%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU634^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 1.67s 1.30s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 65 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 698 ( 198 equ; 0 cnn)
% Maximal formula atoms : 8 ( 10 avg)
% Number of connectives : 727 ( 84 ~; 70 |; 48 &; 489 @)
% ( 6 <=>; 30 =>; 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 : 20 ( 17 usr; 13 con; 0-2 aty)
% Number of variables : 125 ( 0 ^; 93 !; 32 ?; 125 :)
% 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,
subset: $i > $i > $o ).
thf(func_def_15,type,
sK4: $i > $i > $i ).
thf(func_def_19,type,
sK8: $i > $i > $i ).
thf(f80,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f79,f44]) ).
thf(f44,plain,
( $true
!= ( subset @ ( setunion @ ( setadjoin @ sK5 @ emptyset ) ) @ sK5 ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( subsetI2 = $true )
& ( uniqinunit = $true )
& ( $true
!= ( subset @ ( setunion @ ( setadjoin @ sK5 @ emptyset ) ) @ sK5 ) )
& ( setunionE2 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f19,f29]) ).
thf(f29,plain,
( ? [X0: $i] :
( $true
!= ( subset @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) @ X0 ) )
=> ( $true
!= ( subset @ ( setunion @ ( setadjoin @ sK5 @ emptyset ) ) @ sK5 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ( subsetI2 = $true )
& ( uniqinunit = $true )
& ? [X0: $i] :
( $true
!= ( subset @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) @ X0 ) )
& ( setunionE2 = $true ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ? [X0: $i] :
( $true
!= ( subset @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) @ X0 ) )
& ( setunionE2 = $true )
& ( subsetI2 = $true )
& ( uniqinunit = $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
~ ( ( uniqinunit = $true )
=> ( ( subsetI2 = $true )
=> ( ( setunionE2 = $true )
=> ! [X0: $i] :
( $true
= ( subset @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) @ X0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( uniqinunit
=> ( subsetI2
=> ( setunionE2
=> ! [X0: $i] : ( subset @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( uniqinunit
=> ( subsetI2
=> ( setunionE2
=> ! [X2: $i] : ( subset @ ( setunion @ ( setadjoin @ X2 @ emptyset ) ) @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( uniqinunit
=> ( subsetI2
=> ( setunionE2
=> ! [X2: $i] : ( subset @ ( setunion @ ( setadjoin @ X2 @ emptyset ) ) @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xhtAR1lNXn/DTF2THF_5188.p',setunionsingleton1) ).
thf(f79,plain,
( $true
= ( subset @ ( setunion @ ( setadjoin @ sK5 @ emptyset ) ) @ sK5 ) ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
( ( $true != $true )
| ( $true
= ( subset @ ( setunion @ ( setadjoin @ sK5 @ emptyset ) ) @ sK5 ) ) ),
inference(superposition,[status(thm)],[f63,f75]) ).
thf(f75,plain,
( $true
= ( in @ ( sK8 @ ( setunion @ ( setadjoin @ sK5 @ emptyset ) ) @ sK5 ) @ sK5 ) ),
inference(backward_demodulation,[status(thm)],[f71,f74]) ).
thf(f74,plain,
( sK5
= ( sK4 @ ( sK8 @ ( setunion @ ( setadjoin @ sK5 @ emptyset ) ) @ sK5 ) @ ( setadjoin @ sK5 @ emptyset ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ( $true != $true )
| ( sK5
= ( sK4 @ ( sK8 @ ( setunion @ ( setadjoin @ sK5 @ emptyset ) ) @ sK5 ) @ ( setadjoin @ sK5 @ emptyset ) ) ) ),
inference(superposition,[status(thm)],[f62,f72]) ).
thf(f72,plain,
( $true
= ( in @ ( sK4 @ ( sK8 @ ( setunion @ ( setadjoin @ sK5 @ emptyset ) ) @ sK5 ) @ ( setadjoin @ sK5 @ emptyset ) ) @ ( setadjoin @ sK5 @ emptyset ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ( $true
= ( in @ ( sK4 @ ( sK8 @ ( setunion @ ( setadjoin @ sK5 @ emptyset ) ) @ sK5 ) @ ( setadjoin @ sK5 @ emptyset ) ) @ ( setadjoin @ sK5 @ emptyset ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f65,f68]) ).
thf(f68,plain,
( $true
= ( in @ ( sK8 @ ( setunion @ ( setadjoin @ sK5 @ emptyset ) ) @ sK5 ) @ ( setunion @ ( setadjoin @ sK5 @ emptyset ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
( ( $true
= ( in @ ( sK8 @ ( setunion @ ( setadjoin @ sK5 @ emptyset ) ) @ sK5 ) @ ( setunion @ ( setadjoin @ sK5 @ emptyset ) ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f44,f66]) ).
thf(f66,plain,
! [X3: $i,X4: $i] :
( ( $true
= ( subset @ X4 @ X3 ) )
| ( ( in @ ( sK8 @ X4 @ X3 ) @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
! [X3: $i,X4: $i] :
( ( $true != $true )
| ( ( in @ ( sK8 @ X4 @ X3 ) @ X4 )
= $true )
| ( $true
= ( subset @ X4 @ X3 ) ) ),
inference(definition_unfolding,[status(thm)],[f48,f46]) ).
thf(f46,plain,
subsetI2 = $true,
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f48,plain,
! [X3: $i,X4: $i] :
( ( $true
= ( subset @ X4 @ X3 ) )
| ( ( in @ ( sK8 @ X4 @ X3 ) @ X4 )
= $true )
| ( subsetI2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( subsetI2 = $true )
| ( ( $true
!= ( subset @ sK7 @ sK6 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ sK7 )
!= $true )
| ( ( in @ X2 @ sK6 )
= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( $true
= ( subset @ X4 @ X3 ) )
| ( ( ( in @ ( sK8 @ X4 @ X3 ) @ X4 )
= $true )
& ( $true
!= ( in @ ( sK8 @ X4 @ X3 ) @ X3 ) ) ) )
| ( subsetI2 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f32,f34,f33]) ).
thf(f33,plain,
( ? [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
& ! [X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( ( in @ X2 @ X0 )
= $true ) ) )
=> ( ( $true
!= ( subset @ sK7 @ sK6 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ sK7 )
!= $true )
| ( ( in @ X2 @ sK6 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( $true
= ( in @ X5 @ X4 ) )
& ( $true
!= ( in @ X5 @ X3 ) ) )
=> ( ( ( in @ ( sK8 @ X4 @ X3 ) @ X4 )
= $true )
& ( $true
!= ( in @ ( sK8 @ X4 @ X3 ) @ X3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ( ( subsetI2 = $true )
| ? [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
& ! [X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( ( in @ X2 @ X0 )
= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( $true
= ( subset @ X4 @ X3 ) )
| ? [X5: $i] :
( ( $true
= ( in @ X5 @ X4 ) )
& ( $true
!= ( in @ X5 @ X3 ) ) ) )
| ( subsetI2 != $true ) ) ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( subsetI2 = $true )
| ? [X1: $i,X0: $i] :
( ( $true
!= ( subset @ X0 @ X1 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( $true
= ( in @ X2 @ X1 ) ) ) ) )
& ( ! [X1: $i,X0: $i] :
( ( $true
= ( subset @ X0 @ X1 ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( $true
!= ( in @ X2 @ X1 ) ) ) )
| ( subsetI2 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( subsetI2 = $true )
<=> ! [X1: $i,X0: $i] :
( ( $true
= ( subset @ X0 @ X1 ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( $true
!= ( in @ X2 @ X1 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( subsetI2 = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( $true
= ( in @ X2 @ X1 ) ) )
=> ( $true
= ( subset @ X0 @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( subsetI2
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( subsetI2
= ( ! [X2: $i,X3: $i] :
( ! [X0: $i] :
( ( in @ X0 @ X2 )
=> ( in @ X0 @ X3 ) )
=> ( subset @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xhtAR1lNXn/DTF2THF_5188.p',subsetI2) ).
thf(f65,plain,
! [X3: $i,X4: $i] :
( ( $true
!= ( in @ X4 @ ( setunion @ X3 ) ) )
| ( ( in @ ( sK4 @ X4 @ X3 ) @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
! [X3: $i,X4: $i] :
( ( $true
!= ( in @ X4 @ ( setunion @ X3 ) ) )
| ( $true != $true )
| ( ( in @ ( sK4 @ X4 @ X3 ) @ X3 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f39,f43]) ).
thf(f43,plain,
setunionE2 = $true,
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f39,plain,
! [X3: $i,X4: $i] :
( ( $true
!= ( in @ X4 @ ( setunion @ X3 ) ) )
| ( ( in @ ( sK4 @ X4 @ X3 ) @ X3 )
= $true )
| ( setunionE2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( setunionE2 = $true )
| ( ( $true
= ( in @ sK3 @ ( setunion @ sK2 ) ) )
& ! [X2: $i] :
( ( ( in @ sK3 @ X2 )
!= $true )
| ( ( in @ X2 @ sK2 )
!= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( $true
!= ( in @ X4 @ ( setunion @ X3 ) ) )
| ( ( ( in @ X4 @ ( sK4 @ X4 @ X3 ) )
= $true )
& ( ( in @ ( sK4 @ X4 @ X3 ) @ X3 )
= $true ) ) )
| ( setunionE2 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f25,f27,f26]) ).
thf(f26,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ X0 ) ) )
& ! [X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) )
=> ( ( $true
= ( in @ sK3 @ ( setunion @ sK2 ) ) )
& ! [X2: $i] :
( ( ( in @ sK3 @ X2 )
!= $true )
| ( ( in @ X2 @ sK2 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( $true
= ( in @ X4 @ X5 ) )
& ( $true
= ( in @ X5 @ X3 ) ) )
=> ( ( ( in @ X4 @ ( sK4 @ X4 @ X3 ) )
= $true )
& ( ( in @ ( sK4 @ X4 @ X3 ) @ X3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( ( setunionE2 = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ X0 ) ) )
& ! [X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( $true
!= ( in @ X4 @ ( setunion @ X3 ) ) )
| ? [X5: $i] :
( ( $true
= ( in @ X4 @ X5 ) )
& ( $true
= ( in @ X5 @ X3 ) ) ) )
| ( setunionE2 != $true ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( setunionE2 = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ X0 ) ) )
& ! [X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setunion @ X0 ) ) )
| ? [X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) )
| ( setunionE2 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( setunionE2 = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setunion @ X0 ) ) )
| ? [X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( setunionE2 = $true )
<=> ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ X0 ) ) )
=> ? [X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( setunionE2
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X0 )
& ( in @ X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( setunionE2
= ( ! [X2: $i,X0: $i] :
( ( in @ X0 @ ( setunion @ X2 ) )
=> ? [X4: $i] :
( ( in @ X4 @ X2 )
& ( in @ X0 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xhtAR1lNXn/DTF2THF_5188.p',setunionE2) ).
thf(f62,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
| ( X0 = X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
| ( $true != $true )
| ( X0 = X1 ) ),
inference(definition_unfolding,[status(thm)],[f38,f45]) ).
thf(f45,plain,
uniqinunit = $true,
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f38,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
| ( X0 = X1 )
| ( uniqinunit != $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
| ( X0 = X1 ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ( ( $true
= ( in @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) )
& ( sK0 != sK1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f21,f22]) ).
thf(f22,plain,
( ? [X2: $i,X3: $i] :
( ( ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) )
= $true )
& ( X2 != X3 ) )
=> ( ( $true
= ( in @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) )
& ( sK0 != sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
| ( X0 = X1 ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ? [X2: $i,X3: $i] :
( ( ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) )
= $true )
& ( X2 != X3 ) ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
| ( X0 = X1 ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
& ( X0 != X1 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
| ( X0 = X1 ) )
<=> ( uniqinunit = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
=> ( X0 = X1 ) )
<=> ( uniqinunit = $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( uniqinunit
= ( ! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xhtAR1lNXn/DTF2THF_5188.p',uniqinunit) ).
thf(f71,plain,
( $true
= ( in @ ( sK8 @ ( setunion @ ( setadjoin @ sK5 @ emptyset ) ) @ sK5 ) @ ( sK4 @ ( sK8 @ ( setunion @ ( setadjoin @ sK5 @ emptyset ) ) @ sK5 ) @ ( setadjoin @ sK5 @ emptyset ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
( ( $true
= ( in @ ( sK8 @ ( setunion @ ( setadjoin @ sK5 @ emptyset ) ) @ sK5 ) @ ( sK4 @ ( sK8 @ ( setunion @ ( setadjoin @ sK5 @ emptyset ) ) @ sK5 ) @ ( setadjoin @ sK5 @ emptyset ) ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f64,f68]) ).
thf(f64,plain,
! [X3: $i,X4: $i] :
( ( $true
!= ( in @ X4 @ ( setunion @ X3 ) ) )
| ( ( in @ X4 @ ( sK4 @ X4 @ X3 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
! [X3: $i,X4: $i] :
( ( $true
!= ( in @ X4 @ ( setunion @ X3 ) ) )
| ( $true != $true )
| ( ( in @ X4 @ ( sK4 @ X4 @ X3 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f40,f43]) ).
thf(f40,plain,
! [X3: $i,X4: $i] :
( ( $true
!= ( in @ X4 @ ( setunion @ X3 ) ) )
| ( ( in @ X4 @ ( sK4 @ X4 @ X3 ) )
= $true )
| ( setunionE2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f63,plain,
! [X3: $i,X4: $i] :
( ( $true
!= ( in @ ( sK8 @ X4 @ X3 ) @ X3 ) )
| ( $true
= ( subset @ X4 @ X3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
! [X3: $i,X4: $i] :
( ( $true != $true )
| ( $true
!= ( in @ ( sK8 @ X4 @ X3 ) @ X3 ) )
| ( $true
= ( subset @ X4 @ X3 ) ) ),
inference(definition_unfolding,[status(thm)],[f47,f46]) ).
thf(f47,plain,
! [X3: $i,X4: $i] :
( ( $true
= ( subset @ X4 @ X3 ) )
| ( $true
!= ( in @ ( sK8 @ X4 @ X3 ) @ X3 ) )
| ( subsetI2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU634^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Feb 24 12:28:59 EST 2026
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEU634^2 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.46 % Domain : Set Theory
% 0.29/0.46 % Problem : Ordered Pairs - Singletons
% 0.29/0.46 % Version : Especial > Reduced > Especial.
% 0.29/0.46 % English : (! A:i.subset (setunion (setadjoin A emptyset)) A)
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.46 % Source : [Bro08]
% 0.29/0.46 % Names : ZFC136l [Bro08]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 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 v6.0.0, 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 v4.0.1, 0.33 v3.7.0
% 0.29/0.46 % Syntax : Number of formulae : 12 ( 3 unt; 8 typ; 3 def)
% 0.29/0.46 % Number of atoms : 18 ( 4 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.29/0.46 % Number of connectives : 30 ( 0 ~; 0 |; 1 &; 22 @)
% 0.29/0.46 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 10 ( 3 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 9 ( 8 usr; 4 con; 0-2 aty)
% 0.29/0.46 % Number of variables : 9 ( 0 ^; 8 !; 1 ?; 9 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : http://mathgate.info/detsetitem.php?id=191
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(in_type,type,
% 0.29/0.46 in: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset_type,type,
% 0.29/0.46 emptyset: $i ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin_type,type,
% 0.29/0.46 setadjoin: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setunion_type,type,
% 0.29/0.46 setunion: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(uniqinunit_type,type,
% 0.29/0.46 uniqinunit: $o ).
% 0.29/0.46
% 0.29/0.46 thf(uniqinunit,definition,
% 0.29/0.46 ( uniqinunit
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subset_type,type,
% 0.29/0.46 subset: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI2_type,type,
% 0.29/0.46 subsetI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI2,definition,
% 0.29/0.46 ( subsetI2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE2_type,type,
% 0.29/0.46 setunionE2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE2,definition,
% 0.29/0.46 ( setunionE2
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 => ? [X: $i] :
% 0.29/0.46 ( ( in @ X @ A )
% 0.29/0.46 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton1,conjecture,
% 0.29/0.46 ( uniqinunit
% 0.29/0.46 => ( subsetI2
% 0.29/0.46 => ( setunionE2
% 0.29/0.46 => ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.52/1.26 ---- Embedded in THF ---
% 1.52/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.26 %%% Generated on Tue Feb 24 12:29:00 EST 2026
% 1.52/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.26 %%% Logic specification used:
% 1.52/1.26 %%% thf(spec, logic, $$dhol).
% 1.52/1.26
% 1.52/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.xhtAR1lNXn/DTF2DTF5188.p
% See solution above
% 1.52/1.26 ------------------------
% 1.52/1.27 ---- Cleaned THF ---
% 1.52/1.27 thf(in_type,type,
% 1.52/1.27 in: $i > $i > $o ).
% 1.52/1.27
% 1.52/1.27 thf(emptyset_type,type,
% 1.52/1.27 emptyset: $i ).
% 1.52/1.27
% 1.52/1.27 thf(setadjoin_type,type,
% 1.52/1.27 setadjoin: $i > $i > $i ).
% 1.52/1.27
% 1.52/1.27 thf(setunion_type,type,
% 1.52/1.27 setunion: $i > $i ).
% 1.52/1.27
% 1.52/1.27 thf(uniqinunit_type,type,
% 1.52/1.27 uniqinunit: $o ).
% 1.52/1.27
% 1.52/1.27 thf(uniqinunit,definition,
% 1.52/1.27 ( uniqinunit
% 1.52/1.27 = ( ! [Xx: $i,Xy: $i] :
% 1.52/1.27 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.52/1.27 => ( Xx = Xy ) ) ) ) ).
% 1.52/1.27
% 1.52/1.27 thf(subset_type,type,
% 1.52/1.27 subset: $i > $i > $o ).
% 1.52/1.27
% 1.52/1.27 thf(subsetI2_type,type,
% 1.52/1.27 subsetI2: $o ).
% 1.52/1.27
% 1.52/1.27 thf(subsetI2,definition,
% 1.52/1.27 ( subsetI2
% 1.52/1.27 = ( ! [A: $i,B: $i] :
% 1.52/1.27 ( ! [Xx: $i] :
% 1.52/1.27 ( ( in @ Xx @ A )
% 1.52/1.27 => ( in @ Xx @ B ) )
% 1.52/1.27 => ( subset @ A @ B ) ) ) ) ).
% 1.52/1.27
% 1.52/1.27 thf(setunionE2_type,type,
% 1.52/1.27 setunionE2: $o ).
% 1.52/1.27
% 1.52/1.27 thf(setunionE2,definition,
% 1.52/1.27 ( setunionE2
% 1.52/1.27 = ( ! [A: $i,Xx: $i] :
% 1.52/1.27 ( ( in @ Xx @ ( setunion @ A ) )
% 1.52/1.27 => ? [X: $i] :
% 1.52/1.27 ( ( in @ X @ A )
% 1.52/1.27 & ( in @ Xx @ X ) ) ) ) ) ).
% 1.52/1.27
% 1.52/1.27 thf(setunionsingleton1,conjecture,
% 1.52/1.27 ( uniqinunit
% 1.52/1.27 => ( subsetI2
% 1.52/1.27 => ( setunionE2
% 1.52/1.27 => ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ) ).
% 1.52/1.27 ------------------------
% 1.52/1.28 % (5467)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_5188 for (2999ds/27Mi)
% 1.52/1.28 % (5466)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_5188 for (2999ds/4Mi)
% 1.52/1.28 % (5466)Instruction limit reached!
% 1.52/1.28 % (5466)------------------------------
% 1.52/1.28 % (5466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.28 % (5466)Termination reason: Unknown
% 1.52/1.28 % (5466)Termination phase: Saturation
% 1.52/1.28
% 1.52/1.28 % (5466)Memory used [KB]: 5500
% 1.52/1.28 % (5466)Time elapsed: 0.003 s
% 1.52/1.28 % (5466)Instructions burned: 5 (million)
% 1.52/1.28 % (5466)------------------------------
% 1.52/1.28 % (5466)------------------------------
% 1.52/1.29 % (5465)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5188 for (2999ds/183Mi)
% 1.52/1.29 % (5468)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5188 for (2999ds/2Mi)
% 1.52/1.29 % (5469)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_5188 for (2999ds/2Mi)
% 1.52/1.29 % (5470)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_5188 for (2999ds/275Mi)
% 1.52/1.29 % (5471)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5188 for (2999ds/18Mi)
% 1.52/1.29 % (5468)Instruction limit reached!
% 1.52/1.29 % (5468)------------------------------
% 1.52/1.29 % (5468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.29 % (5468)Termination reason: Unknown
% 1.52/1.29 % (5468)Termination phase: Property scanning
% 1.52/1.29
% 1.52/1.29 % (5468)Memory used [KB]: 895
% 1.52/1.29 % (5468)Time elapsed: 0.003 s
% 1.52/1.29 % (5468)Instructions burned: 2 (million)
% 1.52/1.29 % (5468)------------------------------
% 1.52/1.29 % (5468)------------------------------
% 1.52/1.29 % (5469)Instruction limit reached!
% 1.52/1.29 % (5469)------------------------------
% 1.52/1.29 % (5469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.29 % (5469)Termination reason: Unknown
% 1.52/1.29 % (5469)Termination phase: Property scanning
% 1.52/1.29
% 1.52/1.29 % (5469)Memory used [KB]: 895
% 1.52/1.29 % (5469)Time elapsed: 0.003 s
% 1.52/1.29 % (5469)Instructions burned: 2 (million)
% 1.52/1.29 % (5469)------------------------------
% 1.52/1.29 % (5469)------------------------------
% 1.52/1.29 % (5467)Instruction limit reached!
% 1.52/1.29 % (5467)------------------------------
% 1.52/1.29 % (5467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.29 % (5467)Termination reason: Unknown
% 1.52/1.29 % (5467)Termination phase: Saturation
% 1.52/1.29
% 1.52/1.29 % (5467)Memory used [KB]: 5628
% 1.52/1.29 % (5467)Time elapsed: 0.011 s
% 1.52/1.29 % (5467)Instructions burned: 28 (million)
% 1.52/1.29 % (5467)------------------------------
% 1.52/1.29 % (5467)------------------------------
% 1.52/1.29 % (5472)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5188 for (2999ds/3Mi)
% 1.52/1.30 % (5471)First to succeed.
% 1.52/1.30 % (5472)Instruction limit reached!
% 1.52/1.30 % (5472)------------------------------
% 1.52/1.30 % (5472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.30 % (5472)Termination reason: Unknown
% 1.52/1.30 % (5472)Termination phase: Saturation
% 1.52/1.30
% 1.52/1.30 % (5472)Memory used [KB]: 5500
% 1.52/1.30 % (5472)Time elapsed: 0.003 s
% 1.52/1.30 % (5472)Instructions burned: 3 (million)
% 1.52/1.30 % (5472)------------------------------
% 1.52/1.30 % (5472)------------------------------
% 1.67/1.30 % (5471)Refutation found. Thanks to Tanya!
% 1.67/1.30 % SZS status Theorem for DTF2THF_5188
% 1.67/1.30 % SZS output start Proof for DTF2THF_5188
% 1.67/1.30 thf(func_def_0, type, in: $i > $i > $o).
% 1.67/1.30 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.67/1.30 thf(func_def_3, type, setunion: $i > $i).
% 1.67/1.30 thf(func_def_6, type, subset: $i > $i > $o).
% 1.67/1.30 thf(func_def_15, type, sK4: $i > $i > $i).
% 1.67/1.30 thf(func_def_19, type, sK8: $i > $i > $i).
% 1.67/1.30 thf(f80,plain,(
% 1.67/1.30 $false),
% 1.67/1.30 inference(subsumption_resolution,[status(thm)],[f79,f44])).
% 1.67/1.30 thf(f44,plain,(
% 1.67/1.30 ($true != (subset @ (setunion @ (setadjoin @ sK5 @ emptyset)) @ sK5))),
% 1.67/1.30 inference(cnf_transformation,[status(thm)],[f30])).
% 1.67/1.30 thf(f30,plain,(
% 1.67/1.30 (subsetI2 = $true) & (uniqinunit = $true) & ($true != (subset @ (setunion @ (setadjoin @ sK5 @ emptyset)) @ sK5)) & (setunionE2 = $true)),
% 1.67/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f19,f29])).
% 1.67/1.30 thf(f29,plain,(
% 1.67/1.30 ? [X0 : $i] : ($true != (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0)) => ($true != (subset @ (setunion @ (setadjoin @ sK5 @ emptyset)) @ sK5))),
% 1.67/1.30 introduced(definition,[],[choice_axiom])).
% 1.67/1.30 thf(f19,plain,(
% 1.67/1.30 (subsetI2 = $true) & (uniqinunit = $true) & ? [X0 : $i] : ($true != (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0)) & (setunionE2 = $true)),
% 1.67/1.30 inference(flattening,[status(thm)],[f18])).
% 1.67/1.30 thf(f18,plain,(
% 1.67/1.30 ((? [X0 : $i] : ($true != (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0)) & (setunionE2 = $true)) & (subsetI2 = $true)) & (uniqinunit = $true)),
% 1.67/1.30 inference(ennf_transformation,[status(thm)],[f14])).
% 1.67/1.30 thf(f14,plain,(
% 1.67/1.30 ~((uniqinunit = $true) => ((subsetI2 = $true) => ((setunionE2 = $true) => ! [X0 : $i] : ($true = (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0)))))),
% 1.67/1.30 inference(fool_elimination,[status(thm)],[f13])).
% 1.67/1.30 thf(f13,plain,(
% 1.67/1.30 ~(uniqinunit => (subsetI2 => (setunionE2 => ! [X0 : $i] : (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0))))),
% 1.67/1.30 inference(rectify,[status(thm)],[f5])).
% 1.67/1.30 thf(f5,negated_conjecture,(
% 1.67/1.30 ~(uniqinunit => (subsetI2 => (setunionE2 => ! [X2 : $i] : (subset @ (setunion @ (setadjoin @ X2 @ emptyset)) @ X2))))),
% 1.67/1.30 inference(negated_conjecture,[status(cth)],[f4])).
% 1.67/1.30 thf(f4,conjecture,(
% 1.67/1.30 uniqinunit => (subsetI2 => (setunionE2 => ! [X2 : $i] : (subset @ (setunion @ (setadjoin @ X2 @ emptyset)) @ X2)))),
% 1.67/1.30 file('/export/starexec/sandbox2/tmp/tmp.xhtAR1lNXn/DTF2THF_5188.p',setunionsingleton1)).
% 1.67/1.30 thf(f79,plain,(
% 1.67/1.30 ($true = (subset @ (setunion @ (setadjoin @ sK5 @ emptyset)) @ sK5))),
% 1.67/1.30 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 1.67/1.30 thf(f78,plain,(
% 1.67/1.30 ($true != $true) | ($true = (subset @ (setunion @ (setadjoin @ sK5 @ emptyset)) @ sK5))),
% 1.67/1.30 inference(superposition,[status(thm)],[f63,f75])).
% 1.67/1.30 thf(f75,plain,(
% 1.67/1.30 ($true = (in @ (sK8 @ (setunion @ (setadjoin @ sK5 @ emptyset)) @ sK5) @ sK5))),
% 1.67/1.30 inference(backward_demodulation,[status(thm)],[f71,f74])).
% 1.67/1.30 thf(f74,plain,(
% 1.67/1.30 (sK5 = (sK4 @ (sK8 @ (setunion @ (setadjoin @ sK5 @ emptyset)) @ sK5) @ (setadjoin @ sK5 @ emptyset)))),
% 1.67/1.30 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.67/1.30 thf(f73,plain,(
% 1.67/1.30 ($true != $true) | (sK5 = (sK4 @ (sK8 @ (setunion @ (setadjoin @ sK5 @ emptyset)) @ sK5) @ (setadjoin @ sK5 @ emptyset)))),
% 1.67/1.30 inference(superposition,[status(thm)],[f62,f72])).
% 1.67/1.30 thf(f72,plain,(
% 1.67/1.30 ($true = (in @ (sK4 @ (sK8 @ (setunion @ (setadjoin @ sK5 @ emptyset)) @ sK5) @ (setadjoin @ sK5 @ emptyset)) @ (setadjoin @ sK5 @ emptyset)))),
% 1.67/1.30 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.67/1.30 thf(f69,plain,(
% 1.67/1.30 ($true = (in @ (sK4 @ (sK8 @ (setunion @ (setadjoin @ sK5 @ emptyset)) @ sK5) @ (setadjoin @ sK5 @ emptyset)) @ (setadjoin @ sK5 @ emptyset))) | ($true != $true)),
% 1.67/1.30 inference(superposition,[status(thm)],[f65,f68])).
% 1.67/1.30 thf(f68,plain,(
% 1.67/1.30 ($true = (in @ (sK8 @ (setunion @ (setadjoin @ sK5 @ emptyset)) @ sK5) @ (setunion @ (setadjoin @ sK5 @ emptyset))))),
% 1.67/1.30 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.67/1.30 thf(f67,plain,(
% 1.67/1.30 ($true = (in @ (sK8 @ (setunion @ (setadjoin @ sK5 @ emptyset)) @ sK5) @ (setunion @ (setadjoin @ sK5 @ emptyset)))) | ($true != $true)),
% 1.67/1.30 inference(superposition,[status(thm)],[f44,f66])).
% 1.67/1.30 thf(f66,plain,(
% 1.67/1.30 ( ! [X3 : $i,X4 : $i] : (($true = (subset @ X4 @ X3)) | ((in @ (sK8 @ X4 @ X3) @ X4) = $true)) )),
% 1.67/1.30 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.67/1.30 thf(f60,plain,(
% 1.67/1.30 ( ! [X3 : $i,X4 : $i] : (($true != $true) | ((in @ (sK8 @ X4 @ X3) @ X4) = $true) | ($true = (subset @ X4 @ X3))) )),
% 1.67/1.30 inference(definition_unfolding,[status(thm)],[f48,f46])).
% 1.67/1.30 thf(f46,plain,(
% 1.67/1.30 (subsetI2 = $true)),
% 1.67/1.30 inference(cnf_transformation,[status(thm)],[f30])).
% 1.67/1.30 thf(f48,plain,(
% 1.67/1.30 ( ! [X3 : $i,X4 : $i] : (($true = (subset @ X4 @ X3)) | ((in @ (sK8 @ X4 @ X3) @ X4) = $true) | (subsetI2 != $true)) )),
% 1.67/1.30 inference(cnf_transformation,[status(thm)],[f35])).
% 1.67/1.30 thf(f35,plain,(
% 1.67/1.30 ((subsetI2 = $true) | (($true != (subset @ sK7 @ sK6)) & ! [X2 : $i] : (((in @ X2 @ sK7) != $true) | ((in @ X2 @ sK6) = $true)))) & (! [X3 : $i,X4 : $i] : (($true = (subset @ X4 @ X3)) | (((in @ (sK8 @ X4 @ X3) @ X4) = $true) & ($true != (in @ (sK8 @ X4 @ X3) @ X3)))) | (subsetI2 != $true))),
% 1.67/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f32,f34,f33])).
% 1.67/1.30 thf(f33,plain,(
% 1.67/1.30 ? [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X0)) & ! [X2 : $i] : (($true != (in @ X2 @ X1)) | ((in @ X2 @ X0) = $true))) => (($true != (subset @ sK7 @ sK6)) & ! [X2 : $i] : (((in @ X2 @ sK7) != $true) | ((in @ X2 @ sK6) = $true)))),
% 1.67/1.30 introduced(definition,[],[choice_axiom])).
% 1.67/1.30 thf(f34,plain,(
% 1.67/1.30 ! [X3 : $i,X4 : $i] : (? [X5 : $i] : (($true = (in @ X5 @ X4)) & ($true != (in @ X5 @ X3))) => (((in @ (sK8 @ X4 @ X3) @ X4) = $true) & ($true != (in @ (sK8 @ X4 @ X3) @ X3))))),
% 1.67/1.30 introduced(definition,[],[choice_axiom])).
% 1.67/1.30 thf(f32,plain,(
% 1.67/1.30 ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X0)) & ! [X2 : $i] : (($true != (in @ X2 @ X1)) | ((in @ X2 @ X0) = $true)))) & (! [X3 : $i,X4 : $i] : (($true = (subset @ X4 @ X3)) | ? [X5 : $i] : (($true = (in @ X5 @ X4)) & ($true != (in @ X5 @ X3)))) | (subsetI2 != $true))),
% 1.67/1.30 inference(rectify,[status(thm)],[f31])).
% 1.67/1.30 thf(f31,plain,(
% 1.67/1.30 ((subsetI2 = $true) | ? [X1 : $i,X0 : $i] : (($true != (subset @ X0 @ X1)) & ! [X2 : $i] : (((in @ X2 @ X0) != $true) | ($true = (in @ X2 @ X1))))) & (! [X1 : $i,X0 : $i] : (($true = (subset @ X0 @ X1)) | ? [X2 : $i] : (((in @ X2 @ X0) = $true) & ($true != (in @ X2 @ X1)))) | (subsetI2 != $true))),
% 1.67/1.30 inference(nnf_transformation,[status(thm)],[f15])).
% 1.67/1.30 thf(f15,plain,(
% 1.67/1.30 (subsetI2 = $true) <=> ! [X1 : $i,X0 : $i] : (($true = (subset @ X0 @ X1)) | ? [X2 : $i] : (((in @ X2 @ X0) = $true) & ($true != (in @ X2 @ X1))))),
% 1.67/1.30 inference(ennf_transformation,[status(thm)],[f12])).
% 1.67/1.30 thf(f12,plain,(
% 1.67/1.30 (subsetI2 = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) => ($true = (in @ X2 @ X1))) => ($true = (subset @ X0 @ X1)))),
% 1.67/1.30 inference(fool_elimination,[status(thm)],[f11])).
% 1.67/1.30 thf(f11,plain,(
% 1.67/1.30 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 1.67/1.30 inference(rectify,[status(thm)],[f2])).
% 1.67/1.30 thf(f2,axiom,(
% 1.67/1.30 (subsetI2 = ! [X2 : $i,X3 : $i] : (! [X0 : $i] : ((in @ X0 @ X2) => (in @ X0 @ X3)) => (subset @ X2 @ X3)))),
% 1.67/1.30 file('/export/starexec/sandbox2/tmp/tmp.xhtAR1lNXn/DTF2THF_5188.p',subsetI2)).
% 1.67/1.30 thf(f65,plain,(
% 1.67/1.30 ( ! [X3 : $i,X4 : $i] : (($true != (in @ X4 @ (setunion @ X3))) | ((in @ (sK4 @ X4 @ X3) @ X3) = $true)) )),
% 1.67/1.30 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.67/1.30 thf(f57,plain,(
% 1.67/1.30 ( ! [X3 : $i,X4 : $i] : (($true != (in @ X4 @ (setunion @ X3))) | ($true != $true) | ((in @ (sK4 @ X4 @ X3) @ X3) = $true)) )),
% 1.67/1.30 inference(definition_unfolding,[status(thm)],[f39,f43])).
% 1.67/1.30 thf(f43,plain,(
% 1.67/1.30 (setunionE2 = $true)),
% 1.67/1.30 inference(cnf_transformation,[status(thm)],[f30])).
% 1.67/1.30 thf(f39,plain,(
% 1.67/1.30 ( ! [X3 : $i,X4 : $i] : (($true != (in @ X4 @ (setunion @ X3))) | ((in @ (sK4 @ X4 @ X3) @ X3) = $true) | (setunionE2 != $true)) )),
% 1.67/1.30 inference(cnf_transformation,[status(thm)],[f28])).
% 1.67/1.30 thf(f28,plain,(
% 1.67/1.30 ((setunionE2 = $true) | (($true = (in @ sK3 @ (setunion @ sK2))) & ! [X2 : $i] : (((in @ sK3 @ X2) != $true) | ((in @ X2 @ sK2) != $true)))) & (! [X3 : $i,X4 : $i] : (($true != (in @ X4 @ (setunion @ X3))) | (((in @ X4 @ (sK4 @ X4 @ X3)) = $true) & ((in @ (sK4 @ X4 @ X3) @ X3) = $true))) | (setunionE2 != $true))),
% 1.67/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f25,f27,f26])).
% 1.67/1.30 thf(f26,plain,(
% 1.67/1.30 ? [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (setunion @ X0))) & ! [X2 : $i] : (((in @ X1 @ X2) != $true) | ((in @ X2 @ X0) != $true))) => (($true = (in @ sK3 @ (setunion @ sK2))) & ! [X2 : $i] : (((in @ sK3 @ X2) != $true) | ((in @ X2 @ sK2) != $true)))),
% 1.67/1.30 introduced(definition,[],[choice_axiom])).
% 1.67/1.30 thf(f27,plain,(
% 1.67/1.30 ! [X3 : $i,X4 : $i] : (? [X5 : $i] : (($true = (in @ X4 @ X5)) & ($true = (in @ X5 @ X3))) => (((in @ X4 @ (sK4 @ X4 @ X3)) = $true) & ((in @ (sK4 @ X4 @ X3) @ X3) = $true)))),
% 1.67/1.30 introduced(definition,[],[choice_axiom])).
% 1.67/1.30 thf(f25,plain,(
% 1.67/1.30 ((setunionE2 = $true) | ? [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (setunion @ X0))) & ! [X2 : $i] : (((in @ X1 @ X2) != $true) | ((in @ X2 @ X0) != $true)))) & (! [X3 : $i,X4 : $i] : (($true != (in @ X4 @ (setunion @ X3))) | ? [X5 : $i] : (($true = (in @ X4 @ X5)) & ($true = (in @ X5 @ X3)))) | (setunionE2 != $true))),
% 1.67/1.30 inference(rectify,[status(thm)],[f24])).
% 1.67/1.30 thf(f24,plain,(
% 1.67/1.30 ((setunionE2 = $true) | ? [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (setunion @ X0))) & ! [X2 : $i] : (((in @ X1 @ X2) != $true) | ((in @ X2 @ X0) != $true)))) & (! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (setunion @ X0))) | ? [X2 : $i] : (((in @ X1 @ X2) = $true) & ((in @ X2 @ X0) = $true))) | (setunionE2 != $true))),
% 1.67/1.30 inference(nnf_transformation,[status(thm)],[f16])).
% 1.67/1.30 thf(f16,plain,(
% 1.67/1.30 (setunionE2 = $true) <=> ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (setunion @ X0))) | ? [X2 : $i] : (((in @ X1 @ X2) = $true) & ((in @ X2 @ X0) = $true)))),
% 1.67/1.30 inference(ennf_transformation,[status(thm)],[f10])).
% 1.67/1.30 thf(f10,plain,(
% 1.67/1.30 (setunionE2 = $true) <=> ! [X1 : $i,X0 : $i] : (($true = (in @ X1 @ (setunion @ X0))) => ? [X2 : $i] : (((in @ X1 @ X2) = $true) & ((in @ X2 @ X0) = $true)))),
% 1.67/1.30 inference(fool_elimination,[status(thm)],[f9])).
% 1.67/1.30 thf(f9,plain,(
% 1.67/1.30 (setunionE2 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ? [X2 : $i] : ((in @ X2 @ X0) & (in @ X1 @ X2))))),
% 1.67/1.30 inference(rectify,[status(thm)],[f3])).
% 1.67/1.30 thf(f3,axiom,(
% 1.67/1.30 (setunionE2 = ! [X2 : $i,X0 : $i] : ((in @ X0 @ (setunion @ X2)) => ? [X4 : $i] : ((in @ X4 @ X2) & (in @ X0 @ X4))))),
% 1.67/1.30 file('/export/starexec/sandbox2/tmp/tmp.xhtAR1lNXn/DTF2THF_5188.p',setunionE2)).
% 1.67/1.30 thf(f62,plain,(
% 1.67/1.30 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (setadjoin @ X0 @ emptyset))) | (X0 = X1)) )),
% 1.67/1.30 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.67/1.30 thf(f51,plain,(
% 1.67/1.30 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (setadjoin @ X0 @ emptyset))) | ($true != $true) | (X0 = X1)) )),
% 1.67/1.30 inference(definition_unfolding,[status(thm)],[f38,f45])).
% 1.67/1.30 thf(f45,plain,(
% 1.67/1.30 (uniqinunit = $true)),
% 1.67/1.30 inference(cnf_transformation,[status(thm)],[f30])).
% 1.67/1.30 thf(f38,plain,(
% 1.67/1.30 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (setadjoin @ X0 @ emptyset))) | (X0 = X1) | (uniqinunit != $true)) )),
% 1.67/1.30 inference(cnf_transformation,[status(thm)],[f23])).
% 1.67/1.30 thf(f23,plain,(
% 1.67/1.30 (! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (setadjoin @ X0 @ emptyset))) | (X0 = X1)) | (uniqinunit != $true)) & ((uniqinunit = $true) | (($true = (in @ sK1 @ (setadjoin @ sK0 @ emptyset))) & (sK0 != sK1)))),
% 1.67/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f21,f22])).
% 1.67/1.30 thf(f22,plain,(
% 1.67/1.30 ? [X2 : $i,X3 : $i] : (((in @ X3 @ (setadjoin @ X2 @ emptyset)) = $true) & (X2 != X3)) => (($true = (in @ sK1 @ (setadjoin @ sK0 @ emptyset))) & (sK0 != sK1))),
% 1.67/1.30 introduced(definition,[],[choice_axiom])).
% 1.67/1.30 thf(f21,plain,(
% 1.67/1.30 (! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (setadjoin @ X0 @ emptyset))) | (X0 = X1)) | (uniqinunit != $true)) & ((uniqinunit = $true) | ? [X2 : $i,X3 : $i] : (((in @ X3 @ (setadjoin @ X2 @ emptyset)) = $true) & (X2 != X3)))),
% 1.67/1.30 inference(rectify,[status(thm)],[f20])).
% 1.67/1.30 thf(f20,plain,(
% 1.67/1.30 (! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (setadjoin @ X0 @ emptyset))) | (X0 = X1)) | (uniqinunit != $true)) & ((uniqinunit = $true) | ? [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (setadjoin @ X0 @ emptyset))) & (X0 != X1)))),
% 1.67/1.30 inference(nnf_transformation,[status(thm)],[f17])).
% 1.67/1.30 thf(f17,plain,(
% 1.67/1.30 ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (setadjoin @ X0 @ emptyset))) | (X0 = X1)) <=> (uniqinunit = $true)),
% 1.67/1.30 inference(ennf_transformation,[status(thm)],[f8])).
% 1.67/1.30 thf(f8,plain,(
% 1.67/1.30 ! [X1 : $i,X0 : $i] : (($true = (in @ X1 @ (setadjoin @ X0 @ emptyset))) => (X0 = X1)) <=> (uniqinunit = $true)),
% 1.67/1.30 inference(fool_elimination,[status(thm)],[f7])).
% 1.67/1.30 thf(f7,plain,(
% 1.67/1.30 (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X0 @ emptyset)) => (X0 = X1)))),
% 1.67/1.30 inference(rectify,[status(thm)],[f1])).
% 1.67/1.30 thf(f1,axiom,(
% 1.67/1.30 (uniqinunit = ! [X1 : $i,X0 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 1.67/1.30 file('/export/starexec/sandbox2/tmp/tmp.xhtAR1lNXn/DTF2THF_5188.p',uniqinunit)).
% 1.67/1.30 thf(f71,plain,(
% 1.67/1.30 ($true = (in @ (sK8 @ (setunion @ (setadjoin @ sK5 @ emptyset)) @ sK5) @ (sK4 @ (sK8 @ (setunion @ (setadjoin @ sK5 @ emptyset)) @ sK5) @ (setadjoin @ sK5 @ emptyset))))),
% 1.67/1.30 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.67/1.30 thf(f70,plain,(
% 1.67/1.30 ($true = (in @ (sK8 @ (setunion @ (setadjoin @ sK5 @ emptyset)) @ sK5) @ (sK4 @ (sK8 @ (setunion @ (setadjoin @ sK5 @ emptyset)) @ sK5) @ (setadjoin @ sK5 @ emptyset)))) | ($true != $true)),
% 1.67/1.30 inference(superposition,[status(thm)],[f64,f68])).
% 1.67/1.30 thf(f64,plain,(
% 1.67/1.30 ( ! [X3 : $i,X4 : $i] : (($true != (in @ X4 @ (setunion @ X3))) | ((in @ X4 @ (sK4 @ X4 @ X3)) = $true)) )),
% 1.67/1.30 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.67/1.30 thf(f56,plain,(
% 1.67/1.30 ( ! [X3 : $i,X4 : $i] : (($true != (in @ X4 @ (setunion @ X3))) | ($true != $true) | ((in @ X4 @ (sK4 @ X4 @ X3)) = $true)) )),
% 1.67/1.30 inference(definition_unfolding,[status(thm)],[f40,f43])).
% 1.67/1.30 thf(f40,plain,(
% 1.67/1.30 ( ! [X3 : $i,X4 : $i] : (($true != (in @ X4 @ (setunion @ X3))) | ((in @ X4 @ (sK4 @ X4 @ X3)) = $true) | (setunionE2 != $true)) )),
% 1.67/1.30 inference(cnf_transformation,[status(thm)],[f28])).
% 1.67/1.30 thf(f63,plain,(
% 1.67/1.30 ( ! [X3 : $i,X4 : $i] : (($true != (in @ (sK8 @ X4 @ X3) @ X3)) | ($true = (subset @ X4 @ X3))) )),
% 1.67/1.30 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.67/1.30 thf(f61,plain,(
% 1.67/1.30 ( ! [X3 : $i,X4 : $i] : (($true != $true) | ($true != (in @ (sK8 @ X4 @ X3) @ X3)) | ($true = (subset @ X4 @ X3))) )),
% 1.67/1.30 inference(definition_unfolding,[status(thm)],[f47,f46])).
% 1.67/1.30 thf(f47,plain,(
% 1.67/1.30 ( ! [X3 : $i,X4 : $i] : (($true = (subset @ X4 @ X3)) | ($true != (in @ (sK8 @ X4 @ X3) @ X3)) | (subsetI2 != $true)) )),
% 1.67/1.30 inference(cnf_transformation,[status(thm)],[f35])).
% 1.67/1.30 % SZS output end Proof for DTF2THF_5188
% 1.67/1.30 % (5471)------------------------------
% 1.67/1.30 % (5471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.30 % (5471)Termination reason: Refutation
% 1.67/1.30
% 1.67/1.30 % (5471)Memory used [KB]: 5500
% 1.67/1.30 % (5471)Time elapsed: 0.010 s
% 1.67/1.30 % (5471)Instructions burned: 7 (million)
% 1.67/1.30 % (5471)------------------------------
% 1.67/1.30 % (5471)------------------------------
% 1.67/1.30 % (5464)Success in time 0.025 s
%------------------------------------------------------------------------------