%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU589^2 : 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 : n029.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 09:35:27 AM UTC 2026
% Result : Theorem 1.66s 1.45s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 263 ( 60 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 359 ( 12 ~; 8 |; 13 &; 270 @)
% ( 0 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 9 usr; 7 con; 0-2 aty)
% ( 18 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 89 ( 44 ^; 36 !; 9 ?; 89 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
binintersect: $i > $i > $i ).
thf(func_def_5,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_18,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f40,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
$true = $false,
inference(backward_demodulation,[status(thm)],[f19,f38]) ).
thf(f38,plain,
( ( in @ sK0 @ sK2 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( in @ sK0 @ sK2 )
= $false )
| ( $true = $false ) ),
inference(forward_demodulation,[status(thm)],[f36,f20]) ).
thf(f20,plain,
( $true
= ( in @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $true
= ( in @ sK0 @ sK1 ) )
& ( $true
= ( in @ sK0 @ sK2 ) )
& ( $true
!= ( in @ sK0 @ ( binintersect @ sK1 @ sK2 ) ) )
& ( dsetconstrI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
& ( $true
= ( in @ X0 @ X2 ) )
& ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
!= $true ) )
=> ( ( $true
= ( in @ sK0 @ sK1 ) )
& ( $true
= ( in @ sK0 @ sK2 ) )
& ( $true
!= ( in @ sK0 @ ( binintersect @ sK1 @ sK2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
& ( $true
= ( in @ X0 @ X2 ) )
& ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
!= $true ) )
& ( dsetconstrI = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
!= $true )
& ( $true
= ( in @ X0 @ X2 ) )
& ( $true
= ( in @ X0 @ X1 ) ) )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( dsetconstrI = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
=> ( ( $true
= ( in @ X0 @ X2 ) )
=> ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( dsetconstrI
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X1 )
=> ( ( in @ X0 @ X2 )
=> ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( dsetconstrI
=> ! [X2: $i,X0: $i,X4: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binintersect @ X0 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( dsetconstrI
=> ! [X2: $i,X0: $i,X4: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( binintersect @ X0 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.K0hJJSmEbc/DTF2THF_6822.p',binintersectI) ).
thf(f36,plain,
( ( ( in @ sK0 @ sK2 )
= $false )
| ( ( in @ sK0 @ sK1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( ^ [Y0: $i] : ( in @ Y0 @ sK2 )
@ sK0 )
= $false )
| ( ( in @ sK0 @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( in @ sK0 @ sK1 )
= $false )
| ( $true != $true )
| ( ( ^ [Y0: $i] : ( in @ Y0 @ sK2 )
@ sK0 )
= $false ) ),
inference(superposition,[status(thm)],[f33,f32]) ).
thf(f32,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) )
| ( ( in @ X1 @ X3 )
= $false )
| ( ( X2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( ( X2 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) )
= $true )
| ( ( in @ X1 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( in @ X1 @ X3 )
=> ( ( X2 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( X2 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( X2 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( Y0 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( Y0 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ Y2 @ Y1 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f17,f16]) ).
thf(f16,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( dsetconstrI
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( dsetconstrI
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.K0hJJSmEbc/DTF2THF_6822.p',dsetconstrI) ).
thf(f17,plain,
dsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f33,plain,
( $true
!= ( in @ sK0
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ Y0 @ sK2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
!= ( in @ sK0
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
@ sK1
@ sK2 ) ) ),
inference(definition_unfolding,[status(thm)],[f18,f21]) ).
thf(f21,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( binintersect
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( binintersect
= ( ^ [X0: $i,X4: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.K0hJJSmEbc/DTF2THF_6822.p',binintersect) ).
thf(f18,plain,
( $true
!= ( in @ sK0 @ ( binintersect @ sK1 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f19,plain,
( $true
= ( in @ sK0 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU589^2 : 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
% 0.15/0.33 % Computer : n029.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % 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 12:27:59 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
% 0.32/0.48 ---- Original DTF file ---
% 0.32/0.48 thf(spec,logic,$$dhol).
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 % File : SEU589^2 : TPTP v9.2.1. Released v3.7.0.
% 0.32/0.48 % Domain : Set Theory
% 0.32/0.48 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.32/0.48 % Version : Especial > Reduced > Especial.
% 0.32/0.48 % English : (! A:i.! B:i.! x:i.in x A -> in x B -> in x (binintersect A B))
% 0.32/0.48
% 0.32/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.32/0.48 % Source : [Bro08]
% 0.32/0.48 % Names : ZFC091l [Bro08]
% 0.32/0.48
% 0.32/0.48 % Status : Theorem
% 0.32/0.48 % Rating : 0.00 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0, 0.20 v5.1.0, 0.40 v4.1.0, 0.33 v3.7.0
% 0.32/0.48 % Syntax : Number of formulae : 7 ( 2 unt; 4 typ; 2 def)
% 0.32/0.48 % Number of atoms : 10 ( 2 equ; 0 cnn)
% 0.32/0.48 % Maximal formula atoms : 4 ( 3 avg)
% 0.32/0.48 % Number of connectives : 25 ( 0 ~; 0 |; 0 &; 20 @)
% 0.32/0.48 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.32/0.49 % Maximal formula depth : 10 ( 4 avg)
% 0.32/0.49 % Number of types : 2 ( 0 usr)
% 0.32/0.49 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.32/0.49 % Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% 0.32/0.49 % Number of variables : 10 ( 4 ^; 6 !; 0 ?; 10 :)
% 0.32/0.49 % SPC : TH0_THM_EQU_NAR
% 0.32/0.49
% 0.32/0.49 % Comments : http://mathgate.info/detsetitem.php?id=166
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 thf(in_type,type,
% 0.32/0.49 in: $i > $i > $o ).
% 0.32/0.49
% 0.32/0.49 thf(dsetconstr_type,type,
% 0.32/0.49 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.32/0.49
% 0.32/0.49 thf(dsetconstrI_type,type,
% 0.32/0.49 dsetconstrI: $o ).
% 0.32/0.49
% 0.32/0.49 thf(dsetconstrI,definition,
% 0.32/0.49 ( dsetconstrI
% 0.32/0.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( Xphi @ Xx )
% 0.32/0.49 => ( in @ Xx
% 0.32/0.49 @ ( dsetconstr @ A
% 0.32/0.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(binintersect_type,type,
% 0.32/0.49 binintersect: $i > $i > $i ).
% 0.32/0.49
% 0.32/0.49 thf(binintersect,definition,
% 0.32/0.49 ( binintersect
% 0.32/0.49 = ( ^ [A: $i,B: $i] :
% 0.32/0.49 ( dsetconstr @ A
% 0.32/0.49 @ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(binintersectI,conjecture,
% 0.32/0.49 ( dsetconstrI
% 0.32/0.49 => ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ B )
% 0.32/0.49 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 ------------------------
% 1.66/1.42 ---- Embedded in THF ---
% 1.66/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.42 %%% Generated on Tue Feb 24 12:28:00 EST 2026
% 1.66/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.42 %%% Logic specification used:
% 1.66/1.42 %%% thf(spec, logic, $$dhol).
% 1.66/1.42
% 1.66/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.K0hJJSmEbc/DTF2DTF6822.p
% See solution above
% 1.66/1.42 ------------------------
% 1.66/1.43 ---- Cleaned THF ---
% 1.66/1.43 thf(in_type,type,
% 1.66/1.43 in: $i > $i > $o ).
% 1.66/1.43
% 1.66/1.43 thf(dsetconstr_type,type,
% 1.66/1.43 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.66/1.43
% 1.66/1.43 thf(dsetconstrI_type,type,
% 1.66/1.43 dsetconstrI: $o ).
% 1.66/1.43
% 1.66/1.43 thf(dsetconstrI,definition,
% 1.66/1.43 ( dsetconstrI
% 1.66/1.43 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.66/1.43 ( ( in @ Xx @ A )
% 1.66/1.43 => ( ( Xphi @ Xx )
% 1.66/1.43 => ( in @ Xx
% 1.66/1.43 @ ( dsetconstr @ A
% 1.66/1.43 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.66/1.43
% 1.66/1.43 thf(binintersect_type,type,
% 1.66/1.43 binintersect: $i > $i > $i ).
% 1.66/1.43
% 1.66/1.43 thf(binintersect,definition,
% 1.66/1.43 ( binintersect
% 1.66/1.43 = ( ^ [A: $i,B: $i] :
% 1.66/1.43 ( dsetconstr @ A
% 1.66/1.43 @ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ) ).
% 1.66/1.43
% 1.66/1.43 thf(binintersectI,conjecture,
% 1.66/1.43 ( dsetconstrI
% 1.66/1.43 => ! [A: $i,B: $i,Xx: $i] :
% 1.66/1.43 ( ( in @ Xx @ A )
% 1.66/1.43 => ( ( in @ Xx @ B )
% 1.66/1.43 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ).
% 1.66/1.43 ------------------------
% 1.66/1.45 % (6936)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_6822 for (3000ds/27Mi)
% 1.66/1.45 % (6934)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6822 for (3000ds/183Mi)
% 1.66/1.45 % (6935)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_6822 for (3000ds/4Mi)
% 1.66/1.45 % (6937)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6822 for (3000ds/2Mi)
% 1.66/1.45 % (6938)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_6822 for (3000ds/2Mi)
% 1.66/1.45 % (6939)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_6822 for (3000ds/275Mi)
% 1.66/1.45 % (6940)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6822 for (3000ds/18Mi)
% 1.66/1.45 % (6937)Instruction limit reached!
% 1.66/1.45 % (6937)------------------------------
% 1.66/1.45 % (6937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (6937)Termination reason: Unknown
% 1.66/1.45 % (6937)Termination phase: Saturation
% 1.66/1.45 % (6938)Instruction limit reached!
% 1.66/1.45 % (6938)------------------------------
% 1.66/1.45 % (6938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (6938)Termination reason: Unknown
% 1.66/1.45 % (6938)Termination phase: Saturation
% 1.66/1.45
% 1.66/1.45 % (6938)Memory used [KB]: 5500
% 1.66/1.45 % (6938)Time elapsed: 0.003 s
% 1.66/1.45 % (6938)Instructions burned: 3 (million)
% 1.66/1.45 % (6938)------------------------------
% 1.66/1.45 % (6938)------------------------------
% 1.66/1.45
% 1.66/1.45 % (6937)Memory used [KB]: 5500
% 1.66/1.45 % (6937)Time elapsed: 0.003 s
% 1.66/1.45 % (6937)Instructions burned: 3 (million)
% 1.66/1.45 % (6937)------------------------------
% 1.66/1.45 % (6937)------------------------------
% 1.66/1.45 % (6939)Refutation not found, incomplete strategy
% 1.66/1.45 % (6939)------------------------------
% 1.66/1.45 % (6939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (6939)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.45
% 1.66/1.45
% 1.66/1.45 % (6939)Memory used [KB]: 5500
% 1.66/1.45 % (6939)Time elapsed: 0.003 s
% 1.66/1.45 % (6939)Instructions burned: 2 (million)
% 1.66/1.45 % (6939)------------------------------
% 1.66/1.45 % (6939)------------------------------
% 1.66/1.45 % (6935)Instruction limit reached!
% 1.66/1.45 % (6935)------------------------------
% 1.66/1.45 % (6935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (6935)Termination reason: Unknown
% 1.66/1.45 % (6935)Termination phase: Saturation
% 1.66/1.45
% 1.66/1.45 % (6935)Memory used [KB]: 5500
% 1.66/1.45 % (6935)Time elapsed: 0.004 s
% 1.66/1.45 % (6935)Instructions burned: 4 (million)
% 1.66/1.45 % (6935)------------------------------
% 1.66/1.45 % (6935)------------------------------
% 1.66/1.45 % (6936)First to succeed.
% 1.66/1.45 % (6934)Also succeeded, but the first one will report.
% 1.66/1.45 % (6936)Refutation found. Thanks to Tanya!
% 1.66/1.45 % SZS status Theorem for DTF2THF_6822
% 1.66/1.45 % SZS output start Proof for DTF2THF_6822
% 1.66/1.45 thf(func_def_0, type, in: $i > $i > $o).
% 1.66/1.45 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 1.66/1.45 thf(func_def_4, type, binintersect: $i > $i > $i).
% 1.66/1.45 thf(func_def_5, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.66/1.45 thf(func_def_18, type, ph4: !>[X0: $tType]:(X0)).
% 1.66/1.45 thf(f40,plain,(
% 1.66/1.45 $false),
% 1.66/1.45 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.66/1.45 thf(f39,plain,(
% 1.66/1.45 ($true = $false)),
% 1.66/1.45 inference(backward_demodulation,[status(thm)],[f19,f38])).
% 1.66/1.45 thf(f38,plain,(
% 1.66/1.45 ((in @ sK0 @ sK2) = $false)),
% 1.66/1.45 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.66/1.45 thf(f37,plain,(
% 1.66/1.45 ((in @ sK0 @ sK2) = $false) | ($true = $false)),
% 1.66/1.45 inference(forward_demodulation,[status(thm)],[f36,f20])).
% 1.66/1.45 thf(f20,plain,(
% 1.66/1.45 ($true = (in @ sK0 @ sK1))),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f15])).
% 1.66/1.45 thf(f15,plain,(
% 1.66/1.45 (($true = (in @ sK0 @ sK1)) & ($true = (in @ sK0 @ sK2)) & ($true != (in @ sK0 @ (binintersect @ sK1 @ sK2)))) & (dsetconstrI = $true)),
% 1.66/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f14])).
% 1.66/1.45 thf(f14,plain,(
% 1.66/1.45 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) & ($true = (in @ X0 @ X2)) & ((in @ X0 @ (binintersect @ X1 @ X2)) != $true)) => (($true = (in @ sK0 @ sK1)) & ($true = (in @ sK0 @ sK2)) & ($true != (in @ sK0 @ (binintersect @ sK1 @ sK2))))),
% 1.66/1.45 introduced(definition,[],[choice_axiom])).
% 1.66/1.45 thf(f13,plain,(
% 1.66/1.45 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) & ($true = (in @ X0 @ X2)) & ((in @ X0 @ (binintersect @ X1 @ X2)) != $true)) & (dsetconstrI = $true)),
% 1.66/1.45 inference(flattening,[status(thm)],[f12])).
% 1.66/1.45 thf(f12,plain,(
% 1.66/1.45 ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (binintersect @ X1 @ X2)) != $true) & ($true = (in @ X0 @ X2))) & ($true = (in @ X0 @ X1))) & (dsetconstrI = $true)),
% 1.66/1.45 inference(ennf_transformation,[status(thm)],[f11])).
% 1.66/1.45 thf(f11,plain,(
% 1.66/1.45 ~((dsetconstrI = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) => (($true = (in @ X0 @ X2)) => ((in @ X0 @ (binintersect @ X1 @ X2)) = $true))))),
% 1.66/1.45 inference(fool_elimination,[status(thm)],[f10])).
% 1.66/1.45 thf(f10,plain,(
% 1.66/1.45 ~(dsetconstrI => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => ((in @ X0 @ X2) => (in @ X0 @ (binintersect @ X1 @ X2)))))),
% 1.66/1.45 inference(rectify,[status(thm)],[f4])).
% 1.66/1.45 thf(f4,negated_conjecture,(
% 1.66/1.45 ~(dsetconstrI => ! [X2 : $i,X0 : $i,X4 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X4) => (in @ X2 @ (binintersect @ X0 @ X4)))))),
% 1.66/1.45 inference(negated_conjecture,[status(cth)],[f3])).
% 1.66/1.45 thf(f3,conjecture,(
% 1.66/1.45 dsetconstrI => ! [X2 : $i,X0 : $i,X4 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X4) => (in @ X2 @ (binintersect @ X0 @ X4))))),
% 1.66/1.45 file('/export/starexec/sandbox/tmp/tmp.K0hJJSmEbc/DTF2THF_6822.p',binintersectI)).
% 1.66/1.45 thf(f36,plain,(
% 1.66/1.45 ((in @ sK0 @ sK2) = $false) | ((in @ sK0 @ sK1) = $false)),
% 1.66/1.45 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.66/1.45 thf(f35,plain,(
% 1.66/1.45 (((^[Y0 : $i]: (in @ Y0 @ sK2)) @ sK0) = $false) | ((in @ sK0 @ sK1) = $false)),
% 1.66/1.45 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.66/1.45 thf(f34,plain,(
% 1.66/1.45 ((in @ sK0 @ sK1) = $false) | ($true != $true) | (((^[Y0 : $i]: (in @ Y0 @ sK2)) @ sK0) = $false)),
% 1.66/1.45 inference(superposition,[status(thm)],[f33,f32])).
% 1.66/1.45 thf(f32,plain,(
% 1.66/1.45 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = (in @ X1 @ (dsetconstr @ X3 @ X2))) | ((in @ X1 @ X3) = $false) | ((X2 @ X1) = $false)) )),
% 1.66/1.45 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.66/1.45 thf(f31,plain,(
% 1.66/1.45 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : ((((X2 @ X1) => (in @ X1 @ (dsetconstr @ X3 @ X2))) = $true) | ((in @ X1 @ X3) = $false)) )),
% 1.66/1.45 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.66/1.45 thf(f30,plain,(
% 1.66/1.45 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : ((((in @ X1 @ X3) => ((X2 @ X1) => (in @ X1 @ (dsetconstr @ X3 @ X2)))) = $true)) )),
% 1.66/1.45 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.66/1.45 thf(f29,plain,(
% 1.66/1.45 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X1 @ Y0) => ((X2 @ X1) => (in @ X1 @ (dsetconstr @ Y0 @ X2))))) @ X3))) )),
% 1.66/1.45 inference(pi_clausification,[status(thm)],[f28])).
% 1.66/1.45 thf(f28,plain,(
% 1.66/1.45 ( ! [X2 : $i > $o,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ Y0) => ((X2 @ X1) => (in @ X1 @ (dsetconstr @ Y0 @ X2)))))))) )),
% 1.66/1.45 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.66/1.45 thf(f27,plain,(
% 1.66/1.45 ( ! [X2 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => ((Y0 @ X1) => (in @ X1 @ (dsetconstr @ Y1 @ Y0))))))) @ X2))) )),
% 1.66/1.45 inference(pi_clausification,[status(thm)],[f26])).
% 1.66/1.45 thf(f26,plain,(
% 1.66/1.45 ( ! [X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => ((Y0 @ X1) => (in @ X1 @ (dsetconstr @ Y1 @ Y0)))))))) = $true)) )),
% 1.66/1.45 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.66/1.45 thf(f25,plain,(
% 1.66/1.45 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1))))))))) @ X1) = $true)) )),
% 1.66/1.45 inference(pi_clausification,[status(thm)],[f24])).
% 1.66/1.45 thf(f24,plain,(
% 1.66/1.45 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))))),
% 1.66/1.45 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.66/1.45 thf(f23,plain,(
% 1.66/1.45 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))) = $true)),
% 1.66/1.45 inference(definition_unfolding,[status(thm)],[f17,f16])).
% 1.66/1.45 thf(f16,plain,(
% 1.66/1.45 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f7])).
% 1.66/1.45 thf(f7,plain,(
% 1.66/1.45 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 1.66/1.45 inference(fool_elimination,[status(thm)],[f6])).
% 1.66/1.45 thf(f6,plain,(
% 1.66/1.45 (dsetconstrI = ! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))))),
% 1.66/1.45 inference(rectify,[status(thm)],[f1])).
% 1.66/1.45 thf(f1,axiom,(
% 1.66/1.45 (dsetconstrI = ! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))))),
% 1.66/1.45 file('/export/starexec/sandbox/tmp/tmp.K0hJJSmEbc/DTF2THF_6822.p',dsetconstrI)).
% 1.66/1.45 thf(f17,plain,(
% 1.66/1.45 (dsetconstrI = $true)),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f15])).
% 1.66/1.45 thf(f33,plain,(
% 1.66/1.45 ($true != (in @ sK0 @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (in @ Y0 @ sK2)))))),
% 1.66/1.45 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.66/1.45 thf(f22,plain,(
% 1.66/1.45 ($true != (in @ sK0 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))) @ sK1 @ sK2)))),
% 1.66/1.45 inference(definition_unfolding,[status(thm)],[f18,f21])).
% 1.66/1.45 thf(f21,plain,(
% 1.66/1.45 (binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))))),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f9])).
% 1.66/1.45 thf(f9,plain,(
% 1.66/1.45 (binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))))),
% 1.66/1.45 inference(fool_elimination,[status(thm)],[f8])).
% 1.66/1.45 thf(f8,plain,(
% 1.66/1.45 (binintersect = (^[X0 : $i, X1 : $i] : (dsetconstr @ X0 @ (^[X2 : $i] : (in @ X2 @ X1)))))),
% 1.66/1.45 inference(rectify,[status(thm)],[f2])).
% 1.66/1.45 thf(f2,axiom,(
% 1.66/1.45 (binintersect = (^[X0 : $i, X4 : $i] : (dsetconstr @ X0 @ (^[X2 : $i] : (in @ X2 @ X4)))))),
% 1.66/1.45 file('/export/starexec/sandbox/tmp/tmp.K0hJJSmEbc/DTF2THF_6822.p',binintersect)).
% 1.66/1.45 thf(f18,plain,(
% 1.66/1.45 ($true != (in @ sK0 @ (binintersect @ sK1 @ sK2)))),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f15])).
% 1.66/1.45 thf(f19,plain,(
% 1.66/1.45 ($true = (in @ sK0 @ sK2))),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f15])).
% 1.66/1.45 % SZS output end Proof for DTF2THF_6822
% 1.66/1.45 % (6936)------------------------------
% 1.66/1.45 % (6936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (6936)Termination reason: Refutation
% 1.66/1.45
% 1.66/1.45 % (6936)Memory used [KB]: 5500
% 1.66/1.45 % (6936)Time elapsed: 0.005 s
% 1.66/1.45 % (6936)Instructions burned: 4 (million)
% 1.66/1.45 % (6936)------------------------------
% 1.66/1.45 % (6936)------------------------------
% 1.66/1.45 % (6933)Success in time 0.018 s
%------------------------------------------------------------------------------