%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU584^2 : 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 : n007.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 09:35:25 AM UTC 2026
% Result : Theorem 1.66s 1.42s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 46 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 291 ( 64 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 401 ( 12 ~; 7 |; 11 &; 312 @)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 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)
% ( 23 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 95 ( 38 ^; 48 !; 9 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setunion: $i > $i ).
thf(func_def_6,type,
binunion: $i > $i > $i ).
thf(f51,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
$true = $false,
inference(superposition,[status(thm)],[f48,f22]) ).
thf(f22,plain,
( $true
= ( in @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $true
= ( in @ sK0 @ sK1 ) )
& ( $true
!= ( in @ sK0 @ ( binunion @ sK2 @ sK1 ) ) )
& ( setunionI = $true )
& ( upairset2IR = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f16,f17]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
& ( $true
!= ( in @ X0 @ ( binunion @ X2 @ X1 ) ) ) )
=> ( ( $true
= ( in @ sK0 @ sK1 ) )
& ( $true
!= ( in @ sK0 @ ( binunion @ sK2 @ sK1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
& ( $true
!= ( in @ X0 @ ( binunion @ X2 @ X1 ) ) ) )
& ( setunionI = $true )
& ( upairset2IR = $true ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
& ( $true
!= ( in @ X0 @ ( binunion @ X2 @ X1 ) ) ) )
& ( upairset2IR = $true )
& ( setunionI = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( setunionI = $true )
=> ( ( upairset2IR = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
=> ( $true
= ( in @ X0 @ ( binunion @ X2 @ X1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( setunionI
=> ( upairset2IR
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X1 )
=> ( in @ X0 @ ( binunion @ X2 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( setunionI
=> ( upairset2IR
=> ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( binunion @ X0 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( setunionI
=> ( upairset2IR
=> ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( binunion @ X0 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dDm7TSe8sr/DTF2THF_29133.p',binunionIR) ).
thf(f48,plain,
( ( in @ sK0 @ sK1 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ( in @ sK0 @ sK1 )
= $false )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f32,f44]) ).
thf(f44,plain,
! [X0: $i] :
( ( ( in @ X0 @ ( setadjoin @ sK2 @ ( setadjoin @ sK1 @ emptyset ) ) )
= $false )
| ( $false
= ( in @ sK0 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
! [X0: $i] :
( ( ( in @ X0 @ ( setadjoin @ sK2 @ ( setadjoin @ sK1 @ emptyset ) ) )
= $false )
| ( $false
= ( in @ sK0 @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f41,f40]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X3 @ ( setunion @ X1 ) ) )
| ( ( in @ X2 @ X1 )
= $false )
| ( ( in @ X3 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( in @ X2 @ X1 )
=> ( in @ X3 @ ( setunion @ X1 ) ) ) )
| ( ( in @ X3 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X3 @ X2 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X3 @ ( setunion @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ X2 @ X1 )
=> ( in @ Y0 @ ( setunion @ X1 ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ X2 @ X1 )
=> ( in @ Y0 @ ( setunion @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y1 @ ( setunion @ X1 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y1 @ ( setunion @ X1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f24,f20]) ).
thf(f20,plain,
setunionI = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f24,plain,
( setunionI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( setunionI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( setunionI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X1 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X0 @ ( setunion @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setunionI
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X1 @ ( setunion @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dDm7TSe8sr/DTF2THF_29133.p',setunionI) ).
thf(f41,plain,
( $true
!= ( in @ sK0 @ ( setunion @ ( setadjoin @ sK2 @ ( setadjoin @ sK1 @ emptyset ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
( $true
!= ( in @ sK0
@ ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) )
@ sK2
@ sK1 ) ) ),
inference(definition_unfolding,[status(thm)],[f21,f23]) ).
thf(f23,plain,
( binunion
= ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( binunion
= ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [X0: $i,X1: $i] : ( setunion @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) )
= binunion ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X1: $i,X3: $i] : ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) ) )
= binunion ),
file('/export/starexec/sandbox/tmp/tmp.dDm7TSe8sr/DTF2THF_29133.p',binunion) ).
thf(f21,plain,
( $true
!= ( in @ sK0 @ ( binunion @ sK2 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f32,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f25,f19]) ).
thf(f19,plain,
upairset2IR = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f25,plain,
( upairset2IR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( upairset2IR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( upairset2IR
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( upairset2IR
= ( ! [X3: $i,X1: $i] : ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dDm7TSe8sr/DTF2THF_29133.p',upairset2IR) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU584^2 : 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 : n007.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 12:27:08 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 : SEU584^2 : 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 B -> in x (binunion A 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 : ZFC086l [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 : 11 ( 3 unt; 7 typ; 3 def)
% 0.19/0.47 % Number of atoms : 13 ( 3 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 4 ( 3 avg)
% 0.19/0.47 % Number of connectives : 29 ( 0 ~; 0 |; 0 &; 24 @)
% 0.19/0.47 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 10 ( 3 avg)
% 0.19/0.47 % Number of types : 2 ( 0 usr)
% 0.19/0.47 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 8 ( 7 usr; 3 con; 0-2 aty)
% 0.19/0.47 % Number of variables : 10 ( 2 ^; 8 !; 0 ?; 10 :)
% 0.19/0.47 % SPC : TH0_THM_EQU_NAR
% 0.19/0.47
% 0.19/0.47 % Comments : http://mathgate.info/detsetitem.php?id=160
% 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(emptyset_type,type,
% 0.19/0.47 emptyset: $i ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoin_type,type,
% 0.19/0.47 setadjoin: $i > $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(setunion_type,type,
% 0.19/0.47 setunion: $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(setunionI_type,type,
% 0.19/0.47 setunionI: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setunionI,definition,
% 0.19/0.47 ( setunionI
% 0.19/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.19/0.47 ( ( in @ Xx @ B )
% 0.19/0.47 => ( ( in @ B @ A )
% 0.19/0.47 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 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(binunion,definition,
% 0.19/0.47 ( binunion
% 0.19/0.47 = ( ^ [Xx: $i,Xy: $i] : ( setunion @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(upairset2IR_type,type,
% 0.19/0.47 upairset2IR: $o ).
% 0.19/0.47
% 0.19/0.47 thf(upairset2IR,definition,
% 0.19/0.47 ( upairset2IR
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binunionIR,conjecture,
% 0.19/0.47 ( setunionI
% 0.19/0.47 => ( upairset2IR
% 0.19/0.47 => ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ B )
% 0.19/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.47/1.39 ---- Embedded in THF ---
% 1.47/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.39 %%% Generated on Tue Feb 24 12:27:09 EST 2026
% 1.47/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.39 %%% Logic specification used:
% 1.47/1.39 %%% thf(spec, logic, $$dhol).
% 1.47/1.39
% 1.47/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.dDm7TSe8sr/DTF2DTF29133.p
% See solution above
% 1.47/1.39 ------------------------
% 1.47/1.40 ---- Cleaned THF ---
% 1.47/1.40 thf(in_type,type,
% 1.47/1.40 in: $i > $i > $o ).
% 1.47/1.40
% 1.47/1.40 thf(emptyset_type,type,
% 1.47/1.40 emptyset: $i ).
% 1.47/1.40
% 1.47/1.40 thf(setadjoin_type,type,
% 1.47/1.40 setadjoin: $i > $i > $i ).
% 1.47/1.40
% 1.47/1.40 thf(setunion_type,type,
% 1.47/1.40 setunion: $i > $i ).
% 1.47/1.40
% 1.47/1.40 thf(setunionI_type,type,
% 1.47/1.40 setunionI: $o ).
% 1.47/1.40
% 1.47/1.40 thf(setunionI,definition,
% 1.47/1.40 ( setunionI
% 1.47/1.40 = ( ! [A: $i,Xx: $i,B: $i] :
% 1.47/1.40 ( ( in @ Xx @ B )
% 1.47/1.40 => ( ( in @ B @ A )
% 1.47/1.40 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 1.47/1.40
% 1.47/1.40 thf(binunion_type,type,
% 1.47/1.40 binunion: $i > $i > $i ).
% 1.47/1.40
% 1.47/1.40 thf(binunion,definition,
% 1.47/1.40 ( binunion
% 1.47/1.40 = ( ^ [Xx: $i,Xy: $i] : ( setunion @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.47/1.40
% 1.47/1.40 thf(upairset2IR_type,type,
% 1.47/1.40 upairset2IR: $o ).
% 1.47/1.40
% 1.47/1.40 thf(upairset2IR,definition,
% 1.47/1.40 ( upairset2IR
% 1.47/1.40 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.47/1.40
% 1.47/1.40 thf(binunionIR,conjecture,
% 1.47/1.40 ( setunionI
% 1.47/1.40 => ( upairset2IR
% 1.47/1.40 => ! [A: $i,B: $i,Xx: $i] :
% 1.47/1.40 ( ( in @ Xx @ B )
% 1.47/1.40 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 1.47/1.40 ------------------------
% 1.66/1.42 % (29237)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29133 for (2999ds/18Mi)
% 1.66/1.42 % (29235)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_29133 for (2999ds/2Mi)
% 1.66/1.42 % (29231)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29133 for (2999ds/183Mi)
% 1.66/1.42 % (29232)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_29133 for (2999ds/4Mi)
% 1.66/1.42 % (29234)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29133 for (2999ds/2Mi)
% 1.66/1.42 % (29233)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_29133 for (2999ds/27Mi)
% 1.66/1.42 % (29236)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_29133 for (2999ds/275Mi)
% 1.66/1.42 % (29235)Instruction limit reached!
% 1.66/1.42 % (29235)------------------------------
% 1.66/1.42 % (29235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.42 % (29235)Termination reason: Unknown
% 1.66/1.42 % (29235)Termination phase: Property scanning
% 1.66/1.42
% 1.66/1.42 % (29235)Memory used [KB]: 895
% 1.66/1.42 % (29235)Time elapsed: 0.002 s
% 1.66/1.42 % (29235)Instructions burned: 2 (million)
% 1.66/1.42 % (29235)------------------------------
% 1.66/1.42 % (29235)------------------------------
% 1.66/1.42 % (29234)Instruction limit reached!
% 1.66/1.42 % (29234)------------------------------
% 1.66/1.42 % (29234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.42 % (29234)Termination reason: Unknown
% 1.66/1.42 % (29234)Termination phase: Saturation
% 1.66/1.42
% 1.66/1.42 % (29234)Memory used [KB]: 5500
% 1.66/1.42 % (29234)Time elapsed: 0.003 s
% 1.66/1.42 % (29234)Instructions burned: 3 (million)
% 1.66/1.42 % (29234)------------------------------
% 1.66/1.42 % (29234)------------------------------
% 1.66/1.42 % (29236)Refutation not found, incomplete strategy
% 1.66/1.42 % (29236)------------------------------
% 1.66/1.42 % (29236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.42 % (29232)Instruction limit reached!
% 1.66/1.42 % (29232)------------------------------
% 1.66/1.42 % (29232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.42 % (29232)Termination reason: Unknown
% 1.66/1.42 % (29232)Termination phase: Saturation
% 1.66/1.42
% 1.66/1.42 % (29232)Memory used [KB]: 5500
% 1.66/1.42 % (29232)Time elapsed: 0.004 s
% 1.66/1.42 % (29232)Instructions burned: 4 (million)
% 1.66/1.42 % (29232)------------------------------
% 1.66/1.42 % (29232)------------------------------
% 1.66/1.42 % (29236)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.42
% 1.66/1.42
% 1.66/1.42 % (29236)Memory used [KB]: 5500
% 1.66/1.42 % (29236)Time elapsed: 0.003 s
% 1.66/1.42 % (29236)Instructions burned: 3 (million)
% 1.66/1.42 % (29236)------------------------------
% 1.66/1.42 % (29236)------------------------------
% 1.66/1.42 % (29231)First to succeed.
% 1.66/1.42 % (29237)Also succeeded, but the first one will report.
% 1.66/1.42 % (29231)Refutation found. Thanks to Tanya!
% 1.66/1.42 % SZS status Theorem for DTF2THF_29133
% 1.66/1.42 % SZS output start Proof for DTF2THF_29133
% 1.66/1.42 thf(func_def_0, type, in: $i > $i > $o).
% 1.66/1.42 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.66/1.42 thf(func_def_3, type, setunion: $i > $i).
% 1.66/1.42 thf(func_def_6, type, binunion: $i > $i > $i).
% 1.66/1.42 thf(f51,plain,(
% 1.66/1.42 $false),
% 1.66/1.42 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.66/1.42 thf(f49,plain,(
% 1.66/1.42 ($true = $false)),
% 1.66/1.42 inference(superposition,[status(thm)],[f48,f22])).
% 1.66/1.42 thf(f22,plain,(
% 1.66/1.42 ($true = (in @ sK0 @ sK1))),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f18])).
% 1.66/1.42 thf(f18,plain,(
% 1.66/1.42 (($true = (in @ sK0 @ sK1)) & ($true != (in @ sK0 @ (binunion @ sK2 @ sK1)))) & (setunionI = $true) & (upairset2IR = $true)),
% 1.66/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f16,f17])).
% 1.66/1.42 thf(f17,plain,(
% 1.66/1.42 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) & ($true != (in @ X0 @ (binunion @ X2 @ X1)))) => (($true = (in @ sK0 @ sK1)) & ($true != (in @ sK0 @ (binunion @ sK2 @ sK1))))),
% 1.66/1.42 introduced(definition,[],[choice_axiom])).
% 1.66/1.42 thf(f16,plain,(
% 1.66/1.42 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) & ($true != (in @ X0 @ (binunion @ X2 @ X1)))) & (setunionI = $true) & (upairset2IR = $true)),
% 1.66/1.42 inference(flattening,[status(thm)],[f15])).
% 1.66/1.42 thf(f15,plain,(
% 1.66/1.42 (? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) & ($true != (in @ X0 @ (binunion @ X2 @ X1)))) & (upairset2IR = $true)) & (setunionI = $true)),
% 1.66/1.42 inference(ennf_transformation,[status(thm)],[f12])).
% 1.66/1.42 thf(f12,plain,(
% 1.66/1.42 ~((setunionI = $true) => ((upairset2IR = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) => ($true = (in @ X0 @ (binunion @ X2 @ X1))))))),
% 1.66/1.42 inference(fool_elimination,[status(thm)],[f11])).
% 1.66/1.42 thf(f11,plain,(
% 1.66/1.42 ~(setunionI => (upairset2IR => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => (in @ X0 @ (binunion @ X2 @ X1)))))),
% 1.66/1.42 inference(rectify,[status(thm)],[f5])).
% 1.66/1.42 thf(f5,negated_conjecture,(
% 1.66/1.42 ~(setunionI => (upairset2IR => ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X1 @ X2) => (in @ X1 @ (binunion @ X0 @ X2)))))),
% 1.66/1.42 inference(negated_conjecture,[status(cth)],[f4])).
% 1.66/1.42 thf(f4,conjecture,(
% 1.66/1.42 setunionI => (upairset2IR => ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X1 @ X2) => (in @ X1 @ (binunion @ X0 @ X2))))),
% 1.66/1.42 file('/export/starexec/sandbox/tmp/tmp.dDm7TSe8sr/DTF2THF_29133.p',binunionIR)).
% 1.66/1.42 thf(f48,plain,(
% 1.66/1.42 ((in @ sK0 @ sK1) = $false)),
% 1.66/1.42 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 1.66/1.42 thf(f46,plain,(
% 1.66/1.42 ((in @ sK0 @ sK1) = $false) | ($true = $false)),
% 1.66/1.42 inference(superposition,[status(thm)],[f32,f44])).
% 1.66/1.42 thf(f44,plain,(
% 1.66/1.42 ( ! [X0 : $i] : (((in @ X0 @ (setadjoin @ sK2 @ (setadjoin @ sK1 @ emptyset))) = $false) | ($false = (in @ sK0 @ X0))) )),
% 1.66/1.42 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.66/1.42 thf(f42,plain,(
% 1.66/1.42 ( ! [X0 : $i] : (((in @ X0 @ (setadjoin @ sK2 @ (setadjoin @ sK1 @ emptyset))) = $false) | ($false = (in @ sK0 @ X0)) | ($true != $true)) )),
% 1.66/1.42 inference(superposition,[status(thm)],[f41,f40])).
% 1.66/1.42 thf(f40,plain,(
% 1.66/1.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (in @ X3 @ (setunion @ X1))) | ((in @ X2 @ X1) = $false) | ((in @ X3 @ X2) = $false)) )),
% 1.66/1.42 inference(binary_proxy_clausification,[status(thm)],[f39])).
% 1.66/1.42 thf(f39,plain,(
% 1.66/1.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X2 @ X1) => (in @ X3 @ (setunion @ X1)))) | ((in @ X3 @ X2) = $false)) )),
% 1.66/1.42 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 1.66/1.42 thf(f38,plain,(
% 1.66/1.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X3 @ X2) => ((in @ X2 @ X1) => (in @ X3 @ (setunion @ X1)))))) )),
% 1.66/1.42 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.66/1.42 thf(f37,plain,(
% 1.66/1.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ X2 @ X1) => (in @ Y0 @ (setunion @ X1))))) @ X3))) )),
% 1.66/1.42 inference(pi_clausification,[status(thm)],[f36])).
% 1.66/1.42 thf(f36,plain,(
% 1.66/1.42 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ X2 @ X1) => (in @ Y0 @ (setunion @ X1)))))))) )),
% 1.66/1.42 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.66/1.42 thf(f35,plain,(
% 1.66/1.42 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ X1) => (in @ Y1 @ (setunion @ X1))))))) @ X2))) )),
% 1.66/1.42 inference(pi_clausification,[status(thm)],[f34])).
% 1.66/1.42 thf(f34,plain,(
% 1.66/1.42 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ X1) => (in @ Y1 @ (setunion @ X1)))))))))) )),
% 1.66/1.42 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.66/1.42 thf(f33,plain,(
% 1.66/1.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0))))))))) @ X1))) )),
% 1.66/1.42 inference(pi_clausification,[status(thm)],[f27])).
% 1.66/1.42 thf(f27,plain,(
% 1.66/1.42 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))))),
% 1.66/1.42 inference(definition_unfolding,[status(thm)],[f24,f20])).
% 1.66/1.42 thf(f20,plain,(
% 1.66/1.42 (setunionI = $true)),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f18])).
% 1.66/1.42 thf(f24,plain,(
% 1.66/1.42 (setunionI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))))),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f14])).
% 1.66/1.42 thf(f14,plain,(
% 1.66/1.42 (setunionI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))))),
% 1.66/1.42 inference(fool_elimination,[status(thm)],[f13])).
% 1.66/1.42 thf(f13,plain,(
% 1.66/1.42 (setunionI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => ((in @ X1 @ X2) => (in @ X0 @ (setunion @ X2)))))),
% 1.66/1.42 inference(rectify,[status(thm)],[f1])).
% 1.66/1.42 thf(f1,axiom,(
% 1.66/1.42 (setunionI = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X1 @ X2) => ((in @ X2 @ X0) => (in @ X1 @ (setunion @ X0)))))),
% 1.66/1.42 file('/export/starexec/sandbox/tmp/tmp.dDm7TSe8sr/DTF2THF_29133.p',setunionI)).
% 1.66/1.42 thf(f41,plain,(
% 1.66/1.42 ($true != (in @ sK0 @ (setunion @ (setadjoin @ sK2 @ (setadjoin @ sK1 @ emptyset)))))),
% 1.66/1.42 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.66/1.42 thf(f26,plain,(
% 1.66/1.42 ($true != (in @ sK0 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setunion @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))) @ sK2 @ sK1)))),
% 1.66/1.42 inference(definition_unfolding,[status(thm)],[f21,f23])).
% 1.66/1.42 thf(f23,plain,(
% 1.66/1.42 (binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (setunion @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f10])).
% 1.66/1.42 thf(f10,plain,(
% 1.66/1.42 (binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (setunion @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))),
% 1.66/1.42 inference(fool_elimination,[status(thm)],[f9])).
% 1.66/1.42 thf(f9,plain,(
% 1.66/1.42 ((^[X0 : $i, X1 : $i] : (setunion @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) = binunion)),
% 1.66/1.42 inference(rectify,[status(thm)],[f2])).
% 1.66/1.42 thf(f2,axiom,(
% 1.66/1.42 ((^[X1 : $i, X3 : $i] : (setunion @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)))) = binunion)),
% 1.66/1.42 file('/export/starexec/sandbox/tmp/tmp.dDm7TSe8sr/DTF2THF_29133.p',binunion)).
% 1.66/1.42 thf(f21,plain,(
% 1.66/1.42 ($true != (in @ sK0 @ (binunion @ sK2 @ sK1)))),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f18])).
% 1.66/1.42 thf(f32,plain,(
% 1.66/1.42 ( ! [X2 : $i,X1 : $i] : (($true = (in @ X2 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))))) )),
% 1.66/1.42 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.66/1.42 thf(f31,plain,(
% 1.66/1.42 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (in @ Y0 @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)))) @ X2))) )),
% 1.66/1.42 inference(pi_clausification,[status(thm)],[f30])).
% 1.66/1.42 thf(f30,plain,(
% 1.66/1.42 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset))))))) )),
% 1.66/1.42 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.66/1.42 thf(f29,plain,(
% 1.66/1.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))) @ X1))) )),
% 1.66/1.42 inference(pi_clausification,[status(thm)],[f28])).
% 1.66/1.42 thf(f28,plain,(
% 1.66/1.42 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))),
% 1.66/1.42 inference(definition_unfolding,[status(thm)],[f25,f19])).
% 1.66/1.42 thf(f19,plain,(
% 1.66/1.42 (upairset2IR = $true)),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f18])).
% 1.66/1.42 thf(f25,plain,(
% 1.66/1.42 (upairset2IR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))),
% 1.66/1.42 inference(cnf_transformation,[status(thm)],[f8])).
% 1.66/1.42 thf(f8,plain,(
% 1.66/1.42 (upairset2IR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))),
% 1.66/1.42 inference(fool_elimination,[status(thm)],[f7])).
% 1.66/1.42 thf(f7,plain,(
% 1.66/1.42 (upairset2IR = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))))),
% 1.66/1.42 inference(rectify,[status(thm)],[f3])).
% 1.66/1.42 thf(f3,axiom,(
% 1.66/1.42 (upairset2IR = ! [X3 : $i,X1 : $i] : (in @ X3 @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset))))),
% 1.66/1.42 file('/export/starexec/sandbox/tmp/tmp.dDm7TSe8sr/DTF2THF_29133.p',upairset2IR)).
% 1.66/1.42 % SZS output end Proof for DTF2THF_29133
% 1.66/1.42 % (29231)------------------------------
% 1.66/1.42 % (29231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.42 % (29231)Termination reason: Refutation
% 1.66/1.42
% 1.66/1.42 % (29231)Memory used [KB]: 5500
% 1.66/1.42 % (29231)Time elapsed: 0.006 s
% 1.66/1.42 % (29231)Instructions burned: 4 (million)
% 1.66/1.42 % (29231)------------------------------
% 1.66/1.42 % (29231)------------------------------
% 1.66/1.42 % (29230)Success in time 0.019 s
%------------------------------------------------------------------------------