%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU638^2 : 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 : n002.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 09:35:49 AM UTC 2026
% Result : Theorem 1.57s 1.31s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 62 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 525 ( 155 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 565 ( 59 ~; 43 |; 41 &; 389 @)
% ( 4 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 18 usr; 12 con; 0-2 aty)
% ( 0 !!; 5 ??; 0 @@+; 0 @@-)
% Number of variables : 184 ( 69 ^; 84 !; 31 ?; 184 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_7,type,
singleton: $i > $o ).
thf(func_def_8,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_17,type,
sK0: $i > $o ).
thf(func_def_19,type,
sK2: $i > $o ).
thf(func_def_24,type,
sK7: $i > $o ).
thf(func_def_28,type,
ph10:
!>[X0: $tType] : X0 ).
thf(f71,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f70,f65]) ).
thf(f65,plain,
( ( sK0 @ sK9 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
( ( $true != $true )
| ( ( sK0 @ sK9 )
= $true ) ),
inference(superposition,[status(thm)],[f63,f62]) ).
thf(f62,plain,
( ( in @ sK9 @ ( setadjoin @ sK9 @ emptyset ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f56,f57]) ).
thf(f57,plain,
( ( setadjoin @ sK9 @ emptyset )
= ( dsetconstr @ sK1 @ sK0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( setadjoin @ sK9 @ emptyset )
= ( dsetconstr @ sK1 @ sK0 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ( in @ sK9 @ ( dsetconstr @ sK1 @ sK0 ) )
& ( ( setadjoin @ sK9 @ emptyset )
= ( dsetconstr @ sK1 @ sK0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK1 @ sK0 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK1 @ sK0 ) ) )
@ sK9 )
= $true ),
inference(sigma_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK1 @ sK0 ) )
& ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK1 @ sK0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( ( setadjoin @ Y3 @ emptyset )
= Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) )
@ sK1
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f33,f44]) ).
thf(f44,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( ( setadjoin @ Y3 @ emptyset )
= Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f43,f42]) ).
thf(f42,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= X0 )
& ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( singleton
= ( ^ [X0: $i] :
? [X2: $i] :
( ( ( setadjoin @ X2 @ emptyset )
= X0 )
& ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fMCN0PTsuP/DTF2THF_396.p',singleton) ).
thf(f43,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) )
= ex1 ),
file('/export/starexec/sandbox/tmp/tmp.fMCN0PTsuP/DTF2THF_396.p',ex1) ).
thf(f33,plain,
( ( ex1 @ sK1
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( ( ex1 @ sK1
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ sK1 )
!= $true )
| ( ( sK0 @ X2 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f19,f22]) ).
thf(f22,plain,
( ? [X0: $i > $o,X1: $i] :
( ( ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( X0 @ X2 )
!= $true ) ) )
=> ( ( ( ex1 @ sK1
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ sK1 )
!= $true )
| ( ( sK0 @ X2 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ? [X0: $i > $o,X1: $i] :
( ( ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( X0 @ X2 )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ? [X0: $i > $o,X1: $i] :
( ( ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( X0 @ X2 )
!= $true ) ) )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
~ ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ! [X0: $i > $o,X1: $i] :
( ( ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
=> ? [X2: $i] :
( ( ( X0 @ X2 )
= $true )
& ( ( in @ X2 @ X1 )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
~ ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ! [X0: $i > $o,X1: $i] :
( ( ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
=> ? [X3: $i] :
( ( $true
= ( X0 @ X3 ) )
& ( ( in @ X3 @ X1 )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
~ ( dsetconstrEL
=> ( dsetconstrER
=> ! [X0: $i > $o,X1: $i] :
( ( ex1 @ X1
@ ^ [X2: $i] : ( X0 @ X2 ) )
=> ? [X3: $i] :
( ( X0 @ X3 )
& ( in @ X3 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( dsetconstrEL
=> ( dsetconstrER
=> ! [X1: $i > $o,X0: $i] :
( ( ex1 @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ( in @ X2 @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( dsetconstrEL
=> ( dsetconstrER
=> ! [X1: $i > $o,X0: $i] :
( ( ex1 @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ( in @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fMCN0PTsuP/DTF2THF_396.p',ex1E1) ).
thf(f56,plain,
( ( in @ sK9 @ ( dsetconstr @ sK1 @ sK0 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f63,plain,
! [X0: $i] :
( ( ( in @ X0 @ ( setadjoin @ sK9 @ emptyset ) )
!= $true )
| ( $true
= ( sK0 @ X0 ) ) ),
inference(superposition,[status(thm)],[f61,f57]) ).
thf(f61,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( dsetconstr @ X4 @ X3 ) )
!= $true )
| ( ( X3 @ X5 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) )
| ( ( X3 @ X5 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( X3 @ X5 )
= $true )
| ( $true
!= ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f36,f35]) ).
thf(f35,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f36,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( X3 @ X5 )
= $true )
| ( $true
!= ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( dsetconstrER = $true )
| ( ( ( sK2 @ sK4 )
!= $true )
& ( ( in @ sK4
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) )
= $true ) ) )
& ( ! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( X3 @ X5 )
= $true )
| ( $true
!= ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f25,f26]) ).
thf(f26,plain,
( ? [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X2 )
!= $true )
& ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true ) )
=> ( ( ( sK2 @ sK4 )
!= $true )
& ( ( in @ sK4
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( ( dsetconstrER = $true )
| ? [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X2 )
!= $true )
& ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true ) ) )
& ( ! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( X3 @ X5 )
= $true )
| ( $true
!= ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( dsetconstrER = $true )
| ? [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X2 )
!= $true )
& ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true ) ) )
& ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X2 )
= $true )
| ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( dsetconstrER = $true )
<=> ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X2 )
= $true )
| ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true )
=> ( ( X0 @ X2 )
= $true ) )
<=> ( dsetconstrER = $true ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( X0 @ X2 ) )
= dsetconstrER ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: $i > $o,X0: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
file('/export/starexec/sandbox/tmp/tmp.fMCN0PTsuP/DTF2THF_396.p',dsetconstrER) ).
thf(f70,plain,
( ( sK0 @ sK9 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ( $true != $true )
| ( ( sK0 @ sK9 )
!= $true ) ),
inference(superposition,[status(thm)],[f32,f68]) ).
thf(f68,plain,
( ( in @ sK9 @ sK1 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
( ( $true != $true )
| ( ( in @ sK9 @ sK1 )
= $true ) ),
inference(superposition,[status(thm)],[f66,f62]) ).
thf(f66,plain,
! [X0: $i] :
( ( ( in @ X0 @ ( setadjoin @ sK9 @ emptyset ) )
!= $true )
| ( ( in @ X0 @ sK1 )
= $true ) ),
inference(superposition,[status(thm)],[f59,f57]) ).
thf(f59,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( dsetconstr @ X1 @ X2 ) ) )
| ( ( in @ X0 @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( ( in @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( $true != $true )
| ( $true
!= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f41,f34]) ).
thf(f34,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f41,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( ( in @ X0 @ X1 )
= $true )
| ( dsetconstrEL != $true ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( ( in @ X0 @ X1 )
= $true ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ( ( ( in @ sK5
@ ( dsetconstr @ sK6
@ ^ [Y0: $i] : ( sK7 @ Y0 ) ) )
= $true )
& ( ( in @ sK5 @ sK6 )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f29,f30]) ).
thf(f30,plain,
( ? [X3: $i,X4: $i,X5: $i > $o] :
( ( ( in @ X3
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
= $true )
& ( ( in @ X3 @ X4 )
!= $true ) )
=> ( ( ( in @ sK5
@ ( dsetconstr @ sK6
@ ^ [Y0: $i] : ( sK7 @ Y0 ) ) )
= $true )
& ( ( in @ sK5 @ sK6 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( ( in @ X0 @ X1 )
= $true ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ? [X3: $i,X4: $i,X5: $i > $o] :
( ( ( in @ X3
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
= $true )
& ( ( in @ X3 @ X4 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( ( in @ X0 @ X1 )
= $true ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ? [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
& ( ( in @ X0 @ X1 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( ( in @ X0 @ X1 )
= $true ) )
<=> ( dsetconstrEL = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( dsetconstrEL = $true )
<=> ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
=> ( ( in @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( in @ X0 @ X1 ) )
= dsetconstrEL ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) )
= dsetconstrEL ),
file('/export/starexec/sandbox/tmp/tmp.fMCN0PTsuP/DTF2THF_396.p',dsetconstrEL) ).
thf(f32,plain,
! [X2: $i] :
( ( ( in @ X2 @ sK1 )
!= $true )
| ( ( sK0 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU638^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n002.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:29:33 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.37 ---- Original DTF file ---
% 0.15/0.38 thf(spec,logic,$$dhol).
% 0.15/0.38 %------------------------------------------------------------------------------
% 0.15/0.38 % File : SEU638^2 : TPTP v9.2.1. Released v3.7.0.
% 0.15/0.38 % Domain : Set Theory
% 0.15/0.38 % Problem : Ordered Pairs - Singletons
% 0.15/0.38 % Version : Especial > Reduced > Especial.
% 0.15/0.38 % English : (! A:i.! phi:i>o.ex1 A (^ x:i.phi x) -> (? x:i.in x A & phi x))
% 0.15/0.38
% 0.15/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.15/0.38 % Source : [Bro08]
% 0.15/0.38 % Names : ZFC140l [Bro08]
% 0.15/0.38
% 0.15/0.38 % Status : Theorem
% 0.15/0.38 % Rating : 0.00 v8.2.0, 0.23 v8.1.0, 0.09 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v4.1.0, 0.33 v3.7.0
% 0.15/0.38 % Syntax : Number of formulae : 13 ( 4 unt; 8 typ; 4 def)
% 0.15/0.38 % Number of atoms : 18 ( 5 equ; 0 cnn)
% 0.15/0.38 % Maximal formula atoms : 4 ( 3 avg)
% 0.15/0.38 % Number of connectives : 34 ( 0 ~; 0 |; 2 &; 27 @)
% 0.15/0.38 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.15/0.38 % Maximal formula depth : 10 ( 3 avg)
% 0.15/0.38 % Number of types : 2 ( 0 usr)
% 0.15/0.38 % Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% 0.15/0.38 % Number of symbols : 9 ( 8 usr; 3 con; 0-2 aty)
% 0.15/0.38 % Number of variables : 17 ( 7 ^; 8 !; 2 ?; 17 :)
% 0.15/0.38 % SPC : TH0_THM_EQU_NAR
% 0.15/0.38
% 0.15/0.38 % Comments : http://mathgate.info/detsetitem.php?id=403
% 0.15/0.38 %------------------------------------------------------------------------------
% 0.15/0.38 thf(in_type,type,
% 0.15/0.38 in: $i > $i > $o ).
% 0.15/0.38
% 0.15/0.38 thf(emptyset_type,type,
% 0.15/0.38 emptyset: $i ).
% 0.15/0.38
% 0.15/0.38 thf(setadjoin_type,type,
% 0.15/0.38 setadjoin: $i > $i > $i ).
% 0.15/0.38
% 0.15/0.38 thf(dsetconstr_type,type,
% 0.15/0.38 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.15/0.38
% 0.15/0.38 thf(dsetconstrEL_type,type,
% 0.15/0.38 dsetconstrEL: $o ).
% 0.15/0.38
% 0.15/0.38 thf(dsetconstrEL,definition,
% 0.15/0.38 ( dsetconstrEL
% 0.15/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.15/0.38 ( ( in @ Xx
% 0.15/0.38 @ ( dsetconstr @ A
% 0.15/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.15/0.38 => ( in @ Xx @ A ) ) ) ) ).
% 0.15/0.38
% 0.15/0.38 thf(dsetconstrER_type,type,
% 0.15/0.38 dsetconstrER: $o ).
% 0.15/0.38
% 0.15/0.38 thf(dsetconstrER,definition,
% 0.15/0.38 ( dsetconstrER
% 0.15/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.15/0.38 ( ( in @ Xx
% 0.15/0.38 @ ( dsetconstr @ A
% 0.15/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.15/0.38 => ( Xphi @ Xx ) ) ) ) ).
% 0.15/0.38
% 0.15/0.38 thf(singleton_type,type,
% 0.15/0.38 singleton: $i > $o ).
% 0.15/0.38
% 0.15/0.38 thf(singleton,definition,
% 0.15/0.38 ( singleton
% 0.15/0.38 = ( ^ [A: $i] :
% 0.15/0.38 ? [Xx: $i] :
% 0.15/0.38 ( ( in @ Xx @ A )
% 0.15/0.38 & ( A
% 0.15/0.38 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.15/0.38
% 0.15/0.38 thf(ex1_type,type,
% 0.15/0.38 ex1: $i > ( $i > $o ) > $o ).
% 0.15/0.38
% 0.15/0.38 thf(ex1,definition,
% 0.15/0.38 ( ex1
% 0.15/0.38 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.15/0.38 ( singleton
% 0.15/0.38 @ ( dsetconstr @ A
% 0.15/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.38
% 0.15/0.38 thf(ex1E1,conjecture,
% 0.15/0.38 ( dsetconstrEL
% 0.15/0.38 => ( dsetconstrER
% 0.15/0.38 => ! [A: $i,Xphi: $i > $o] :
% 0.15/0.38 ( ( ex1 @ A
% 0.15/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.38 => ? [Xx: $i] :
% 0.15/0.38 ( ( in @ Xx @ A )
% 0.15/0.38 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.38
% 0.15/0.38 %------------------------------------------------------------------------------
% 0.15/0.38 ------------------------
% 1.40/1.28 ---- Embedded in THF ---
% 1.40/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.40/1.28 %%% Generated on Tue Feb 24 12:29:34 EST 2026
% 1.40/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.40/1.28 %%% Logic specification used:
% 1.40/1.28 %%% thf(spec, logic, $$dhol).
% 1.40/1.28
% 1.40/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.fMCN0PTsuP/DTF2DTF396.p
% See solution above
% 1.40/1.28 ------------------------
% 1.40/1.29 ---- Cleaned THF ---
% 1.40/1.29 thf(in_type,type,
% 1.40/1.29 in: $i > $i > $o ).
% 1.40/1.29
% 1.40/1.29 thf(emptyset_type,type,
% 1.40/1.29 emptyset: $i ).
% 1.40/1.29
% 1.40/1.29 thf(setadjoin_type,type,
% 1.40/1.29 setadjoin: $i > $i > $i ).
% 1.40/1.29
% 1.40/1.29 thf(dsetconstr_type,type,
% 1.40/1.29 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.40/1.29
% 1.40/1.29 thf(dsetconstrEL_type,type,
% 1.40/1.29 dsetconstrEL: $o ).
% 1.40/1.29
% 1.40/1.29 thf(dsetconstrEL,definition,
% 1.40/1.29 ( dsetconstrEL
% 1.40/1.29 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.40/1.29 ( ( in @ Xx
% 1.40/1.29 @ ( dsetconstr @ A
% 1.40/1.29 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.40/1.29 => ( in @ Xx @ A ) ) ) ) ).
% 1.40/1.29
% 1.40/1.29 thf(dsetconstrER_type,type,
% 1.40/1.29 dsetconstrER: $o ).
% 1.40/1.29
% 1.40/1.29 thf(dsetconstrER,definition,
% 1.40/1.29 ( dsetconstrER
% 1.40/1.29 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.40/1.29 ( ( in @ Xx
% 1.40/1.29 @ ( dsetconstr @ A
% 1.40/1.29 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.40/1.29 => ( Xphi @ Xx ) ) ) ) ).
% 1.40/1.29
% 1.40/1.29 thf(singleton_type,type,
% 1.40/1.29 singleton: $i > $o ).
% 1.40/1.29
% 1.40/1.29 thf(singleton,definition,
% 1.40/1.29 ( singleton
% 1.40/1.29 = ( ^ [A: $i] :
% 1.40/1.29 ? [Xx: $i] :
% 1.40/1.29 ( ( in @ Xx @ A )
% 1.40/1.29 & ( A
% 1.40/1.29 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.40/1.29
% 1.40/1.29 thf(ex1_type,type,
% 1.40/1.29 ex1: $i > ( $i > $o ) > $o ).
% 1.40/1.29
% 1.40/1.29 thf(ex1,definition,
% 1.40/1.29 ( ex1
% 1.40/1.29 = ( ^ [A: $i,Xphi: $i > $o] :
% 1.40/1.29 ( singleton
% 1.40/1.29 @ ( dsetconstr @ A
% 1.40/1.29 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 1.40/1.29
% 1.40/1.29 thf(ex1E1,conjecture,
% 1.40/1.29 ( dsetconstrEL
% 1.40/1.29 => ( dsetconstrER
% 1.40/1.29 => ! [A: $i,Xphi: $i > $o] :
% 1.40/1.29 ( ( ex1 @ A
% 1.40/1.29 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.40/1.29 => ? [Xx: $i] :
% 1.40/1.29 ( ( in @ Xx @ A )
% 1.40/1.29 & ( Xphi @ Xx ) ) ) ) ) ).
% 1.40/1.29 ------------------------
% 1.57/1.31 % (515)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_396 for (2999ds/4Mi)
% 1.57/1.31 % (517)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_396 for (2999ds/2Mi)
% 1.57/1.31 % (519)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_396 for (2999ds/275Mi)
% 1.57/1.31 % (518)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_396 for (2999ds/2Mi)
% 1.57/1.31 % (516)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_396 for (2999ds/27Mi)
% 1.57/1.31 % (514)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_396 for (2999ds/183Mi)
% 1.57/1.31 % (520)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_396 for (2999ds/18Mi)
% 1.57/1.31 % (517)Instruction limit reached!
% 1.57/1.31 % (517)------------------------------
% 1.57/1.31 % (517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.31 % (517)Termination reason: Unknown
% 1.57/1.31 % (517)Termination phase: Property scanning
% 1.57/1.31 % (518)Instruction limit reached!
% 1.57/1.31 % (518)------------------------------
% 1.57/1.31 % (518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.31 % (518)Termination reason: Unknown
% 1.57/1.31 % (518)Termination phase: Property scanning
% 1.57/1.31
% 1.57/1.31 % (518)Memory used [KB]: 1023
% 1.57/1.31 % (518)Time elapsed: 0.003 s
% 1.57/1.31 % (518)Instructions burned: 3 (million)
% 1.57/1.31 % (518)------------------------------
% 1.57/1.31 % (518)------------------------------
% 1.57/1.31
% 1.57/1.31 % (517)Memory used [KB]: 1023
% 1.57/1.31 % (517)Time elapsed: 0.003 s
% 1.57/1.31 % (517)Instructions burned: 3 (million)
% 1.57/1.31 % (517)------------------------------
% 1.57/1.31 % (517)------------------------------
% 1.57/1.31 % (515)Instruction limit reached!
% 1.57/1.31 % (515)------------------------------
% 1.57/1.31 % (515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.31 % (515)Termination reason: Unknown
% 1.57/1.31 % (515)Termination phase: Saturation
% 1.57/1.31
% 1.57/1.31 % (515)Memory used [KB]: 5500
% 1.57/1.31 % (515)Time elapsed: 0.004 s
% 1.57/1.31 % (515)Instructions burned: 4 (million)
% 1.57/1.31 % (515)------------------------------
% 1.57/1.31 % (515)------------------------------
% 1.57/1.31 % (519)Refutation not found, incomplete strategy
% 1.57/1.31 % (519)------------------------------
% 1.57/1.31 % (519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.31 % (519)Termination reason: Refutation not found, incomplete strategy
% 1.57/1.31
% 1.57/1.31
% 1.57/1.31 % (519)Memory used [KB]: 5500
% 1.57/1.31 % (519)Time elapsed: 0.004 s
% 1.57/1.31 % (519)Instructions burned: 4 (million)
% 1.57/1.31 % (519)------------------------------
% 1.57/1.31 % (519)------------------------------
% 1.57/1.31 % (520)First to succeed.
% 1.57/1.31 % (514)Also succeeded, but the first one will report.
% 1.57/1.31 % (520)Refutation found. Thanks to Tanya!
% 1.57/1.31 % SZS status Theorem for DTF2THF_396
% 1.57/1.31 % SZS output start Proof for DTF2THF_396
% 1.57/1.31 thf(func_def_0, type, in: $i > $i > $o).
% 1.57/1.31 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.57/1.31 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i).
% 1.57/1.31 thf(func_def_7, type, singleton: $i > $o).
% 1.57/1.31 thf(func_def_8, type, ex1: $i > ($i > $o) > $o).
% 1.57/1.31 thf(func_def_17, type, sK0: $i > $o).
% 1.57/1.31 thf(func_def_19, type, sK2: $i > $o).
% 1.57/1.31 thf(func_def_24, type, sK7: $i > $o).
% 1.57/1.31 thf(func_def_28, type, ph10: !>[X0: $tType]:(X0)).
% 1.57/1.31 thf(f71,plain,(
% 1.57/1.31 $false),
% 1.57/1.31 inference(subsumption_resolution,[status(thm)],[f70,f65])).
% 1.57/1.31 thf(f65,plain,(
% 1.57/1.31 ((sK0 @ sK9) = $true)),
% 1.57/1.31 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.57/1.31 thf(f64,plain,(
% 1.57/1.31 ($true != $true) | ((sK0 @ sK9) = $true)),
% 1.57/1.31 inference(superposition,[status(thm)],[f63,f62])).
% 1.57/1.31 thf(f62,plain,(
% 1.57/1.31 ((in @ sK9 @ (setadjoin @ sK9 @ emptyset)) = $true)),
% 1.57/1.31 inference(forward_demodulation,[status(thm)],[f56,f57])).
% 1.57/1.31 thf(f57,plain,(
% 1.57/1.31 ((setadjoin @ sK9 @ emptyset) = (dsetconstr @ sK1 @ sK0))),
% 1.57/1.31 inference(equality_proxy_clausification,[status(thm)],[f55])).
% 1.57/1.31 thf(f55,plain,(
% 1.57/1.31 (((setadjoin @ sK9 @ emptyset) = (dsetconstr @ sK1 @ sK0)) = $true)),
% 1.57/1.31 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.57/1.31 thf(f54,plain,(
% 1.57/1.31 (((in @ sK9 @ (dsetconstr @ sK1 @ sK0)) & ((setadjoin @ sK9 @ emptyset) = (dsetconstr @ sK1 @ sK0))) = $true)),
% 1.57/1.31 inference(beta_eta_normalization,[status(thm)],[f53])).
% 1.57/1.31 thf(f53,plain,(
% 1.57/1.31 (((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK1 @ sK0)) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK1 @ sK0)))) @ sK9) = $true)),
% 1.57/1.31 inference(sigma_clausification,[status(thm)],[f52])).
% 1.57/1.31 thf(f52,plain,(
% 1.57/1.31 ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK1 @ sK0)) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK1 @ sK0))))) = $true)),
% 1.57/1.31 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.57/1.31 thf(f45,plain,(
% 1.57/1.31 (((^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) & ((setadjoin @ Y3 @ emptyset) = Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))) @ sK1 @ (^[Y0 : $i]: (sK0 @ Y0))) = $true)),
% 1.57/1.31 inference(definition_unfolding,[status(thm)],[f33,f44])).
% 1.57/1.31 thf(f44,plain,(
% 1.57/1.31 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) & ((setadjoin @ Y3 @ emptyset) = Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.57/1.31 inference(definition_unfolding,[status(thm)],[f43,f42])).
% 1.57/1.31 thf(f42,plain,(
% 1.57/1.31 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 1.57/1.31 inference(cnf_transformation,[status(thm)],[f14])).
% 1.57/1.31 thf(f14,plain,(
% 1.57/1.31 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 1.57/1.31 inference(fool_elimination,[status(thm)],[f13])).
% 1.57/1.31 thf(f13,plain,(
% 1.57/1.31 (singleton = (^[X0 : $i] : (? [X1 : $i] : (((setadjoin @ X1 @ emptyset) = X0) & (in @ X1 @ X0)))))),
% 1.57/1.31 inference(rectify,[status(thm)],[f3])).
% 1.57/1.31 thf(f3,axiom,(
% 1.57/1.31 (singleton = (^[X0 : $i] : (? [X2 : $i] : (((setadjoin @ X2 @ emptyset) = X0) & (in @ X2 @ X0)))))),
% 1.57/1.31 file('/export/starexec/sandbox/tmp/tmp.fMCN0PTsuP/DTF2THF_396.p',singleton)).
% 1.57/1.31 thf(f43,plain,(
% 1.57/1.31 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.57/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.57/1.31 thf(f8,plain,(
% 1.57/1.31 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.57/1.31 inference(fool_elimination,[status(thm)],[f4])).
% 1.57/1.31 thf(f4,axiom,(
% 1.57/1.31 ((^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))) = ex1)),
% 1.57/1.31 file('/export/starexec/sandbox/tmp/tmp.fMCN0PTsuP/DTF2THF_396.p',ex1)).
% 1.57/1.31 thf(f33,plain,(
% 1.57/1.31 ((ex1 @ sK1 @ (^[Y0 : $i]: (sK0 @ Y0))) = $true)),
% 1.57/1.31 inference(cnf_transformation,[status(thm)],[f23])).
% 1.57/1.31 thf(f23,plain,(
% 1.57/1.31 (dsetconstrER = $true) & (dsetconstrEL = $true) & (((ex1 @ sK1 @ (^[Y0 : $i]: (sK0 @ Y0))) = $true) & ! [X2 : $i] : (((in @ X2 @ sK1) != $true) | ((sK0 @ X2) != $true)))),
% 1.57/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f19,f22])).
% 1.57/1.31 thf(f22,plain,(
% 1.57/1.31 ? [X0 : $i > $o,X1 : $i] : (((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) = $true) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((X0 @ X2) != $true))) => (((ex1 @ sK1 @ (^[Y0 : $i]: (sK0 @ Y0))) = $true) & ! [X2 : $i] : (((in @ X2 @ sK1) != $true) | ((sK0 @ X2) != $true)))),
% 1.57/1.31 introduced(definition,[],[choice_axiom])).
% 1.57/1.31 thf(f19,plain,(
% 1.57/1.31 (dsetconstrER = $true) & (dsetconstrEL = $true) & ? [X0 : $i > $o,X1 : $i] : (((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) = $true) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((X0 @ X2) != $true)))),
% 1.57/1.31 inference(flattening,[status(thm)],[f18])).
% 1.57/1.31 thf(f18,plain,(
% 1.57/1.31 (? [X0 : $i > $o,X1 : $i] : (((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) = $true) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((X0 @ X2) != $true))) & (dsetconstrER = $true)) & (dsetconstrEL = $true)),
% 1.57/1.31 inference(ennf_transformation,[status(thm)],[f17])).
% 1.57/1.31 thf(f17,plain,(
% 1.57/1.31 ~((dsetconstrEL = $true) => ((dsetconstrER = $true) => ! [X0 : $i > $o,X1 : $i] : (((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) = $true) => ? [X2 : $i] : (((X0 @ X2) = $true) & ((in @ X2 @ X1) = $true)))))),
% 1.57/1.31 inference(rectify,[status(thm)],[f16])).
% 1.57/1.31 thf(f16,plain,(
% 1.57/1.31 ~((dsetconstrEL = $true) => ((dsetconstrER = $true) => ! [X0 : $i > $o,X1 : $i] : (((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) = $true) => ? [X3 : $i] : (($true = (X0 @ X3)) & ((in @ X3 @ X1) = $true)))))),
% 1.57/1.31 inference(fool_elimination,[status(thm)],[f15])).
% 1.57/1.31 thf(f15,plain,(
% 1.57/1.31 ~(dsetconstrEL => (dsetconstrER => ! [X0 : $i > $o,X1 : $i] : ((ex1 @ X1 @ (^[X2 : $i] : (X0 @ X2))) => ? [X3 : $i] : ((X0 @ X3) & (in @ X3 @ X1)))))),
% 1.57/1.31 inference(rectify,[status(thm)],[f6])).
% 1.57/1.31 thf(f6,negated_conjecture,(
% 1.57/1.31 ~(dsetconstrEL => (dsetconstrER => ! [X1 : $i > $o,X0 : $i] : ((ex1 @ X0 @ (^[X2 : $i] : (X1 @ X2))) => ? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0)))))),
% 1.57/1.31 inference(negated_conjecture,[status(cth)],[f5])).
% 1.57/1.31 thf(f5,conjecture,(
% 1.57/1.31 dsetconstrEL => (dsetconstrER => ! [X1 : $i > $o,X0 : $i] : ((ex1 @ X0 @ (^[X2 : $i] : (X1 @ X2))) => ? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0))))),
% 1.57/1.31 file('/export/starexec/sandbox/tmp/tmp.fMCN0PTsuP/DTF2THF_396.p',ex1E1)).
% 1.57/1.31 thf(f56,plain,(
% 1.57/1.31 ((in @ sK9 @ (dsetconstr @ sK1 @ sK0)) = $true)),
% 1.57/1.31 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.57/1.31 thf(f63,plain,(
% 1.57/1.31 ( ! [X0 : $i] : (((in @ X0 @ (setadjoin @ sK9 @ emptyset)) != $true) | ($true = (sK0 @ X0))) )),
% 1.57/1.31 inference(superposition,[status(thm)],[f61,f57])).
% 1.57/1.31 thf(f61,plain,(
% 1.57/1.31 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (((in @ X5 @ (dsetconstr @ X4 @ X3)) != $true) | ((X3 @ X5) = $true)) )),
% 1.57/1.31 inference(beta_eta_normalization,[status(thm)],[f60])).
% 1.57/1.31 thf(f60,plain,(
% 1.57/1.31 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0))))) | ((X3 @ X5) = $true)) )),
% 1.57/1.31 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.57/1.31 thf(f48,plain,(
% 1.57/1.31 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (((X3 @ X5) = $true) | ($true != (in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0))))) | ($true != $true)) )),
% 1.57/1.31 inference(definition_unfolding,[status(thm)],[f36,f35])).
% 1.57/1.31 thf(f35,plain,(
% 1.57/1.31 (dsetconstrER = $true)),
% 1.57/1.31 inference(cnf_transformation,[status(thm)],[f23])).
% 1.57/1.31 thf(f36,plain,(
% 1.57/1.31 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (((X3 @ X5) = $true) | ($true != (in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0))))) | (dsetconstrER != $true)) )),
% 1.57/1.31 inference(cnf_transformation,[status(thm)],[f27])).
% 1.57/1.31 thf(f27,plain,(
% 1.57/1.31 ((dsetconstrER = $true) | (((sK2 @ sK4) != $true) & ((in @ sK4 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (sK2 @ Y0)))) = $true))) & (! [X3 : $i > $o,X4 : $i,X5 : $i] : (((X3 @ X5) = $true) | ($true != (in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0)))))) | (dsetconstrER != $true))),
% 1.57/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f25,f26])).
% 1.57/1.31 thf(f26,plain,(
% 1.57/1.31 ? [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X2) != $true) & ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true)) => (((sK2 @ sK4) != $true) & ((in @ sK4 @ (dsetconstr @ sK3 @ (^[Y0 : $i]: (sK2 @ Y0)))) = $true))),
% 1.57/1.31 introduced(definition,[],[choice_axiom])).
% 1.57/1.31 thf(f25,plain,(
% 1.57/1.31 ((dsetconstrER = $true) | ? [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X2) != $true) & ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true))) & (! [X3 : $i > $o,X4 : $i,X5 : $i] : (((X3 @ X5) = $true) | ($true != (in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0)))))) | (dsetconstrER != $true))),
% 1.57/1.31 inference(rectify,[status(thm)],[f24])).
% 1.57/1.31 thf(f24,plain,(
% 1.57/1.31 ((dsetconstrER = $true) | ? [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X2) != $true) & ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true))) & (! [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X2) = $true) | ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true)) | (dsetconstrER != $true))),
% 1.57/1.31 inference(nnf_transformation,[status(thm)],[f20])).
% 1.57/1.31 thf(f20,plain,(
% 1.57/1.31 (dsetconstrER = $true) <=> ! [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X2) = $true) | ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true))),
% 1.57/1.31 inference(ennf_transformation,[status(thm)],[f10])).
% 1.57/1.31 thf(f10,plain,(
% 1.57/1.31 ! [X0 : $i > $o,X1 : $i,X2 : $i] : (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) => ((X0 @ X2) = $true)) <=> (dsetconstrER = $true)),
% 1.57/1.31 inference(fool_elimination,[status(thm)],[f9])).
% 1.57/1.31 thf(f9,plain,(
% 1.57/1.31 (! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X0 @ X3)))) => (X0 @ X2)) = dsetconstrER)),
% 1.57/1.31 inference(rectify,[status(thm)],[f2])).
% 1.57/1.31 thf(f2,axiom,(
% 1.57/1.31 (! [X1 : $i > $o,X0 : $i,X2 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 1.57/1.31 file('/export/starexec/sandbox/tmp/tmp.fMCN0PTsuP/DTF2THF_396.p',dsetconstrER)).
% 1.57/1.31 thf(f70,plain,(
% 1.57/1.31 ((sK0 @ sK9) != $true)),
% 1.57/1.31 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.57/1.31 thf(f69,plain,(
% 1.57/1.31 ($true != $true) | ((sK0 @ sK9) != $true)),
% 1.57/1.31 inference(superposition,[status(thm)],[f32,f68])).
% 1.57/1.31 thf(f68,plain,(
% 1.57/1.31 ((in @ sK9 @ sK1) = $true)),
% 1.57/1.31 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.57/1.31 thf(f67,plain,(
% 1.57/1.31 ($true != $true) | ((in @ sK9 @ sK1) = $true)),
% 1.57/1.31 inference(superposition,[status(thm)],[f66,f62])).
% 1.57/1.31 thf(f66,plain,(
% 1.57/1.31 ( ! [X0 : $i] : (((in @ X0 @ (setadjoin @ sK9 @ emptyset)) != $true) | ((in @ X0 @ sK1) = $true)) )),
% 1.57/1.31 inference(superposition,[status(thm)],[f59,f57])).
% 1.57/1.31 thf(f59,plain,(
% 1.57/1.31 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (dsetconstr @ X1 @ X2))) | ((in @ X0 @ X1) = $true)) )),
% 1.57/1.31 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.57/1.31 thf(f58,plain,(
% 1.57/1.31 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0))))) | ((in @ X0 @ X1) = $true)) )),
% 1.57/1.31 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.57/1.31 thf(f49,plain,(
% 1.57/1.31 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (((in @ X0 @ X1) = $true) | ($true != $true) | ($true != (in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))))) )),
% 1.57/1.31 inference(definition_unfolding,[status(thm)],[f41,f34])).
% 1.57/1.31 thf(f34,plain,(
% 1.57/1.31 (dsetconstrEL = $true)),
% 1.57/1.31 inference(cnf_transformation,[status(thm)],[f23])).
% 1.57/1.31 thf(f41,plain,(
% 1.57/1.31 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0))))) | ((in @ X0 @ X1) = $true) | (dsetconstrEL != $true)) )),
% 1.57/1.31 inference(cnf_transformation,[status(thm)],[f31])).
% 1.57/1.31 thf(f31,plain,(
% 1.57/1.31 (! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true != (in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0))))) | ((in @ X0 @ X1) = $true)) | (dsetconstrEL != $true)) & ((dsetconstrEL = $true) | (((in @ sK5 @ (dsetconstr @ sK6 @ (^[Y0 : $i]: (sK7 @ Y0)))) = $true) & ((in @ sK5 @ sK6) != $true)))),
% 1.57/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f29,f30])).
% 1.57/1.31 thf(f30,plain,(
% 1.57/1.31 ? [X3 : $i,X4 : $i,X5 : $i > $o] : (((in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0)))) = $true) & ((in @ X3 @ X4) != $true)) => (((in @ sK5 @ (dsetconstr @ sK6 @ (^[Y0 : $i]: (sK7 @ Y0)))) = $true) & ((in @ sK5 @ sK6) != $true))),
% 1.57/1.31 introduced(definition,[],[choice_axiom])).
% 1.57/1.31 thf(f29,plain,(
% 1.57/1.31 (! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true != (in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0))))) | ((in @ X0 @ X1) = $true)) | (dsetconstrEL != $true)) & ((dsetconstrEL = $true) | ? [X3 : $i,X4 : $i,X5 : $i > $o] : (((in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0)))) = $true) & ((in @ X3 @ X4) != $true)))),
% 1.57/1.31 inference(rectify,[status(thm)],[f28])).
% 1.57/1.31 thf(f28,plain,(
% 1.57/1.31 (! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true != (in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0))))) | ((in @ X0 @ X1) = $true)) | (dsetconstrEL != $true)) & ((dsetconstrEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $o] : (($true = (in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0))))) & ((in @ X0 @ X1) != $true)))),
% 1.57/1.31 inference(nnf_transformation,[status(thm)],[f21])).
% 1.57/1.31 thf(f21,plain,(
% 1.57/1.31 ! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true != (in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0))))) | ((in @ X0 @ X1) = $true)) <=> (dsetconstrEL = $true)),
% 1.57/1.31 inference(ennf_transformation,[status(thm)],[f12])).
% 1.57/1.31 thf(f12,plain,(
% 1.57/1.31 (dsetconstrEL = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true = (in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0))))) => ((in @ X0 @ X1) = $true))),
% 1.57/1.31 inference(fool_elimination,[status(thm)],[f11])).
% 1.57/1.31 thf(f11,plain,(
% 1.57/1.31 (! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X0 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X2 @ X3)))) => (in @ X0 @ X1)) = dsetconstrEL)),
% 1.57/1.31 inference(rectify,[status(thm)],[f1])).
% 1.57/1.31 thf(f1,axiom,(
% 1.57/1.31 (! [X2 : $i,X0 : $i,X1 : $i > $o] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X2 @ X0)) = dsetconstrEL)),
% 1.57/1.31 file('/export/starexec/sandbox/tmp/tmp.fMCN0PTsuP/DTF2THF_396.p',dsetconstrEL)).
% 1.57/1.31 thf(f32,plain,(
% 1.57/1.31 ( ! [X2 : $i] : (((in @ X2 @ sK1) != $true) | ((sK0 @ X2) != $true)) )),
% 1.57/1.31 inference(cnf_transformation,[status(thm)],[f23])).
% 1.57/1.31 % SZS output end Proof for DTF2THF_396
% 1.57/1.31 % (520)------------------------------
% 1.57/1.31 % (520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.31 % (520)Termination reason: Refutation
% 1.57/1.31
% 1.57/1.31 % (520)Memory used [KB]: 5500
% 1.57/1.31 % (520)Time elapsed: 0.007 s
% 1.57/1.31 % (520)Instructions burned: 5 (million)
% 1.57/1.31 % (520)------------------------------
% 1.57/1.31 % (520)------------------------------
% 1.57/1.31 % (513)Success in time 0.021 s
%------------------------------------------------------------------------------