%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU738^2 : 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 : n014.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 09:36:48 AM UTC 2026
% Result : Theorem 1.67s 1.48s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 372 ( 98 equ; 0 cnn)
% Maximal formula atoms : 10 ( 13 avg)
% Number of connectives : 413 ( 44 ~; 16 |; 41 &; 278 @)
% ( 2 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 77 ( 0 ^; 50 !; 27 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
binunion: $i > $i > $i ).
thf(f36,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f35,f26]) ).
thf(f26,plain,
( ( in @ sK6 @ sK3 )
= $true ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( in @ sK3 @ ( powerset @ sK4 ) )
= $true )
& ( ( in @ sK5 @ ( powerset @ sK4 ) )
= $true )
& ( ( in @ sK6 @ sK4 )
= $true )
& ( ( in @ sK6 @ sK3 )
= $true )
& ( ( in @ sK6 @ ( binunion @ sK3 @ sK5 ) )
!= $true )
& ( binunionIL = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f12,f19,f18,f17]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true ) ) ) )
=> ( ( ( in @ sK3 @ ( powerset @ sK4 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK4 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ sK4 )
= $true )
& ( ( in @ X3 @ sK3 )
= $true )
& ( ( in @ X3 @ ( binunion @ sK3 @ X2 ) )
!= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK4 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ sK4 )
= $true )
& ( ( in @ X3 @ sK3 )
= $true )
& ( ( in @ X3 @ ( binunion @ sK3 @ X2 ) )
!= $true ) ) )
=> ( ( ( in @ sK5 @ ( powerset @ sK4 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ sK4 )
= $true )
& ( ( in @ X3 @ sK3 )
= $true )
& ( ( in @ X3 @ ( binunion @ sK3 @ sK5 ) )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ sK4 )
= $true )
& ( ( in @ X3 @ sK3 )
= $true )
& ( ( in @ X3 @ ( binunion @ sK3 @ sK5 ) )
!= $true ) )
=> ( ( ( in @ sK6 @ sK4 )
= $true )
& ( ( in @ sK6 @ sK3 )
= $true )
& ( ( in @ sK6 @ ( binunion @ sK3 @ sK5 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true ) ) ) )
& ( binunionIL = $true ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( binunionIL = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( binunionIL = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
=> ( ( in @ X3 @ X0 )
!= $true ) ) ) ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( binunionIL = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
!= $true )
=> ( ( in @ X3 @ X0 )
!= $true ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( binunionIL
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ ( binunion @ X0 @ X2 ) )
=> ~ ( in @ X3 @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( binunionIL
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ ( binunion @ X3 @ X4 ) )
=> ~ ( in @ X2 @ X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( binunionIL
=> ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ ( binunion @ X3 @ X4 ) )
=> ~ ( in @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xE9zOS66gU/DTF2THF_6653.p',binunionTILcontra) ).
thf(f35,plain,
( ( in @ sK6 @ sK3 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true != $true )
| ( ( in @ sK6 @ sK3 )
!= $true ) ),
inference(superposition,[status(thm)],[f25,f33]) ).
thf(f33,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( binunion @ X5 @ X4 ) )
= $true )
| ( ( in @ X3 @ X5 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X5 )
!= $true )
| ( $true != $true )
| ( ( in @ X3 @ ( binunion @ X5 @ X4 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f21,f24]) ).
thf(f24,plain,
binunionIL = $true,
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f21,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X5 )
!= $true )
| ( ( in @ X3 @ ( binunion @ X5 @ X4 ) )
= $true )
| ( binunionIL != $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( binunionIL = $true )
| ( ( ( in @ sK0 @ sK2 )
= $true )
& ( ( in @ sK0 @ ( binunion @ sK2 @ sK1 ) )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X5 )
!= $true )
| ( ( in @ X3 @ ( binunion @ X5 @ X4 ) )
= $true ) )
| ( binunionIL != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f14,f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
& ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
!= $true ) )
=> ( ( ( in @ sK0 @ sK2 )
= $true )
& ( ( in @ sK0 @ ( binunion @ sK2 @ sK1 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ( ( binunionIL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
& ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X5 )
!= $true )
| ( ( in @ X3 @ ( binunion @ X5 @ X4 ) )
= $true ) )
| ( binunionIL != $true ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( binunionIL = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
!= $true ) ) )
& ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
= $true ) )
| ( binunionIL != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( binunionIL = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
= $true ) )
<=> ( binunionIL = $true ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binunion @ X1 @ X0 ) ) )
= binunionIL ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) )
= binunionIL ),
file('/export/starexec/sandbox/tmp/tmp.xE9zOS66gU/DTF2THF_6653.p',binunionIL) ).
thf(f25,plain,
( ( in @ sK6 @ ( binunion @ sK3 @ sK5 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU738^2 : 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
% 0.15/0.34 % Computer : n014.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:32:42 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.33/0.49 ---- Original DTF file ---
% 0.33/0.49 thf(spec,logic,$$dhol).
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 % File : SEU738^2 : TPTP v9.2.1. Released v3.7.0.
% 0.33/0.49 % Domain : Set Theory
% 0.33/0.49 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.33/0.49 % Version : Especial > Reduced > Especial.
% 0.33/0.49 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.33/0.49 % (! x:i.in x A -> ~(in x (binunion X Y)) -> ~(in x X))))
% 0.33/0.49
% 0.33/0.49 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.33/0.49 % Source : [Bro08]
% 0.33/0.49 % Names : ZFC240l [Bro08]
% 0.33/0.49
% 0.33/0.49 % Status : Theorem
% 0.33/0.49 % 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
% 0.33/0.49 % Syntax : Number of formulae : 6 ( 1 unt; 4 typ; 1 def)
% 0.33/0.49 % Number of atoms : 10 ( 1 equ; 0 cnn)
% 0.33/0.49 % Maximal formula atoms : 6 ( 5 avg)
% 0.33/0.49 % Number of connectives : 28 ( 2 ~; 0 |; 0 &; 20 @)
% 0.33/0.49 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.33/0.49 % Maximal formula depth : 14 ( 8 avg)
% 0.33/0.49 % Number of types : 2 ( 0 usr)
% 0.33/0.49 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.33/0.49 % Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% 0.33/0.49 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.33/0.49 % SPC : TH0_THM_EQU_NAR
% 0.33/0.49
% 0.33/0.49 % Comments : http://mathgate.info/detsetitem.php?id=300
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 thf(in_type,type,
% 0.33/0.49 in: $i > $i > $o ).
% 0.33/0.49
% 0.33/0.49 thf(powerset_type,type,
% 0.33/0.49 powerset: $i > $i ).
% 0.33/0.49
% 0.33/0.49 thf(binunion_type,type,
% 0.33/0.49 binunion: $i > $i > $i ).
% 0.33/0.49
% 0.33/0.49 thf(binunionIL_type,type,
% 0.33/0.49 binunionIL: $o ).
% 0.33/0.49
% 0.33/0.49 thf(binunionIL,definition,
% 0.33/0.49 ( binunionIL
% 0.33/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.49 ( ( in @ Xx @ A )
% 0.33/0.49 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 thf(binunionTILcontra,conjecture,
% 0.33/0.49 ( binunionIL
% 0.33/0.49 => ! [A: $i,X: $i] :
% 0.33/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.49 => ! [Y: $i] :
% 0.33/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.49 => ! [Xx: $i] :
% 0.33/0.49 ( ( in @ Xx @ A )
% 0.33/0.49 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.33/0.49 => ~ ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 ------------------------
% 1.67/1.44 ---- Embedded in THF ---
% 1.67/1.44 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.67/1.44 %%% Generated on Tue Feb 24 12:32:43 EST 2026
% 1.67/1.44 %%% using '$$dhol' embedding, version 1.3.0.
% 1.67/1.44 %%% Logic specification used:
% 1.67/1.44 %%% thf(spec, logic, $$dhol).
% 1.67/1.44
% 1.67/1.44 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.xE9zOS66gU/DTF2DTF6653.p
% See solution above
% 1.67/1.44 ------------------------
% 1.67/1.45 ---- Cleaned THF ---
% 1.67/1.45 thf(in_type,type,
% 1.67/1.45 in: $i > $i > $o ).
% 1.67/1.45
% 1.67/1.45 thf(powerset_type,type,
% 1.67/1.45 powerset: $i > $i ).
% 1.67/1.45
% 1.67/1.45 thf(binunion_type,type,
% 1.67/1.45 binunion: $i > $i > $i ).
% 1.67/1.45
% 1.67/1.45 thf(binunionIL_type,type,
% 1.67/1.45 binunionIL: $o ).
% 1.67/1.45
% 1.67/1.45 thf(binunionIL,definition,
% 1.67/1.45 ( binunionIL
% 1.67/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.67/1.45 ( ( in @ Xx @ A )
% 1.67/1.45 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 1.67/1.45
% 1.67/1.45 thf(binunionTILcontra,conjecture,
% 1.67/1.45 ( binunionIL
% 1.67/1.45 => ! [A: $i,X: $i] :
% 1.67/1.45 ( ( in @ X @ ( powerset @ A ) )
% 1.67/1.45 => ! [Y: $i] :
% 1.67/1.45 ( ( in @ Y @ ( powerset @ A ) )
% 1.67/1.45 => ! [Xx: $i] :
% 1.67/1.45 ( ( in @ Xx @ A )
% 1.67/1.45 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 1.67/1.45 => ~ ( in @ Xx @ X ) ) ) ) ) ) ).
% 1.67/1.45 ------------------------
% 1.67/1.47 % (6774)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_6653 for (2999ds/2Mi)
% 1.67/1.47 % (6772)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_6653 for (2999ds/27Mi)
% 1.67/1.47 % (6776)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6653 for (2999ds/18Mi)
% 1.67/1.47 % (6773)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6653 for (2999ds/2Mi)
% 1.67/1.47 % (6771)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_6653 for (2999ds/4Mi)
% 1.67/1.47 % (6775)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_6653 for (2999ds/275Mi)
% 1.67/1.47 % (6770)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6653 for (2999ds/183Mi)
% 1.67/1.47 % (6773)Instruction limit reached!
% 1.67/1.47 % (6773)------------------------------
% 1.67/1.47 % (6773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.47 % (6773)Termination reason: Unknown
% 1.67/1.47 % (6773)Termination phase: Function definition elimination
% 1.67/1.47
% 1.67/1.47 % (6773)Memory used [KB]: 895
% 1.67/1.47 % (6773)Time elapsed: 0.003 s
% 1.67/1.47 % (6773)Instructions burned: 2 (million)
% 1.67/1.47 % (6773)------------------------------
% 1.67/1.47 % (6773)------------------------------
% 1.67/1.47 % (6774)Instruction limit reached!
% 1.67/1.47 % (6774)------------------------------
% 1.67/1.47 % (6774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.47 % (6774)Termination reason: Unknown
% 1.67/1.47 % (6774)Termination phase: Property scanning
% 1.67/1.47
% 1.67/1.47 % (6774)Memory used [KB]: 895
% 1.67/1.47 % (6774)Time elapsed: 0.003 s
% 1.67/1.47 % (6774)Instructions burned: 2 (million)
% 1.67/1.47 % (6774)------------------------------
% 1.67/1.47 % (6774)------------------------------
% 1.67/1.47 % (6775)First to succeed.
% 1.67/1.48 % (6772)Also succeeded, but the first one will report.
% 1.67/1.48 % (6770)Also succeeded, but the first one will report.
% 1.67/1.48 % (6775)Refutation found. Thanks to Tanya!
% 1.67/1.48 % SZS status Theorem for DTF2THF_6653
% 1.67/1.48 % SZS output start Proof for DTF2THF_6653
% 1.67/1.48 thf(func_def_0, type, in: $i > $i > $o).
% 1.67/1.48 thf(func_def_1, type, powerset: $i > $i).
% 1.67/1.48 thf(func_def_2, type, binunion: $i > $i > $i).
% 1.67/1.48 thf(f36,plain,(
% 1.67/1.48 $false),
% 1.67/1.48 inference(subsumption_resolution,[status(thm)],[f35,f26])).
% 1.67/1.48 thf(f26,plain,(
% 1.67/1.48 ((in @ sK6 @ sK3) = $true)),
% 1.67/1.48 inference(cnf_transformation,[status(thm)],[f20])).
% 1.67/1.48 thf(f20,plain,(
% 1.67/1.48 (((in @ sK3 @ (powerset @ sK4)) = $true) & (((in @ sK5 @ (powerset @ sK4)) = $true) & (((in @ sK6 @ sK4) = $true) & ((in @ sK6 @ sK3) = $true) & ((in @ sK6 @ (binunion @ sK3 @ sK5)) != $true)))) & (binunionIL = $true)),
% 1.67/1.48 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f12,f19,f18,f17])).
% 1.67/1.48 thf(f17,plain,(
% 1.67/1.48 ? [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((in @ X3 @ X0) = $true) & ((in @ X3 @ (binunion @ X0 @ X2)) != $true)))) => (((in @ sK3 @ (powerset @ sK4)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ sK4)) = $true) & ? [X3 : $i] : (((in @ X3 @ sK4) = $true) & ((in @ X3 @ sK3) = $true) & ((in @ X3 @ (binunion @ sK3 @ X2)) != $true))))),
% 1.67/1.48 introduced(definition,[],[choice_axiom])).
% 1.67/1.48 thf(f18,plain,(
% 1.67/1.48 ? [X2 : $i] : (((in @ X2 @ (powerset @ sK4)) = $true) & ? [X3 : $i] : (((in @ X3 @ sK4) = $true) & ((in @ X3 @ sK3) = $true) & ((in @ X3 @ (binunion @ sK3 @ X2)) != $true))) => (((in @ sK5 @ (powerset @ sK4)) = $true) & ? [X3 : $i] : (((in @ X3 @ sK4) = $true) & ((in @ X3 @ sK3) = $true) & ((in @ X3 @ (binunion @ sK3 @ sK5)) != $true)))),
% 1.67/1.48 introduced(definition,[],[choice_axiom])).
% 1.67/1.48 thf(f19,plain,(
% 1.67/1.48 ? [X3 : $i] : (((in @ X3 @ sK4) = $true) & ((in @ X3 @ sK3) = $true) & ((in @ X3 @ (binunion @ sK3 @ sK5)) != $true)) => (((in @ sK6 @ sK4) = $true) & ((in @ sK6 @ sK3) = $true) & ((in @ sK6 @ (binunion @ sK3 @ sK5)) != $true))),
% 1.67/1.48 introduced(definition,[],[choice_axiom])).
% 1.67/1.48 thf(f12,plain,(
% 1.67/1.48 ? [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((in @ X3 @ X0) = $true) & ((in @ X3 @ (binunion @ X0 @ X2)) != $true)))) & (binunionIL = $true)),
% 1.67/1.48 inference(flattening,[status(thm)],[f11])).
% 1.67/1.48 thf(f11,plain,(
% 1.67/1.48 ? [X1 : $i,X0 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ X0) = $true) & ((in @ X3 @ (binunion @ X0 @ X2)) != $true)) & ((in @ X3 @ X1) = $true)) & ((in @ X2 @ (powerset @ X1)) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) & (binunionIL = $true)),
% 1.67/1.48 inference(ennf_transformation,[status(thm)],[f9])).
% 1.67/1.48 thf(f9,plain,(
% 1.67/1.48 ~((binunionIL = $true) => ! [X1 : $i,X0 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => (((in @ X3 @ (binunion @ X0 @ X2)) != $true) => ((in @ X3 @ X0) != $true))))))),
% 1.67/1.48 inference(flattening,[status(thm)],[f8])).
% 1.67/1.48 thf(f8,plain,(
% 1.67/1.48 ~((binunionIL = $true) => ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => (~((in @ X3 @ (binunion @ X0 @ X2)) = $true) => ~((in @ X3 @ X0) = $true))))))),
% 1.67/1.48 inference(fool_elimination,[status(thm)],[f7])).
% 1.67/1.48 thf(f7,plain,(
% 1.67/1.48 ~(binunionIL => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => (~(in @ X3 @ (binunion @ X0 @ X2)) => ~(in @ X3 @ X0))))))),
% 1.67/1.48 inference(rectify,[status(thm)],[f3])).
% 1.67/1.48 thf(f3,negated_conjecture,(
% 1.67/1.48 ~(binunionIL => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ (binunion @ X3 @ X4)) => ~(in @ X2 @ X3))))))),
% 1.67/1.48 inference(negated_conjecture,[status(cth)],[f2])).
% 1.67/1.48 thf(f2,conjecture,(
% 1.67/1.48 binunionIL => ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ (binunion @ X3 @ X4)) => ~(in @ X2 @ X3)))))),
% 1.67/1.48 file('/export/starexec/sandbox/tmp/tmp.xE9zOS66gU/DTF2THF_6653.p',binunionTILcontra)).
% 1.67/1.48 thf(f35,plain,(
% 1.67/1.48 ((in @ sK6 @ sK3) != $true)),
% 1.67/1.48 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.67/1.48 thf(f34,plain,(
% 1.67/1.48 ($true != $true) | ((in @ sK6 @ sK3) != $true)),
% 1.67/1.48 inference(superposition,[status(thm)],[f25,f33])).
% 1.67/1.48 thf(f33,plain,(
% 1.67/1.48 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (binunion @ X5 @ X4)) = $true) | ((in @ X3 @ X5) != $true)) )),
% 1.67/1.48 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.67/1.48 thf(f32,plain,(
% 1.67/1.48 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X5) != $true) | ($true != $true) | ((in @ X3 @ (binunion @ X5 @ X4)) = $true)) )),
% 1.67/1.48 inference(definition_unfolding,[status(thm)],[f21,f24])).
% 1.67/1.48 thf(f24,plain,(
% 1.67/1.48 (binunionIL = $true)),
% 1.67/1.48 inference(cnf_transformation,[status(thm)],[f20])).
% 1.67/1.48 thf(f21,plain,(
% 1.67/1.48 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X5) != $true) | ((in @ X3 @ (binunion @ X5 @ X4)) = $true) | (binunionIL != $true)) )),
% 1.67/1.48 inference(cnf_transformation,[status(thm)],[f16])).
% 1.67/1.48 thf(f16,plain,(
% 1.67/1.48 ((binunionIL = $true) | (((in @ sK0 @ sK2) = $true) & ((in @ sK0 @ (binunion @ sK2 @ sK1)) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X5) != $true) | ((in @ X3 @ (binunion @ X5 @ X4)) = $true)) | (binunionIL != $true))),
% 1.67/1.48 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f14,f15])).
% 1.67/1.48 thf(f15,plain,(
% 1.67/1.48 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X2) = $true) & ((in @ X0 @ (binunion @ X2 @ X1)) != $true)) => (((in @ sK0 @ sK2) = $true) & ((in @ sK0 @ (binunion @ sK2 @ sK1)) != $true))),
% 1.67/1.48 introduced(definition,[],[choice_axiom])).
% 1.67/1.48 thf(f14,plain,(
% 1.67/1.48 ((binunionIL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X2) = $true) & ((in @ X0 @ (binunion @ X2 @ X1)) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X5) != $true) | ((in @ X3 @ (binunion @ X5 @ X4)) = $true)) | (binunionIL != $true))),
% 1.67/1.48 inference(rectify,[status(thm)],[f13])).
% 1.67/1.48 thf(f13,plain,(
% 1.67/1.48 ((binunionIL = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ (binunion @ X1 @ X0)) != $true))) & (! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ (binunion @ X1 @ X0)) = $true)) | (binunionIL != $true))),
% 1.67/1.48 inference(nnf_transformation,[status(thm)],[f10])).
% 1.67/1.48 thf(f10,plain,(
% 1.67/1.48 (binunionIL = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ (binunion @ X1 @ X0)) = $true))),
% 1.67/1.48 inference(ennf_transformation,[status(thm)],[f6])).
% 1.67/1.48 thf(f6,plain,(
% 1.67/1.48 ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X1) = $true) => ((in @ X2 @ (binunion @ X1 @ X0)) = $true)) <=> (binunionIL = $true)),
% 1.67/1.48 inference(fool_elimination,[status(thm)],[f5])).
% 1.67/1.48 thf(f5,plain,(
% 1.67/1.48 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (binunion @ X1 @ X0))) = binunionIL)),
% 1.67/1.48 inference(rectify,[status(thm)],[f1])).
% 1.67/1.48 thf(f1,axiom,(
% 1.67/1.48 (! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ (binunion @ X0 @ X1))) = binunionIL)),
% 1.67/1.48 file('/export/starexec/sandbox/tmp/tmp.xE9zOS66gU/DTF2THF_6653.p',binunionIL)).
% 1.67/1.48 thf(f25,plain,(
% 1.67/1.48 ((in @ sK6 @ (binunion @ sK3 @ sK5)) != $true)),
% 1.67/1.48 inference(cnf_transformation,[status(thm)],[f20])).
% 1.67/1.48 % SZS output end Proof for DTF2THF_6653
% 1.67/1.48 % (6775)------------------------------
% 1.67/1.48 % (6775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.48 % (6775)Termination reason: Refutation
% 1.67/1.48
% 1.67/1.48 % (6775)Memory used [KB]: 5500
% 1.67/1.48 % (6775)Time elapsed: 0.005 s
% 1.67/1.48 % (6775)Instructions burned: 3 (million)
% 1.67/1.48 % (6775)------------------------------
% 1.67/1.48 % (6775)------------------------------
% 1.67/1.48 % (6769)Success in time 0.021 s
%------------------------------------------------------------------------------