%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU586^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.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 09:35:26 AM UTC 2026
% Result : Theorem 1.67s 1.42s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 442 ( 132 equ; 0 cnn)
% Maximal formula atoms : 14 ( 11 avg)
% Number of connectives : 434 ( 67 ~; 62 |; 41 &; 234 @)
% ( 5 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 12 con; 0-2 aty)
% Number of variables : 85 ( 0 ^; 64 !; 21 ?; 85 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
binunion: $i > $i > $i ).
thf(f65,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f50,f55,f64]) ).
thf(f64,plain,
~ spl7_1,
inference(avatar_contradiction_clause,[status(thm)],[f63]) ).
thf(f63,plain,
( $false
| ~ spl7_1 ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ( $true != $true )
| ~ spl7_1 ),
inference(superposition,[status(thm)],[f29,f46]) ).
thf(f46,plain,
( ! [X5: $o] : ( $true = X5 )
| ~ spl7_1 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f45,definition,
( spl7_1
<=> ! [X5: $o] : ( $true = X5 ) ),
introduced(definition,[new_symbols(naming,[spl7_1])],[avatar_definition]) ).
thf(f29,plain,
( $true
!= ( in @ sK4 @ sK5 ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( in @ sK4 @ sK6 )
!= $true )
& ( $true
!= ( in @ sK4 @ sK5 ) )
& ( ( in @ sK4 @ ( binunion @ sK5 @ sK6 ) )
= $true )
& ( binunionEcases = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f10,f17]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
& ( ( in @ X0 @ X1 )
!= $true )
& ( ( in @ X0 @ ( binunion @ X1 @ X2 ) )
= $true ) )
=> ( ( ( in @ sK4 @ sK6 )
!= $true )
& ( $true
!= ( in @ sK4 @ sK5 ) )
& ( ( in @ sK4 @ ( binunion @ sK5 @ sK6 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
& ( ( in @ X0 @ X1 )
!= $true )
& ( ( in @ X0 @ ( binunion @ X1 @ X2 ) )
= $true ) )
& ( binunionEcases = $true ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ? [X2: $i,X1: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
& ( ( in @ X0 @ X1 )
!= $true )
& ( ( in @ X0 @ ( binunion @ X1 @ X2 ) )
= $true ) )
& ( binunionEcases = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( binunionEcases = $true )
=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ ( binunion @ X1 @ X2 ) )
= $true )
=> ( ( $true
= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( binunionEcases
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( binunion @ X1 @ X2 ) )
=> ( ( in @ X0 @ X1 )
| ( in @ X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( binunionEcases
=> ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X0 )
| ( in @ X2 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( binunionEcases
=> ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X0 )
| ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BsANC4lOnc/DTF2THF_17597.p',binunionE) ).
thf(f55,plain,
~ spl7_2,
inference(avatar_contradiction_clause,[status(thm)],[f54]) ).
thf(f54,plain,
( $false
| ~ spl7_2 ),
inference(subsumption_resolution,[status(thm)],[f53,f29]) ).
thf(f53,plain,
( ( $true
= ( in @ sK4 @ sK5 ) )
| ~ spl7_2 ),
inference(subsumption_resolution,[status(thm)],[f52,f30]) ).
thf(f30,plain,
( ( in @ sK4 @ sK6 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f52,plain,
( ( ( in @ sK4 @ sK6 )
= $true )
| ( $true
= ( in @ sK4 @ sK5 ) )
| ~ spl7_2 ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
( ( $true
= ( in @ sK4 @ sK5 ) )
| ( $true != $true )
| ( ( in @ sK4 @ sK6 )
= $true )
| ~ spl7_2 ),
inference(superposition,[status(thm)],[f49,f28]) ).
thf(f28,plain,
( ( in @ sK4 @ ( binunion @ sK5 @ sK6 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f49,plain,
( ! [X6: $i,X7: $i,X4: $i] :
( ( ( in @ X6 @ ( binunion @ X7 @ X4 ) )
!= $true )
| ( ( in @ X6 @ X4 )
= $true )
| ( ( in @ X6 @ X7 )
= $true ) )
| ~ spl7_2 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f48,definition,
( spl7_2
<=> ! [X6: $i,X4: $i,X7: $i] :
( ( ( in @ X6 @ ( binunion @ X7 @ X4 ) )
!= $true )
| ( ( in @ X6 @ X7 )
= $true )
| ( ( in @ X6 @ X4 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl7_2])],[avatar_definition]) ).
thf(f50,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[status(thm)],[f43,f48,f45]) ).
thf(f43,plain,
! [X6: $i,X7: $i,X4: $i,X5: $o] :
( ( ( in @ X6 @ ( binunion @ X7 @ X4 ) )
!= $true )
| ( ( in @ X6 @ X4 )
= $true )
| ( $true = X5 )
| ( ( in @ X6 @ X7 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
! [X6: $i,X7: $i,X4: $i,X5: $o] :
( ( ( in @ X6 @ X7 )
= $true )
| ( ( in @ X6 @ X4 )
= $true )
| ( ( in @ X6 @ ( binunion @ X7 @ X4 ) )
!= $true )
| ( $true = X5 )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f19,f27]) ).
thf(f27,plain,
binunionEcases = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f19,plain,
! [X6: $i,X7: $i,X4: $i,X5: $o] :
( ( ( in @ X6 @ X4 )
= $true )
| ( ( in @ X6 @ ( binunion @ X7 @ X4 ) )
!= $true )
| ( $true = X5 )
| ( ( in @ X6 @ X7 )
= $true )
| ( binunionEcases != $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( binunionEcases = $true )
| ( ( ( sK1 = $true )
| ( ( in @ sK2 @ sK0 )
!= $true ) )
& ( ( in @ sK2 @ ( binunion @ sK3 @ sK0 ) )
= $true )
& ( sK1 != $true )
& ( ( sK1 = $true )
| ( ( in @ sK2 @ sK3 )
!= $true ) ) ) )
& ( ! [X4: $i,X5: $o,X6: $i,X7: $i] :
( ( ( $true != X5 )
& ( ( in @ X6 @ X4 )
= $true ) )
| ( ( in @ X6 @ ( binunion @ X7 @ X4 ) )
!= $true )
| ( $true = X5 )
| ( ( $true != X5 )
& ( ( in @ X6 @ X7 )
= $true ) ) )
| ( binunionEcases != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f14,f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( ( $true = X1 )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ( ( in @ X2 @ ( binunion @ X3 @ X0 ) )
= $true )
& ( $true != X1 )
& ( ( $true = X1 )
| ( ( in @ X2 @ X3 )
!= $true ) ) )
=> ( ( ( sK1 = $true )
| ( ( in @ sK2 @ sK0 )
!= $true ) )
& ( ( in @ sK2 @ ( binunion @ sK3 @ sK0 ) )
= $true )
& ( sK1 != $true )
& ( ( sK1 = $true )
| ( ( in @ sK2 @ sK3 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ( ( binunionEcases = $true )
| ? [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( ( $true = X1 )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ( ( in @ X2 @ ( binunion @ X3 @ X0 ) )
= $true )
& ( $true != X1 )
& ( ( $true = X1 )
| ( ( in @ X2 @ X3 )
!= $true ) ) ) )
& ( ! [X4: $i,X5: $o,X6: $i,X7: $i] :
( ( ( $true != X5 )
& ( ( in @ X6 @ X4 )
= $true ) )
| ( ( in @ X6 @ ( binunion @ X7 @ X4 ) )
!= $true )
| ( $true = X5 )
| ( ( $true != X5 )
& ( ( in @ X6 @ X7 )
= $true ) ) )
| ( binunionEcases != $true ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( binunionEcases = $true )
| ? [X2: $i,X1: $o,X0: $i,X3: $i] :
( ( ( $true = X1 )
| ( $true
!= ( in @ X0 @ X2 ) ) )
& ( ( in @ X0 @ ( binunion @ X3 @ X2 ) )
= $true )
& ( $true != X1 )
& ( ( $true = X1 )
| ( ( in @ X0 @ X3 )
!= $true ) ) ) )
& ( ! [X2: $i,X1: $o,X0: $i,X3: $i] :
( ( ( $true != X1 )
& ( $true
= ( in @ X0 @ X2 ) ) )
| ( ( in @ X0 @ ( binunion @ X3 @ X2 ) )
!= $true )
| ( $true = X1 )
| ( ( $true != X1 )
& ( ( in @ X0 @ X3 )
= $true ) ) )
| ( binunionEcases != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( binunionEcases = $true )
<=> ! [X2: $i,X1: $o,X0: $i,X3: $i] :
( ( ( $true != X1 )
& ( $true
= ( in @ X0 @ X2 ) ) )
| ( ( in @ X0 @ ( binunion @ X3 @ X2 ) )
!= $true )
| ( $true = X1 )
| ( ( $true != X1 )
& ( ( in @ X0 @ X3 )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( $true = X1 )
| ( ( $true != X1 )
& ( $true
= ( in @ X0 @ X2 ) ) )
| ( ( $true != X1 )
& ( ( in @ X0 @ X3 )
= $true ) )
| ( ( in @ X0 @ ( binunion @ X3 @ X2 ) )
!= $true ) )
<=> ( binunionEcases = $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( ( in @ X0 @ ( binunion @ X3 @ X2 ) )
= $true )
=> ( ( ( ( in @ X0 @ X3 )
= $true )
=> ( $true = X1 ) )
=> ( ( ( $true
= ( in @ X0 @ X2 ) )
=> ( $true = X1 ) )
=> ( $true = X1 ) ) ) )
<=> ( binunionEcases = $true ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( binunionEcases
= ( ! [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( in @ X0 @ ( binunion @ X3 @ X2 ) )
=> ( ( ( in @ X0 @ X3 )
=> X1 )
=> ( ( ( in @ X0 @ X2 )
=> X1 )
=> X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( binunionEcases
= ( ! [X2: $i,X3: $o,X1: $i,X0: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( ( in @ X2 @ X0 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BsANC4lOnc/DTF2THF_17597.p',binunionEcases) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU586^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n013.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 12:27:23 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
% 0.19/0.47 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : SEU586^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.47 % Domain : Set Theory
% 0.19/0.47 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.19/0.47 % Version : Especial > Reduced > Especial.
% 0.19/0.47 % English : (! A:i.! B:i.! x:i.in x (binunion A B) -> in x A | in x B)
% 0.19/0.47
% 0.19/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.47 % Source : [Bro08]
% 0.19/0.47 % Names : ZFC088l [Bro08]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.19/0.47 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.19/0.47 % Number of atoms : 9 ( 1 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 4 ( 4 avg)
% 0.19/0.47 % Number of connectives : 24 ( 0 ~; 1 |; 0 &; 16 @)
% 0.19/0.47 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 9 ( 5 avg)
% 0.19/0.47 % Number of types : 2 ( 0 usr)
% 0.19/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.19/0.47 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.19/0.47 % SPC : TH0_THM_EQU_NAR
% 0.19/0.47
% 0.19/0.47 % Comments : http://mathgate.info/detsetitem.php?id=162
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(in_type,type,
% 0.19/0.47 in: $i > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(binunion_type,type,
% 0.19/0.47 binunion: $i > $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(binunionEcases_type,type,
% 0.19/0.47 binunionEcases: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binunionEcases,definition,
% 0.19/0.47 ( binunionEcases
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.19/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.19/0.47 => ( ( ( in @ Xx @ A )
% 0.19/0.47 => Xphi )
% 0.19/0.47 => ( ( ( in @ Xx @ B )
% 0.19/0.47 => Xphi )
% 0.19/0.47 => Xphi ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binunionE,conjecture,
% 0.19/0.47 ( binunionEcases
% 0.19/0.47 => ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.19/0.47 => ( ( in @ Xx @ A )
% 0.19/0.47 | ( in @ Xx @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.48/1.38 ---- Embedded in THF ---
% 1.48/1.38 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.38 %%% Generated on Tue Feb 24 12:27:24 EST 2026
% 1.48/1.38 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.38 %%% Logic specification used:
% 1.48/1.38 %%% thf(spec, logic, $$dhol).
% 1.48/1.38
% 1.48/1.38 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.BsANC4lOnc/DTF2DTF17597.p
% See solution above
% 1.48/1.38 ------------------------
% 1.48/1.39 ---- Cleaned THF ---
% 1.48/1.39 thf(in_type,type,
% 1.48/1.39 in: $i > $i > $o ).
% 1.48/1.39
% 1.48/1.39 thf(binunion_type,type,
% 1.48/1.39 binunion: $i > $i > $i ).
% 1.48/1.39
% 1.48/1.39 thf(binunionEcases_type,type,
% 1.48/1.39 binunionEcases: $o ).
% 1.48/1.39
% 1.48/1.39 thf(binunionEcases,definition,
% 1.48/1.39 ( binunionEcases
% 1.48/1.39 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 1.48/1.39 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 1.48/1.39 => ( ( ( in @ Xx @ A )
% 1.48/1.39 => Xphi )
% 1.48/1.39 => ( ( ( in @ Xx @ B )
% 1.48/1.39 => Xphi )
% 1.48/1.39 => Xphi ) ) ) ) ) ).
% 1.48/1.39
% 1.48/1.39 thf(binunionE,conjecture,
% 1.48/1.39 ( binunionEcases
% 1.48/1.39 => ! [A: $i,B: $i,Xx: $i] :
% 1.48/1.39 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 1.48/1.39 => ( ( in @ Xx @ A )
% 1.48/1.39 | ( in @ Xx @ B ) ) ) ) ).
% 1.48/1.39 ------------------------
% 1.67/1.41 % (17695)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_17597 for (2999ds/4Mi)
% 1.67/1.41 % (17697)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17597 for (2999ds/2Mi)
% 1.67/1.41 % (17698)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_17597 for (2999ds/2Mi)
% 1.67/1.41 % (17696)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_17597 for (2999ds/27Mi)
% 1.67/1.41 % (17699)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_17597 for (2999ds/275Mi)
% 1.67/1.41 % (17694)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17597 for (2999ds/183Mi)
% 1.67/1.41 % (17700)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17597 for (2999ds/18Mi)
% 1.67/1.41 % (17697)Instruction limit reached!
% 1.67/1.41 % (17697)------------------------------
% 1.67/1.41 % (17697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.41 % (17697)Termination reason: Unknown
% 1.67/1.41 % (17697)Termination phase: Saturation
% 1.67/1.41 % (17698)Instruction limit reached!
% 1.67/1.41 % (17698)------------------------------
% 1.67/1.41 % (17698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.41 % (17698)Termination reason: Unknown
% 1.67/1.41 % (17698)Termination phase: Saturation
% 1.67/1.41
% 1.67/1.41 % (17698)Memory used [KB]: 5500
% 1.67/1.41 % (17698)Time elapsed: 0.003 s
% 1.67/1.41 % (17698)Instructions burned: 3 (million)
% 1.67/1.41 % (17698)------------------------------
% 1.67/1.41 % (17698)------------------------------
% 1.67/1.41
% 1.67/1.41 % (17697)Memory used [KB]: 5500
% 1.67/1.41 % (17697)Time elapsed: 0.003 s
% 1.67/1.41 % (17697)Instructions burned: 3 (million)
% 1.67/1.41 % (17697)------------------------------
% 1.67/1.41 % (17697)------------------------------
% 1.67/1.41 % (17695)Instruction limit reached!
% 1.67/1.41 % (17695)------------------------------
% 1.67/1.41 % (17695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.41 % (17695)Termination reason: Unknown
% 1.67/1.41 % (17695)Termination phase: Saturation
% 1.67/1.41
% 1.67/1.41 % (17695)Memory used [KB]: 5500
% 1.67/1.41 % (17695)Time elapsed: 0.004 s
% 1.67/1.41 % (17695)Instructions burned: 4 (million)
% 1.67/1.41 % (17695)------------------------------
% 1.67/1.41 % (17695)------------------------------
% 1.67/1.41 % (17699)First to succeed.
% 1.67/1.41 % (17700)Also succeeded, but the first one will report.
% 1.67/1.42 % (17699)Refutation found. Thanks to Tanya!
% 1.67/1.42 % SZS status Theorem for DTF2THF_17597
% 1.67/1.42 % SZS output start Proof for DTF2THF_17597
% 1.67/1.42 thf(func_def_0, type, in: $i > $i > $o).
% 1.67/1.42 thf(func_def_1, type, binunion: $i > $i > $i).
% 1.67/1.42 thf(f65,plain,(
% 1.67/1.42 $false),
% 1.67/1.42 inference(avatar_sat_refutation,[status(thm)],[f50,f55,f64])).
% 1.67/1.42 thf(f64,plain,(
% 1.67/1.42 ~spl7_1),
% 1.67/1.42 inference(avatar_contradiction_clause,[status(thm)],[f63])).
% 1.67/1.42 thf(f63,plain,(
% 1.67/1.42 $false | ~spl7_1),
% 1.67/1.42 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.67/1.42 thf(f57,plain,(
% 1.67/1.42 ($true != $true) | ~spl7_1),
% 1.67/1.42 inference(superposition,[status(thm)],[f29,f46])).
% 1.67/1.42 thf(f46,plain,(
% 1.67/1.42 ( ! [X5 : $o] : (($true = X5)) ) | ~spl7_1),
% 1.67/1.42 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.67/1.42 thf(f45,definition,(
% 1.67/1.42 spl7_1 <=> ! [X5 : $o] : ($true = X5)),
% 1.67/1.42 introduced(definition,[new_symbols(naming,[spl7_1])],[avatar_definition])).
% 1.67/1.42 thf(f29,plain,(
% 1.67/1.42 ($true != (in @ sK4 @ sK5))),
% 1.67/1.42 inference(cnf_transformation,[status(thm)],[f18])).
% 1.67/1.42 thf(f18,plain,(
% 1.67/1.42 (((in @ sK4 @ sK6) != $true) & ($true != (in @ sK4 @ sK5)) & ((in @ sK4 @ (binunion @ sK5 @ sK6)) = $true)) & (binunionEcases = $true)),
% 1.67/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f10,f17])).
% 1.67/1.42 thf(f17,plain,(
% 1.67/1.42 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X2)) & ((in @ X0 @ X1) != $true) & ((in @ X0 @ (binunion @ X1 @ X2)) = $true)) => (((in @ sK4 @ sK6) != $true) & ($true != (in @ sK4 @ sK5)) & ((in @ sK4 @ (binunion @ sK5 @ sK6)) = $true))),
% 1.67/1.42 introduced(definition,[],[choice_axiom])).
% 1.67/1.42 thf(f10,plain,(
% 1.67/1.42 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X2)) & ((in @ X0 @ X1) != $true) & ((in @ X0 @ (binunion @ X1 @ X2)) = $true)) & (binunionEcases = $true)),
% 1.67/1.42 inference(flattening,[status(thm)],[f9])).
% 1.67/1.42 thf(f9,plain,(
% 1.67/1.42 ? [X2 : $i,X1 : $i,X0 : $i] : ((($true != (in @ X0 @ X2)) & ((in @ X0 @ X1) != $true)) & ((in @ X0 @ (binunion @ X1 @ X2)) = $true)) & (binunionEcases = $true)),
% 1.67/1.42 inference(ennf_transformation,[status(thm)],[f8])).
% 1.67/1.42 thf(f8,plain,(
% 1.67/1.42 ~((binunionEcases = $true) => ! [X2 : $i,X1 : $i,X0 : $i] : (((in @ X0 @ (binunion @ X1 @ X2)) = $true) => (($true = (in @ X0 @ X2)) | ((in @ X0 @ X1) = $true))))),
% 1.67/1.42 inference(fool_elimination,[status(thm)],[f7])).
% 1.67/1.42 thf(f7,plain,(
% 1.67/1.42 ~(binunionEcases => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (binunion @ X1 @ X2)) => ((in @ X0 @ X1) | (in @ X0 @ X2))))),
% 1.67/1.42 inference(rectify,[status(thm)],[f3])).
% 1.67/1.42 thf(f3,negated_conjecture,(
% 1.67/1.42 ~(binunionEcases => ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ (binunion @ X0 @ X1)) => ((in @ X2 @ X0) | (in @ X2 @ X1))))),
% 1.67/1.42 inference(negated_conjecture,[status(cth)],[f2])).
% 1.67/1.42 thf(f2,conjecture,(
% 1.67/1.42 binunionEcases => ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ (binunion @ X0 @ X1)) => ((in @ X2 @ X0) | (in @ X2 @ X1)))),
% 1.67/1.42 file('/export/starexec/sandbox/tmp/tmp.BsANC4lOnc/DTF2THF_17597.p',binunionE)).
% 1.67/1.42 thf(f55,plain,(
% 1.67/1.42 ~spl7_2),
% 1.67/1.42 inference(avatar_contradiction_clause,[status(thm)],[f54])).
% 1.67/1.42 thf(f54,plain,(
% 1.67/1.42 $false | ~spl7_2),
% 1.67/1.42 inference(subsumption_resolution,[status(thm)],[f53,f29])).
% 1.67/1.42 thf(f53,plain,(
% 1.67/1.42 ($true = (in @ sK4 @ sK5)) | ~spl7_2),
% 1.67/1.42 inference(subsumption_resolution,[status(thm)],[f52,f30])).
% 1.67/1.42 thf(f30,plain,(
% 1.67/1.42 ((in @ sK4 @ sK6) != $true)),
% 1.67/1.42 inference(cnf_transformation,[status(thm)],[f18])).
% 1.67/1.42 thf(f52,plain,(
% 1.67/1.42 ((in @ sK4 @ sK6) = $true) | ($true = (in @ sK4 @ sK5)) | ~spl7_2),
% 1.67/1.42 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.67/1.42 thf(f51,plain,(
% 1.67/1.42 ($true = (in @ sK4 @ sK5)) | ($true != $true) | ((in @ sK4 @ sK6) = $true) | ~spl7_2),
% 1.67/1.42 inference(superposition,[status(thm)],[f49,f28])).
% 1.67/1.42 thf(f28,plain,(
% 1.67/1.42 ((in @ sK4 @ (binunion @ sK5 @ sK6)) = $true)),
% 1.67/1.42 inference(cnf_transformation,[status(thm)],[f18])).
% 1.67/1.42 thf(f49,plain,(
% 1.67/1.42 ( ! [X6 : $i,X7 : $i,X4 : $i] : (((in @ X6 @ (binunion @ X7 @ X4)) != $true) | ((in @ X6 @ X4) = $true) | ((in @ X6 @ X7) = $true)) ) | ~spl7_2),
% 1.67/1.42 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.67/1.42 thf(f48,definition,(
% 1.67/1.42 spl7_2 <=> ! [X6 : $i,X4 : $i,X7 : $i] : (((in @ X6 @ (binunion @ X7 @ X4)) != $true) | ((in @ X6 @ X7) = $true) | ((in @ X6 @ X4) = $true))),
% 1.67/1.42 introduced(definition,[new_symbols(naming,[spl7_2])],[avatar_definition])).
% 1.67/1.42 thf(f50,plain,(
% 1.67/1.42 spl7_1 | spl7_2),
% 1.67/1.42 inference(avatar_split_clause,[status(thm)],[f43,f48,f45])).
% 1.67/1.42 thf(f43,plain,(
% 1.67/1.42 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $o] : (((in @ X6 @ (binunion @ X7 @ X4)) != $true) | ((in @ X6 @ X4) = $true) | ($true = X5) | ((in @ X6 @ X7) = $true)) )),
% 1.67/1.42 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.67/1.42 thf(f38,plain,(
% 1.67/1.42 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $o] : (((in @ X6 @ X7) = $true) | ((in @ X6 @ X4) = $true) | ((in @ X6 @ (binunion @ X7 @ X4)) != $true) | ($true = X5) | ($true != $true)) )),
% 1.67/1.42 inference(definition_unfolding,[status(thm)],[f19,f27])).
% 1.67/1.42 thf(f27,plain,(
% 1.67/1.42 (binunionEcases = $true)),
% 1.67/1.42 inference(cnf_transformation,[status(thm)],[f18])).
% 1.67/1.42 thf(f19,plain,(
% 1.67/1.42 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $o] : (((in @ X6 @ X4) = $true) | ((in @ X6 @ (binunion @ X7 @ X4)) != $true) | ($true = X5) | ((in @ X6 @ X7) = $true) | (binunionEcases != $true)) )),
% 1.67/1.42 inference(cnf_transformation,[status(thm)],[f16])).
% 1.67/1.42 thf(f16,plain,(
% 1.67/1.42 ((binunionEcases = $true) | (((sK1 = $true) | ((in @ sK2 @ sK0) != $true)) & ((in @ sK2 @ (binunion @ sK3 @ sK0)) = $true) & (sK1 != $true) & ((sK1 = $true) | ((in @ sK2 @ sK3) != $true)))) & (! [X4 : $i,X5 : $o,X6 : $i,X7 : $i] : ((($true != X5) & ((in @ X6 @ X4) = $true)) | ((in @ X6 @ (binunion @ X7 @ X4)) != $true) | ($true = X5) | (($true != X5) & ((in @ X6 @ X7) = $true))) | (binunionEcases != $true))),
% 1.67/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f14,f15])).
% 1.67/1.42 thf(f15,plain,(
% 1.67/1.42 ? [X0 : $i,X1 : $o,X2 : $i,X3 : $i] : ((($true = X1) | ((in @ X2 @ X0) != $true)) & ((in @ X2 @ (binunion @ X3 @ X0)) = $true) & ($true != X1) & (($true = X1) | ((in @ X2 @ X3) != $true))) => (((sK1 = $true) | ((in @ sK2 @ sK0) != $true)) & ((in @ sK2 @ (binunion @ sK3 @ sK0)) = $true) & (sK1 != $true) & ((sK1 = $true) | ((in @ sK2 @ sK3) != $true)))),
% 1.67/1.42 introduced(definition,[],[choice_axiom])).
% 1.67/1.42 thf(f14,plain,(
% 1.67/1.42 ((binunionEcases = $true) | ? [X0 : $i,X1 : $o,X2 : $i,X3 : $i] : ((($true = X1) | ((in @ X2 @ X0) != $true)) & ((in @ X2 @ (binunion @ X3 @ X0)) = $true) & ($true != X1) & (($true = X1) | ((in @ X2 @ X3) != $true)))) & (! [X4 : $i,X5 : $o,X6 : $i,X7 : $i] : ((($true != X5) & ((in @ X6 @ X4) = $true)) | ((in @ X6 @ (binunion @ X7 @ X4)) != $true) | ($true = X5) | (($true != X5) & ((in @ X6 @ X7) = $true))) | (binunionEcases != $true))),
% 1.67/1.42 inference(rectify,[status(thm)],[f13])).
% 1.67/1.42 thf(f13,plain,(
% 1.67/1.42 ((binunionEcases = $true) | ? [X2 : $i,X1 : $o,X0 : $i,X3 : $i] : ((($true = X1) | ($true != (in @ X0 @ X2))) & ((in @ X0 @ (binunion @ X3 @ X2)) = $true) & ($true != X1) & (($true = X1) | ((in @ X0 @ X3) != $true)))) & (! [X2 : $i,X1 : $o,X0 : $i,X3 : $i] : ((($true != X1) & ($true = (in @ X0 @ X2))) | ((in @ X0 @ (binunion @ X3 @ X2)) != $true) | ($true = X1) | (($true != X1) & ((in @ X0 @ X3) = $true))) | (binunionEcases != $true))),
% 1.67/1.42 inference(nnf_transformation,[status(thm)],[f12])).
% 1.67/1.42 thf(f12,plain,(
% 1.67/1.42 (binunionEcases = $true) <=> ! [X2 : $i,X1 : $o,X0 : $i,X3 : $i] : ((($true != X1) & ($true = (in @ X0 @ X2))) | ((in @ X0 @ (binunion @ X3 @ X2)) != $true) | ($true = X1) | (($true != X1) & ((in @ X0 @ X3) = $true)))),
% 1.67/1.42 inference(flattening,[status(thm)],[f11])).
% 1.67/1.42 thf(f11,plain,(
% 1.67/1.42 ! [X0 : $i,X1 : $o,X2 : $i,X3 : $i] : (((($true = X1) | (($true != X1) & ($true = (in @ X0 @ X2)))) | (($true != X1) & ((in @ X0 @ X3) = $true))) | ((in @ X0 @ (binunion @ X3 @ X2)) != $true)) <=> (binunionEcases = $true)),
% 1.67/1.42 inference(ennf_transformation,[status(thm)],[f6])).
% 1.67/1.42 thf(f6,plain,(
% 1.67/1.42 ! [X0 : $i,X1 : $o,X2 : $i,X3 : $i] : (((in @ X0 @ (binunion @ X3 @ X2)) = $true) => ((((in @ X0 @ X3) = $true) => ($true = X1)) => ((($true = (in @ X0 @ X2)) => ($true = X1)) => ($true = X1)))) <=> (binunionEcases = $true)),
% 1.67/1.42 inference(fool_elimination,[status(thm)],[f5])).
% 1.67/1.42 thf(f5,plain,(
% 1.67/1.42 (binunionEcases = ! [X0 : $i,X1 : $o,X2 : $i,X3 : $i] : ((in @ X0 @ (binunion @ X3 @ X2)) => (((in @ X0 @ X3) => X1) => (((in @ X0 @ X2) => X1) => X1))))),
% 1.67/1.42 inference(rectify,[status(thm)],[f1])).
% 1.67/1.42 thf(f1,axiom,(
% 1.67/1.42 (binunionEcases = ! [X2 : $i,X3 : $o,X1 : $i,X0 : $i] : ((in @ X2 @ (binunion @ X0 @ X1)) => (((in @ X2 @ X0) => X3) => (((in @ X2 @ X1) => X3) => X3))))),
% 1.67/1.42 file('/export/starexec/sandbox/tmp/tmp.BsANC4lOnc/DTF2THF_17597.p',binunionEcases)).
% 1.67/1.42 % SZS output end Proof for DTF2THF_17597
% 1.67/1.42 % (17699)------------------------------
% 1.67/1.42 % (17699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.42 % (17699)Termination reason: Refutation
% 1.67/1.42
% 1.67/1.42 % (17699)Memory used [KB]: 5500
% 1.67/1.42 % (17699)Time elapsed: 0.005 s
% 1.67/1.42 % (17699)Instructions burned: 2 (million)
% 1.67/1.42 % (17699)------------------------------
% 1.67/1.42 % (17699)------------------------------
% 1.67/1.42 % (17693)Success in time 0.018 s
%------------------------------------------------------------------------------