%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU636^2 : 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 : 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 09:35:48 AM UTC 2026
% Result : Theorem 1.46s 1.29s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 244 ( 76 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 276 ( 10 ~; 9 |; 9 &; 202 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 9 usr; 8 con; 0-2 aty)
% ( 14 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 53 ( 18 ^; 32 !; 3 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
setadjoin: $i > $i > $i ).
thf(func_def_2,type,
setunion: $i > $i ).
thf(func_def_3,type,
subset: $i > $i > $o ).
thf(func_def_8,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(f56,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
sK0 != sK0,
inference(superposition,[status(thm)],[f23,f51]) ).
thf(f51,plain,
! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) ),
inference(superposition,[status(thm)],[f45,f37]) ).
thf(f37,plain,
! [X1: $i] :
( ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( subset @ Y0 @ ( setunion @ ( setadjoin @ Y0 @ emptyset ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( subset @ Y0 @ ( setunion @ ( setadjoin @ Y0 @ emptyset ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f25,f19]) ).
thf(f19,plain,
( setunionsingleton2
= ( !! @ $i
@ ^ [Y0: $i] : ( subset @ Y0 @ ( setunion @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( setunionsingleton2
= ( !! @ $i
@ ^ [Y0: $i] : ( subset @ Y0 @ ( setunion @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i] :
( ( subset @ X0 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) )
= setunionsingleton2 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $i] :
( ( subset @ X0 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) )
= setunionsingleton2 ),
file('/export/starexec/sandbox/tmp/tmp.t0CoxlCKMV/DTF2THF_16715.p',setunionsingleton2) ).
thf(f25,plain,
setunionsingleton2 = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( ( setunion @ ( setadjoin @ sK0 @ emptyset ) )
!= sK0 )
& ( setextsub = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f16,f17]) ).
thf(f17,plain,
( ? [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
!= X0 )
=> ( ( setunion @ ( setadjoin @ sK0 @ emptyset ) )
!= sK0 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ? [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
!= X0 )
& ( setextsub = $true ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
!= X0 )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setextsub = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( setextsub = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( setextsub
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( setextsub
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( setextsub
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ! [X2: $i] :
( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
= X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.t0CoxlCKMV/DTF2THF_16715.p',setunionsingleton) ).
thf(f45,plain,
! [X0: $i] :
( ( ( subset @ X0 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) )
= $false )
| ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: $i] :
( ( ( subset @ X0 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) )
= $false )
| ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f35,f39]) ).
thf(f39,plain,
! [X1: $i] :
( ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( subset @ ( setunion @ ( setadjoin @ Y0 @ emptyset ) ) @ Y0 )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( subset @ ( setunion @ ( setadjoin @ Y0 @ emptyset ) ) @ Y0 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f24,f21]) ).
thf(f21,plain,
( setunionsingleton1
= ( !! @ $i
@ ^ [Y0: $i] : ( subset @ ( setunion @ ( setadjoin @ Y0 @ emptyset ) ) @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( setunionsingleton1
= ( !! @ $i
@ ^ [Y0: $i] : ( subset @ ( setunion @ ( setadjoin @ Y0 @ emptyset ) ) @ Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i] :
( ( subset @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) @ X0 )
= setunionsingleton1 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i] :
( ( subset @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) @ X0 )
= setunionsingleton1 ),
file('/export/starexec/sandbox/tmp/tmp.t0CoxlCKMV/DTF2THF_16715.p',setunionsingleton1) ).
thf(f24,plain,
setunionsingleton1 = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f35,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
= $false )
| ( ( subset @ X1 @ X2 )
= $false )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X1: $i] :
( ( ( X2 = X1 )
= $true )
| ( ( subset @ X2 @ X1 )
= $false )
| ( ( subset @ X1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
= $false )
| ( ( ( subset @ X1 @ X2 )
=> ( X2 = X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
=> ( ( subset @ X1 @ X2 )
=> ( X2 = X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( subset @ X1 @ Y0 )
=> ( Y0 = X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ Y0 @ X1 )
=> ( ( subset @ X1 @ Y0 )
=> ( Y0 = X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f22,f20]) ).
thf(f20,plain,
( setextsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( setextsub
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y1 @ Y0 )
=> ( ( subset @ Y0 @ Y1 )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( setextsub
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setextsub
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.t0CoxlCKMV/DTF2THF_16715.p',setextsub) ).
thf(f22,plain,
setextsub = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f23,plain,
( ( setunion @ ( setadjoin @ sK0 @ emptyset ) )
!= sK0 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU636^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n025.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 12:29:27 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
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SEU636^2 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.46 % Domain : Set Theory
% 0.31/0.46 % Problem : Ordered Pairs - Singletons
% 0.31/0.46 % Version : Especial > Reduced > Especial.
% 0.31/0.46 % English : (! x:i.setunion (setadjoin x emptyset) = x)
% 0.31/0.46
% 0.31/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.31/0.46 % Source : [Bro08]
% 0.31/0.46 % Names : ZFC138l [Bro08]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 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
% 0.31/0.46 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.31/0.46 % Number of atoms : 15 ( 5 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 4 ( 3 avg)
% 0.31/0.46 % Number of connectives : 22 ( 0 ~; 0 |; 0 &; 17 @)
% 0.31/0.46 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 5 ( 2 avg)
% 0.31/0.46 % Number of types : 2 ( 0 usr)
% 0.31/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 8 ( 7 usr; 4 con; 0-2 aty)
% 0.31/0.46 % Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : http://mathgate.info/detsetitem.php?id=193
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(emptyset_type,type,
% 0.31/0.46 emptyset: $i ).
% 0.31/0.46
% 0.31/0.46 thf(setadjoin_type,type,
% 0.31/0.46 setadjoin: $i > $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(setunion_type,type,
% 0.31/0.46 setunion: $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(subset_type,type,
% 0.31/0.46 subset: $i > $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(setextsub_type,type,
% 0.31/0.46 setextsub: $o ).
% 0.31/0.46
% 0.31/0.46 thf(setextsub,definition,
% 0.31/0.46 ( setextsub
% 0.31/0.46 = ( ! [A: $i,B: $i] :
% 0.31/0.46 ( ( subset @ A @ B )
% 0.31/0.46 => ( ( subset @ B @ A )
% 0.31/0.46 => ( A = B ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(setunionsingleton1_type,type,
% 0.31/0.46 setunionsingleton1: $o ).
% 0.31/0.46
% 0.31/0.46 thf(setunionsingleton1,definition,
% 0.31/0.46 ( setunionsingleton1
% 0.31/0.46 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(setunionsingleton2_type,type,
% 0.31/0.46 setunionsingleton2: $o ).
% 0.31/0.46
% 0.31/0.46 thf(setunionsingleton2,definition,
% 0.31/0.46 ( setunionsingleton2
% 0.31/0.46 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(setunionsingleton,conjecture,
% 0.31/0.46 ( setextsub
% 0.31/0.46 => ( setunionsingleton1
% 0.31/0.46 => ( setunionsingleton2
% 0.31/0.46 => ! [Xx: $i] :
% 0.31/0.46 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.31/0.46 = Xx ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.46/1.26 ---- Embedded in THF ---
% 1.46/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.26 %%% Generated on Tue Feb 24 12:29:28 EST 2026
% 1.46/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.26 %%% Logic specification used:
% 1.46/1.26 %%% thf(spec, logic, $$dhol).
% 1.46/1.26
% 1.46/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.t0CoxlCKMV/DTF2DTF16715.p
% See solution above
% 1.46/1.27 ------------------------
% 1.46/1.27 ---- Cleaned THF ---
% 1.46/1.27 thf(emptyset_type,type,
% 1.46/1.27 emptyset: $i ).
% 1.46/1.27
% 1.46/1.27 thf(setadjoin_type,type,
% 1.46/1.27 setadjoin: $i > $i > $i ).
% 1.46/1.27
% 1.46/1.27 thf(setunion_type,type,
% 1.46/1.27 setunion: $i > $i ).
% 1.46/1.27
% 1.46/1.27 thf(subset_type,type,
% 1.46/1.27 subset: $i > $i > $o ).
% 1.46/1.27
% 1.46/1.27 thf(setextsub_type,type,
% 1.46/1.27 setextsub: $o ).
% 1.46/1.27
% 1.46/1.27 thf(setextsub,definition,
% 1.46/1.27 ( setextsub
% 1.46/1.27 = ( ! [A: $i,B: $i] :
% 1.46/1.27 ( ( subset @ A @ B )
% 1.46/1.27 => ( ( subset @ B @ A )
% 1.46/1.27 => ( A = B ) ) ) ) ) ).
% 1.46/1.27
% 1.46/1.27 thf(setunionsingleton1_type,type,
% 1.46/1.27 setunionsingleton1: $o ).
% 1.46/1.27
% 1.46/1.27 thf(setunionsingleton1,definition,
% 1.46/1.27 ( setunionsingleton1
% 1.46/1.27 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 1.46/1.27
% 1.46/1.27 thf(setunionsingleton2_type,type,
% 1.46/1.27 setunionsingleton2: $o ).
% 1.46/1.27
% 1.46/1.27 thf(setunionsingleton2,definition,
% 1.46/1.27 ( setunionsingleton2
% 1.46/1.27 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 1.46/1.27
% 1.46/1.27 thf(setunionsingleton,conjecture,
% 1.46/1.27 ( setextsub
% 1.46/1.27 => ( setunionsingleton1
% 1.46/1.27 => ( setunionsingleton2
% 1.46/1.27 => ! [Xx: $i] :
% 1.46/1.27 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 1.46/1.27 = Xx ) ) ) ) ).
% 1.46/1.27 ------------------------
% 1.46/1.29 % (16994)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_16715 for (2999ds/4Mi)
% 1.46/1.29 % (16995)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_16715 for (2999ds/27Mi)
% 1.46/1.29 % (16994)Instruction limit reached!
% 1.46/1.29 % (16994)------------------------------
% 1.46/1.29 % (16994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (16994)Termination reason: Unknown
% 1.46/1.29 % (16994)Termination phase: Saturation
% 1.46/1.29
% 1.46/1.29 % (16994)Memory used [KB]: 5500
% 1.46/1.29 % (16994)Time elapsed: 0.003 s
% 1.46/1.29 % (16994)Instructions burned: 4 (million)
% 1.46/1.29 % (16994)------------------------------
% 1.46/1.29 % (16994)------------------------------
% 1.46/1.29 % (16995)First to succeed.
% 1.46/1.29 % (16995)Refutation found. Thanks to Tanya!
% 1.46/1.29 % SZS status Theorem for DTF2THF_16715
% 1.46/1.29 % SZS output start Proof for DTF2THF_16715
% 1.46/1.29 thf(func_def_1, type, setadjoin: $i > $i > $i).
% 1.46/1.29 thf(func_def_2, type, setunion: $i > $i).
% 1.46/1.29 thf(func_def_3, type, subset: $i > $i > $o).
% 1.46/1.29 thf(func_def_8, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.46/1.29 thf(f56,plain,(
% 1.46/1.29 $false),
% 1.46/1.29 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.46/1.29 thf(f55,plain,(
% 1.46/1.29 (sK0 != sK0)),
% 1.46/1.29 inference(superposition,[status(thm)],[f23,f51])).
% 1.46/1.29 thf(f51,plain,(
% 1.46/1.29 ( ! [X0 : $i] : (((setunion @ (setadjoin @ X0 @ emptyset)) = X0)) )),
% 1.46/1.29 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.46/1.29 thf(f49,plain,(
% 1.46/1.29 ( ! [X0 : $i] : (($true = $false) | ((setunion @ (setadjoin @ X0 @ emptyset)) = X0)) )),
% 1.46/1.29 inference(superposition,[status(thm)],[f45,f37])).
% 1.46/1.29 thf(f37,plain,(
% 1.46/1.29 ( ! [X1 : $i] : (((subset @ X1 @ (setunion @ (setadjoin @ X1 @ emptyset))) = $true)) )),
% 1.46/1.29 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.46/1.29 thf(f36,plain,(
% 1.46/1.29 ( ! [X1 : $i] : ((((^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset)))) @ X1) = $true)) )),
% 1.46/1.29 inference(pi_clausification,[status(thm)],[f26])).
% 1.46/1.29 thf(f26,plain,(
% 1.46/1.29 ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) = $true)),
% 1.46/1.29 inference(definition_unfolding,[status(thm)],[f25,f19])).
% 1.46/1.29 thf(f19,plain,(
% 1.46/1.29 (setunionsingleton2 = (!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))))),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f14])).
% 1.46/1.29 thf(f14,plain,(
% 1.46/1.29 (setunionsingleton2 = (!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))))),
% 1.46/1.29 inference(fool_elimination,[status(thm)],[f13])).
% 1.46/1.29 thf(f13,plain,(
% 1.46/1.29 (! [X0 : $i] : (subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset))) = setunionsingleton2)),
% 1.46/1.29 inference(rectify,[status(thm)],[f3])).
% 1.46/1.29 thf(f3,axiom,(
% 1.46/1.29 (! [X0 : $i] : (subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset))) = setunionsingleton2)),
% 1.46/1.29 file('/export/starexec/sandbox/tmp/tmp.t0CoxlCKMV/DTF2THF_16715.p',setunionsingleton2)).
% 1.46/1.29 thf(f25,plain,(
% 1.46/1.29 (setunionsingleton2 = $true)),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f18])).
% 1.46/1.29 thf(f18,plain,(
% 1.46/1.29 (setunionsingleton2 = $true) & (setunionsingleton1 = $true) & ((setunion @ (setadjoin @ sK0 @ emptyset)) != sK0) & (setextsub = $true)),
% 1.46/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f16,f17])).
% 1.46/1.29 thf(f17,plain,(
% 1.46/1.29 ? [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) != X0) => ((setunion @ (setadjoin @ sK0 @ emptyset)) != sK0)),
% 1.46/1.29 introduced(definition,[],[choice_axiom])).
% 1.46/1.29 thf(f16,plain,(
% 1.46/1.29 (setunionsingleton2 = $true) & (setunionsingleton1 = $true) & ? [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) != X0) & (setextsub = $true)),
% 1.46/1.29 inference(flattening,[status(thm)],[f15])).
% 1.46/1.29 thf(f15,plain,(
% 1.46/1.29 ((? [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) != X0) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setextsub = $true)),
% 1.46/1.29 inference(ennf_transformation,[status(thm)],[f8])).
% 1.46/1.29 thf(f8,plain,(
% 1.46/1.29 ~((setextsub = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ! [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0))))),
% 1.46/1.29 inference(fool_elimination,[status(thm)],[f7])).
% 1.46/1.29 thf(f7,plain,(
% 1.46/1.29 ~(setextsub => (setunionsingleton1 => (setunionsingleton2 => ! [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0))))),
% 1.46/1.29 inference(rectify,[status(thm)],[f5])).
% 1.46/1.29 thf(f5,negated_conjecture,(
% 1.46/1.29 ~(setextsub => (setunionsingleton1 => (setunionsingleton2 => ! [X2 : $i] : ((setunion @ (setadjoin @ X2 @ emptyset)) = X2))))),
% 1.46/1.29 inference(negated_conjecture,[status(cth)],[f4])).
% 1.46/1.29 thf(f4,conjecture,(
% 1.46/1.29 setextsub => (setunionsingleton1 => (setunionsingleton2 => ! [X2 : $i] : ((setunion @ (setadjoin @ X2 @ emptyset)) = X2)))),
% 1.46/1.29 file('/export/starexec/sandbox/tmp/tmp.t0CoxlCKMV/DTF2THF_16715.p',setunionsingleton)).
% 1.46/1.29 thf(f45,plain,(
% 1.46/1.29 ( ! [X0 : $i] : (((subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset))) = $false) | ((setunion @ (setadjoin @ X0 @ emptyset)) = X0)) )),
% 1.46/1.29 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.46/1.29 thf(f41,plain,(
% 1.46/1.29 ( ! [X0 : $i] : (((subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset))) = $false) | ((setunion @ (setadjoin @ X0 @ emptyset)) = X0) | ($true = $false)) )),
% 1.46/1.29 inference(superposition,[status(thm)],[f35,f39])).
% 1.46/1.29 thf(f39,plain,(
% 1.46/1.29 ( ! [X1 : $i] : (((subset @ (setunion @ (setadjoin @ X1 @ emptyset)) @ X1) = $true)) )),
% 1.46/1.29 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.46/1.29 thf(f38,plain,(
% 1.46/1.29 ( ! [X1 : $i] : ((((^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0)) @ X1) = $true)) )),
% 1.46/1.29 inference(pi_clausification,[status(thm)],[f27])).
% 1.46/1.29 thf(f27,plain,(
% 1.46/1.29 ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) = $true)),
% 1.46/1.29 inference(definition_unfolding,[status(thm)],[f24,f21])).
% 1.46/1.29 thf(f21,plain,(
% 1.46/1.29 (setunionsingleton1 = (!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))))),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f12])).
% 1.46/1.29 thf(f12,plain,(
% 1.46/1.29 (setunionsingleton1 = (!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))))),
% 1.46/1.29 inference(fool_elimination,[status(thm)],[f11])).
% 1.46/1.29 thf(f11,plain,(
% 1.46/1.29 (! [X0 : $i] : (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0) = setunionsingleton1)),
% 1.46/1.29 inference(rectify,[status(thm)],[f2])).
% 1.46/1.29 thf(f2,axiom,(
% 1.46/1.29 (! [X0 : $i] : (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0) = setunionsingleton1)),
% 1.46/1.29 file('/export/starexec/sandbox/tmp/tmp.t0CoxlCKMV/DTF2THF_16715.p',setunionsingleton1)).
% 1.46/1.29 thf(f24,plain,(
% 1.46/1.29 (setunionsingleton1 = $true)),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f18])).
% 1.46/1.29 thf(f35,plain,(
% 1.46/1.29 ( ! [X2 : $i,X1 : $i] : (((subset @ X2 @ X1) = $false) | ((subset @ X1 @ X2) = $false) | (X1 = X2)) )),
% 1.46/1.29 inference(equality_proxy_clausification,[status(thm)],[f34])).
% 1.46/1.29 thf(f34,plain,(
% 1.46/1.29 ( ! [X2 : $i,X1 : $i] : (((X2 = X1) = $true) | ((subset @ X2 @ X1) = $false) | ((subset @ X1 @ X2) = $false)) )),
% 1.46/1.29 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.46/1.29 thf(f33,plain,(
% 1.46/1.29 ( ! [X2 : $i,X1 : $i] : (((subset @ X2 @ X1) = $false) | (((subset @ X1 @ X2) => (X2 = X1)) = $true)) )),
% 1.46/1.29 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.46/1.29 thf(f32,plain,(
% 1.46/1.29 ( ! [X2 : $i,X1 : $i] : ((((subset @ X2 @ X1) => ((subset @ X1 @ X2) => (X2 = X1))) = $true)) )),
% 1.46/1.29 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.46/1.29 thf(f31,plain,(
% 1.46/1.29 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((subset @ Y0 @ X1) => ((subset @ X1 @ Y0) => (Y0 = X1)))) @ X2) = $true)) )),
% 1.46/1.29 inference(pi_clausification,[status(thm)],[f30])).
% 1.46/1.29 thf(f30,plain,(
% 1.46/1.29 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ X1) => ((subset @ X1 @ Y0) => (Y0 = X1))))))) )),
% 1.46/1.29 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.46/1.29 thf(f29,plain,(
% 1.46/1.29 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0)))))) @ X1) = $true)) )),
% 1.46/1.29 inference(pi_clausification,[status(thm)],[f28])).
% 1.46/1.29 thf(f28,plain,(
% 1.46/1.29 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) = $true)),
% 1.46/1.29 inference(definition_unfolding,[status(thm)],[f22,f20])).
% 1.46/1.29 thf(f20,plain,(
% 1.46/1.29 (setextsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))))),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f10])).
% 1.46/1.29 thf(f10,plain,(
% 1.46/1.29 (setextsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))))),
% 1.46/1.29 inference(fool_elimination,[status(thm)],[f9])).
% 1.46/1.29 thf(f9,plain,(
% 1.46/1.29 (setextsub = ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))))),
% 1.46/1.29 inference(rectify,[status(thm)],[f1])).
% 1.46/1.29 thf(f1,axiom,(
% 1.46/1.29 (setextsub = ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))))),
% 1.46/1.29 file('/export/starexec/sandbox/tmp/tmp.t0CoxlCKMV/DTF2THF_16715.p',setextsub)).
% 1.46/1.29 thf(f22,plain,(
% 1.46/1.29 (setextsub = $true)),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f18])).
% 1.46/1.29 thf(f23,plain,(
% 1.46/1.29 ((setunion @ (setadjoin @ sK0 @ emptyset)) != sK0)),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f18])).
% 1.46/1.29 % SZS output end Proof for DTF2THF_16715
% 1.46/1.29 % (16995)------------------------------
% 1.46/1.29 % (16995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (16995)Termination reason: Refutation
% 1.46/1.29
% 1.46/1.29 % (16995)Memory used [KB]: 5500
% 1.46/1.29 % (16995)Time elapsed: 0.004 s
% 1.46/1.29 % (16995)Instructions burned: 5 (million)
% 1.46/1.29 % (16995)------------------------------
% 1.46/1.29 % (16995)------------------------------
% 1.46/1.29 % (16992)Success in time 0.013 s
%------------------------------------------------------------------------------