%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU783^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n025.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 09:37:10 AM UTC 2026
% Result : Theorem 1.65s 1.30s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 375 ( 84 equ; 0 cnn)
% Maximal formula atoms : 12 ( 12 avg)
% Number of connectives : 487 ( 16 ~; 2 |; 46 &; 369 @)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 10 usr; 9 con; 0-2 aty)
% ( 15 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 86 ( 18 ^; 41 !; 27 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
binunion: $i > $i > $i ).
thf(func_def_4,type,
kpair: $i > $i > $i ).
thf(func_def_5,type,
breln1: $i > $i > $o ).
thf(f36,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f35]) ).
thf(f35,plain,
$true = $false,
inference(superposition,[status(thm)],[f19,f33]) ).
thf(f33,plain,
( ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 )
= $false )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f18,f31]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( binunion @ X2 @ X1 ) )
= $true )
| ( ( in @ X3 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( binunion @ X2 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ ( binunion @ X2 @ X1 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ ( binunion @ X2 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ ( binunion @ Y0 @ X1 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ ( binunion @ Y0 @ X1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( binunion @ Y1 @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( binunion @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f23,f22]) ).
thf(f22,plain,
binunionIL = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( binunionIL = $true )
& ( ( breln1 @ sK0 @ sK1 )
= $true )
& ( ( in @ sK4 @ sK0 )
= $true )
& ( ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 )
= $true )
& ( ( in @ ( kpair @ sK3 @ sK4 ) @ ( binunion @ sK1 @ sK2 ) )
!= $true )
& ( ( in @ sK3 @ sK0 )
= $true )
& ( ( breln1 @ sK0 @ sK2 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f10,f14,f13,f12,f11]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ X0 ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
!= $true ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( $true
= ( breln1 @ X0 @ X2 ) ) ) )
=> ( ( ( breln1 @ sK0 @ sK1 )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK0 ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ sK1 )
= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ sK1 @ X2 ) )
!= $true ) )
& ( ( in @ X3 @ sK0 )
= $true ) )
& ( ( breln1 @ sK0 @ X2 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK0 ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ sK1 )
= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ sK1 @ X2 ) )
!= $true ) )
& ( ( in @ X3 @ sK0 )
= $true ) )
& ( ( breln1 @ sK0 @ X2 )
= $true ) )
=> ( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK0 ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ sK1 )
= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ sK1 @ sK2 ) )
!= $true ) )
& ( ( in @ X3 @ sK0 )
= $true ) )
& ( ( breln1 @ sK0 @ sK2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK0 ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ sK1 )
= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ sK1 @ sK2 ) )
!= $true ) )
& ( ( in @ X3 @ sK0 )
= $true ) )
=> ( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK0 ) )
& ( ( in @ ( kpair @ sK3 @ X4 ) @ sK1 )
= $true )
& ( ( in @ ( kpair @ sK3 @ X4 ) @ ( binunion @ sK1 @ sK2 ) )
!= $true ) )
& ( ( in @ sK3 @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK0 ) )
& ( ( in @ ( kpair @ sK3 @ X4 ) @ sK1 )
= $true )
& ( ( in @ ( kpair @ sK3 @ X4 ) @ ( binunion @ sK1 @ sK2 ) )
!= $true ) )
=> ( ( ( in @ sK4 @ sK0 )
= $true )
& ( ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 )
= $true )
& ( ( in @ ( kpair @ sK3 @ sK4 ) @ ( binunion @ sK1 @ sK2 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ( binunionIL = $true )
& ? [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ X0 ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
!= $true ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( $true
= ( breln1 @ X0 @ X2 ) ) ) ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
& ( $true
= ( in @ X4 @ X0 ) ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( $true
= ( breln1 @ X0 @ X2 ) ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) )
& ( binunionIL = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( binunionIL = $true )
=> ! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
=> ! [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X0 ) )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( binunionIL
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( binunionIL
=> ! [X0: $i,X3: $i] :
( ( breln1 @ X0 @ X3 )
=> ! [X4: $i] :
( ( breln1 @ X0 @ X4 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( ( in @ ( kpair @ X2 @ X5 ) @ X3 )
=> ( in @ ( kpair @ X2 @ X5 ) @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( binunionIL
=> ! [X0: $i,X3: $i] :
( ( breln1 @ X0 @ X3 )
=> ! [X4: $i] :
( ( breln1 @ X0 @ X4 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( ( in @ ( kpair @ X2 @ X5 ) @ X3 )
=> ( in @ ( kpair @ X2 @ X5 ) @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HIk6QMu6ba/DTF2THF_1467.p',breln1unionIL) ).
thf(f23,plain,
( binunionIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( binunion @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( binunionIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ ( binunion @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
=> ( in @ X0 @ ( binunion @ X1 @ X2 ) ) )
= binunionIL ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) )
= binunionIL ),
file('/export/starexec/sandbox2/tmp/tmp.HIk6QMu6ba/DTF2THF_1467.p',binunionIL) ).
thf(f18,plain,
( ( in @ ( kpair @ sK3 @ sK4 ) @ ( binunion @ sK1 @ sK2 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f19,plain,
( ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU783^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n025.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:33:57 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.45 thf(spec,logic,$$dhol).
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % File : SEU783^2 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.45 % Domain : Set Theory
% 0.20/0.45 % Problem : Binary Relations on a Set
% 0.20/0.45 % Version : Especial > Reduced > Especial.
% 0.20/0.45 % English : (! A:i.! R:i.breln1 A R -> (! S:i.breln1 A S -> (! x:i.in x A ->
% 0.20/0.45 % (! y:i.in y A -> in (kpair x y) R ->
% 0.20/0.45 % in (kpair x y) (binunion R S)))))
% 0.20/0.45
% 0.20/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.45 % Source : [Bro08]
% 0.20/0.45 % Names : ZFC285l [Bro08]
% 0.20/0.45
% 0.20/0.45 % Status : Theorem
% 0.20/0.45 % 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
% 0.20/0.45 % Syntax : Number of formulae : 7 ( 1 unt; 5 typ; 1 def)
% 0.20/0.45 % Number of atoms : 11 ( 1 equ; 0 cnn)
% 0.20/0.45 % Maximal formula atoms : 7 ( 5 avg)
% 0.20/0.45 % Number of connectives : 31 ( 0 ~; 0 |; 0 &; 24 @)
% 0.20/0.45 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.20/0.45 % Maximal formula depth : 16 ( 9 avg)
% 0.20/0.45 % Number of types : 2 ( 0 usr)
% 0.20/0.45 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.20/0.45 % Number of symbols : 6 ( 5 usr; 1 con; 0-2 aty)
% 0.20/0.45 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.20/0.45 % SPC : TH0_THM_EQU_NAR
% 0.20/0.45
% 0.20/0.45 % Comments : http://mathgate.info/detsetitem.php?id=348
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 thf(in_type,type,
% 0.20/0.45 in: $i > $i > $o ).
% 0.20/0.45
% 0.20/0.45 thf(binunion_type,type,
% 0.20/0.45 binunion: $i > $i > $i ).
% 0.20/0.45
% 0.20/0.45 thf(binunionIL_type,type,
% 0.20/0.45 binunionIL: $o ).
% 0.20/0.45
% 0.20/0.45 thf(binunionIL,definition,
% 0.20/0.45 ( binunionIL
% 0.20/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ A )
% 0.20/0.45 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(kpair_type,type,
% 0.20/0.45 kpair: $i > $i > $i ).
% 0.20/0.45
% 0.20/0.45 thf(breln1_type,type,
% 0.20/0.45 breln1: $i > $i > $o ).
% 0.20/0.45
% 0.20/0.45 thf(breln1unionIL,conjecture,
% 0.20/0.45 ( binunionIL
% 0.20/0.45 => ! [A: $i,R: $i] :
% 0.20/0.45 ( ( breln1 @ A @ R )
% 0.20/0.45 => ! [S: $i] :
% 0.20/0.45 ( ( breln1 @ A @ S )
% 0.20/0.45 => ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ A )
% 0.20/0.45 => ! [Xy: $i] :
% 0.20/0.45 ( ( in @ Xy @ A )
% 0.20/0.45 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.20/0.45 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 ------------------------
% 1.50/1.27 ---- Embedded in THF ---
% 1.50/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.27 %%% Generated on Tue Feb 24 12:33:58 EST 2026
% 1.50/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.27 %%% Logic specification used:
% 1.50/1.27 %%% thf(spec, logic, $$dhol).
% 1.50/1.27
% 1.50/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.HIk6QMu6ba/DTF2DTF1467.p
% See solution above
% 1.50/1.27 ------------------------
% 1.50/1.28 ---- Cleaned THF ---
% 1.50/1.28 thf(in_type,type,
% 1.50/1.28 in: $i > $i > $o ).
% 1.50/1.28
% 1.50/1.28 thf(binunion_type,type,
% 1.50/1.28 binunion: $i > $i > $i ).
% 1.50/1.28
% 1.50/1.28 thf(binunionIL_type,type,
% 1.50/1.28 binunionIL: $o ).
% 1.50/1.28
% 1.50/1.28 thf(binunionIL,definition,
% 1.50/1.28 ( binunionIL
% 1.50/1.28 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.50/1.28 ( ( in @ Xx @ A )
% 1.50/1.28 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 1.50/1.28
% 1.50/1.28 thf(kpair_type,type,
% 1.50/1.28 kpair: $i > $i > $i ).
% 1.50/1.28
% 1.50/1.28 thf(breln1_type,type,
% 1.50/1.28 breln1: $i > $i > $o ).
% 1.50/1.28
% 1.50/1.28 thf(breln1unionIL,conjecture,
% 1.50/1.28 ( binunionIL
% 1.50/1.28 => ! [A: $i,R: $i] :
% 1.50/1.28 ( ( breln1 @ A @ R )
% 1.50/1.28 => ! [S: $i] :
% 1.50/1.28 ( ( breln1 @ A @ S )
% 1.50/1.28 => ! [Xx: $i] :
% 1.50/1.28 ( ( in @ Xx @ A )
% 1.50/1.28 => ! [Xy: $i] :
% 1.50/1.28 ( ( in @ Xy @ A )
% 1.50/1.28 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 1.50/1.28 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ).
% 1.50/1.28 ------------------------
% 1.50/1.29 % (1629)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_1467 for (3000ds/4Mi)
% 1.50/1.29 % (1628)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1467 for (3000ds/183Mi)
% 1.50/1.29 % (1629)Instruction limit reached!
% 1.50/1.29 % (1629)------------------------------
% 1.50/1.29 % (1629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (1629)Termination reason: Unknown
% 1.50/1.29 % (1629)Termination phase: Saturation
% 1.50/1.29
% 1.50/1.29 % (1629)Memory used [KB]: 5500
% 1.50/1.29 % (1629)Time elapsed: 0.003 s
% 1.50/1.29 % (1629)Instructions burned: 4 (million)
% 1.50/1.29 % (1629)------------------------------
% 1.50/1.29 % (1629)------------------------------
% 1.50/1.29 % (1628)First to succeed.
% 1.65/1.30 % (1628)Refutation found. Thanks to Tanya!
% 1.65/1.30 % SZS status Theorem for DTF2THF_1467
% 1.65/1.30 % SZS output start Proof for DTF2THF_1467
% 1.65/1.30 thf(func_def_0, type, in: $i > $i > $o).
% 1.65/1.30 thf(func_def_1, type, binunion: $i > $i > $i).
% 1.65/1.30 thf(func_def_4, type, kpair: $i > $i > $i).
% 1.65/1.30 thf(func_def_5, type, breln1: $i > $i > $o).
% 1.65/1.30 thf(f36,plain,(
% 1.65/1.30 $false),
% 1.65/1.30 inference(trivial_inequality_removal,[status(thm)],[f35])).
% 1.65/1.30 thf(f35,plain,(
% 1.65/1.30 ($true = $false)),
% 1.65/1.30 inference(superposition,[status(thm)],[f19,f33])).
% 1.65/1.30 thf(f33,plain,(
% 1.65/1.30 ((in @ (kpair @ sK3 @ sK4) @ sK1) = $false)),
% 1.65/1.30 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.65/1.30 thf(f32,plain,(
% 1.65/1.30 ((in @ (kpair @ sK3 @ sK4) @ sK1) = $false) | ($true != $true)),
% 1.65/1.30 inference(superposition,[status(thm)],[f18,f31])).
% 1.65/1.30 thf(f31,plain,(
% 1.65/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X3 @ (binunion @ X2 @ X1)) = $true) | ((in @ X3 @ X2) = $false)) )),
% 1.65/1.30 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.65/1.30 thf(f30,plain,(
% 1.65/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X3 @ X2) => (in @ X3 @ (binunion @ X2 @ X1))) = $true)) )),
% 1.65/1.30 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.65/1.30 thf(f29,plain,(
% 1.65/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ (binunion @ X2 @ X1)))) @ X3))) )),
% 1.65/1.30 inference(pi_clausification,[status(thm)],[f28])).
% 1.65/1.30 thf(f28,plain,(
% 1.65/1.30 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ (binunion @ X2 @ X1))))) = $true)) )),
% 1.65/1.30 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.65/1.30 thf(f27,plain,(
% 1.65/1.30 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (binunion @ Y0 @ X1)))))) @ X2) = $true)) )),
% 1.65/1.30 inference(pi_clausification,[status(thm)],[f26])).
% 1.65/1.30 thf(f26,plain,(
% 1.65/1.30 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (binunion @ Y0 @ X1))))))) = $true)) )),
% 1.65/1.30 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.65/1.30 thf(f25,plain,(
% 1.65/1.30 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0)))))))) @ X1))) )),
% 1.65/1.30 inference(pi_clausification,[status(thm)],[f24])).
% 1.65/1.30 thf(f24,plain,(
% 1.65/1.30 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))))),
% 1.65/1.30 inference(definition_unfolding,[status(thm)],[f23,f22])).
% 1.65/1.30 thf(f22,plain,(
% 1.65/1.30 (binunionIL = $true)),
% 1.65/1.30 inference(cnf_transformation,[status(thm)],[f15])).
% 1.65/1.30 thf(f15,plain,(
% 1.65/1.30 (binunionIL = $true) & (((breln1 @ sK0 @ sK1) = $true) & (((((in @ sK4 @ sK0) = $true) & ((in @ (kpair @ sK3 @ sK4) @ sK1) = $true) & ((in @ (kpair @ sK3 @ sK4) @ (binunion @ sK1 @ sK2)) != $true)) & ((in @ sK3 @ sK0) = $true)) & ((breln1 @ sK0 @ sK2) = $true)))),
% 1.65/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f10,f14,f13,f12,f11])).
% 1.65/1.30 thf(f11,plain,(
% 1.65/1.30 ? [X0 : $i,X1 : $i] : (((breln1 @ X0 @ X1) = $true) & ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ X0)) & ((in @ (kpair @ X3 @ X4) @ X1) = $true) & ((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) != $true)) & ((in @ X3 @ X0) = $true)) & ($true = (breln1 @ X0 @ X2)))) => (((breln1 @ sK0 @ sK1) = $true) & ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ sK0)) & ((in @ (kpair @ X3 @ X4) @ sK1) = $true) & ((in @ (kpair @ X3 @ X4) @ (binunion @ sK1 @ X2)) != $true)) & ((in @ X3 @ sK0) = $true)) & ((breln1 @ sK0 @ X2) = $true)))),
% 1.65/1.30 introduced(definition,[],[choice_axiom])).
% 1.65/1.30 thf(f12,plain,(
% 1.65/1.30 ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ sK0)) & ((in @ (kpair @ X3 @ X4) @ sK1) = $true) & ((in @ (kpair @ X3 @ X4) @ (binunion @ sK1 @ X2)) != $true)) & ((in @ X3 @ sK0) = $true)) & ((breln1 @ sK0 @ X2) = $true)) => (? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ sK0)) & ((in @ (kpair @ X3 @ X4) @ sK1) = $true) & ((in @ (kpair @ X3 @ X4) @ (binunion @ sK1 @ sK2)) != $true)) & ((in @ X3 @ sK0) = $true)) & ((breln1 @ sK0 @ sK2) = $true))),
% 1.65/1.30 introduced(definition,[],[choice_axiom])).
% 1.65/1.30 thf(f13,plain,(
% 1.65/1.30 ? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ sK0)) & ((in @ (kpair @ X3 @ X4) @ sK1) = $true) & ((in @ (kpair @ X3 @ X4) @ (binunion @ sK1 @ sK2)) != $true)) & ((in @ X3 @ sK0) = $true)) => (? [X4 : $i] : (($true = (in @ X4 @ sK0)) & ((in @ (kpair @ sK3 @ X4) @ sK1) = $true) & ((in @ (kpair @ sK3 @ X4) @ (binunion @ sK1 @ sK2)) != $true)) & ((in @ sK3 @ sK0) = $true))),
% 1.65/1.30 introduced(definition,[],[choice_axiom])).
% 1.65/1.30 thf(f14,plain,(
% 1.65/1.30 ? [X4 : $i] : (($true = (in @ X4 @ sK0)) & ((in @ (kpair @ sK3 @ X4) @ sK1) = $true) & ((in @ (kpair @ sK3 @ X4) @ (binunion @ sK1 @ sK2)) != $true)) => (((in @ sK4 @ sK0) = $true) & ((in @ (kpair @ sK3 @ sK4) @ sK1) = $true) & ((in @ (kpair @ sK3 @ sK4) @ (binunion @ sK1 @ sK2)) != $true))),
% 1.65/1.30 introduced(definition,[],[choice_axiom])).
% 1.65/1.30 thf(f10,plain,(
% 1.65/1.30 (binunionIL = $true) & ? [X0 : $i,X1 : $i] : (((breln1 @ X0 @ X1) = $true) & ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ X0)) & ((in @ (kpair @ X3 @ X4) @ X1) = $true) & ((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) != $true)) & ((in @ X3 @ X0) = $true)) & ($true = (breln1 @ X0 @ X2))))),
% 1.65/1.30 inference(flattening,[status(thm)],[f9])).
% 1.65/1.30 thf(f9,plain,(
% 1.65/1.30 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : ((((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) != $true) & ((in @ (kpair @ X3 @ X4) @ X1) = $true)) & ($true = (in @ X4 @ X0))) & ((in @ X3 @ X0) = $true)) & ($true = (breln1 @ X0 @ X2))) & ((breln1 @ X0 @ X1) = $true)) & (binunionIL = $true)),
% 1.65/1.30 inference(ennf_transformation,[status(thm)],[f8])).
% 1.65/1.30 thf(f8,plain,(
% 1.65/1.30 ~((binunionIL = $true) => ! [X0 : $i,X1 : $i] : (((breln1 @ X0 @ X1) = $true) => ! [X2 : $i] : (($true = (breln1 @ X0 @ X2)) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => ! [X4 : $i] : (($true = (in @ X4 @ X0)) => (((in @ (kpair @ X3 @ X4) @ X1) = $true) => ((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) = $true)))))))),
% 1.65/1.30 inference(fool_elimination,[status(thm)],[f7])).
% 1.65/1.30 thf(f7,plain,(
% 1.65/1.30 ~(binunionIL => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2))))))))),
% 1.65/1.30 inference(rectify,[status(thm)],[f3])).
% 1.65/1.30 thf(f3,negated_conjecture,(
% 1.65/1.30 ~(binunionIL => ! [X0 : $i,X3 : $i] : ((breln1 @ X0 @ X3) => ! [X4 : $i] : ((breln1 @ X0 @ X4) => ! [X2 : $i] : ((in @ X2 @ X0) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ (kpair @ X2 @ X5) @ X3) => (in @ (kpair @ X2 @ X5) @ (binunion @ X3 @ X4))))))))),
% 1.65/1.30 inference(negated_conjecture,[status(cth)],[f2])).
% 1.65/1.30 thf(f2,conjecture,(
% 1.65/1.30 binunionIL => ! [X0 : $i,X3 : $i] : ((breln1 @ X0 @ X3) => ! [X4 : $i] : ((breln1 @ X0 @ X4) => ! [X2 : $i] : ((in @ X2 @ X0) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ (kpair @ X2 @ X5) @ X3) => (in @ (kpair @ X2 @ X5) @ (binunion @ X3 @ X4)))))))),
% 1.65/1.30 file('/export/starexec/sandbox2/tmp/tmp.HIk6QMu6ba/DTF2THF_1467.p',breln1unionIL)).
% 1.65/1.30 thf(f23,plain,(
% 1.65/1.30 (binunionIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))))),
% 1.65/1.30 inference(cnf_transformation,[status(thm)],[f6])).
% 1.65/1.30 thf(f6,plain,(
% 1.65/1.30 (binunionIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))))),
% 1.65/1.30 inference(fool_elimination,[status(thm)],[f5])).
% 1.65/1.30 thf(f5,plain,(
% 1.65/1.30 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => (in @ X0 @ (binunion @ X1 @ X2))) = binunionIL)),
% 1.65/1.30 inference(rectify,[status(thm)],[f1])).
% 1.65/1.30 thf(f1,axiom,(
% 1.65/1.30 (! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ X0) => (in @ X2 @ (binunion @ X0 @ X1))) = binunionIL)),
% 1.65/1.30 file('/export/starexec/sandbox2/tmp/tmp.HIk6QMu6ba/DTF2THF_1467.p',binunionIL)).
% 1.65/1.30 thf(f18,plain,(
% 1.65/1.30 ((in @ (kpair @ sK3 @ sK4) @ (binunion @ sK1 @ sK2)) != $true)),
% 1.65/1.30 inference(cnf_transformation,[status(thm)],[f15])).
% 1.65/1.30 thf(f19,plain,(
% 1.65/1.30 ((in @ (kpair @ sK3 @ sK4) @ sK1) = $true)),
% 1.65/1.30 inference(cnf_transformation,[status(thm)],[f15])).
% 1.65/1.30 % SZS output end Proof for DTF2THF_1467
% 1.65/1.30 % (1628)------------------------------
% 1.65/1.30 % (1628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.30 % (1628)Termination reason: Refutation
% 1.65/1.30
% 1.65/1.30 % (1628)Memory used [KB]: 5500
% 1.65/1.30 % (1628)Time elapsed: 0.003 s
% 1.65/1.30 % (1628)Instructions burned: 3 (million)
% 1.65/1.30 % (1628)------------------------------
% 1.65/1.30 % (1628)------------------------------
% 1.65/1.30 % (1627)Success in time 0.014 s
%------------------------------------------------------------------------------