%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU621^2 : 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 : n004.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 09:35:40 AM UTC 2026
% Result : Theorem 1.70s 1.44s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 457 ( 135 equ; 0 cnn)
% Maximal formula atoms : 8 ( 10 avg)
% Number of connectives : 440 ( 55 ~; 45 |; 33 &; 278 @)
% ( 4 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 90 ( 0 ^; 68 !; 22 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_5,type,
subset: $i > $i > $o ).
thf(func_def_15,type,
sK6: $i > $i > $i ).
thf(f58,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f57,f29]) ).
thf(f29,plain,
( ( subset @ ( setadjoin @ sK0 @ emptyset ) @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $true
= ( in @ sK0 @ sK1 ) )
& ( ( subset @ ( setadjoin @ sK0 @ emptyset ) @ sK1 )
!= $true )
& ( subsetI2 = $true )
& ( uniqinunit = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f16]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( ( subset @ ( setadjoin @ X0 @ emptyset ) @ X1 )
!= $true ) )
=> ( ( $true
= ( in @ sK0 @ sK1 ) )
& ( ( subset @ ( setadjoin @ sK0 @ emptyset ) @ sK1 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( ( subset @ ( setadjoin @ X0 @ emptyset ) @ X1 )
!= $true ) )
& ( subsetI2 = $true )
& ( uniqinunit = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( ( subset @ ( setadjoin @ X0 @ emptyset ) @ X1 )
!= $true ) )
& ( subsetI2 = $true )
& ( uniqinunit = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( uniqinunit = $true )
=> ( ( subsetI2 = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( subset @ ( setadjoin @ X0 @ emptyset ) @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( uniqinunit
=> ( subsetI2
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ X1 )
=> ( subset @ ( setadjoin @ X0 @ emptyset ) @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( uniqinunit
=> ( subsetI2
=> ! [X0: $i,X2: $i] :
( ( in @ X0 @ X2 )
=> ( subset @ ( setadjoin @ X0 @ emptyset ) @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( uniqinunit
=> ( subsetI2
=> ! [X0: $i,X2: $i] :
( ( in @ X0 @ X2 )
=> ( subset @ ( setadjoin @ X0 @ emptyset ) @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.d1PGr4SD66/DTF2THF_5301.p',singletonsubset) ).
thf(f57,plain,
( ( subset @ ( setadjoin @ sK0 @ emptyset ) @ sK1 )
= $true ),
inference(subsumption_resolution,[status(thm)],[f56,f30]) ).
thf(f30,plain,
( $true
= ( in @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f56,plain,
( ( $true
!= ( in @ sK0 @ sK1 ) )
| ( ( subset @ ( setadjoin @ sK0 @ emptyset ) @ sK1 )
= $true ) ),
inference(superposition,[status(thm)],[f46,f54]) ).
thf(f54,plain,
( sK0
= ( sK6 @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( sK0
= ( sK6 @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f29,f52]) ).
thf(f52,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( setadjoin @ X1 @ emptyset ) @ X0 )
= $true )
| ( ( sK6 @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( setadjoin @ X1 @ emptyset ) @ X0 )
= $true )
| ( $true != $true )
| ( ( sK6 @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= X1 ) ),
inference(superposition,[status(thm)],[f45,f47]) ).
thf(f47,plain,
! [X3: $i,X4: $i] :
( ( $true
= ( in @ ( sK6 @ X4 @ X3 ) @ X3 ) )
| ( $true
= ( subset @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
! [X3: $i,X4: $i] :
( ( $true != $true )
| ( $true
= ( subset @ X3 @ X4 ) )
| ( $true
= ( in @ ( sK6 @ X4 @ X3 ) @ X3 ) ) ),
inference(definition_unfolding,[status(thm)],[f34,f28]) ).
thf(f28,plain,
subsetI2 = $true,
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f34,plain,
! [X3: $i,X4: $i] :
( ( $true
= ( in @ ( sK6 @ X4 @ X3 ) @ X3 ) )
| ( $true
= ( subset @ X3 @ X4 ) )
| ( subsetI2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( subsetI2 = $true )
| ( ! [X2: $i] :
( ( $true
= ( in @ X2 @ sK5 ) )
| ( $true
!= ( in @ X2 @ sK4 ) ) )
& ( ( subset @ sK4 @ sK5 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( $true
!= ( in @ ( sK6 @ X4 @ X3 ) @ X4 ) )
& ( $true
= ( in @ ( sK6 @ X4 @ X3 ) @ X3 ) ) )
| ( $true
= ( subset @ X3 @ X4 ) ) )
| ( subsetI2 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f23,f25,f24]) ).
thf(f24,plain,
( ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ( ( subset @ X0 @ X1 )
!= $true ) )
=> ( ! [X2: $i] :
( ( $true
= ( in @ X2 @ sK5 ) )
| ( $true
!= ( in @ X2 @ sK4 ) ) )
& ( ( subset @ sK4 @ sK5 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
& ( $true
= ( in @ X5 @ X3 ) ) )
=> ( ( $true
!= ( in @ ( sK6 @ X4 @ X3 ) @ X4 ) )
& ( $true
= ( in @ ( sK6 @ X4 @ X3 ) @ X3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ( ( subsetI2 = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ( ( subset @ X0 @ X1 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
& ( $true
= ( in @ X5 @ X3 ) ) )
| ( $true
= ( subset @ X3 @ X4 ) ) )
| ( subsetI2 != $true ) ) ),
inference(rectify,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( subsetI2 = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ( ( subset @ X0 @ X1 )
!= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
& ( ( in @ X2 @ X0 )
= $true ) )
| ( ( subset @ X0 @ X1 )
= $true ) )
| ( subsetI2 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( subsetI2 = $true )
<=> ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
& ( ( in @ X2 @ X0 )
= $true ) )
| ( ( subset @ X0 @ X1 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( $true
= ( in @ X2 @ X1 ) ) )
=> ( ( subset @ X0 @ X1 )
= $true ) )
<=> ( subsetI2 = $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI2 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X2: $i,X3: $i] :
( ( ! [X0: $i] :
( ( in @ X0 @ X2 )
=> ( in @ X0 @ X3 ) )
=> ( subset @ X2 @ X3 ) )
= subsetI2 ),
file('/export/starexec/sandbox/tmp/tmp.d1PGr4SD66/DTF2THF_5301.p',subsetI2) ).
thf(f45,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f33,f27]) ).
thf(f27,plain,
uniqinunit = $true,
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f33,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 )
| ( uniqinunit != $true ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ( ( ( in @ sK2 @ ( setadjoin @ sK3 @ emptyset ) )
= $true )
& ( sK3 != sK2 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f19,f20]) ).
thf(f20,plain,
( ? [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= $true )
& ( X2 != X3 ) )
=> ( ( ( in @ sK2 @ ( setadjoin @ sK3 @ emptyset ) )
= $true )
& ( sK3 != sK2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ? [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= $true )
& ( X2 != X3 ) ) ) ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
& ( X0 != X1 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
<=> ( uniqinunit = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
=> ( X0 = X1 ) )
<=> ( uniqinunit = $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.d1PGr4SD66/DTF2THF_5301.p',uniqinunit) ).
thf(f46,plain,
! [X3: $i,X4: $i] :
( ( $true
!= ( in @ ( sK6 @ X4 @ X3 ) @ X4 ) )
| ( $true
= ( subset @ X3 @ X4 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
! [X3: $i,X4: $i] :
( ( $true
!= ( in @ ( sK6 @ X4 @ X3 ) @ X4 ) )
| ( $true != $true )
| ( $true
= ( subset @ X3 @ X4 ) ) ),
inference(definition_unfolding,[status(thm)],[f35,f28]) ).
thf(f35,plain,
! [X3: $i,X4: $i] :
( ( $true
!= ( in @ ( sK6 @ X4 @ X3 ) @ X4 ) )
| ( $true
= ( subset @ X3 @ X4 ) )
| ( subsetI2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU621^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n004.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:28:26 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
% 0.31/0.48 ---- Original DTF file ---
% 0.31/0.48 thf(spec,logic,$$dhol).
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 % File : SEU621^2 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.48 % Domain : Set Theory
% 0.31/0.48 % Problem : Ordered Pairs - Cartesian Products
% 0.31/0.48 % Version : Especial > Reduced > Especial.
% 0.31/0.48 % English : (! A:i.! x:i.in x A -> subset (setadjoin x emptyset) A)
% 0.31/0.48
% 0.31/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.31/0.48 % Source : [Bro08]
% 0.31/0.48 % Names : ZFC123l [Bro08]
% 0.31/0.48
% 0.31/0.48 % Status : Theorem
% 0.31/0.48 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 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 v4.0.0, 0.33 v3.7.0
% 0.31/0.48 % Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 2 def)
% 0.31/0.48 % Number of atoms : 13 ( 3 equ; 0 cnn)
% 0.31/0.48 % Maximal formula atoms : 4 ( 4 avg)
% 0.31/0.48 % Number of connectives : 22 ( 0 ~; 0 |; 0 &; 16 @)
% 0.31/0.48 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.31/0.48 % Maximal formula depth : 10 ( 4 avg)
% 0.31/0.48 % Number of types : 2 ( 0 usr)
% 0.31/0.48 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.31/0.48 % Number of symbols : 7 ( 6 usr; 3 con; 0-2 aty)
% 0.31/0.48 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.31/0.48 % SPC : TH0_THM_EQU_NAR
% 0.31/0.48
% 0.31/0.48 % Comments : http://mathgate.info/detsetitem.php?id=178
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 thf(in_type,type,
% 0.31/0.48 in: $i > $i > $o ).
% 0.31/0.48
% 0.31/0.48 thf(emptyset_type,type,
% 0.31/0.48 emptyset: $i ).
% 0.31/0.48
% 0.31/0.48 thf(setadjoin_type,type,
% 0.31/0.48 setadjoin: $i > $i > $i ).
% 0.31/0.48
% 0.31/0.48 thf(uniqinunit_type,type,
% 0.31/0.48 uniqinunit: $o ).
% 0.31/0.48
% 0.31/0.48 thf(uniqinunit,definition,
% 0.31/0.48 ( uniqinunit
% 0.31/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.31/0.48 => ( Xx = Xy ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(subset_type,type,
% 0.31/0.48 subset: $i > $i > $o ).
% 0.31/0.48
% 0.31/0.48 thf(subsetI2_type,type,
% 0.31/0.48 subsetI2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(subsetI2,definition,
% 0.31/0.48 ( subsetI2
% 0.31/0.48 = ( ! [A: $i,B: $i] :
% 0.31/0.48 ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( in @ Xx @ B ) )
% 0.31/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(singletonsubset,conjecture,
% 0.31/0.48 ( uniqinunit
% 0.31/0.48 => ( subsetI2
% 0.31/0.48 => ! [A: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 ------------------------
% 1.70/1.40 ---- Embedded in THF ---
% 1.70/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.70/1.41 %%% Generated on Tue Feb 24 12:28:27 EST 2026
% 1.70/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.70/1.41 %%% Logic specification used:
% 1.70/1.41 %%% thf(spec, logic, $$dhol).
% 1.70/1.41
% 1.70/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.d1PGr4SD66/DTF2DTF5301.p
% See solution above
% 1.70/1.41 ------------------------
% 1.70/1.41 ---- Cleaned THF ---
% 1.70/1.41 thf(in_type,type,
% 1.70/1.41 in: $i > $i > $o ).
% 1.70/1.41
% 1.70/1.41 thf(emptyset_type,type,
% 1.70/1.41 emptyset: $i ).
% 1.70/1.41
% 1.70/1.41 thf(setadjoin_type,type,
% 1.70/1.41 setadjoin: $i > $i > $i ).
% 1.70/1.41
% 1.70/1.41 thf(uniqinunit_type,type,
% 1.70/1.41 uniqinunit: $o ).
% 1.70/1.41
% 1.70/1.41 thf(uniqinunit,definition,
% 1.70/1.41 ( uniqinunit
% 1.70/1.41 = ( ! [Xx: $i,Xy: $i] :
% 1.70/1.41 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.70/1.41 => ( Xx = Xy ) ) ) ) ).
% 1.70/1.41
% 1.70/1.41 thf(subset_type,type,
% 1.70/1.41 subset: $i > $i > $o ).
% 1.70/1.41
% 1.70/1.41 thf(subsetI2_type,type,
% 1.70/1.41 subsetI2: $o ).
% 1.70/1.41
% 1.70/1.41 thf(subsetI2,definition,
% 1.70/1.41 ( subsetI2
% 1.70/1.41 = ( ! [A: $i,B: $i] :
% 1.70/1.41 ( ! [Xx: $i] :
% 1.70/1.41 ( ( in @ Xx @ A )
% 1.70/1.41 => ( in @ Xx @ B ) )
% 1.70/1.41 => ( subset @ A @ B ) ) ) ) ).
% 1.70/1.41
% 1.70/1.41 thf(singletonsubset,conjecture,
% 1.70/1.41 ( uniqinunit
% 1.70/1.41 => ( subsetI2
% 1.70/1.41 => ! [A: $i,Xx: $i] :
% 1.70/1.41 ( ( in @ Xx @ A )
% 1.70/1.41 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 1.70/1.41 ------------------------
% 1.70/1.43 % (5442)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5301 for (2999ds/18Mi)
% 1.70/1.43 % (5437)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_5301 for (2999ds/4Mi)
% 1.70/1.43 % (5441)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_5301 for (2999ds/275Mi)
% 1.70/1.43 % (5436)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5301 for (2999ds/183Mi)
% 1.70/1.43 % (5439)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5301 for (2999ds/2Mi)
% 1.70/1.43 % (5438)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_5301 for (2999ds/27Mi)
% 1.70/1.43 % (5440)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_5301 for (2999ds/2Mi)
% 1.70/1.44 % (5439)Instruction limit reached!
% 1.70/1.44 % (5439)------------------------------
% 1.70/1.44 % (5439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.44 % (5439)Termination reason: Unknown
% 1.70/1.44 % (5440)Instruction limit reached!
% 1.70/1.44 % (5440)------------------------------
% 1.70/1.44 % (5440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.44 % (5439)Termination phase: Saturation
% 1.70/1.44
% 1.70/1.44 % (5439)Memory used [KB]: 5500
% 1.70/1.44 % (5439)Time elapsed: 0.003 s
% 1.70/1.44 % (5439)Instructions burned: 2 (million)
% 1.70/1.44 % (5439)------------------------------
% 1.70/1.44 % (5439)------------------------------
% 1.70/1.44 % (5440)Termination reason: Unknown
% 1.70/1.44 % (5440)Termination phase: Saturation
% 1.70/1.44
% 1.70/1.44 % (5440)Memory used [KB]: 895
% 1.70/1.44 % (5440)Time elapsed: 0.003 s
% 1.70/1.44 % (5440)Instructions burned: 2 (million)
% 1.70/1.44 % (5440)------------------------------
% 1.70/1.44 % (5440)------------------------------
% 1.70/1.44 % (5437)Instruction limit reached!
% 1.70/1.44 % (5437)------------------------------
% 1.70/1.44 % (5437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.44 % (5437)Termination reason: Unknown
% 1.70/1.44 % (5437)Termination phase: Saturation
% 1.70/1.44
% 1.70/1.44 % (5437)Memory used [KB]: 5500
% 1.70/1.44 % (5437)Time elapsed: 0.004 s
% 1.70/1.44 % (5437)Instructions burned: 4 (million)
% 1.70/1.44 % (5437)------------------------------
% 1.70/1.44 % (5437)------------------------------
% 1.70/1.44 % (5441)First to succeed.
% 1.70/1.44 % (5436)Also succeeded, but the first one will report.
% 1.70/1.44 % (5441)Refutation found. Thanks to Tanya!
% 1.70/1.44 % SZS status Theorem for DTF2THF_5301
% 1.70/1.44 % SZS output start Proof for DTF2THF_5301
% 1.70/1.44 thf(func_def_0, type, in: $i > $i > $o).
% 1.70/1.44 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.70/1.44 thf(func_def_5, type, subset: $i > $i > $o).
% 1.70/1.44 thf(func_def_15, type, sK6: $i > $i > $i).
% 1.70/1.44 thf(f58,plain,(
% 1.70/1.44 $false),
% 1.70/1.44 inference(subsumption_resolution,[status(thm)],[f57,f29])).
% 1.70/1.44 thf(f29,plain,(
% 1.70/1.44 ((subset @ (setadjoin @ sK0 @ emptyset) @ sK1) != $true)),
% 1.70/1.44 inference(cnf_transformation,[status(thm)],[f17])).
% 1.70/1.44 thf(f17,plain,(
% 1.70/1.44 (($true = (in @ sK0 @ sK1)) & ((subset @ (setadjoin @ sK0 @ emptyset) @ sK1) != $true)) & (subsetI2 = $true) & (uniqinunit = $true)),
% 1.70/1.44 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f16])).
% 1.70/1.44 thf(f16,plain,(
% 1.70/1.44 ? [X0 : $i,X1 : $i] : (((in @ X0 @ X1) = $true) & ((subset @ (setadjoin @ X0 @ emptyset) @ X1) != $true)) => (($true = (in @ sK0 @ sK1)) & ((subset @ (setadjoin @ sK0 @ emptyset) @ sK1) != $true))),
% 1.70/1.44 introduced(definition,[],[choice_axiom])).
% 1.70/1.44 thf(f13,plain,(
% 1.70/1.44 ? [X0 : $i,X1 : $i] : (((in @ X0 @ X1) = $true) & ((subset @ (setadjoin @ X0 @ emptyset) @ X1) != $true)) & (subsetI2 = $true) & (uniqinunit = $true)),
% 1.70/1.44 inference(flattening,[status(thm)],[f12])).
% 1.70/1.44 thf(f12,plain,(
% 1.70/1.44 (? [X0 : $i,X1 : $i] : (((in @ X0 @ X1) = $true) & ((subset @ (setadjoin @ X0 @ emptyset) @ X1) != $true)) & (subsetI2 = $true)) & (uniqinunit = $true)),
% 1.70/1.44 inference(ennf_transformation,[status(thm)],[f7])).
% 1.70/1.44 thf(f7,plain,(
% 1.70/1.44 ~((uniqinunit = $true) => ((subsetI2 = $true) => ! [X0 : $i,X1 : $i] : (((in @ X0 @ X1) = $true) => ((subset @ (setadjoin @ X0 @ emptyset) @ X1) = $true))))),
% 1.70/1.44 inference(fool_elimination,[status(thm)],[f6])).
% 1.70/1.44 thf(f6,plain,(
% 1.70/1.44 ~(uniqinunit => (subsetI2 => ! [X0 : $i,X1 : $i] : ((in @ X0 @ X1) => (subset @ (setadjoin @ X0 @ emptyset) @ X1))))),
% 1.70/1.44 inference(rectify,[status(thm)],[f4])).
% 1.70/1.44 thf(f4,negated_conjecture,(
% 1.70/1.44 ~(uniqinunit => (subsetI2 => ! [X0 : $i,X2 : $i] : ((in @ X0 @ X2) => (subset @ (setadjoin @ X0 @ emptyset) @ X2))))),
% 1.70/1.44 inference(negated_conjecture,[status(cth)],[f3])).
% 1.70/1.44 thf(f3,conjecture,(
% 1.70/1.44 uniqinunit => (subsetI2 => ! [X0 : $i,X2 : $i] : ((in @ X0 @ X2) => (subset @ (setadjoin @ X0 @ emptyset) @ X2)))),
% 1.70/1.44 file('/export/starexec/sandbox/tmp/tmp.d1PGr4SD66/DTF2THF_5301.p',singletonsubset)).
% 1.70/1.44 thf(f57,plain,(
% 1.70/1.44 ((subset @ (setadjoin @ sK0 @ emptyset) @ sK1) = $true)),
% 1.70/1.44 inference(subsumption_resolution,[status(thm)],[f56,f30])).
% 1.70/1.44 thf(f30,plain,(
% 1.70/1.44 ($true = (in @ sK0 @ sK1))),
% 1.70/1.44 inference(cnf_transformation,[status(thm)],[f17])).
% 1.70/1.44 thf(f56,plain,(
% 1.70/1.44 ($true != (in @ sK0 @ sK1)) | ((subset @ (setadjoin @ sK0 @ emptyset) @ sK1) = $true)),
% 1.70/1.44 inference(superposition,[status(thm)],[f46,f54])).
% 1.70/1.44 thf(f54,plain,(
% 1.70/1.44 (sK0 = (sK6 @ sK1 @ (setadjoin @ sK0 @ emptyset)))),
% 1.70/1.44 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.70/1.44 thf(f53,plain,(
% 1.70/1.44 (sK0 = (sK6 @ sK1 @ (setadjoin @ sK0 @ emptyset))) | ($true != $true)),
% 1.70/1.44 inference(superposition,[status(thm)],[f29,f52])).
% 1.70/1.44 thf(f52,plain,(
% 1.70/1.44 ( ! [X0 : $i,X1 : $i] : (((subset @ (setadjoin @ X1 @ emptyset) @ X0) = $true) | ((sK6 @ X0 @ (setadjoin @ X1 @ emptyset)) = X1)) )),
% 1.70/1.44 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.70/1.44 thf(f49,plain,(
% 1.70/1.44 ( ! [X0 : $i,X1 : $i] : (((subset @ (setadjoin @ X1 @ emptyset) @ X0) = $true) | ($true != $true) | ((sK6 @ X0 @ (setadjoin @ X1 @ emptyset)) = X1)) )),
% 1.70/1.44 inference(superposition,[status(thm)],[f45,f47])).
% 1.70/1.44 thf(f47,plain,(
% 1.70/1.44 ( ! [X3 : $i,X4 : $i] : (($true = (in @ (sK6 @ X4 @ X3) @ X3)) | ($true = (subset @ X3 @ X4))) )),
% 1.70/1.44 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.70/1.44 thf(f44,plain,(
% 1.70/1.44 ( ! [X3 : $i,X4 : $i] : (($true != $true) | ($true = (subset @ X3 @ X4)) | ($true = (in @ (sK6 @ X4 @ X3) @ X3))) )),
% 1.70/1.44 inference(definition_unfolding,[status(thm)],[f34,f28])).
% 1.70/1.44 thf(f28,plain,(
% 1.70/1.44 (subsetI2 = $true)),
% 1.70/1.44 inference(cnf_transformation,[status(thm)],[f17])).
% 1.70/1.44 thf(f34,plain,(
% 1.70/1.44 ( ! [X3 : $i,X4 : $i] : (($true = (in @ (sK6 @ X4 @ X3) @ X3)) | ($true = (subset @ X3 @ X4)) | (subsetI2 != $true)) )),
% 1.70/1.44 inference(cnf_transformation,[status(thm)],[f26])).
% 1.70/1.44 thf(f26,plain,(
% 1.70/1.44 ((subsetI2 = $true) | (! [X2 : $i] : (($true = (in @ X2 @ sK5)) | ($true != (in @ X2 @ sK4))) & ((subset @ sK4 @ sK5) != $true))) & (! [X3 : $i,X4 : $i] : ((($true != (in @ (sK6 @ X4 @ X3) @ X4)) & ($true = (in @ (sK6 @ X4 @ X3) @ X3))) | ($true = (subset @ X3 @ X4))) | (subsetI2 != $true))),
% 1.70/1.44 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f23,f25,f24])).
% 1.70/1.44 thf(f24,plain,(
% 1.70/1.44 ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true = (in @ X2 @ X1)) | ((in @ X2 @ X0) != $true)) & ((subset @ X0 @ X1) != $true)) => (! [X2 : $i] : (($true = (in @ X2 @ sK5)) | ($true != (in @ X2 @ sK4))) & ((subset @ sK4 @ sK5) != $true))),
% 1.70/1.44 introduced(definition,[],[choice_axiom])).
% 1.70/1.44 thf(f25,plain,(
% 1.70/1.44 ! [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X4) != $true) & ($true = (in @ X5 @ X3))) => (($true != (in @ (sK6 @ X4 @ X3) @ X4)) & ($true = (in @ (sK6 @ X4 @ X3) @ X3))))),
% 1.70/1.44 introduced(definition,[],[choice_axiom])).
% 1.70/1.44 thf(f23,plain,(
% 1.70/1.44 ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true = (in @ X2 @ X1)) | ((in @ X2 @ X0) != $true)) & ((subset @ X0 @ X1) != $true))) & (! [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X4) != $true) & ($true = (in @ X5 @ X3))) | ($true = (subset @ X3 @ X4))) | (subsetI2 != $true))),
% 1.70/1.44 inference(rectify,[status(thm)],[f22])).
% 1.70/1.44 thf(f22,plain,(
% 1.70/1.44 ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true = (in @ X2 @ X1)) | ((in @ X2 @ X0) != $true)) & ((subset @ X0 @ X1) != $true))) & (! [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true != (in @ X2 @ X1)) & ((in @ X2 @ X0) = $true)) | ((subset @ X0 @ X1) = $true)) | (subsetI2 != $true))),
% 1.70/1.44 inference(nnf_transformation,[status(thm)],[f14])).
% 1.70/1.44 thf(f14,plain,(
% 1.70/1.44 (subsetI2 = $true) <=> ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true != (in @ X2 @ X1)) & ((in @ X2 @ X0) = $true)) | ((subset @ X0 @ X1) = $true))),
% 1.70/1.44 inference(ennf_transformation,[status(thm)],[f9])).
% 1.70/1.44 thf(f9,plain,(
% 1.70/1.44 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) => ($true = (in @ X2 @ X1))) => ((subset @ X0 @ X1) = $true)) <=> (subsetI2 = $true)),
% 1.70/1.44 inference(fool_elimination,[status(thm)],[f8])).
% 1.70/1.44 thf(f8,plain,(
% 1.70/1.44 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 1.70/1.44 inference(rectify,[status(thm)],[f2])).
% 1.70/1.44 thf(f2,axiom,(
% 1.70/1.44 (! [X2 : $i,X3 : $i] : (! [X0 : $i] : ((in @ X0 @ X2) => (in @ X0 @ X3)) => (subset @ X2 @ X3)) = subsetI2)),
% 1.70/1.44 file('/export/starexec/sandbox/tmp/tmp.d1PGr4SD66/DTF2THF_5301.p',subsetI2)).
% 1.70/1.44 thf(f45,plain,(
% 1.70/1.44 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true) | (X0 = X1)) )),
% 1.70/1.44 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.70/1.44 thf(f38,plain,(
% 1.70/1.44 ( ! [X0 : $i,X1 : $i] : ((X0 = X1) | ((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true) | ($true != $true)) )),
% 1.70/1.44 inference(definition_unfolding,[status(thm)],[f33,f27])).
% 1.70/1.44 thf(f27,plain,(
% 1.70/1.44 (uniqinunit = $true)),
% 1.70/1.44 inference(cnf_transformation,[status(thm)],[f17])).
% 1.70/1.44 thf(f33,plain,(
% 1.70/1.44 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true) | (X0 = X1) | (uniqinunit != $true)) )),
% 1.70/1.44 inference(cnf_transformation,[status(thm)],[f21])).
% 1.70/1.44 thf(f21,plain,(
% 1.70/1.44 (! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true) | (X0 = X1)) | (uniqinunit != $true)) & ((uniqinunit = $true) | (((in @ sK2 @ (setadjoin @ sK3 @ emptyset)) = $true) & (sK3 != sK2)))),
% 1.70/1.44 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f19,f20])).
% 1.70/1.44 thf(f20,plain,(
% 1.70/1.44 ? [X2 : $i,X3 : $i] : (((in @ X2 @ (setadjoin @ X3 @ emptyset)) = $true) & (X2 != X3)) => (((in @ sK2 @ (setadjoin @ sK3 @ emptyset)) = $true) & (sK3 != sK2))),
% 1.70/1.44 introduced(definition,[],[choice_axiom])).
% 1.70/1.44 thf(f19,plain,(
% 1.70/1.44 (! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true) | (X0 = X1)) | (uniqinunit != $true)) & ((uniqinunit = $true) | ? [X2 : $i,X3 : $i] : (((in @ X2 @ (setadjoin @ X3 @ emptyset)) = $true) & (X2 != X3)))),
% 1.70/1.44 inference(rectify,[status(thm)],[f18])).
% 1.70/1.44 thf(f18,plain,(
% 1.70/1.44 (! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true) | (X0 = X1)) | (uniqinunit != $true)) & ((uniqinunit = $true) | ? [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true) & (X0 != X1)))),
% 1.70/1.44 inference(nnf_transformation,[status(thm)],[f15])).
% 1.70/1.44 thf(f15,plain,(
% 1.70/1.44 ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true) | (X0 = X1)) <=> (uniqinunit = $true)),
% 1.70/1.44 inference(ennf_transformation,[status(thm)],[f11])).
% 1.70/1.44 thf(f11,plain,(
% 1.70/1.44 ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true) => (X0 = X1)) <=> (uniqinunit = $true)),
% 1.70/1.44 inference(fool_elimination,[status(thm)],[f10])).
% 1.70/1.44 thf(f10,plain,(
% 1.70/1.44 (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 1.70/1.44 inference(rectify,[status(thm)],[f1])).
% 1.70/1.44 thf(f1,axiom,(
% 1.70/1.44 (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 1.70/1.44 file('/export/starexec/sandbox/tmp/tmp.d1PGr4SD66/DTF2THF_5301.p',uniqinunit)).
% 1.70/1.44 thf(f46,plain,(
% 1.70/1.44 ( ! [X3 : $i,X4 : $i] : (($true != (in @ (sK6 @ X4 @ X3) @ X4)) | ($true = (subset @ X3 @ X4))) )),
% 1.70/1.44 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.70/1.44 thf(f43,plain,(
% 1.70/1.44 ( ! [X3 : $i,X4 : $i] : (($true != (in @ (sK6 @ X4 @ X3) @ X4)) | ($true != $true) | ($true = (subset @ X3 @ X4))) )),
% 1.70/1.44 inference(definition_unfolding,[status(thm)],[f35,f28])).
% 1.70/1.44 thf(f35,plain,(
% 1.70/1.44 ( ! [X3 : $i,X4 : $i] : (($true != (in @ (sK6 @ X4 @ X3) @ X4)) | ($true = (subset @ X3 @ X4)) | (subsetI2 != $true)) )),
% 1.70/1.44 inference(cnf_transformation,[status(thm)],[f26])).
% 1.70/1.44 % SZS output end Proof for DTF2THF_5301
% 1.70/1.44 % (5441)------------------------------
% 1.70/1.44 % (5441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.44 % (5441)Termination reason: Refutation
% 1.70/1.44
% 1.70/1.44 % (5441)Memory used [KB]: 5500
% 1.70/1.44 % (5441)Time elapsed: 0.006 s
% 1.70/1.44 % (5441)Instructions burned: 4 (million)
% 1.70/1.44 % (5441)------------------------------
% 1.70/1.44 % (5441)------------------------------
% 1.70/1.44 % (5435)Success in time 0.02 s
%------------------------------------------------------------------------------