0.32/0.49 % Version : Especial.
% 0.32/0.49 % English : Trybulec's 32nd Boolean property of sets
% 0.32/0.49
% 0.32/0.49 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.32/0.49 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.32/0.49 % Source : [Bro09]
% 0.32/0.49 % Names : tps_0151 [Bro09]
% 0.32/0.49 % : BOOL-PROP-32 [TPS]
% 0.32/0.49
% 0.32/0.49 % Status : Theorem
% 0.32/0.49 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.32/0.49 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.32/0.49 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.32/0.49 % Maximal formula atoms : 0 ( 0 avg)
% 0.32/0.49 % Number of connectives : 13 ( 0 ~; 1 |; 1 &; 7 @)
% 0.32/0.49 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.32/0.49 % Maximal formula depth : 9 ( 9 avg)
% 0.32/0.49 % Number of types : 2 ( 1 usr)
% 0.32/0.49 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.32/0.49 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.32/0.49 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.32/0.49 % SPC : TH0_THM_NEQ_NAR
% 0.32/0.49
% 0.32/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.32/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.32/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.32/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.32/0.49 % : Polymorphic definitions expanded.
% 0.32/0.49 % :
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 thf(a_type,type,
% 0.32/0.49 a: $tType ).
% 0.32/0.49
% 0.32/0.49 thf(cBOOL_PROP_32_pme,conjecture,
% 0.32/0.49 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.32/0.49 ( ( ! [Xx: a] :
% 0.32/0.49 ( ( X @ Xx )
% 0.32/0.49 => ( Z @ Xx ) )
% 0.32/0.49 & ! [Xx: a] :
% 0.32/0.49 ( ( Y @ Xx )
% 0.32/0.49 => ( Z @ Xx ) ) )
% 0.32/0.49 => ! [Xx: a] :
% 0.32/0.49 ( ( ( X @ Xx )
% 0.32/0.49 | ( Y @ Xx ) )
% 0.32/0.49 => ( Z @ Xx ) ) ) ).
% 0.32/0.49
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 ------------------------
% 1.68/1.41 ---- Embedded in THF ---
% 1.68/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.68/1.41 %%% Generated on Tue Feb 24 11:49:50 EST 2026
% 1.68/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.68/1.41 %%% Logic specification used:
% 1.68/1.41 %%% thf(spec, logic, $$dhol).
% 1.68/1.41
% 1.68/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Vi6xzMhfdl/DTF2DTF31689.p
% See solution above
% 1.68/1.41 ------------------------
% 1.68/1.42 ---- Cleaned THF ---
% 1.68/1.42 thf(a_type,type,
% 1.68/1.42 a: $tType ).
% 1.68/1.42
% 1.68/1.42 thf(cBOOL_PROP_32_pme,conjecture,
% 1.68/1.42 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.68/1.42 ( ( ! [Xx: a] :
% 1.68/1.42 ( ( X @ Xx )
% 1.68/1.42 => ( Z @ Xx ) )
% 1.68/1.42 & ! [Xx: a] :
% 1.68/1.42 ( ( Y @ Xx )
% 1.68/1.42 => ( Z @ Xx ) ) )
% 1.68/1.42 => ! [Xx: a] :
% 1.68/1.42 ( ( ( X @ Xx )
% 1.68/1.42 | ( Y @ Xx ) )
% 1.68/1.42 => ( Z @ Xx ) ) ) ).
% 1.68/1.42 ------------------------
% 1.68/1.44 % (31803)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_31689 for (3000ds/27Mi)
% 1.68/1.44 % (31805)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_31689 for (3000ds/2Mi)
% 1.68/1.44 % (31801)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31689 for (3000ds/183Mi)
% 1.68/1.44 % (31806)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_31689 for (3000ds/275Mi)
% 1.68/1.44 % (31802)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_31689 for (3000ds/4Mi)
% 1.68/1.44 % (31807)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31689 for (3000ds/18Mi)
% 1.68/1.44 % (31804)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_31689 for (3000ds/2Mi)
% 1.68/1.44 % (31804)Instruction limit reached!
% 1.68/1.44 % (31804)------------------------------
% 1.68/1.44 % (31804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.44 % (31804)Termination reason: Unknown
% 1.68/1.44 % (31804)Termination phase: Saturation
% 1.68/1.44 % (31805)Instruction limit reached!
% 1.68/1.44 % (31805)------------------------------
% 1.68/1.44 % (31805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.44
% 1.68/1.44 % (31804)Memory used [KB]: 5500
% 1.68/1.44 % (31804)Time elapsed: 0.003 s
% 1.68/1.44 % (31804)Instructions burned: 2 (million)
% 1.68/1.44 % (31804)------------------------------
% 1.68/1.44 % (31804)------------------------------
% 1.68/1.44 % (31805)Termination reason: Unknown
% 1.68/1.44 % (31805)Termination phase: Saturation
% 1.68/1.44
% 1.68/1.44 % (31805)Memory used [KB]: 5500
% 1.68/1.44 % (31805)Time elapsed: 0.003 s
% 1.68/1.44 % (31805)Instructions burned: 2 (million)
% 1.68/1.44 % (31805)------------------------------
% 1.68/1.44 % (31805)------------------------------
% 1.68/1.44 % (31806)First to succeed.
% 1.68/1.44 % (31801)Also succeeded, but the first one will report.
% 1.68/1.44 % (31806)Refutation found. Thanks to Tanya!
% 1.68/1.44 % SZS status Theorem for DTF2THF_31689
% 1.68/1.44 % SZS output start Proof for DTF2THF_31689
% 1.68/1.44 thf(type_def_5, type, a: $tType).
% 1.68/1.44 thf(func_def_0, type, a: $tType).
% 1.68/1.44 thf(func_def_4, type, sK0: a > $o).
% 1.68/1.44 thf(func_def_5, type, sK1: a > $o).
% 1.68/1.44 thf(func_def_6, type, sK2: a > $o).
% 1.68/1.44 thf(func_def_7, type, sK3: a).
% 1.68/1.44 thf(f32,plain,(
% 1.68/1.44 $false),
% 1.68/1.44 inference(avatar_sat_refutation,[status(thm)],[f24,f27,f31])).
% 1.68/1.44 thf(f31,plain,(
% 1.68/1.44 ~spl4_2),
% 1.68/1.44 inference(avatar_contradiction_clause,[status(thm)],[f30])).
% 1.68/1.44 thf(f30,plain,(
% 1.68/1.44 $false | ~spl4_2),
% 1.68/1.44 inference(subsumption_resolution,[status(thm)],[f29,f23])).
% 1.68/1.44 thf(f23,plain,(
% 1.68/1.44 ($true = (sK0 @ sK3)) | ~spl4_2),
% 1.68/1.44 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.68/1.44 thf(f21,definition,(
% 1.68/1.44 spl4_2 <=> ($true = (sK0 @ sK3))),
% 1.68/1.44 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.68/1.44 thf(f29,plain,(
% 1.68/1.44 ($true != (sK0 @ sK3))),
% 1.68/1.44 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.68/1.44 thf(f28,plain,(
% 1.68/1.44 ($true != $true) | ($true != (sK0 @ sK3))),
% 1.68/1.44 inference(superposition,[status(thm)],[f12,f15])).
% 1.68/1.44 thf(f15,plain,(
% 1.68/1.44 ( ! [X3 : a] : (($true = (sK2 @ X3)) | ($true != (sK0 @ X3))) )),
% 1.68/1.44 inference(cnf_transformation,[status(thm)],[f11])).
% 1.68/1.44 thf(f11,plain,(
% 1.68/1.44 ! [X3 : a] : (($true = (sK2 @ X3)) | ($true != (sK0 @ X3))) & ! [X4 : a] : (((sK2 @ X4) = $true) | ($true != (sK1 @ X4))) & ((($true = (sK1 @ sK3)) | ($true = (sK0 @ sK3))) & ($true != (sK2 @ sK3)))),
% 1.68/1.44 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f10,f9])).
% 1.68/1.44 thf(f9,plain,(
% 1.68/1.44 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : (((X2 @ X3) = $true) | ((X0 @ X3) != $true)) & ! [X4 : a] : (($true = (X2 @ X4)) | ($true != (X1 @ X4))) & ? [X5 : a] : ((($true = (X1 @ X5)) | ($true = (X0 @ X5))) & ($true != (X2 @ X5)))) => (! [X3 : a] : (($true = (sK2 @ X3)) | ($true != (sK0 @ X3))) & ! [X4 : a] : (((sK2 @ X4) = $true) | ($true != (sK1 @ X4))) & ? [X5 : a] : ((($true = (sK1 @ X5)) | ($true = (sK0 @ X5))) & ($true != (sK2 @ X5))))),
% 1.68/1.44 introduced(definition,[],[choice_axiom])).
% 1.68/1.44 thf(f10,plain,(
% 1.68/1.44 ? [X5 : a] : ((($true = (sK1 @ X5)) | ($true = (sK0 @ X5))) & ($true != (sK2 @ X5))) => ((($true = (sK1 @ sK3)) | ($true = (sK0 @ sK3))) & ($true != (sK2 @ sK3)))),
% 1.68/1.44 introduced(definition,[],[choice_axiom])).
% 1.68/1.44 thf(f8,plain,(
% 1.68/1.44 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : (((X2 @ X3) = $true) | ((X0 @ X3) != $true)) & ! [X4 : a] : (($true = (X2 @ X4)) | ($true != (X1 @ X4))) & ? [X5 : a] : ((($true = (X1 @ X5)) | ($true = (X0 @ X5))) & ($true != (X2 @ X5))))),
% 1.68/1.44 inference(rectify,[status(thm)],[f7])).
% 1.68/1.44 thf(f7,plain,(
% 1.68/1.44 ? [X2 : a > $o,X0 : a > $o,X1 : a > $o] : (! [X3 : a] : (((X1 @ X3) = $true) | ((X2 @ X3) != $true)) & ! [X4 : a] : (($true = (X1 @ X4)) | ($true != (X0 @ X4))) & ? [X5 : a] : ((($true = (X0 @ X5)) | ($true = (X2 @ X5))) & ($true != (X1 @ X5))))),
% 1.68/1.44 inference(flattening,[status(thm)],[f6])).
% 1.68/1.44 thf(f6,plain,(
% 1.68/1.44 ? [X1 : a > $o,X2 : a > $o,X0 : a > $o] : (? [X5 : a] : ((($true = (X0 @ X5)) | ($true = (X2 @ X5))) & ($true != (X1 @ X5))) & (! [X3 : a] : (((X1 @ X3) = $true) | ((X2 @ X3) != $true)) & ! [X4 : a] : (($true = (X1 @ X4)) | ($true != (X0 @ X4)))))),
% 1.68/1.44 inference(ennf_transformation,[status(thm)],[f5])).
% 1.68/1.44 thf(f5,plain,(
% 1.68/1.44 ~! [X1 : a > $o,X2 : a > $o,X0 : a > $o] : ((! [X3 : a] : (((X2 @ X3) = $true) => ((X1 @ X3) = $true)) & ! [X4 : a] : (($true = (X0 @ X4)) => ($true = (X1 @ X4)))) => ! [X5 : a] : ((($true = (X0 @ X5)) | ($true = (X2 @ X5))) => ($true = (X1 @ X5))))),
% 1.68/1.44 inference(fool_elimination,[status(thm)],[f4])).
% 1.68/1.44 thf(f4,plain,(
% 1.68/1.44 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X3 : a] : ((X2 @ X3) => (X1 @ X3)) & ! [X4 : a] : ((X0 @ X4) => (X1 @ X4))) => ! [X5 : a] : (((X2 @ X5) | (X0 @ X5)) => (X1 @ X5)))),
% 1.68/1.44 inference(rectify,[status(thm)],[f2])).
% 1.68/1.44 thf(f2,negated_conjecture,(
% 1.68/1.44 ~! [X1 : a > $o,X2 : a > $o,X0 : a > $o] : ((! [X3 : a] : ((X0 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X1 @ X3) => (X2 @ X3))) => ! [X3 : a] : (((X0 @ X3) | (X1 @ X3)) => (X2 @ X3)))),
% 1.68/1.44 inference(negated_conjecture,[status(cth)],[f1])).
% 1.68/1.44 thf(f1,conjecture,(
% 1.68/1.44 ! [X1 : a > $o,X2 : a > $o,X0 : a > $o] : ((! [X3 : a] : ((X0 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X1 @ X3) => (X2 @ X3))) => ! [X3 : a] : (((X0 @ X3) | (X1 @ X3)) => (X2 @ X3)))),
% 1.68/1.44 file('/export/starexec/sandbox/tmp/tmp.Vi6xzMhfdl/DTF2THF_31689.p',cBOOL_PROP_32_pme)).
% 1.68/1.44 thf(f12,plain,(
% 1.68/1.44 ($true != (sK2 @ sK3))),
% 1.68/1.44 inference(cnf_transformation,[status(thm)],[f11])).
% 1.68/1.44 thf(f27,plain,(
% 1.68/1.44 ~spl4_1),
% 1.68/1.44 inference(avatar_split_clause,[status(thm)],[f26,f17])).
% 1.68/1.44 thf(f17,definition,(
% 1.68/1.44 spl4_1 <=> ($true = (sK1 @ sK3))),
% 1.68/1.44 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.68/1.44 thf(f26,plain,(
% 1.68/1.44 ($true != (sK1 @ sK3))),
% 1.68/1.44 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.68/1.44 thf(f25,plain,(
% 1.68/1.44 ($true != $true) | ($true != (sK1 @ sK3))),
% 1.68/1.44 inference(superposition,[status(thm)],[f12,f14])).
% 1.68/1.44 thf(f14,plain,(
% 1.68/1.44 ( ! [X4 : a] : (((sK2 @ X4) = $true) | ($true != (sK1 @ X4))) )),
% 1.68/1.44 inference(cnf_transformation,[status(thm)],[f11])).
% 1.68/1.44 thf(f24,plain,(
% 1.68/1.44 spl4_1 | spl4_2),
% 1.68/1.44 inference(avatar_split_clause,[status(thm)],[f13,f21,f17])).
% 1.68/1.44 thf(f13,plain,(
% 1.68/1.44 ($true = (sK1 @ sK3)) | ($true = (sK0 @ sK3))),
% 1.68/1.44 inference(cnf_transformation,[status(thm)],[f11])).
% 1.68/1.44 % SZS output end Proof for DTF2THF_31689
% 1.68/1.44 % (31806)------------------------------
% 1.68/1.44 % (31806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.44 % (31806)Termination reason: Refutation
% 1.68/1.44
% 1.68/1.44 % (31806)Memory used [KB]: 5500
% 1.68/1.44 % (31806)Time elapsed: 0.004 s
% 1.68/1.44 % (31806)Instructions burned: 2 (million)
% 1.68/1.44 % (31806)------------------------------
% 1.68/1.44 % (31806)------------------------------
% 1.68/1.44 % (31800)Success in time 0.018 s
%------------------------------------------------------------------------------