%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET201^5 : 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 : n031.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 09:31:25 AM UTC 2026
% Result : Theorem 1.62s 1.30s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 5 unt; 0 typ; 2 def)
% Number of atoms : 239 ( 82 equ; 0 cnn)
% Maximal formula atoms : 16 ( 8 avg)
% Number of connectives : 243 ( 45 ~; 34 |; 40 &; 104 @)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 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_1,type,
cV: a > $o ).
thf(func_def_5,type,
sK0: a > $o ).
thf(func_def_6,type,
sK1: a > $o ).
thf(func_def_7,type,
sK2: a > $o ).
thf(func_def_8,type,
sK3: a ).
thf(f34,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f25,f29,f33]) ).
thf(f33,plain,
spl4_2,
inference(avatar_contradiction_clause,[status(thm)],[f32]) ).
thf(f32,plain,
( $false
| spl4_2 ),
inference(subsumption_resolution,[status(thm)],[f31,f14]) ).
thf(f14,plain,
( $true
= ( sK0 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( sK2 @ sK3 )
= $true )
& ( ( $true
!= ( sK1 @ sK3 ) )
| ( ( cV @ sK3 )
!= $true ) )
& ( $true
= ( sK0 @ sK3 ) )
& ! [X4: a] :
( ( $true
= ( sK1 @ X4 ) )
| ( $true
!= ( sK2 @ X4 ) ) )
& ! [X5: a] :
( ( $true
!= ( sK0 @ X5 ) )
| ( $true
= ( cV @ X5 ) ) ) ),
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 )
& ( ( ( X1 @ X3 )
!= $true )
| ( ( cV @ X3 )
!= $true ) )
& ( ( X0 @ X3 )
= $true ) )
& ! [X4: a] :
( ( $true
= ( X1 @ X4 ) )
| ( $true
!= ( X2 @ X4 ) ) )
& ! [X5: a] :
( ( $true
!= ( X0 @ X5 ) )
| ( $true
= ( cV @ X5 ) ) ) )
=> ( ? [X3: a] :
( ( $true
= ( sK2 @ X3 ) )
& ( ( ( sK1 @ X3 )
!= $true )
| ( ( cV @ X3 )
!= $true ) )
& ( $true
= ( sK0 @ X3 ) ) )
& ! [X4: a] :
( ( $true
= ( sK1 @ X4 ) )
| ( $true
!= ( sK2 @ X4 ) ) )
& ! [X5: a] :
( ( $true
!= ( sK0 @ X5 ) )
| ( $true
= ( cV @ X5 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X3: a] :
( ( $true
= ( sK2 @ X3 ) )
& ( ( ( sK1 @ X3 )
!= $true )
| ( ( cV @ X3 )
!= $true ) )
& ( $true
= ( sK0 @ X3 ) ) )
=> ( ( ( sK2 @ sK3 )
= $true )
& ( ( $true
!= ( sK1 @ sK3 ) )
| ( ( cV @ sK3 )
!= $true ) )
& ( $true
= ( sK0 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X3: a] :
( ( ( X2 @ X3 )
= $true )
& ( ( ( X1 @ X3 )
!= $true )
| ( ( cV @ X3 )
!= $true ) )
& ( ( X0 @ X3 )
= $true ) )
& ! [X4: a] :
( ( $true
= ( X1 @ X4 ) )
| ( $true
!= ( X2 @ X4 ) ) )
& ! [X5: a] :
( ( $true
!= ( X0 @ X5 ) )
| ( $true
= ( cV @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X1: a > $o,X0: a > $o,X2: a > $o] :
( ? [X5: a] :
( ( $true
= ( X2 @ X5 ) )
& ( ( $true
!= ( X0 @ X5 ) )
| ( $true
!= ( cV @ X5 ) ) )
& ( ( X1 @ X5 )
= $true ) )
& ! [X4: a] :
( ( $true
= ( X0 @ X4 ) )
| ( $true
!= ( X2 @ X4 ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( cV @ X3 )
= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X2: a > $o,X0: a > $o,X1: a > $o] :
( ? [X5: a] :
( ( ( $true
!= ( X0 @ X5 ) )
| ( $true
!= ( cV @ X5 ) ) )
& ( $true
= ( X2 @ X5 ) )
& ( ( X1 @ X5 )
= $true ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( cV @ X3 )
= $true ) )
& ! [X4: a] :
( ( $true
= ( X0 @ X4 ) )
| ( $true
!= ( X2 @ X4 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( cV @ X3 )
= $true ) )
& ! [X4: a] :
( ( $true
= ( X2 @ X4 ) )
=> ( $true
= ( X0 @ X4 ) ) ) )
=> ! [X5: a] :
( ( ( $true
= ( X2 @ X5 ) )
& ( ( X1 @ X5 )
= $true ) )
=> ( ( $true
= ( cV @ X5 ) )
& ( $true
= ( X0 @ X5 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( cV @ X3 ) )
& ! [X4: a] :
( ( X2 @ X4 )
=> ( X0 @ X4 ) ) )
=> ! [X5: a] :
( ( ( X1 @ X5 )
& ( X2 @ X5 ) )
=> ( ( X0 @ X5 )
& ( cV @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( X2 @ X3 )
=> ( cV @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) )
=> ! [X3: a] :
( ( ( X2 @ X3 )
& ( X0 @ X3 ) )
=> ( ( X1 @ X3 )
& ( cV @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( X2 @ X3 )
=> ( cV @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) )
=> ! [X3: a] :
( ( ( X2 @ X3 )
& ( X0 @ X3 ) )
=> ( ( X1 @ X3 )
& ( cV @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.n9dBVkV9Fq/DTF2THF_32397.p',cBOOL_PROP_41_pme) ).
thf(f31,plain,
( ( $true
!= ( sK0 @ sK3 ) )
| spl4_2 ),
inference(trivial_inequality_removal,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $true
!= ( sK0 @ sK3 ) )
| ( $true != $true )
| spl4_2 ),
inference(superposition,[status(thm)],[f24,f12]) ).
thf(f12,plain,
! [X5: a] :
( ( $true
= ( cV @ X5 ) )
| ( $true
!= ( sK0 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f24,plain,
( ( ( cV @ sK3 )
!= $true )
| spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f22]) ).
thf(f22,definition,
( spl4_2
<=> ( ( cV @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f29,plain,
spl4_1,
inference(avatar_contradiction_clause,[status(thm)],[f28]) ).
thf(f28,plain,
( $false
| spl4_1 ),
inference(subsumption_resolution,[status(thm)],[f27,f16]) ).
thf(f16,plain,
( ( sK2 @ sK3 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f27,plain,
( ( ( sK2 @ sK3 )
!= $true )
| spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( sK2 @ sK3 )
!= $true )
| ( $true != $true )
| spl4_1 ),
inference(superposition,[status(thm)],[f20,f13]) ).
thf(f13,plain,
! [X4: a] :
( ( $true
= ( sK1 @ X4 ) )
| ( $true
!= ( sK2 @ X4 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f20,plain,
( ( $true
!= ( sK1 @ sK3 ) )
| spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f18]) ).
thf(f18,definition,
( spl4_1
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f25,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f15,f22,f18]) ).
thf(f15,plain,
( ( ( cV @ sK3 )
!= $true )
| ( $true
!= ( sK1 @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET201^5 : TPTP v9.2.1. Released v4.0.0.
% 0.14/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n031.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 11:56:03 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SET201^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.46 % Domain : Set Theory
% 0.31/0.46 % Problem : TPS problem BOOL-PROP-41
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English : Trybulec's 41st Boolean property of sets
% 0.31/0.46
% 0.31/0.46 % Refs : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of
% 0.31/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Bro09]
% 0.31/0.46 % Names : tps_0254 [Bro09]
% 0.31/0.46 % : BOOL-PROP-41 [TPS]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.31/0.46 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.31/0.46 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.31/0.46 % Number of connectives : 15 ( 0 ~; 0 |; 3 &; 8 @)
% 0.31/0.46 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 9 ( 9 avg)
% 0.31/0.46 % Number of types : 2 ( 1 usr)
% 0.31/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 1 ( 1 usr; 0 con; 1-1 aty)
% 0.31/0.46 % Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 0.31/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.46 % : Polymorphic definitions expanded.
% 0.31/0.46 % :
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(a_type,type,
% 0.31/0.46 a: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(cV,type,
% 0.31/0.46 cV: a > $o ).
% 0.31/0.46
% 0.31/0.46 thf(cBOOL_PROP_41_pme,conjecture,
% 0.31/0.46 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 0.31/0.46 ( ( ! [Xx: a] :
% 0.31/0.46 ( ( X @ Xx )
% 0.31/0.46 => ( Y @ Xx ) )
% 0.31/0.46 & ! [Xx: a] :
% 0.31/0.46 ( ( Z @ Xx )
% 0.31/0.46 => ( cV @ Xx ) ) )
% 0.31/0.46 => ! [Xx: a] :
% 0.31/0.46 ( ( ( X @ Xx )
% 0.31/0.46 & ( Z @ Xx ) )
% 0.31/0.46 => ( ( Y @ Xx )
% 0.31/0.46 & ( cV @ Xx ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.47/1.28 ---- Embedded in THF ---
% 1.47/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.28 %%% Generated on Tue Feb 24 11:56:04 EST 2026
% 1.47/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.28 %%% Logic specification used:
% 1.47/1.28 %%% thf(spec, logic, $$dhol).
% 1.47/1.28
% 1.47/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.n9dBVkV9Fq/DTF2DTF32397.p
% See solution above
% 1.47/1.28 ------------------------
% 1.47/1.29 ---- Cleaned THF ---
% 1.47/1.29 thf(a_type,type,
% 1.47/1.29 a: $tType ).
% 1.47/1.29
% 1.47/1.29 thf(cV,type,
% 1.47/1.29 cV: a > $o ).
% 1.47/1.29
% 1.47/1.29 thf(cBOOL_PROP_41_pme,conjecture,
% 1.47/1.29 ! [X: a > $o,Y: a > $o,Z: a > $o] :
% 1.47/1.29 ( ( ! [Xx: a] :
% 1.47/1.29 ( ( X @ Xx )
% 1.47/1.29 => ( Y @ Xx ) )
% 1.47/1.29 & ! [Xx: a] :
% 1.47/1.29 ( ( Z @ Xx )
% 1.47/1.29 => ( cV @ Xx ) ) )
% 1.47/1.29 => ! [Xx: a] :
% 1.47/1.29 ( ( ( X @ Xx )
% 1.47/1.29 & ( Z @ Xx ) )
% 1.47/1.29 => ( ( Y @ Xx )
% 1.47/1.29 & ( cV @ Xx ) ) ) ) ).
% 1.47/1.29 ------------------------
% 1.62/1.30 % (32678)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32397 for (2999ds/183Mi)
% 1.62/1.30 % (32679)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_32397 for (2999ds/4Mi)
% 1.62/1.30 % (32678)First to succeed.
% 1.62/1.30 % (32679)Also succeeded, but the first one will report.
% 1.62/1.30 % (32678)Refutation found. Thanks to Tanya!
% 1.62/1.30 % SZS status Theorem for DTF2THF_32397
% 1.62/1.30 % SZS output start Proof for DTF2THF_32397
% 1.62/1.30 thf(type_def_5, type, a: $tType).
% 1.62/1.30 thf(func_def_0, type, a: $tType).
% 1.62/1.30 thf(func_def_1, type, cV: a > $o).
% 1.62/1.30 thf(func_def_5, type, sK0: a > $o).
% 1.62/1.30 thf(func_def_6, type, sK1: a > $o).
% 1.62/1.30 thf(func_def_7, type, sK2: a > $o).
% 1.62/1.30 thf(func_def_8, type, sK3: a).
% 1.62/1.30 thf(f34,plain,(
% 1.62/1.30 $false),
% 1.62/1.30 inference(avatar_sat_refutation,[status(thm)],[f25,f29,f33])).
% 1.62/1.30 thf(f33,plain,(
% 1.62/1.30 spl4_2),
% 1.62/1.30 inference(avatar_contradiction_clause,[status(thm)],[f32])).
% 1.62/1.30 thf(f32,plain,(
% 1.62/1.30 $false | spl4_2),
% 1.62/1.30 inference(subsumption_resolution,[status(thm)],[f31,f14])).
% 1.62/1.30 thf(f14,plain,(
% 1.62/1.30 ($true = (sK0 @ sK3))),
% 1.62/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.62/1.30 thf(f11,plain,(
% 1.62/1.30 (((sK2 @ sK3) = $true) & (($true != (sK1 @ sK3)) | ((cV @ sK3) != $true)) & ($true = (sK0 @ sK3))) & ! [X4 : a] : (($true = (sK1 @ X4)) | ($true != (sK2 @ X4))) & ! [X5 : a] : (($true != (sK0 @ X5)) | ($true = (cV @ X5)))),
% 1.62/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f10,f9])).
% 1.62/1.30 thf(f9,plain,(
% 1.62/1.30 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (? [X3 : a] : (((X2 @ X3) = $true) & (((X1 @ X3) != $true) | ((cV @ X3) != $true)) & ((X0 @ X3) = $true)) & ! [X4 : a] : (($true = (X1 @ X4)) | ($true != (X2 @ X4))) & ! [X5 : a] : (($true != (X0 @ X5)) | ($true = (cV @ X5)))) => (? [X3 : a] : (($true = (sK2 @ X3)) & (((sK1 @ X3) != $true) | ((cV @ X3) != $true)) & ($true = (sK0 @ X3))) & ! [X4 : a] : (($true = (sK1 @ X4)) | ($true != (sK2 @ X4))) & ! [X5 : a] : (($true != (sK0 @ X5)) | ($true = (cV @ X5))))),
% 1.62/1.30 introduced(definition,[],[choice_axiom])).
% 1.62/1.30 thf(f10,plain,(
% 1.62/1.30 ? [X3 : a] : (($true = (sK2 @ X3)) & (((sK1 @ X3) != $true) | ((cV @ X3) != $true)) & ($true = (sK0 @ X3))) => (((sK2 @ sK3) = $true) & (($true != (sK1 @ sK3)) | ((cV @ sK3) != $true)) & ($true = (sK0 @ sK3)))),
% 1.62/1.30 introduced(definition,[],[choice_axiom])).
% 1.62/1.30 thf(f8,plain,(
% 1.62/1.30 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (? [X3 : a] : (((X2 @ X3) = $true) & (((X1 @ X3) != $true) | ((cV @ X3) != $true)) & ((X0 @ X3) = $true)) & ! [X4 : a] : (($true = (X1 @ X4)) | ($true != (X2 @ X4))) & ! [X5 : a] : (($true != (X0 @ X5)) | ($true = (cV @ X5))))),
% 1.62/1.30 inference(rectify,[status(thm)],[f7])).
% 1.62/1.30 thf(f7,plain,(
% 1.62/1.30 ? [X1 : a > $o,X0 : a > $o,X2 : a > $o] : (? [X5 : a] : (($true = (X2 @ X5)) & (($true != (X0 @ X5)) | ($true != (cV @ X5))) & ((X1 @ X5) = $true)) & ! [X4 : a] : (($true = (X0 @ X4)) | ($true != (X2 @ X4))) & ! [X3 : a] : (((X1 @ X3) != $true) | ((cV @ X3) = $true)))),
% 1.62/1.30 inference(flattening,[status(thm)],[f6])).
% 1.62/1.30 thf(f6,plain,(
% 1.62/1.30 ? [X2 : a > $o,X0 : a > $o,X1 : a > $o] : (? [X5 : a] : ((($true != (X0 @ X5)) | ($true != (cV @ X5))) & (($true = (X2 @ X5)) & ((X1 @ X5) = $true))) & (! [X3 : a] : (((X1 @ X3) != $true) | ((cV @ X3) = $true)) & ! [X4 : a] : (($true = (X0 @ X4)) | ($true != (X2 @ X4)))))),
% 1.62/1.30 inference(ennf_transformation,[status(thm)],[f5])).
% 1.62/1.30 thf(f5,plain,(
% 1.62/1.30 ~! [X2 : a > $o,X0 : a > $o,X1 : a > $o] : ((! [X3 : a] : (((X1 @ X3) = $true) => ((cV @ X3) = $true)) & ! [X4 : a] : (($true = (X2 @ X4)) => ($true = (X0 @ X4)))) => ! [X5 : a] : ((($true = (X2 @ X5)) & ((X1 @ X5) = $true)) => (($true = (cV @ X5)) & ($true = (X0 @ X5)))))),
% 1.62/1.30 inference(fool_elimination,[status(thm)],[f4])).
% 1.62/1.30 thf(f4,plain,(
% 1.62/1.30 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X3 : a] : ((X1 @ X3) => (cV @ X3)) & ! [X4 : a] : ((X2 @ X4) => (X0 @ X4))) => ! [X5 : a] : (((X1 @ X5) & (X2 @ X5)) => ((X0 @ X5) & (cV @ X5))))),
% 1.62/1.30 inference(rectify,[status(thm)],[f2])).
% 1.62/1.30 thf(f2,negated_conjecture,(
% 1.62/1.30 ~! [X1 : a > $o,X2 : a > $o,X0 : a > $o] : ((! [X3 : a] : ((X2 @ X3) => (cV @ X3)) & ! [X3 : a] : ((X0 @ X3) => (X1 @ X3))) => ! [X3 : a] : (((X2 @ X3) & (X0 @ X3)) => ((X1 @ X3) & (cV @ X3))))),
% 1.62/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.62/1.30 thf(f1,conjecture,(
% 1.62/1.30 ! [X1 : a > $o,X2 : a > $o,X0 : a > $o] : ((! [X3 : a] : ((X2 @ X3) => (cV @ X3)) & ! [X3 : a] : ((X0 @ X3) => (X1 @ X3))) => ! [X3 : a] : (((X2 @ X3) & (X0 @ X3)) => ((X1 @ X3) & (cV @ X3))))),
% 1.62/1.30 file('/export/starexec/sandbox/tmp/tmp.n9dBVkV9Fq/DTF2THF_32397.p',cBOOL_PROP_41_pme)).
% 1.62/1.30 thf(f31,plain,(
% 1.62/1.30 ($true != (sK0 @ sK3)) | spl4_2),
% 1.62/1.30 inference(trivial_inequality_removal,[status(thm)],[f30])).
% 1.62/1.30 thf(f30,plain,(
% 1.62/1.30 ($true != (sK0 @ sK3)) | ($true != $true) | spl4_2),
% 1.62/1.30 inference(superposition,[status(thm)],[f24,f12])).
% 1.62/1.30 thf(f12,plain,(
% 1.62/1.30 ( ! [X5 : a] : (($true = (cV @ X5)) | ($true != (sK0 @ X5))) )),
% 1.62/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.62/1.30 thf(f24,plain,(
% 1.62/1.30 ((cV @ sK3) != $true) | spl4_2),
% 1.62/1.30 inference(avatar_component_clause,[status(thm)],[f22])).
% 1.62/1.30 thf(f22,definition,(
% 1.62/1.30 spl4_2 <=> ((cV @ sK3) = $true)),
% 1.62/1.30 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.62/1.30 thf(f29,plain,(
% 1.62/1.30 spl4_1),
% 1.62/1.30 inference(avatar_contradiction_clause,[status(thm)],[f28])).
% 1.62/1.30 thf(f28,plain,(
% 1.62/1.30 $false | spl4_1),
% 1.62/1.30 inference(subsumption_resolution,[status(thm)],[f27,f16])).
% 1.62/1.30 thf(f16,plain,(
% 1.62/1.30 ((sK2 @ sK3) = $true)),
% 1.62/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.62/1.30 thf(f27,plain,(
% 1.62/1.30 ((sK2 @ sK3) != $true) | spl4_1),
% 1.62/1.30 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.62/1.30 thf(f26,plain,(
% 1.62/1.30 ((sK2 @ sK3) != $true) | ($true != $true) | spl4_1),
% 1.62/1.30 inference(superposition,[status(thm)],[f20,f13])).
% 1.62/1.30 thf(f13,plain,(
% 1.62/1.30 ( ! [X4 : a] : (($true = (sK1 @ X4)) | ($true != (sK2 @ X4))) )),
% 1.62/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.62/1.30 thf(f20,plain,(
% 1.62/1.30 ($true != (sK1 @ sK3)) | spl4_1),
% 1.62/1.30 inference(avatar_component_clause,[status(thm)],[f18])).
% 1.62/1.30 thf(f18,definition,(
% 1.62/1.30 spl4_1 <=> ($true = (sK1 @ sK3))),
% 1.62/1.30 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.62/1.30 thf(f25,plain,(
% 1.62/1.30 ~spl4_1 | ~spl4_2),
% 1.62/1.30 inference(avatar_split_clause,[status(thm)],[f15,f22,f18])).
% 1.62/1.30 thf(f15,plain,(
% 1.62/1.30 ((cV @ sK3) != $true) | ($true != (sK1 @ sK3))),
% 1.62/1.30 inference(cnf_transformation,[status(thm)],[f11])).
% 1.62/1.30 % SZS output end Proof for DTF2THF_32397
% 1.62/1.30 % (32678)------------------------------
% 1.62/1.30 % (32678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (32678)Termination reason: Refutation
% 1.62/1.30
% 1.62/1.30 % (32678)Memory used [KB]: 5500
% 1.62/1.30 % (32678)Time elapsed: 0.003 s
% 1.62/1.30 % (32678)Instructions burned: 1 (million)
% 1.62/1.30 % (32678)------------------------------
% 1.62/1.30 % (32678)------------------------------
% 1.62/1.30 % (32677)Success in time 0.013 s
%------------------------------------------------------------------------------