%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU708^2 : 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 : n011.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 09:36:33 AM UTC 2026
% Result : Theorem 1.37s 1.25s
% Output : Refutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 13
% Syntax : Number of formulae : 105 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 1396 ( 550 equ; 0 cnn)
% Maximal formula atoms : 10 ( 13 avg)
% Number of connectives : 1334 ( 230 ~; 230 |; 237 &; 567 @)
% ( 8 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 19 con; 0-4 aty)
% Number of variables : 309 ( 81 ^; 178 !; 50 ?; 309 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setunion: $i > $i ).
thf(func_def_2,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_3,type,
singleton: $i > $o ).
thf(func_def_7,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_35,type,
ph15:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
sK16: $o > $i ).
thf(f363,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f362,f332]) ).
thf(f332,plain,
! [X2: $i,X3: $i] :
( ( setunion @ X2 )
= X3 ),
inference(subsumption_resolution,[status(thm)],[f323,f301]) ).
thf(f301,plain,
! [X0: $o] : ( $true = X0 ),
inference(subsumption_resolution,[status(thm)],[f300,f293]) ).
thf(f293,plain,
! [X0: $o] :
( ( ( sK16 @ X0 )
= sK5 )
| ( $true = X0 ) ),
inference(subsumption_resolution,[status(thm)],[f237,f50]) ).
thf(f50,plain,
$true != sK2,
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( theeq = $true )
& ( ifSingleton = $true )
& ( $true
= ( in @ sK3 @ sK4 ) )
& ( ( in @ sK5 @ sK4 )
= $true )
& ( $true != sK2 )
& ( ( if @ sK4 @ sK2 @ sK3 @ sK5 )
!= sK5 )
& ( iffalseProp1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f25,f32,f31]) ).
thf(f31,plain,
( ? [X0: $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
& ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( $true != X0 )
& ( ( if @ X2 @ X0 @ X1 @ X3 )
!= X3 ) ) )
=> ( ( $true
= ( in @ sK3 @ sK4 ) )
& ? [X3: $i] :
( ( ( in @ X3 @ sK4 )
= $true )
& ( $true != sK2 )
& ( ( if @ sK4 @ sK2 @ sK3 @ X3 )
!= X3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ sK4 )
= $true )
& ( $true != sK2 )
& ( ( if @ sK4 @ sK2 @ sK3 @ X3 )
!= X3 ) )
=> ( ( ( in @ sK5 @ sK4 )
= $true )
& ( $true != sK2 )
& ( ( if @ sK4 @ sK2 @ sK3 @ sK5 )
!= sK5 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( theeq = $true )
& ( ifSingleton = $true )
& ? [X0: $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
& ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( $true != X0 )
& ( ( if @ X2 @ X0 @ X1 @ X3 )
!= X3 ) ) )
& ( iffalseProp1 = $true ) ),
inference(flattening,[status(thm)],[f24]) ).
thf(f24,plain,
( ? [X0: $o,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( if @ X2 @ X0 @ X1 @ X3 )
!= X3 )
& ( $true != X0 )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( $true
= ( in @ X1 @ X2 ) ) )
& ( theeq = $true )
& ( ifSingleton = $true )
& ( iffalseProp1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
~ ( ( iffalseProp1 = $true )
=> ( ( ifSingleton = $true )
=> ( ( theeq = $true )
=> ! [X0: $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
=> ( ( $true != X0 )
=> ( ( if @ X2 @ X0 @ X1 @ X3 )
= X3 ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( iffalseProp1 = $true )
=> ( ( ifSingleton = $true )
=> ( ( theeq = $true )
=> ! [X0: $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
=> ( ( $true != X0 )
=> ( ( if @ X2 @ X0 @ X1 @ X3 )
= X3 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( iffalseProp1
=> ( ifSingleton
=> ( theeq
=> ! [X0: $o,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( ~ X0
=> ( ( if @ X2 @ X0 @ X1 @ X3 )
= X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( iffalseProp1
=> ( ifSingleton
=> ( theeq
=> ! [X1: $o,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ X1
=> ( ( if @ X0 @ X1 @ X2 @ X3 )
= X3 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( iffalseProp1
=> ( ifSingleton
=> ( theeq
=> ! [X1: $o,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ X1
=> ( ( if @ X0 @ X1 @ X2 @ X3 )
= X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hNHQIJkcF9/DTF2THF_23592.p',iffalse) ).
thf(f237,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $true = sK2 )
| ( ( sK16 @ X0 )
= sK5 ) ),
inference(duplicate_literal_removal,[status(thm)],[f236]) ).
thf(f236,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $true = sK2 )
| ( ( sK16 @ X0 )
= sK5 )
| ( ( sK16 @ X0 )
= sK5 ) ),
inference(equality_proxy_clausification,[status(thm)],[f233]) ).
thf(f233,plain,
! [X0: $o] :
( ( $true = sK2 )
| ( ( sK5
= ( sK16 @ X0 ) )
= $true )
| ( ( sK16 @ X0 )
= sK5 )
| ( $true = X0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f232]) ).
thf(f232,plain,
! [X0: $o] :
( ( $true
= ( ~ X0
& ( sK5
= ( sK16 @ X0 ) ) ) )
| ( $true = X0 )
| ( ( sK16 @ X0 )
= sK5 )
| ( $true = sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f231]) ).
thf(f231,plain,
! [X0: $o] :
( ( ( sK5
= ( sK16 @ X0 ) )
= $true )
| ( $true
= ( ~ X0
& ( sK5
= ( sK16 @ X0 ) ) ) )
| ( $true = X0 )
| ( $true = sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f215]) ).
thf(f215,plain,
! [X0: $o] :
( ( $true
= ( sK2
& ( sK3
= ( sK16 @ X0 ) ) ) )
| ( $true = X0 )
| ( ( sK5
= ( sK16 @ X0 ) )
= $true )
| ( $true
= ( ~ X0
& ( sK5
= ( sK16 @ X0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f214]) ).
thf(f214,plain,
! [X0: $o] :
( ( $true
= ( ~ sK2
& ( sK5
= ( sK16 @ X0 ) ) ) )
| ( $true
= ( sK2
& ( sK3
= ( sK16 @ X0 ) ) ) )
| ( $true = X0 )
| ( $true
= ( ~ X0
& ( sK5
= ( sK16 @ X0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f213]) ).
thf(f213,plain,
! [X0: $o] :
( ( $true = X0 )
| ( ( ( sK2
& ( sK3
= ( sK16 @ X0 ) ) )
| ( ~ sK2
& ( sK5
= ( sK16 @ X0 ) ) ) )
= $true )
| ( $true
= ( ~ X0
& ( sK5
= ( sK16 @ X0 ) ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f212]) ).
thf(f212,plain,
! [X0: $o] :
( ( ( ( sK2
& ( sK3
= ( sK16 @ X0 ) ) )
| ( ~ sK2
& ( sK5
= ( sK16 @ X0 ) ) ) )
= $true )
| ( $true
= ( ~ X0
& ( sK5
= ( sK16 @ X0 ) ) ) )
| ( $true = X0 )
| ( $true = X0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f210]) ).
thf(f210,plain,
! [X0: $o] :
( ( $true
= ( X0
& ( sK3
= ( sK16 @ X0 ) ) ) )
| ( $true = X0 )
| ( $true
= ( ~ X0
& ( sK5
= ( sK16 @ X0 ) ) ) )
| ( ( ( sK2
& ( sK3
= ( sK16 @ X0 ) ) )
| ( ~ sK2
& ( sK5
= ( sK16 @ X0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f181]) ).
thf(f181,plain,
! [X0: $o] :
( ( ( ( X0
& ( sK3
= ( sK16 @ X0 ) ) )
| ( ~ X0
& ( sK5
= ( sK16 @ X0 ) ) ) )
= $true )
| ( $true = X0 )
| ( ( ( sK2
& ( sK3
= ( sK16 @ X0 ) ) )
| ( ~ sK2
& ( sK5
= ( sK16 @ X0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f180]) ).
thf(f180,plain,
! [X0: $o] :
( ( $true = X0 )
| ( ( ( sK2
& ( sK3
= ( sK16 @ X0 ) ) )
| ( ~ sK2
& ( sK5
= ( sK16 @ X0 ) ) ) )
!= ( ( X0
& ( sK3
= ( sK16 @ X0 ) ) )
| ( ~ X0
& ( sK5
= ( sK16 @ X0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f179]) ).
thf(f179,plain,
! [X0: $o] :
( ( $true = X0 )
| ( ( ^ [Y0: $i] :
( ( sK2
& ( sK3 = Y0 ) )
| ( ~ sK2
& ( sK5 = Y0 ) ) )
@ ( sK16 @ X0 ) )
!= ( ^ [Y0: $i] :
( ( X0
& ( sK3 = Y0 ) )
| ( ~ X0
& ( sK5 = Y0 ) ) )
@ ( sK16 @ X0 ) ) ) ),
inference(negative_extensionality,[status(thm)],[f168]) ).
thf(f168,plain,
! [X0: $o] :
( ( ( ^ [Y0: $i] :
( ( X0
& ( sK3 = Y0 ) )
| ( ~ X0
& ( sK5 = Y0 ) ) ) )
!= ( ^ [Y0: $i] :
( ( sK2
& ( sK3 = Y0 ) )
| ( ~ sK2
& ( sK5 = Y0 ) ) ) ) )
| ( $true = X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f167]) ).
thf(f167,plain,
! [X0: $o] :
( ( sK5 != sK5 )
| ( $true = X0 )
| ( ( ^ [Y0: $i] :
( ( X0
& ( sK3 = Y0 ) )
| ( ~ X0
& ( sK5 = Y0 ) ) ) )
!= ( ^ [Y0: $i] :
( ( sK2
& ( sK3 = Y0 ) )
| ( ~ sK2
& ( sK5 = Y0 ) ) ) ) ) ),
inference(constrained_superposition,[status(thm)],[f80,f154]) ).
thf(f154,plain,
! [X0: $o] :
( ( ( setunion
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] :
( ( X0
& ( sK3 = Y0 ) )
| ( ~ X0
& ( sK5 = Y0 ) ) ) ) )
= sK5 )
| ( $true = X0 ) ),
inference(subsumption_resolution,[status(thm)],[f152,f115]) ).
thf(f115,plain,
! [X0: $o] :
( ( singleton
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] :
( ( X0
& ( sK3 = Y0 ) )
| ( ~ X0
& ( sK5 = Y0 ) ) ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f114]) ).
thf(f114,plain,
! [X0: $o] :
( ( $true != $true )
| ( ( singleton
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] :
( ( X0
& ( sK3 = Y0 ) )
| ( ~ X0
& ( sK5 = Y0 ) ) ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f104,f52]) ).
thf(f52,plain,
( $true
= ( in @ sK3 @ sK4 ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f104,plain,
! [X0: $o,X1: $i] :
( ( $true
!= ( in @ X1 @ sK4 ) )
| ( ( singleton
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] :
( ( X0
& ( X1 = Y0 ) )
| ( ~ X0
& ( sK5 = Y0 ) ) ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f101]) ).
thf(f101,plain,
! [X0: $o,X1: $i] :
( ( $true
!= ( in @ X1 @ sK4 ) )
| ( $true != $true )
| ( ( singleton
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] :
( ( X0
& ( X1 = Y0 ) )
| ( ~ X0
& ( sK5 = Y0 ) ) ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f82,f51]) ).
thf(f51,plain,
( ( in @ sK5 @ sK4 )
= $true ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f82,plain,
! [X6: $o,X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X7 @ X4 ) )
| ( ( singleton
@ ( dsetconstr @ X4
@ ^ [Y0: $i] :
( ( X6
& ( X5 = Y0 ) )
| ( ~ X6
& ( X7 = Y0 ) ) ) ) )
= $true )
| ( ( in @ X5 @ X4 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
! [X6: $o,X7: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X5 @ X4 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ X4
@ ^ [Y0: $i] :
( ( X6
& ( X5 = Y0 ) )
| ( ~ X6
& ( X7 = Y0 ) ) ) ) )
= $true )
| ( $true
!= ( in @ X7 @ X4 ) ) ),
inference(definition_unfolding,[status(thm)],[f55,f53]) ).
thf(f53,plain,
ifSingleton = $true,
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f55,plain,
! [X6: $o,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ X4
@ ^ [Y0: $i] :
( ( X6
& ( X5 = Y0 ) )
| ( ~ X6
& ( X7 = Y0 ) ) ) ) )
= $true )
| ( $true
!= ( in @ X7 @ X4 ) )
| ( ifSingleton != $true ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( ifSingleton = $true )
| ( ( $true
= ( in @ sK7 @ sK6 ) )
& ( ( singleton
@ ( dsetconstr @ sK6
@ ^ [Y0: $i] :
( ( sK8
& ( sK7 = Y0 ) )
| ( ~ sK8
& ( sK9 = Y0 ) ) ) ) )
!= $true )
& ( $true
= ( in @ sK9 @ sK6 ) ) ) )
& ( ! [X4: $i,X5: $i,X6: $o] :
( ( ( in @ X5 @ X4 )
!= $true )
| ! [X7: $i] :
( ( ( singleton
@ ( dsetconstr @ X4
@ ^ [Y0: $i] :
( ( X6
& ( X5 = Y0 ) )
| ( ~ X6
& ( X7 = Y0 ) ) ) ) )
= $true )
| ( $true
!= ( in @ X7 @ X4 ) ) ) )
| ( ifSingleton != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f35,f37,f36]) ).
thf(f36,plain,
( ? [X0: $i,X1: $i,X2: $o] :
( ( ( in @ X1 @ X0 )
= $true )
& ? [X3: $i] :
( ( $true
!= ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( ( X2
& ( X1 = Y0 ) )
| ( ~ X2
& ( X3 = Y0 ) ) ) ) ) )
& ( ( in @ X3 @ X0 )
= $true ) ) )
=> ( ( $true
= ( in @ sK7 @ sK6 ) )
& ? [X3: $i] :
( ( ( singleton
@ ( dsetconstr @ sK6
@ ^ [Y0: $i] :
( ( sK8
& ( sK7 = Y0 ) )
| ( ~ sK8
& ( X3 = Y0 ) ) ) ) )
!= $true )
& ( ( in @ X3 @ sK6 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f37,plain,
( ? [X3: $i] :
( ( ( singleton
@ ( dsetconstr @ sK6
@ ^ [Y0: $i] :
( ( sK8
& ( sK7 = Y0 ) )
| ( ~ sK8
& ( X3 = Y0 ) ) ) ) )
!= $true )
& ( ( in @ X3 @ sK6 )
= $true ) )
=> ( ( ( singleton
@ ( dsetconstr @ sK6
@ ^ [Y0: $i] :
( ( sK8
& ( sK7 = Y0 ) )
| ( ~ sK8
& ( sK9 = Y0 ) ) ) ) )
!= $true )
& ( $true
= ( in @ sK9 @ sK6 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f35,plain,
( ( ( ifSingleton = $true )
| ? [X0: $i,X1: $i,X2: $o] :
( ( ( in @ X1 @ X0 )
= $true )
& ? [X3: $i] :
( ( $true
!= ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( ( X2
& ( X1 = Y0 ) )
| ( ~ X2
& ( X3 = Y0 ) ) ) ) ) )
& ( ( in @ X3 @ X0 )
= $true ) ) ) )
& ( ! [X4: $i,X5: $i,X6: $o] :
( ( ( in @ X5 @ X4 )
!= $true )
| ! [X7: $i] :
( ( ( singleton
@ ( dsetconstr @ X4
@ ^ [Y0: $i] :
( ( X6
& ( X5 = Y0 ) )
| ( ~ X6
& ( X7 = Y0 ) ) ) ) )
= $true )
| ( $true
!= ( in @ X7 @ X4 ) ) ) )
| ( ifSingleton != $true ) ) ),
inference(rectify,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( ifSingleton = $true )
| ? [X0: $i,X1: $i,X2: $o] :
( ( ( in @ X1 @ X0 )
= $true )
& ? [X3: $i] :
( ( $true
!= ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( ( X2
& ( X1 = Y0 ) )
| ( ~ X2
& ( X3 = Y0 ) ) ) ) ) )
& ( ( in @ X3 @ X0 )
= $true ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $o] :
( ( ( in @ X1 @ X0 )
!= $true )
| ! [X3: $i] :
( ( $true
= ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( ( X2
& ( X1 = Y0 ) )
| ( ~ X2
& ( X3 = Y0 ) ) ) ) ) )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
| ( ifSingleton != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ifSingleton = $true )
<=> ! [X0: $i,X1: $i,X2: $o] :
( ( ( in @ X1 @ X0 )
!= $true )
| ! [X3: $i] :
( ( $true
= ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( ( X2
& ( X1 = Y0 ) )
| ( ~ X2
& ( X3 = Y0 ) ) ) ) ) )
| ( ( in @ X3 @ X0 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ifSingleton = $true )
<=> ! [X0: $i,X1: $i,X2: $o] :
( ( ( in @ X1 @ X0 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( $true
= ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( ( X2
& ( X1 = Y0 ) )
| ( ~ X2
& ( X3 = Y0 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i,X1: $i,X2: $o] :
( ( ( in @ X1 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X3 = X4 )
& ~ X2 )
| ( ( X1 = X4 )
& X2 ) ) ) ) ) )
= ifSingleton ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i,X2: $i,X1: $o] :
( ( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X3 = X4 )
& ~ X1 )
| ( ( X2 = X4 )
& X1 ) ) ) ) ) )
= ifSingleton ),
file('/export/starexec/sandbox2/tmp/tmp.hNHQIJkcF9/DTF2THF_23592.p',ifSingleton) ).
thf(f152,plain,
! [X0: $o] :
( ( $true = X0 )
| ( ( setunion
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] :
( ( X0
& ( sK3 = Y0 ) )
| ( ~ X0
& ( sK5 = Y0 ) ) ) ) )
= sK5 )
| ( ( singleton
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] :
( ( X0
& ( sK3 = Y0 ) )
| ( ~ X0
& ( sK5 = Y0 ) ) ) ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f150]) ).
thf(f150,plain,
! [X0: $o] :
( ( ( singleton
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] :
( ( X0
& ( sK3 = Y0 ) )
| ( ~ X0
& ( sK5 = Y0 ) ) ) ) )
!= $true )
| ( ( setunion
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] :
( ( X0
& ( sK3 = Y0 ) )
| ( ~ X0
& ( sK5 = Y0 ) ) ) ) )
= sK5 )
| ( $true != $true )
| ( $true = X0 ) ),
inference(superposition,[status(thm)],[f79,f123]) ).
thf(f123,plain,
! [X0: $o] :
( ( $true
= ( in @ sK5
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] :
( ( X0
& ( sK3 = Y0 ) )
| ( ~ X0
& ( sK5 = Y0 ) ) ) ) ) )
| ( $true = X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f122]) ).
thf(f122,plain,
! [X0: $o] :
( ( $true != $true )
| ( $true = X0 )
| ( $true
= ( in @ sK5
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] :
( ( X0
& ( sK3 = Y0 ) )
| ( ~ X0
& ( sK5 = Y0 ) ) ) ) ) ) ),
inference(superposition,[status(thm)],[f112,f52]) ).
thf(f112,plain,
! [X0: $i,X1: $o] :
( ( $true
!= ( in @ X0 @ sK4 ) )
| ( $true = X1 )
| ( $true
= ( in @ sK5
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] :
( ( X1
& ( X0 = Y0 ) )
| ( ~ X1
& ( sK5 = Y0 ) ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f109]) ).
thf(f109,plain,
! [X0: $i,X1: $o] :
( ( $true != $true )
| ( $true = X1 )
| ( $true
= ( in @ sK5
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] :
( ( X1
& ( X0 = Y0 ) )
| ( ~ X1
& ( sK5 = Y0 ) ) ) ) ) )
| ( $true
!= ( in @ X0 @ sK4 ) ) ),
inference(superposition,[status(thm)],[f81,f51]) ).
thf(f81,plain,
! [X6: $i,X7: $i,X4: $o,X5: $i] :
( ( $true
!= ( in @ X7 @ X6 ) )
| ( ( in @ X5 @ X6 )
!= $true )
| ( $true = X4 )
| ( ( in @ X7
@ ( dsetconstr @ X6
@ ^ [Y0: $i] :
( ( X4
& ( X5 = Y0 ) )
| ( ~ X4
& ( X7 = Y0 ) ) ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
! [X6: $i,X7: $i,X4: $o,X5: $i] :
( ( $true
!= ( in @ X7 @ X6 ) )
| ( $true = X4 )
| ( ( in @ X7
@ ( dsetconstr @ X6
@ ^ [Y0: $i] :
( ( X4
& ( X5 = Y0 ) )
| ( ~ X4
& ( X7 = Y0 ) ) ) ) )
= $true )
| ( ( in @ X5 @ X6 )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f59,f48]) ).
thf(f48,plain,
iffalseProp1 = $true,
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f59,plain,
! [X6: $i,X7: $i,X4: $o,X5: $i] :
( ( $true
!= ( in @ X7 @ X6 ) )
| ( $true = X4 )
| ( ( in @ X7
@ ( dsetconstr @ X6
@ ^ [Y0: $i] :
( ( X4
& ( X5 = Y0 ) )
| ( ~ X4
& ( X7 = Y0 ) ) ) ) )
= $true )
| ( ( in @ X5 @ X6 )
!= $true )
| ( iffalseProp1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( iffalseProp1 = $true )
| ( ( $true
= ( in @ sK13 @ sK12 ) )
& ( $true != sK10 )
& ( ( in @ sK13
@ ( dsetconstr @ sK12
@ ^ [Y0: $i] :
( ( sK10
& ( sK11 = Y0 ) )
| ( ~ sK10
& ( sK13 = Y0 ) ) ) ) )
!= $true )
& ( $true
= ( in @ sK11 @ sK12 ) ) ) )
& ( ! [X4: $o,X5: $i,X6: $i] :
( ! [X7: $i] :
( ( $true
!= ( in @ X7 @ X6 ) )
| ( $true = X4 )
| ( ( in @ X7
@ ( dsetconstr @ X6
@ ^ [Y0: $i] :
( ( X4
& ( X5 = Y0 ) )
| ( ~ X4
& ( X7 = Y0 ) ) ) ) )
= $true ) )
| ( ( in @ X5 @ X6 )
!= $true ) )
| ( iffalseProp1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13])],[f40,f42,f41]) ).
thf(f41,plain,
( ? [X0: $o,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( $true != X0 )
& ( ( in @ X3
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( X0
& ( X1 = Y0 ) )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) )
!= $true ) )
& ( $true
= ( in @ X1 @ X2 ) ) )
=> ( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK12 ) )
& ( $true != sK10 )
& ( $true
!= ( in @ X3
@ ( dsetconstr @ sK12
@ ^ [Y0: $i] :
( ( sK10
& ( sK11 = Y0 ) )
| ( ~ sK10
& ( X3 = Y0 ) ) ) ) ) ) )
& ( $true
= ( in @ sK11 @ sK12 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f42,plain,
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK12 ) )
& ( $true != sK10 )
& ( $true
!= ( in @ X3
@ ( dsetconstr @ sK12
@ ^ [Y0: $i] :
( ( sK10
& ( sK11 = Y0 ) )
| ( ~ sK10
& ( X3 = Y0 ) ) ) ) ) ) )
=> ( ( $true
= ( in @ sK13 @ sK12 ) )
& ( $true != sK10 )
& ( ( in @ sK13
@ ( dsetconstr @ sK12
@ ^ [Y0: $i] :
( ( sK10
& ( sK11 = Y0 ) )
| ( ~ sK10
& ( sK13 = Y0 ) ) ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f40,plain,
( ( ( iffalseProp1 = $true )
| ? [X0: $o,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( $true != X0 )
& ( ( in @ X3
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( X0
& ( X1 = Y0 ) )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) )
!= $true ) )
& ( $true
= ( in @ X1 @ X2 ) ) ) )
& ( ! [X4: $o,X5: $i,X6: $i] :
( ! [X7: $i] :
( ( $true
!= ( in @ X7 @ X6 ) )
| ( $true = X4 )
| ( ( in @ X7
@ ( dsetconstr @ X6
@ ^ [Y0: $i] :
( ( X4
& ( X5 = Y0 ) )
| ( ~ X4
& ( X7 = Y0 ) ) ) ) )
= $true ) )
| ( ( in @ X5 @ X6 )
!= $true ) )
| ( iffalseProp1 != $true ) ) ),
inference(rectify,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( iffalseProp1 = $true )
| ? [X0: $o,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( $true != X0 )
& ( ( in @ X3
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( X0
& ( X1 = Y0 ) )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) )
!= $true ) )
& ( $true
= ( in @ X1 @ X2 ) ) ) )
& ( ! [X0: $o,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( $true = X0 )
| ( ( in @ X3
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( X0
& ( X1 = Y0 ) )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) )
= $true ) )
| ( $true
!= ( in @ X1 @ X2 ) ) )
| ( iffalseProp1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( iffalseProp1 = $true )
<=> ! [X0: $o,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( $true = X0 )
| ( ( in @ X3
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( X0
& ( X1 = Y0 ) )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) )
= $true ) )
| ( $true
!= ( in @ X1 @ X2 ) ) ) ),
inference(flattening,[status(thm)],[f20]) ).
thf(f20,plain,
( ( iffalseProp1 = $true )
<=> ! [X0: $o,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( X0
& ( X1 = Y0 ) )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) )
= $true )
| ( $true = X0 )
| ( ( in @ X3 @ X2 )
!= $true ) )
| ( $true
!= ( in @ X1 @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( iffalseProp1 = $true )
<=> ! [X0: $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
=> ( ( $true != X0 )
=> ( ( in @ X3
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( X0
& ( X1 = Y0 ) )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) )
= $true ) ) ) ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ( iffalseProp1 = $true )
<=> ! [X0: $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
=> ( ( $true != X0 )
=> ( ( in @ X3
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( X0
& ( X1 = Y0 ) )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
( iffalseProp1
= ( ! [X0: $o,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( ~ X0
=> ( in @ X3
@ ( dsetconstr @ X2
@ ^ [X4: $i] :
( ( ( X3 = X4 )
& ~ X0 )
| ( ( X1 = X4 )
& X0 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( iffalseProp1
= ( ! [X1: $o,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ X1
=> ( in @ X3
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X3 = X4 )
& ~ X1 )
| ( ( X2 = X4 )
& X1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hNHQIJkcF9/DTF2THF_23592.p',iffalseProp1) ).
thf(f79,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( ( setunion @ X2 )
= X3 )
| ( ( singleton @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
! [X2: $i,X3: $i] :
( ( ( setunion @ X2 )
= X3 )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true != $true )
| ( ( singleton @ X2 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f44,f54]) ).
thf(f54,plain,
theeq = $true,
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f44,plain,
! [X2: $i,X3: $i] :
( ( ( singleton @ X2 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( setunion @ X2 )
= X3 )
| ( theeq != $true ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( theeq = $true )
| ( ( ( singleton @ sK0 )
= $true )
& ( $true
= ( in @ sK1 @ sK0 ) )
& ( ( setunion @ sK0 )
!= sK1 ) ) )
& ( ! [X2: $i] :
( ( ( singleton @ X2 )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( ( setunion @ X2 )
= X3 ) ) )
| ( theeq != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f27,f29,f28]) ).
thf(f28,plain,
( ? [X0: $i] :
( ( $true
= ( singleton @ X0 ) )
& ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( setunion @ X0 )
!= X1 ) ) )
=> ( ( ( singleton @ sK0 )
= $true )
& ? [X1: $i] :
( ( $true
= ( in @ X1 @ sK0 ) )
& ( ( setunion @ sK0 )
!= X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ? [X1: $i] :
( ( $true
= ( in @ X1 @ sK0 ) )
& ( ( setunion @ sK0 )
!= X1 ) )
=> ( ( $true
= ( in @ sK1 @ sK0 ) )
& ( ( setunion @ sK0 )
!= sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ( ( theeq = $true )
| ? [X0: $i] :
( ( $true
= ( singleton @ X0 ) )
& ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( setunion @ X0 )
!= X1 ) ) ) )
& ( ! [X2: $i] :
( ( ( singleton @ X2 )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( ( setunion @ X2 )
= X3 ) ) )
| ( theeq != $true ) ) ),
inference(rectify,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( theeq = $true )
| ? [X0: $i] :
( ( $true
= ( singleton @ X0 ) )
& ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( setunion @ X0 )
!= X1 ) ) ) )
& ( ! [X0: $i] :
( ( $true
!= ( singleton @ X0 ) )
| ! [X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( setunion @ X0 )
= X1 ) ) )
| ( theeq != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( theeq = $true )
<=> ! [X0: $i] :
( ( $true
!= ( singleton @ X0 ) )
| ! [X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( setunion @ X0 )
= X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X0: $i] :
( ( $true
= ( singleton @ X0 ) )
=> ! [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( setunion @ X0 )
= X1 ) ) )
<=> ( theeq = $true ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i] :
( ( ( singleton @ X0 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( ( setunion @ X0 )
= X1 ) ) )
= theeq ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X5: $i] :
( ( ( singleton @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( ( setunion @ X5 )
= X2 ) ) )
= theeq ),
file('/export/starexec/sandbox2/tmp/tmp.hNHQIJkcF9/DTF2THF_23592.p',theeq) ).
thf(f80,plain,
( ( setunion
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] :
( ( sK2
& ( sK3 = Y0 ) )
| ( ~ sK2
& ( sK5 = Y0 ) ) ) ) )
!= sK5 ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
( ( ^ [Y0: $i,Y1: $o,Y2: $i,Y3: $i] :
( setunion
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( Y1
& ( Y2 = Y4 ) )
| ( ~ Y1
& ( Y3 = Y4 ) ) ) ) )
@ sK4
@ sK2
@ sK3
@ sK5 )
!= sK5 ),
inference(definition_unfolding,[status(thm)],[f49,f64]) ).
thf(f64,plain,
( if
= ( ^ [Y0: $i,Y1: $o,Y2: $i,Y3: $i] :
( setunion
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( Y1
& ( Y2 = Y4 ) )
| ( ~ Y1
& ( Y3 = Y4 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( if
= ( ^ [Y0: $i,Y1: $o,Y2: $i,Y3: $i] :
( setunion
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( Y1
& ( Y2 = Y4 ) )
| ( ~ Y1
& ( Y3 = Y4 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [X0: $i,X1: $o,X2: $i,X3: $i] :
( setunion
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X3 = X4 )
& ~ X1 )
| ( ( X2 = X4 )
& X1 ) ) ) ) )
= if ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X0: $i,X1: $o,X2: $i,X3: $i] :
( setunion
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X3 = X4 )
& ~ X1 )
| ( ( X2 = X4 )
& X1 ) ) ) ) )
= if ),
file('/export/starexec/sandbox2/tmp/tmp.hNHQIJkcF9/DTF2THF_23592.p',if) ).
thf(f49,plain,
( ( if @ sK4 @ sK2 @ sK3 @ sK5 )
!= sK5 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f300,plain,
! [X0: $o] :
( ( $true = X0 )
| ( ( sK16 @ X0 )
!= sK5 ) ),
inference(subsumption_resolution,[status(thm)],[f209,f50]) ).
thf(f209,plain,
! [X0: $o] :
( ( ( sK16 @ X0 )
!= sK5 )
| ( $true = sK2 )
| ( $true = X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f208]) ).
thf(f208,plain,
! [X0: $o] :
( ( $true = X0 )
| ( ( sK5
= ( sK16 @ X0 ) )
= $false )
| ( $true = sK2 ) ),
inference(not_proxy_clausification,[status(thm)],[f207]) ).
thf(f207,plain,
! [X0: $o] :
( ( $true = X0 )
| ( ( ~ sK2 ) = $false )
| ( ( sK5
= ( sK16 @ X0 ) )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f206]) ).
thf(f206,plain,
! [X0: $o] :
( ( ( sK5
= ( sK16 @ X0 ) )
= $false )
| ( $true = X0 )
| ( ( ~ sK2 ) = $false )
| ( $true = X0 ) ),
inference(not_proxy_clausification,[status(thm)],[f205]) ).
thf(f205,plain,
! [X0: $o] :
( ( ( ~ X0 ) = $false )
| ( ( sK5
= ( sK16 @ X0 ) )
= $false )
| ( ( ~ sK2 ) = $false )
| ( $true = X0 ) ),
inference(duplicate_literal_removal,[status(thm)],[f204]) ).
thf(f204,plain,
! [X0: $o] :
( ( $true = X0 )
| ( ( sK5
= ( sK16 @ X0 ) )
= $false )
| ( ( ~ sK2 ) = $false )
| ( ( ~ X0 ) = $false )
| ( ( sK5
= ( sK16 @ X0 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f203]) ).
thf(f203,plain,
! [X0: $o] :
( ( $false
= ( ~ sK2
& ( sK5
= ( sK16 @ X0 ) ) ) )
| ( ( sK5
= ( sK16 @ X0 ) )
= $false )
| ( ( ~ X0 ) = $false )
| ( $true = X0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f195]) ).
thf(f195,plain,
! [X0: $o] :
( ( $false
= ( ~ X0
& ( sK5
= ( sK16 @ X0 ) ) ) )
| ( $false
= ( ~ sK2
& ( sK5
= ( sK16 @ X0 ) ) ) )
| ( $true = X0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f183]) ).
thf(f183,plain,
! [X0: $o] :
( ( ( ( sK2
& ( sK3
= ( sK16 @ X0 ) ) )
| ( ~ sK2
& ( sK5
= ( sK16 @ X0 ) ) ) )
= $false )
| ( $true = X0 )
| ( $false
= ( ~ X0
& ( sK5
= ( sK16 @ X0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f182]) ).
thf(f182,plain,
! [X0: $o] :
( ( ( ( X0
& ( sK3
= ( sK16 @ X0 ) ) )
| ( ~ X0
& ( sK5
= ( sK16 @ X0 ) ) ) )
= $false )
| ( $true = X0 )
| ( ( ( sK2
& ( sK3
= ( sK16 @ X0 ) ) )
| ( ~ sK2
& ( sK5
= ( sK16 @ X0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f180]) ).
thf(f323,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( ( setunion @ X2 )
= X3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f302]) ).
thf(f302,plain,
! [X2: $i,X3: $i] :
( ( ( setunion @ X2 )
= X3 )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true != $true ) ),
inference(backward_demodulation,[status(thm)],[f79,f301]) ).
thf(f362,plain,
! [X0: $i] :
( ( setunion @ X0 )
!= sK5 ),
inference(superposition,[status(thm)],[f80,f332]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU708^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n011.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 12:31:17 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.41 ---- Original DTF file ---
% 0.16/0.41 thf(spec,logic,$$dhol).
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 % File : SEU708^2 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.41 % Domain : Set Theory
% 0.16/0.41 % Problem : Conditionals
% 0.16/0.41 % Version : Especial > Reduced > Especial.
% 0.16/0.41 % English : (! A:i.! phi:o.! x:i.in x A -> (! y:i.in y A -> ~phi ->
% 0.16/0.41 % if A phi x y = y))
% 0.16/0.41
% 0.16/0.41 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.41 % Source : [Bro08]
% 0.16/0.41 % Names : ZFC210l [Bro08]
% 0.16/0.41
% 0.16/0.41 % Status : Theorem
% 0.16/0.41 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.40 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0, 0.43 v7.4.0, 0.22 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v6.1.0, 0.29 v6.0.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% 0.16/0.41 % Syntax : Number of formulae : 13 ( 4 unt; 8 typ; 4 def)
% 0.16/0.41 % Number of atoms : 28 ( 12 equ; 0 cnn)
% 0.16/0.41 % Maximal formula atoms : 6 ( 5 avg)
% 0.16/0.41 % Number of connectives : 57 ( 5 ~; 3 |; 6 &; 30 @)
% 0.16/0.41 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.16/0.41 % Maximal formula depth : 12 ( 3 avg)
% 0.16/0.41 % Number of types : 2 ( 0 usr)
% 0.16/0.41 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.16/0.41 % Number of symbols : 9 ( 8 usr; 3 con; 0-4 aty)
% 0.16/0.41 % Number of variables : 21 ( 7 ^; 14 !; 0 ?; 21 :)
% 0.16/0.41 % SPC : TH0_THM_EQU_NAR
% 0.16/0.41
% 0.16/0.41 % Comments : http://mathgate.info/detsetitem.php?id=264
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 thf(in_type,type,
% 0.16/0.41 in: $i > $i > $o ).
% 0.16/0.41
% 0.16/0.41 thf(setunion_type,type,
% 0.16/0.41 setunion: $i > $i ).
% 0.16/0.41
% 0.16/0.41 thf(dsetconstr_type,type,
% 0.16/0.41 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.16/0.41
% 0.16/0.41 thf(singleton_type,type,
% 0.16/0.41 singleton: $i > $o ).
% 0.16/0.41
% 0.16/0.41 thf(iffalseProp1_type,type,
% 0.16/0.41 iffalseProp1: $o ).
% 0.16/0.41
% 0.16/0.41 thf(iffalseProp1,definition,
% 0.16/0.41 ( iffalseProp1
% 0.16/0.41 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.16/0.41 ( ( in @ Xx @ A )
% 0.16/0.41 => ! [Xy: $i] :
% 0.16/0.41 ( ( in @ Xy @ A )
% 0.16/0.41 => ( ~ Xphi
% 0.16/0.41 => ( in @ Xy
% 0.16/0.41 @ ( dsetconstr @ A
% 0.16/0.41 @ ^ [Xz: $i] :
% 0.16/0.41 ( ( Xphi
% 0.16/0.41 & ( Xz = Xx ) )
% 0.16/0.41 | ( ~ Xphi
% 0.16/0.41 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.41
% 0.16/0.41 thf(ifSingleton_type,type,
% 0.16/0.41 ifSingleton: $o ).
% 0.16/0.41
% 0.16/0.41 thf(ifSingleton,definition,
% 0.16/0.41 ( ifSingleton
% 0.16/0.41 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.16/0.41 ( ( in @ Xx @ A )
% 0.16/0.41 => ! [Xy: $i] :
% 0.16/0.41 ( ( in @ Xy @ A )
% 0.16/0.41 => ( singleton
% 0.16/0.41 @ ( dsetconstr @ A
% 0.16/0.41 @ ^ [Xz: $i] :
% 0.16/0.41 ( ( Xphi
% 0.16/0.41 & ( Xz = Xx ) )
% 0.16/0.41 | ( ~ Xphi
% 0.16/0.41 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.16/0.41
% 0.16/0.41 thf(if_type,type,
% 0.16/0.41 if: $i > $o > $i > $i > $i ).
% 0.16/0.41
% 0.16/0.41 thf(if,definition,
% 0.16/0.41 ( if
% 0.16/0.41 = ( ^ [A: $i,Xphi: $o,Xx: $i,Xy: $i] :
% 0.16/0.41 ( setunion
% 0.16/0.41 @ ( dsetconstr @ A
% 0.16/0.41 @ ^ [Xz: $i] :
% 0.16/0.41 ( ( Xphi
% 0.16/0.41 & ( Xz = Xx ) )
% 0.16/0.41 | ( ~ Xphi
% 0.16/0.41 & ( Xz = Xy ) ) ) ) ) ) ) ).
% 0.16/0.41
% 0.16/0.41 thf(theeq_type,type,
% 0.16/0.41 theeq: $o ).
% 0.16/0.41
% 0.16/0.41 thf(theeq,definition,
% 0.16/0.41 ( theeq
% 0.16/0.41 = ( ! [X: $i] :
% 0.16/0.41 ( ( singleton @ X )
% 0.16/0.41 => ! [Xx: $i] :
% 0.16/0.41 ( ( in @ Xx @ X )
% 0.16/0.41 => ( ( setunion @ X )
% 0.16/0.41 = Xx ) ) ) ) ) ).
% 0.16/0.41
% 0.16/0.41 thf(iffalse,conjecture,
% 0.16/0.41 ( iffalseProp1
% 0.16/0.41 => ( ifSingleton
% 0.16/0.41 => ( theeq
% 0.16/0.41 => ! [A: $i,Xphi: $o,Xx: $i] :
% 0.16/0.41 ( ( in @ Xx @ A )
% 0.16/0.41 => ! [Xy: $i] :
% 0.16/0.41 ( ( in @ Xy @ A )
% 0.16/0.41 => ( ~ Xphi
% 0.16/0.41 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.16/0.41 = Xy ) ) ) ) ) ) ) ).
% 0.16/0.41
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 ------------------------
% 1.36/1.13 ---- Embedded in THF ---
% 1.36/1.13 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.36/1.13 %%% Generated on Tue Feb 24 12:31:18 EST 2026
% 1.36/1.13 %%% using '$$dhol' embedding, version 1.3.0.
% 1.36/1.13 %%% Logic specification used:
% 1.36/1.13 %%% thf(spec, logic, $$dhol).
% 1.36/1.13
% 1.36/1.13 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.hNHQIJkcF9/DTF2DTF23592.p
% See solution above
% 1.36/1.13 ------------------------
% 1.36/1.14 ---- Cleaned THF ---
% 1.36/1.14 thf(in_type,type,
% 1.36/1.14 in: $i > $i > $o ).
% 1.36/1.14
% 1.36/1.14 thf(setunion_type,type,
% 1.36/1.14 setunion: $i > $i ).
% 1.36/1.14
% 1.36/1.14 thf(dsetconstr_type,type,
% 1.36/1.14 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.36/1.14
% 1.36/1.14 thf(singleton_type,type,
% 1.36/1.14 singleton: $i > $o ).
% 1.36/1.14
% 1.36/1.14 thf(iffalseProp1_type,type,
% 1.36/1.14 iffalseProp1: $o ).
% 1.36/1.14
% 1.36/1.14 thf(iffalseProp1,definition,
% 1.36/1.14 ( iffalseProp1
% 1.36/1.14 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 1.36/1.14 ( ( in @ Xx @ A )
% 1.36/1.14 => ! [Xy: $i] :
% 1.36/1.14 ( ( in @ Xy @ A )
% 1.36/1.14 => ( ~ Xphi
% 1.36/1.14 => ( in @ Xy
% 1.36/1.14 @ ( dsetconstr @ A
% 1.36/1.14 @ ^ [Xz: $i] :
% 1.36/1.14 ( ( Xphi
% 1.36/1.14 & ( Xz = Xx ) )
% 1.36/1.14 | ( ~ Xphi
% 1.36/1.14 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 1.36/1.14
% 1.36/1.14 thf(ifSingleton_type,type,
% 1.36/1.14 ifSingleton: $o ).
% 1.36/1.14
% 1.36/1.14 thf(ifSingleton,definition,
% 1.36/1.14 ( ifSingleton
% 1.36/1.14 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 1.36/1.14 ( ( in @ Xx @ A )
% 1.36/1.14 => ! [Xy: $i] :
% 1.36/1.14 ( ( in @ Xy @ A )
% 1.36/1.14 => ( singleton
% 1.36/1.14 @ ( dsetconstr @ A
% 1.36/1.14 @ ^ [Xz: $i] :
% 1.36/1.14 ( ( Xphi
% 1.36/1.14 & ( Xz = Xx ) )
% 1.36/1.14 | ( ~ Xphi
% 1.36/1.14 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 1.36/1.14
% 1.36/1.14 thf(if_type,type,
% 1.36/1.14 if: $i > $o > $i > $i > $i ).
% 1.36/1.14
% 1.36/1.14 thf(if,definition,
% 1.36/1.14 ( if
% 1.36/1.14 = ( ^ [A: $i,Xphi: $o,Xx: $i,Xy: $i] :
% 1.36/1.14 ( setunion
% 1.36/1.14 @ ( dsetconstr @ A
% 1.36/1.14 @ ^ [Xz: $i] :
% 1.36/1.14 ( ( Xphi
% 1.36/1.14 & ( Xz = Xx ) )
% 1.36/1.14 | ( ~ Xphi
% 1.36/1.14 & ( Xz = Xy ) ) ) ) ) ) ) ).
% 1.36/1.14
% 1.36/1.14 thf(theeq_type,type,
% 1.36/1.14 theeq: $o ).
% 1.36/1.14
% 1.36/1.14 thf(theeq,definition,
% 1.36/1.14 ( theeq
% 1.36/1.14 = ( ! [X: $i] :
% 1.36/1.14 ( ( singleton @ X )
% 1.36/1.14 => ! [Xx: $i] :
% 1.36/1.14 ( ( in @ Xx @ X )
% 1.36/1.14 => ( ( setunion @ X )
% 1.36/1.14 = Xx ) ) ) ) ) ).
% 1.36/1.14
% 1.36/1.14 thf(iffalse,conjecture,
% 1.36/1.14 ( iffalseProp1
% 1.36/1.14 => ( ifSingleton
% 1.36/1.14 => ( theeq
% 1.36/1.14 => ! [A: $i,Xphi: $o,Xx: $i] :
% 1.36/1.14 ( ( in @ Xx @ A )
% 1.36/1.14 => ! [Xy: $i] :
% 1.36/1.14 ( ( in @ Xy @ A )
% 1.36/1.14 => ( ~ Xphi
% 1.36/1.14 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 1.36/1.14 = Xy ) ) ) ) ) ) ) ).
% 1.36/1.14 ------------------------
% 1.36/1.15 % (23690)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/183Mi)
% 1.36/1.16 % (23691)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_23592 for (2999ds/4Mi)
% 1.36/1.16 % (23692)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_23592 for (2999ds/27Mi)
% 1.36/1.16 % (23694)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_23592 for (2999ds/2Mi)
% 1.36/1.16 % (23695)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_23592 for (2999ds/275Mi)
% 1.36/1.16 % (23693)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/2Mi)
% 1.36/1.16 % (23696)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/18Mi)
% 1.36/1.16 % (23691)Instruction limit reached!
% 1.36/1.16 % (23691)------------------------------
% 1.36/1.16 % (23691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.16 % (23691)Termination reason: Unknown
% 1.36/1.16 % (23691)Termination phase: Property scanning
% 1.36/1.16
% 1.36/1.16 % (23691)Memory used [KB]: 1023
% 1.36/1.16 % (23691)Time elapsed: 0.003 s
% 1.36/1.16 % (23691)Instructions burned: 4 (million)
% 1.36/1.16 % (23691)------------------------------
% 1.36/1.16 % (23691)------------------------------
% 1.36/1.16 % (23693)Instruction limit reached!
% 1.36/1.16 % (23693)------------------------------
% 1.36/1.16 % (23693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.16 % (23693)Termination reason: Unknown
% 1.36/1.16 % (23693)Termination phase: Property scanning
% 1.36/1.16
% 1.36/1.16 % (23693)Memory used [KB]: 1023
% 1.36/1.16 % (23693)Time elapsed: 0.003 s
% 1.36/1.16 % (23693)Instructions burned: 3 (million)
% 1.36/1.16 % (23693)------------------------------
% 1.36/1.16 % (23693)------------------------------
% 1.36/1.16 % (23694)Instruction limit reached!
% 1.36/1.16 % (23694)------------------------------
% 1.36/1.16 % (23694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.16 % (23694)Termination reason: Unknown
% 1.36/1.16 % (23694)Termination phase: Function definition elimination
% 1.36/1.16
% 1.36/1.16 % (23694)Memory used [KB]: 1023
% 1.36/1.16 % (23694)Time elapsed: 0.003 s
% 1.36/1.16 % (23694)Instructions burned: 4 (million)
% 1.36/1.16 % (23694)------------------------------
% 1.36/1.16 % (23694)------------------------------
% 1.36/1.16 % (23695)Refutation not found, incomplete strategy
% 1.36/1.16 % (23695)------------------------------
% 1.36/1.16 % (23695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.16 % (23695)Termination reason: Refutation not found, incomplete strategy
% 1.36/1.16
% 1.36/1.16
% 1.36/1.16 % (23695)Memory used [KB]: 5500
% 1.36/1.16 % (23695)Time elapsed: 0.006 s
% 1.36/1.16 % (23695)Instructions burned: 8 (million)
% 1.36/1.16 % (23695)------------------------------
% 1.36/1.16 % (23695)------------------------------
% 1.36/1.16 % (23692)Refutation not found, incomplete strategy
% 1.36/1.16 % (23692)------------------------------
% 1.36/1.16 % (23692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.16 % (23692)Termination reason: Refutation not found, incomplete strategy
% 1.36/1.16
% 1.36/1.16
% 1.36/1.16 % (23692)Memory used [KB]: 5628
% 1.36/1.16 % (23692)Time elapsed: 0.008 s
% 1.36/1.16 % (23692)Instructions burned: 13 (million)
% 1.36/1.16 % (23692)------------------------------
% 1.36/1.16 % (23692)------------------------------
% 1.36/1.17 % (23696)Instruction limit reached!
% 1.36/1.17 % (23696)------------------------------
% 1.36/1.17 % (23696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.17 % (23696)Termination reason: Unknown
% 1.36/1.17 % (23696)Termination phase: Saturation
% 1.36/1.17
% 1.36/1.17 % (23696)Memory used [KB]: 5628
% 1.36/1.17 % (23696)Time elapsed: 0.011 s
% 1.36/1.17 % (23696)Instructions burned: 18 (million)
% 1.36/1.17 % (23696)------------------------------
% 1.36/1.17 % (23696)------------------------------
% 1.36/1.18 % (23698)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/37Mi)
% 1.36/1.18 % (23697)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/3Mi)
% 1.36/1.18 % (23699)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/15Mi)
% 1.36/1.18 % (23697)Instruction limit reached!
% 1.36/1.18 % (23697)------------------------------
% 1.36/1.18 % (23697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.18 % (23697)Termination reason: Unknown
% 1.36/1.18 % (23697)Termination phase: Property scanning
% 1.36/1.18
% 1.36/1.18 % (23697)Memory used [KB]: 1023
% 1.36/1.18 % (23697)Time elapsed: 0.003 s
% 1.36/1.18 % (23697)Instructions burned: 4 (million)
% 1.36/1.18 % (23697)------------------------------
% 1.36/1.18 % (23697)------------------------------
% 1.36/1.18 % (23700)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/3Mi)
% 1.36/1.18 % (23700)Instruction limit reached!
% 1.36/1.18 % (23700)------------------------------
% 1.36/1.18 % (23700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.18 % (23700)Termination reason: Unknown
% 1.36/1.18 % (23700)Termination phase: Property scanning
% 1.36/1.18
% 1.36/1.18 % (23700)Memory used [KB]: 1023
% 1.36/1.18 % (23700)Time elapsed: 0.003 s
% 1.36/1.18 % (23700)Instructions burned: 4 (million)
% 1.36/1.18 % (23700)------------------------------
% 1.36/1.18 % (23700)------------------------------
% 1.36/1.18 % (23701)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/1041Mi)
% 1.36/1.18 % (23699)Refutation not found, incomplete strategy
% 1.36/1.18 % (23699)------------------------------
% 1.36/1.18 % (23699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.18 % (23699)Termination reason: Refutation not found, incomplete strategy
% 1.36/1.18
% 1.36/1.18
% 1.36/1.18 % (23699)Memory used [KB]: 5628
% 1.36/1.18 % (23699)Time elapsed: 0.009 s
% 1.36/1.18 % (23699)Instructions burned: 14 (million)
% 1.36/1.18 % (23699)------------------------------
% 1.36/1.18 % (23699)------------------------------
% 1.36/1.19 % (23703)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/16Mi)
% 1.36/1.19 % (23698)Instruction limit reached!
% 1.36/1.19 % (23698)------------------------------
% 1.36/1.19 % (23698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.19 % (23698)Termination reason: Unknown
% 1.36/1.19 % (23698)Termination phase: Saturation
% 1.36/1.19
% 1.36/1.19 % (23698)Memory used [KB]: 5756
% 1.36/1.19 % (23698)Time elapsed: 0.019 s
% 1.36/1.19 % (23698)Instructions burned: 37 (million)
% 1.36/1.19 % (23698)------------------------------
% 1.36/1.19 % (23698)------------------------------
% 1.36/1.19 % (23702)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/7Mi)
% 1.36/1.20 % (23702)Instruction limit reached!
% 1.36/1.20 % (23702)------------------------------
% 1.36/1.20 % (23702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.36/1.20 % (23702)Termination reason: Unknown
% 1.36/1.20 % (23702)Termination phase: Saturation
% 1.36/1.20
% 1.36/1.20 % (23702)Memory used [KB]: 1023
% 1.36/1.20 % (23702)Time elapsed: 0.003 s
% 1.36/1.20 % (23702)Instructions burned: 7 (million)
% 1.36/1.20 % (23702)------------------------------
% 1.36/1.20 % (23702)------------------------------
% 1.37/1.20 % (23704)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/3Mi)
% 1.37/1.20 % (23704)Instruction limit reached!
% 1.37/1.20 % (23704)------------------------------
% 1.37/1.20 % (23704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.20 % (23704)Termination reason: Unknown
% 1.37/1.20 % (23704)Termination phase: Function definition elimination
% 1.37/1.20
% 1.37/1.20 % (23704)Memory used [KB]: 1023
% 1.37/1.20 % (23704)Time elapsed: 0.003 s
% 1.37/1.20 % (23704)Instructions burned: 4 (million)
% 1.37/1.20 % (23704)------------------------------
% 1.37/1.20 % (23704)------------------------------
% 1.37/1.20 % (23705)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/3Mi)
% 1.37/1.20 % (23705)Instruction limit reached!
% 1.37/1.20 % (23705)------------------------------
% 1.37/1.20 % (23705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.20 % (23705)Termination reason: Unknown
% 1.37/1.20 % (23705)Termination phase: Property scanning
% 1.37/1.20
% 1.37/1.20 % (23705)Memory used [KB]: 1023
% 1.37/1.20 % (23705)Time elapsed: 0.003 s
% 1.37/1.20 % (23705)Instructions burned: 4 (million)
% 1.37/1.20 % (23705)------------------------------
% 1.37/1.20 % (23705)------------------------------
% 1.37/1.20 % (23703)Instruction limit reached!
% 1.37/1.20 % (23703)------------------------------
% 1.37/1.20 % (23703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.20 % (23703)Termination reason: Unknown
% 1.37/1.20 % (23703)Termination phase: Saturation
% 1.37/1.20
% 1.37/1.20 % (23703)Memory used [KB]: 5884
% 1.37/1.20 % (23703)Time elapsed: 0.010 s
% 1.37/1.20 % (23703)Instructions burned: 16 (million)
% 1.37/1.20 % (23703)------------------------------
% 1.37/1.20 % (23703)------------------------------
% 1.37/1.20 % (23707)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/3Mi)
% 1.37/1.21 % (23707)Instruction limit reached!
% 1.37/1.21 % (23707)------------------------------
% 1.37/1.21 % (23707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.21 % (23707)Termination reason: Unknown
% 1.37/1.21 % (23707)Termination phase: Property scanning
% 1.37/1.21
% 1.37/1.21 % (23707)Memory used [KB]: 1023
% 1.37/1.21 % (23707)Time elapsed: 0.002 s
% 1.37/1.21 % (23707)Instructions burned: 3 (million)
% 1.37/1.21 % (23707)------------------------------
% 1.37/1.21 % (23707)------------------------------
% 1.37/1.21 % (23706)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/7Mi)
% 1.37/1.21 % (23706)Refutation not found, incomplete strategy
% 1.37/1.21 % (23706)------------------------------
% 1.37/1.21 % (23706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.21 % (23706)Termination reason: Refutation not found, incomplete strategy
% 1.37/1.21
% 1.37/1.21
% 1.37/1.21 % (23706)Memory used [KB]: 5500
% 1.37/1.21 % (23706)Time elapsed: 0.003 s
% 1.37/1.21 % (23706)Instructions burned: 4 (million)
% 1.37/1.21 % (23706)------------------------------
% 1.37/1.21 % (23706)------------------------------
% 1.37/1.21 % (23708)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/4Mi)
% 1.37/1.22 % (23711)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/6Mi)
% 1.37/1.22 % (23708)Instruction limit reached!
% 1.37/1.22 % (23708)------------------------------
% 1.37/1.22 % (23708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.22 % (23708)Termination reason: Unknown
% 1.37/1.22 % (23708)Termination phase: Saturation
% 1.37/1.22
% 1.37/1.22 % (23708)Memory used [KB]: 5500
% 1.37/1.22 % (23708)Time elapsed: 0.004 s
% 1.37/1.22 % (23708)Instructions burned: 5 (million)
% 1.37/1.22 % (23708)------------------------------
% 1.37/1.22 % (23708)------------------------------
% 1.37/1.22 % (23710)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/710Mi)
% 1.37/1.22 % (23711)Instruction limit reached!
% 1.37/1.22 % (23711)------------------------------
% 1.37/1.22 % (23711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.22 % (23711)Termination reason: Unknown
% 1.37/1.22 % (23711)Termination phase: Saturation
% 1.37/1.22
% 1.37/1.22 % (23711)Memory used [KB]: 5500
% 1.37/1.22 % (23711)Time elapsed: 0.004 s
% 1.37/1.22 % (23711)Instructions burned: 8 (million)
% 1.37/1.22 % (23711)------------------------------
% 1.37/1.22 % (23711)------------------------------
% 1.37/1.22 % (23709)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/18Mi)
% 1.37/1.23 % (23690)Instruction limit reached!
% 1.37/1.23 % (23690)------------------------------
% 1.37/1.23 % (23690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.23 % (23690)Termination reason: Unknown
% 1.37/1.23 % (23690)Termination phase: Saturation
% 1.37/1.23
% 1.37/1.23 % (23690)Memory used [KB]: 6012
% 1.37/1.23 % (23690)Time elapsed: 0.068 s
% 1.37/1.23 % (23690)Instructions burned: 183 (million)
% 1.37/1.23 % (23690)------------------------------
% 1.37/1.23 % (23690)------------------------------
% 1.37/1.23 % (23709)Instruction limit reached!
% 1.37/1.23 % (23709)------------------------------
% 1.37/1.23 % (23709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.23 % (23714)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/5Mi)
% 1.37/1.23 % (23709)Termination reason: Unknown
% 1.37/1.23 % (23709)Termination phase: Saturation
% 1.37/1.23
% 1.37/1.23 % (23709)Memory used [KB]: 5628
% 1.37/1.23 % (23709)Time elapsed: 0.011 s
% 1.37/1.23 % (23709)Instructions burned: 18 (million)
% 1.37/1.23 % (23712)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/902Mi)
% 1.37/1.23 % (23709)------------------------------
% 1.37/1.23 % (23709)------------------------------
% 1.37/1.23 % (23714)Instruction limit reached!
% 1.37/1.23 % (23714)------------------------------
% 1.37/1.23 % (23714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.23 % (23714)Termination reason: Unknown
% 1.37/1.23 % (23714)Termination phase: Saturation
% 1.37/1.23
% 1.37/1.23 % (23714)Memory used [KB]: 5500
% 1.37/1.23 % (23714)Time elapsed: 0.003 s
% 1.37/1.23 % (23714)Instructions burned: 7 (million)
% 1.37/1.23 % (23714)------------------------------
% 1.37/1.23 % (23714)------------------------------
% 1.37/1.23 % (23712)Refutation not found, incomplete strategy
% 1.37/1.23 % (23712)------------------------------
% 1.37/1.23 % (23712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.23 % (23712)Termination reason: Refutation not found, incomplete strategy
% 1.37/1.23
% 1.37/1.23
% 1.37/1.23 % (23712)Memory used [KB]: 5500
% 1.37/1.23 % (23712)Time elapsed: 0.004 s
% 1.37/1.23 % (23712)Instructions burned: 5 (million)
% 1.37/1.23 % (23712)------------------------------
% 1.37/1.23 % (23712)------------------------------
% 1.37/1.23 % (23713)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/21Mi)
% 1.37/1.24 % (23717)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/779Mi)
% 1.37/1.24 % (23715)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/6Mi)
% 1.37/1.24 % (23716)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/377Mi)
% 1.37/1.24 % (23713)Instruction limit reached!
% 1.37/1.24 % (23713)------------------------------
% 1.37/1.24 % (23713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.24 % (23713)Termination reason: Unknown
% 1.37/1.24 % (23713)Termination phase: Saturation
% 1.37/1.24
% 1.37/1.24 % (23713)Memory used [KB]: 5628
% 1.37/1.24 % (23713)Time elapsed: 0.013 s
% 1.37/1.24 % (23713)Instructions burned: 22 (million)
% 1.37/1.24 % (23713)------------------------------
% 1.37/1.24 % (23713)------------------------------
% 1.37/1.24 % (23715)Instruction limit reached!
% 1.37/1.24 % (23715)------------------------------
% 1.37/1.24 % (23715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.24 % (23715)Termination reason: Unknown
% 1.37/1.24 % (23715)Termination phase: Saturation
% 1.37/1.24
% 1.37/1.24 % (23715)Memory used [KB]: 5500
% 1.37/1.24 % (23715)Time elapsed: 0.004 s
% 1.37/1.24 % (23715)Instructions burned: 6 (million)
% 1.37/1.24 % (23715)------------------------------
% 1.37/1.24 % (23715)------------------------------
% 1.37/1.24 % (23717)Refutation not found, incomplete strategy
% 1.37/1.24 % (23717)------------------------------
% 1.37/1.24 % (23717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.25 % (23717)Termination reason: Refutation not found, incomplete strategy
% 1.37/1.25
% 1.37/1.25
% 1.37/1.25 % (23717)Memory used [KB]: 5628
% 1.37/1.25 % (23717)Time elapsed: 0.007 s
% 1.37/1.25 % (23717)Instructions burned: 19 (million)
% 1.37/1.25 % (23717)------------------------------
% 1.37/1.25 % (23717)------------------------------
% 1.37/1.25 % (23718)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_23592 for (2999ds/19Mi)
% 1.37/1.25 % (23710)First to succeed.
% 1.37/1.25 % (23716)Refutation not found, incomplete strategy
% 1.37/1.25 % (23716)------------------------------
% 1.37/1.25 % (23716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.25 % (23716)Termination reason: Refutation not found, incomplete strategy
% 1.37/1.25
% 1.37/1.25
% 1.37/1.25 % (23716)Memory used [KB]: 5628
% 1.37/1.25 % (23716)Time elapsed: 0.008 s
% 1.37/1.25 % (23716)Instructions burned: 13 (million)
% 1.37/1.25 % (23716)------------------------------
% 1.37/1.25 % (23716)------------------------------
% 1.37/1.25 % (23710)Refutation found. Thanks to Tanya!
% 1.37/1.25 % SZS status Theorem for DTF2THF_23592
% 1.37/1.25 % SZS output start Proof for DTF2THF_23592
% 1.37/1.25 thf(func_def_0, type, in: $i > $i > $o).
% 1.37/1.25 thf(func_def_1, type, setunion: $i > $i).
% 1.37/1.25 thf(func_def_2, type, dsetconstr: $i > ($i > $o) > $i).
% 1.37/1.25 thf(func_def_3, type, singleton: $i > $o).
% 1.37/1.25 thf(func_def_7, type, if: $i > $o > $i > $i > $i).
% 1.37/1.25 thf(func_def_35, type, ph15: !>[X0: $tType]:(X0)).
% 1.37/1.25 thf(func_def_36, type, sK16: $o > $i).
% 1.37/1.25 thf(f363,plain,(
% 1.37/1.25 $false),
% 1.37/1.25 inference(subsumption_resolution,[status(thm)],[f362,f332])).
% 1.37/1.25 thf(f332,plain,(
% 1.37/1.25 ( ! [X2 : $i,X3 : $i] : (((setunion @ X2) = X3)) )),
% 1.37/1.25 inference(subsumption_resolution,[status(thm)],[f323,f301])).
% 1.37/1.25 thf(f301,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (($true = X0)) )),
% 1.37/1.25 inference(subsumption_resolution,[status(thm)],[f300,f293])).
% 1.37/1.25 thf(f293,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (((sK16 @ X0) = sK5) | ($true = X0)) )),
% 1.37/1.25 inference(subsumption_resolution,[status(thm)],[f237,f50])).
% 1.37/1.25 thf(f50,plain,(
% 1.37/1.25 ($true != sK2)),
% 1.37/1.25 inference(cnf_transformation,[status(thm)],[f33])).
% 1.37/1.25 thf(f33,plain,(
% 1.37/1.25 (theeq = $true) & (ifSingleton = $true) & (($true = (in @ sK3 @ sK4)) & (((in @ sK5 @ sK4) = $true) & ($true != sK2) & ((if @ sK4 @ sK2 @ sK3 @ sK5) != sK5))) & (iffalseProp1 = $true)),
% 1.37/1.25 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f25,f32,f31])).
% 1.37/1.25 thf(f31,plain,(
% 1.37/1.25 ? [X0 : $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) & ? [X3 : $i] : (((in @ X3 @ X2) = $true) & ($true != X0) & ((if @ X2 @ X0 @ X1 @ X3) != X3))) => (($true = (in @ sK3 @ sK4)) & ? [X3 : $i] : (((in @ X3 @ sK4) = $true) & ($true != sK2) & ((if @ sK4 @ sK2 @ sK3 @ X3) != X3)))),
% 1.37/1.25 introduced(definition,[],[choice_axiom])).
% 1.37/1.25 thf(f32,plain,(
% 1.37/1.25 ? [X3 : $i] : (((in @ X3 @ sK4) = $true) & ($true != sK2) & ((if @ sK4 @ sK2 @ sK3 @ X3) != X3)) => (((in @ sK5 @ sK4) = $true) & ($true != sK2) & ((if @ sK4 @ sK2 @ sK3 @ sK5) != sK5))),
% 1.37/1.25 introduced(definition,[],[choice_axiom])).
% 1.37/1.25 thf(f25,plain,(
% 1.37/1.25 (theeq = $true) & (ifSingleton = $true) & ? [X0 : $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) & ? [X3 : $i] : (((in @ X3 @ X2) = $true) & ($true != X0) & ((if @ X2 @ X0 @ X1 @ X3) != X3))) & (iffalseProp1 = $true)),
% 1.37/1.25 inference(flattening,[status(thm)],[f24])).
% 1.37/1.25 thf(f24,plain,(
% 1.37/1.25 ((? [X0 : $o,X1 : $i,X2 : $i] : (? [X3 : $i] : ((((if @ X2 @ X0 @ X1 @ X3) != X3) & ($true != X0)) & ((in @ X3 @ X2) = $true)) & ($true = (in @ X1 @ X2))) & (theeq = $true)) & (ifSingleton = $true)) & (iffalseProp1 = $true)),
% 1.37/1.25 inference(ennf_transformation,[status(thm)],[f18])).
% 1.37/1.25 thf(f18,plain,(
% 1.37/1.25 ~((iffalseProp1 = $true) => ((ifSingleton = $true) => ((theeq = $true) => ! [X0 : $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) => ! [X3 : $i] : (((in @ X3 @ X2) = $true) => (($true != X0) => ((if @ X2 @ X0 @ X1 @ X3) = X3)))))))),
% 1.37/1.25 inference(flattening,[status(thm)],[f11])).
% 1.37/1.25 thf(f11,plain,(
% 1.37/1.25 ~((iffalseProp1 = $true) => ((ifSingleton = $true) => ((theeq = $true) => ! [X0 : $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) => ! [X3 : $i] : (((in @ X3 @ X2) = $true) => (~($true = X0) => ((if @ X2 @ X0 @ X1 @ X3) = X3)))))))),
% 1.37/1.25 inference(fool_elimination,[status(thm)],[f10])).
% 1.37/1.25 thf(f10,plain,(
% 1.37/1.25 ~(iffalseProp1 => (ifSingleton => (theeq => ! [X0 : $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X2) => (~X0 => ((if @ X2 @ X0 @ X1 @ X3) = X3)))))))),
% 1.37/1.25 inference(rectify,[status(thm)],[f6])).
% 1.37/1.25 thf(f6,negated_conjecture,(
% 1.37/1.25 ~(iffalseProp1 => (ifSingleton => (theeq => ! [X1 : $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (~X1 => ((if @ X0 @ X1 @ X2 @ X3) = X3)))))))),
% 1.37/1.25 inference(negated_conjecture,[status(cth)],[f5])).
% 1.37/1.25 thf(f5,conjecture,(
% 1.37/1.25 iffalseProp1 => (ifSingleton => (theeq => ! [X1 : $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (~X1 => ((if @ X0 @ X1 @ X2 @ X3) = X3))))))),
% 1.37/1.25 file('/export/starexec/sandbox2/tmp/tmp.hNHQIJkcF9/DTF2THF_23592.p',iffalse)).
% 1.37/1.25 thf(f237,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (($true = X0) | ($true = sK2) | ((sK16 @ X0) = sK5)) )),
% 1.37/1.25 inference(duplicate_literal_removal,[status(thm)],[f236])).
% 1.37/1.25 thf(f236,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (($true = X0) | ($true = sK2) | ((sK16 @ X0) = sK5) | ((sK16 @ X0) = sK5)) )),
% 1.37/1.25 inference(equality_proxy_clausification,[status(thm)],[f233])).
% 1.37/1.25 thf(f233,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (($true = sK2) | ((sK5 = (sK16 @ X0)) = $true) | ((sK16 @ X0) = sK5) | ($true = X0)) )),
% 1.37/1.25 inference(binary_proxy_clausification,[status(thm)],[f232])).
% 1.37/1.25 thf(f232,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (($true = ((~ X0) & (sK5 = (sK16 @ X0)))) | ($true = X0) | ((sK16 @ X0) = sK5) | ($true = sK2)) )),
% 1.37/1.25 inference(equality_proxy_clausification,[status(thm)],[f231])).
% 1.37/1.25 thf(f231,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (((sK5 = (sK16 @ X0)) = $true) | ($true = ((~ X0) & (sK5 = (sK16 @ X0)))) | ($true = X0) | ($true = sK2)) )),
% 1.37/1.25 inference(binary_proxy_clausification,[status(thm)],[f215])).
% 1.37/1.25 thf(f215,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (($true = (sK2 & (sK3 = (sK16 @ X0)))) | ($true = X0) | ((sK5 = (sK16 @ X0)) = $true) | ($true = ((~ X0) & (sK5 = (sK16 @ X0))))) )),
% 1.37/1.25 inference(binary_proxy_clausification,[status(thm)],[f214])).
% 1.37/1.25 thf(f214,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (($true = ((~ sK2) & (sK5 = (sK16 @ X0)))) | ($true = (sK2 & (sK3 = (sK16 @ X0)))) | ($true = X0) | ($true = ((~ X0) & (sK5 = (sK16 @ X0))))) )),
% 1.37/1.25 inference(binary_proxy_clausification,[status(thm)],[f213])).
% 1.37/1.25 thf(f213,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (($true = X0) | (((sK2 & (sK3 = (sK16 @ X0))) | ((~ sK2) & (sK5 = (sK16 @ X0)))) = $true) | ($true = ((~ X0) & (sK5 = (sK16 @ X0))))) )),
% 1.37/1.25 inference(duplicate_literal_removal,[status(thm)],[f212])).
% 1.37/1.25 thf(f212,plain,(
% 1.37/1.25 ( ! [X0 : $o] : ((((sK2 & (sK3 = (sK16 @ X0))) | ((~ sK2) & (sK5 = (sK16 @ X0)))) = $true) | ($true = ((~ X0) & (sK5 = (sK16 @ X0)))) | ($true = X0) | ($true = X0)) )),
% 1.37/1.25 inference(binary_proxy_clausification,[status(thm)],[f210])).
% 1.37/1.25 thf(f210,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (($true = (X0 & (sK3 = (sK16 @ X0)))) | ($true = X0) | ($true = ((~ X0) & (sK5 = (sK16 @ X0)))) | (((sK2 & (sK3 = (sK16 @ X0))) | ((~ sK2) & (sK5 = (sK16 @ X0)))) = $true)) )),
% 1.37/1.25 inference(binary_proxy_clausification,[status(thm)],[f181])).
% 1.37/1.25 thf(f181,plain,(
% 1.37/1.25 ( ! [X0 : $o] : ((((X0 & (sK3 = (sK16 @ X0))) | ((~ X0) & (sK5 = (sK16 @ X0)))) = $true) | ($true = X0) | (((sK2 & (sK3 = (sK16 @ X0))) | ((~ sK2) & (sK5 = (sK16 @ X0)))) = $true)) )),
% 1.37/1.25 inference(binary_proxy_clausification,[status(thm)],[f180])).
% 1.37/1.25 thf(f180,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (($true = X0) | (((sK2 & (sK3 = (sK16 @ X0))) | ((~ sK2) & (sK5 = (sK16 @ X0)))) != ((X0 & (sK3 = (sK16 @ X0))) | ((~ X0) & (sK5 = (sK16 @ X0)))))) )),
% 1.37/1.25 inference(beta_eta_normalization,[status(thm)],[f179])).
% 1.37/1.25 thf(f179,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (($true = X0) | (((^[Y0 : $i]: ((sK2 & (sK3 = Y0)) | ((~ sK2) & (sK5 = Y0)))) @ (sK16 @ X0)) != ((^[Y0 : $i]: ((X0 & (sK3 = Y0)) | ((~ X0) & (sK5 = Y0)))) @ (sK16 @ X0)))) )),
% 1.37/1.25 inference(negative_extensionality,[status(thm)],[f168])).
% 1.37/1.25 thf(f168,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (((^[Y0 : $i]: ((X0 & (sK3 = Y0)) | ((~ X0) & (sK5 = Y0)))) != (^[Y0 : $i]: ((sK2 & (sK3 = Y0)) | ((~ sK2) & (sK5 = Y0))))) | ($true = X0)) )),
% 1.37/1.25 inference(trivial_inequality_removal,[status(thm)],[f167])).
% 1.37/1.25 thf(f167,plain,(
% 1.37/1.25 ( ! [X0 : $o] : ((sK5 != sK5) | ($true = X0) | ((^[Y0 : $i]: ((X0 & (sK3 = Y0)) | ((~ X0) & (sK5 = Y0)))) != (^[Y0 : $i]: ((sK2 & (sK3 = Y0)) | ((~ sK2) & (sK5 = Y0)))))) )),
% 1.37/1.25 inference(constrained_superposition,[status(thm)],[f80,f154])).
% 1.37/1.25 thf(f154,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (((setunion @ (dsetconstr @ sK4 @ (^[Y0 : $i]: ((X0 & (sK3 = Y0)) | ((~ X0) & (sK5 = Y0)))))) = sK5) | ($true = X0)) )),
% 1.37/1.25 inference(subsumption_resolution,[status(thm)],[f152,f115])).
% 1.37/1.25 thf(f115,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (((singleton @ (dsetconstr @ sK4 @ (^[Y0 : $i]: ((X0 & (sK3 = Y0)) | ((~ X0) & (sK5 = Y0)))))) = $true)) )),
% 1.37/1.25 inference(trivial_inequality_removal,[status(thm)],[f114])).
% 1.37/1.25 thf(f114,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (($true != $true) | ((singleton @ (dsetconstr @ sK4 @ (^[Y0 : $i]: ((X0 & (sK3 = Y0)) | ((~ X0) & (sK5 = Y0)))))) = $true)) )),
% 1.37/1.25 inference(superposition,[status(thm)],[f104,f52])).
% 1.37/1.25 thf(f52,plain,(
% 1.37/1.25 ($true = (in @ sK3 @ sK4))),
% 1.37/1.25 inference(cnf_transformation,[status(thm)],[f33])).
% 1.37/1.25 thf(f104,plain,(
% 1.37/1.25 ( ! [X0 : $o,X1 : $i] : (($true != (in @ X1 @ sK4)) | ((singleton @ (dsetconstr @ sK4 @ (^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((~ X0) & (sK5 = Y0)))))) = $true)) )),
% 1.37/1.25 inference(trivial_inequality_removal,[status(thm)],[f101])).
% 1.37/1.25 thf(f101,plain,(
% 1.37/1.25 ( ! [X0 : $o,X1 : $i] : (($true != (in @ X1 @ sK4)) | ($true != $true) | ((singleton @ (dsetconstr @ sK4 @ (^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((~ X0) & (sK5 = Y0)))))) = $true)) )),
% 1.37/1.25 inference(superposition,[status(thm)],[f82,f51])).
% 1.37/1.25 thf(f51,plain,(
% 1.37/1.25 ((in @ sK5 @ sK4) = $true)),
% 1.37/1.25 inference(cnf_transformation,[status(thm)],[f33])).
% 1.37/1.25 thf(f82,plain,(
% 1.37/1.25 ( ! [X6 : $o,X7 : $i,X4 : $i,X5 : $i] : (($true != (in @ X7 @ X4)) | ((singleton @ (dsetconstr @ X4 @ (^[Y0 : $i]: ((X6 & (X5 = Y0)) | ((~ X6) & (X7 = Y0)))))) = $true) | ((in @ X5 @ X4) != $true)) )),
% 1.37/1.25 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.37/1.25 thf(f73,plain,(
% 1.37/1.25 ( ! [X6 : $o,X7 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((in @ X5 @ X4) != $true) | ((singleton @ (dsetconstr @ X4 @ (^[Y0 : $i]: ((X6 & (X5 = Y0)) | ((~ X6) & (X7 = Y0)))))) = $true) | ($true != (in @ X7 @ X4))) )),
% 1.37/1.25 inference(definition_unfolding,[status(thm)],[f55,f53])).
% 1.37/1.25 thf(f53,plain,(
% 1.37/1.25 (ifSingleton = $true)),
% 1.37/1.25 inference(cnf_transformation,[status(thm)],[f33])).
% 1.37/1.25 thf(f55,plain,(
% 1.37/1.25 ( ! [X6 : $o,X7 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X4) != $true) | ((singleton @ (dsetconstr @ X4 @ (^[Y0 : $i]: ((X6 & (X5 = Y0)) | ((~ X6) & (X7 = Y0)))))) = $true) | ($true != (in @ X7 @ X4)) | (ifSingleton != $true)) )),
% 1.37/1.25 inference(cnf_transformation,[status(thm)],[f38])).
% 1.37/1.25 thf(f38,plain,(
% 1.37/1.25 ((ifSingleton = $true) | (($true = (in @ sK7 @ sK6)) & (((singleton @ (dsetconstr @ sK6 @ (^[Y0 : $i]: ((sK8 & (sK7 = Y0)) | ((~ sK8) & (sK9 = Y0)))))) != $true) & ($true = (in @ sK9 @ sK6))))) & (! [X4 : $i,X5 : $i,X6 : $o] : (((in @ X5 @ X4) != $true) | ! [X7 : $i] : (((singleton @ (dsetconstr @ X4 @ (^[Y0 : $i]: ((X6 & (X5 = Y0)) | ((~ X6) & (X7 = Y0)))))) = $true) | ($true != (in @ X7 @ X4)))) | (ifSingleton != $true))),
% 1.37/1.25 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f35,f37,f36])).
% 1.37/1.25 thf(f36,plain,(
% 1.37/1.25 ? [X0 : $i,X1 : $i,X2 : $o] : (((in @ X1 @ X0) = $true) & ? [X3 : $i] : (($true != (singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: ((X2 & (X1 = Y0)) | ((~ X2) & (X3 = Y0))))))) & ((in @ X3 @ X0) = $true))) => (($true = (in @ sK7 @ sK6)) & ? [X3 : $i] : (((singleton @ (dsetconstr @ sK6 @ (^[Y0 : $i]: ((sK8 & (sK7 = Y0)) | ((~ sK8) & (X3 = Y0)))))) != $true) & ((in @ X3 @ sK6) = $true)))),
% 1.37/1.25 introduced(definition,[],[choice_axiom])).
% 1.37/1.25 thf(f37,plain,(
% 1.37/1.25 ? [X3 : $i] : (((singleton @ (dsetconstr @ sK6 @ (^[Y0 : $i]: ((sK8 & (sK7 = Y0)) | ((~ sK8) & (X3 = Y0)))))) != $true) & ((in @ X3 @ sK6) = $true)) => (((singleton @ (dsetconstr @ sK6 @ (^[Y0 : $i]: ((sK8 & (sK7 = Y0)) | ((~ sK8) & (sK9 = Y0)))))) != $true) & ($true = (in @ sK9 @ sK6)))),
% 1.37/1.25 introduced(definition,[],[choice_axiom])).
% 1.37/1.25 thf(f35,plain,(
% 1.37/1.25 ((ifSingleton = $true) | ? [X0 : $i,X1 : $i,X2 : $o] : (((in @ X1 @ X0) = $true) & ? [X3 : $i] : (($true != (singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: ((X2 & (X1 = Y0)) | ((~ X2) & (X3 = Y0))))))) & ((in @ X3 @ X0) = $true)))) & (! [X4 : $i,X5 : $i,X6 : $o] : (((in @ X5 @ X4) != $true) | ! [X7 : $i] : (((singleton @ (dsetconstr @ X4 @ (^[Y0 : $i]: ((X6 & (X5 = Y0)) | ((~ X6) & (X7 = Y0)))))) = $true) | ($true != (in @ X7 @ X4)))) | (ifSingleton != $true))),
% 1.37/1.25 inference(rectify,[status(thm)],[f34])).
% 1.37/1.25 thf(f34,plain,(
% 1.37/1.25 ((ifSingleton = $true) | ? [X0 : $i,X1 : $i,X2 : $o] : (((in @ X1 @ X0) = $true) & ? [X3 : $i] : (($true != (singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: ((X2 & (X1 = Y0)) | ((~ X2) & (X3 = Y0))))))) & ((in @ X3 @ X0) = $true)))) & (! [X0 : $i,X1 : $i,X2 : $o] : (((in @ X1 @ X0) != $true) | ! [X3 : $i] : (($true = (singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: ((X2 & (X1 = Y0)) | ((~ X2) & (X3 = Y0))))))) | ((in @ X3 @ X0) != $true))) | (ifSingleton != $true))),
% 1.37/1.25 inference(nnf_transformation,[status(thm)],[f23])).
% 1.37/1.25 thf(f23,plain,(
% 1.37/1.25 (ifSingleton = $true) <=> ! [X0 : $i,X1 : $i,X2 : $o] : (((in @ X1 @ X0) != $true) | ! [X3 : $i] : (($true = (singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: ((X2 & (X1 = Y0)) | ((~ X2) & (X3 = Y0))))))) | ((in @ X3 @ X0) != $true)))),
% 1.37/1.25 inference(ennf_transformation,[status(thm)],[f17])).
% 1.37/1.25 thf(f17,plain,(
% 1.37/1.25 (ifSingleton = $true) <=> ! [X0 : $i,X1 : $i,X2 : $o] : (((in @ X1 @ X0) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => ($true = (singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: ((X2 & (X1 = Y0)) | ((~ X2) & (X3 = Y0)))))))))),
% 1.37/1.25 inference(fool_elimination,[status(thm)],[f16])).
% 1.37/1.25 thf(f16,plain,(
% 1.37/1.25 (! [X0 : $i,X1 : $i,X2 : $o] : ((in @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (singleton @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X3 = X4) & ~X2) | ((X1 = X4) & X2))))))) = ifSingleton)),
% 1.37/1.25 inference(rectify,[status(thm)],[f2])).
% 1.37/1.25 thf(f2,axiom,(
% 1.37/1.25 (! [X0 : $i,X2 : $i,X1 : $o] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (singleton @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X3 = X4) & ~X1) | ((X2 = X4) & X1))))))) = ifSingleton)),
% 1.37/1.25 file('/export/starexec/sandbox2/tmp/tmp.hNHQIJkcF9/DTF2THF_23592.p',ifSingleton)).
% 1.37/1.25 thf(f152,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (($true = X0) | ((setunion @ (dsetconstr @ sK4 @ (^[Y0 : $i]: ((X0 & (sK3 = Y0)) | ((~ X0) & (sK5 = Y0)))))) = sK5) | ((singleton @ (dsetconstr @ sK4 @ (^[Y0 : $i]: ((X0 & (sK3 = Y0)) | ((~ X0) & (sK5 = Y0)))))) != $true)) )),
% 1.37/1.25 inference(trivial_inequality_removal,[status(thm)],[f150])).
% 1.37/1.25 thf(f150,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (((singleton @ (dsetconstr @ sK4 @ (^[Y0 : $i]: ((X0 & (sK3 = Y0)) | ((~ X0) & (sK5 = Y0)))))) != $true) | ((setunion @ (dsetconstr @ sK4 @ (^[Y0 : $i]: ((X0 & (sK3 = Y0)) | ((~ X0) & (sK5 = Y0)))))) = sK5) | ($true != $true) | ($true = X0)) )),
% 1.37/1.25 inference(superposition,[status(thm)],[f79,f123])).
% 1.37/1.25 thf(f123,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (($true = (in @ sK5 @ (dsetconstr @ sK4 @ (^[Y0 : $i]: ((X0 & (sK3 = Y0)) | ((~ X0) & (sK5 = Y0))))))) | ($true = X0)) )),
% 1.37/1.25 inference(trivial_inequality_removal,[status(thm)],[f122])).
% 1.37/1.25 thf(f122,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (($true != $true) | ($true = X0) | ($true = (in @ sK5 @ (dsetconstr @ sK4 @ (^[Y0 : $i]: ((X0 & (sK3 = Y0)) | ((~ X0) & (sK5 = Y0)))))))) )),
% 1.37/1.25 inference(superposition,[status(thm)],[f112,f52])).
% 1.37/1.25 thf(f112,plain,(
% 1.37/1.25 ( ! [X0 : $i,X1 : $o] : (($true != (in @ X0 @ sK4)) | ($true = X1) | ($true = (in @ sK5 @ (dsetconstr @ sK4 @ (^[Y0 : $i]: ((X1 & (X0 = Y0)) | ((~ X1) & (sK5 = Y0)))))))) )),
% 1.37/1.25 inference(trivial_inequality_removal,[status(thm)],[f109])).
% 1.37/1.25 thf(f109,plain,(
% 1.37/1.25 ( ! [X0 : $i,X1 : $o] : (($true != $true) | ($true = X1) | ($true = (in @ sK5 @ (dsetconstr @ sK4 @ (^[Y0 : $i]: ((X1 & (X0 = Y0)) | ((~ X1) & (sK5 = Y0))))))) | ($true != (in @ X0 @ sK4))) )),
% 1.37/1.25 inference(superposition,[status(thm)],[f81,f51])).
% 1.37/1.25 thf(f81,plain,(
% 1.37/1.25 ( ! [X6 : $i,X7 : $i,X4 : $o,X5 : $i] : (($true != (in @ X7 @ X6)) | ((in @ X5 @ X6) != $true) | ($true = X4) | ((in @ X7 @ (dsetconstr @ X6 @ (^[Y0 : $i]: ((X4 & (X5 = Y0)) | ((~ X4) & (X7 = Y0)))))) = $true)) )),
% 1.37/1.25 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 1.37/1.25 thf(f78,plain,(
% 1.37/1.25 ( ! [X6 : $i,X7 : $i,X4 : $o,X5 : $i] : (($true != (in @ X7 @ X6)) | ($true = X4) | ((in @ X7 @ (dsetconstr @ X6 @ (^[Y0 : $i]: ((X4 & (X5 = Y0)) | ((~ X4) & (X7 = Y0)))))) = $true) | ((in @ X5 @ X6) != $true) | ($true != $true)) )),
% 1.37/1.25 inference(definition_unfolding,[status(thm)],[f59,f48])).
% 1.37/1.25 thf(f48,plain,(
% 1.37/1.25 (iffalseProp1 = $true)),
% 1.37/1.25 inference(cnf_transformation,[status(thm)],[f33])).
% 1.37/1.25 thf(f59,plain,(
% 1.37/1.25 ( ! [X6 : $i,X7 : $i,X4 : $o,X5 : $i] : (($true != (in @ X7 @ X6)) | ($true = X4) | ((in @ X7 @ (dsetconstr @ X6 @ (^[Y0 : $i]: ((X4 & (X5 = Y0)) | ((~ X4) & (X7 = Y0)))))) = $true) | ((in @ X5 @ X6) != $true) | (iffalseProp1 != $true)) )),
% 1.37/1.25 inference(cnf_transformation,[status(thm)],[f43])).
% 1.37/1.25 thf(f43,plain,(
% 1.37/1.25 ((iffalseProp1 = $true) | ((($true = (in @ sK13 @ sK12)) & ($true != sK10) & ((in @ sK13 @ (dsetconstr @ sK12 @ (^[Y0 : $i]: ((sK10 & (sK11 = Y0)) | ((~ sK10) & (sK13 = Y0)))))) != $true)) & ($true = (in @ sK11 @ sK12)))) & (! [X4 : $o,X5 : $i,X6 : $i] : (! [X7 : $i] : (($true != (in @ X7 @ X6)) | ($true = X4) | ((in @ X7 @ (dsetconstr @ X6 @ (^[Y0 : $i]: ((X4 & (X5 = Y0)) | ((~ X4) & (X7 = Y0)))))) = $true)) | ((in @ X5 @ X6) != $true)) | (iffalseProp1 != $true))),
% 1.37/1.25 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13])],[f40,f42,f41])).
% 1.37/1.25 thf(f41,plain,(
% 1.37/1.25 ? [X0 : $o,X1 : $i,X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X2) = $true) & ($true != X0) & ((in @ X3 @ (dsetconstr @ X2 @ (^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((~ X0) & (X3 = Y0)))))) != $true)) & ($true = (in @ X1 @ X2))) => (? [X3 : $i] : (($true = (in @ X3 @ sK12)) & ($true != sK10) & ($true != (in @ X3 @ (dsetconstr @ sK12 @ (^[Y0 : $i]: ((sK10 & (sK11 = Y0)) | ((~ sK10) & (X3 = Y0)))))))) & ($true = (in @ sK11 @ sK12)))),
% 1.37/1.25 introduced(definition,[],[choice_axiom])).
% 1.37/1.25 thf(f42,plain,(
% 1.37/1.25 ? [X3 : $i] : (($true = (in @ X3 @ sK12)) & ($true != sK10) & ($true != (in @ X3 @ (dsetconstr @ sK12 @ (^[Y0 : $i]: ((sK10 & (sK11 = Y0)) | ((~ sK10) & (X3 = Y0)))))))) => (($true = (in @ sK13 @ sK12)) & ($true != sK10) & ((in @ sK13 @ (dsetconstr @ sK12 @ (^[Y0 : $i]: ((sK10 & (sK11 = Y0)) | ((~ sK10) & (sK13 = Y0)))))) != $true))),
% 1.37/1.25 introduced(definition,[],[choice_axiom])).
% 1.37/1.25 thf(f40,plain,(
% 1.37/1.25 ((iffalseProp1 = $true) | ? [X0 : $o,X1 : $i,X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X2) = $true) & ($true != X0) & ((in @ X3 @ (dsetconstr @ X2 @ (^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((~ X0) & (X3 = Y0)))))) != $true)) & ($true = (in @ X1 @ X2)))) & (! [X4 : $o,X5 : $i,X6 : $i] : (! [X7 : $i] : (($true != (in @ X7 @ X6)) | ($true = X4) | ((in @ X7 @ (dsetconstr @ X6 @ (^[Y0 : $i]: ((X4 & (X5 = Y0)) | ((~ X4) & (X7 = Y0)))))) = $true)) | ((in @ X5 @ X6) != $true)) | (iffalseProp1 != $true))),
% 1.37/1.25 inference(rectify,[status(thm)],[f39])).
% 1.37/1.25 thf(f39,plain,(
% 1.37/1.25 ((iffalseProp1 = $true) | ? [X0 : $o,X1 : $i,X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X2) = $true) & ($true != X0) & ((in @ X3 @ (dsetconstr @ X2 @ (^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((~ X0) & (X3 = Y0)))))) != $true)) & ($true = (in @ X1 @ X2)))) & (! [X0 : $o,X1 : $i,X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X2) != $true) | ($true = X0) | ((in @ X3 @ (dsetconstr @ X2 @ (^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((~ X0) & (X3 = Y0)))))) = $true)) | ($true != (in @ X1 @ X2))) | (iffalseProp1 != $true))),
% 1.37/1.25 inference(nnf_transformation,[status(thm)],[f21])).
% 1.37/1.25 thf(f21,plain,(
% 1.37/1.25 (iffalseProp1 = $true) <=> ! [X0 : $o,X1 : $i,X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X2) != $true) | ($true = X0) | ((in @ X3 @ (dsetconstr @ X2 @ (^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((~ X0) & (X3 = Y0)))))) = $true)) | ($true != (in @ X1 @ X2)))),
% 1.37/1.25 inference(flattening,[status(thm)],[f20])).
% 1.37/1.25 thf(f20,plain,(
% 1.37/1.25 (iffalseProp1 = $true) <=> ! [X0 : $o,X1 : $i,X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ (dsetconstr @ X2 @ (^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((~ X0) & (X3 = Y0)))))) = $true) | ($true = X0)) | ((in @ X3 @ X2) != $true)) | ($true != (in @ X1 @ X2)))),
% 1.37/1.25 inference(ennf_transformation,[status(thm)],[f19])).
% 1.37/1.25 thf(f19,plain,(
% 1.37/1.25 (iffalseProp1 = $true) <=> ! [X0 : $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) => ! [X3 : $i] : (((in @ X3 @ X2) = $true) => (($true != X0) => ((in @ X3 @ (dsetconstr @ X2 @ (^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((~ X0) & (X3 = Y0)))))) = $true))))),
% 1.37/1.25 inference(flattening,[status(thm)],[f15])).
% 1.37/1.25 thf(f15,plain,(
% 1.37/1.25 (iffalseProp1 = $true) <=> ! [X0 : $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) => ! [X3 : $i] : (((in @ X3 @ X2) = $true) => (~($true = X0) => ((in @ X3 @ (dsetconstr @ X2 @ (^[Y0 : $i]: ((X0 & (X1 = Y0)) | ((~ X0) & (X3 = Y0)))))) = $true))))),
% 1.37/1.25 inference(fool_elimination,[status(thm)],[f14])).
% 1.37/1.25 thf(f14,plain,(
% 1.37/1.25 (iffalseProp1 = ! [X0 : $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X2) => (~X0 => (in @ X3 @ (dsetconstr @ X2 @ (^[X4 : $i] : (((X3 = X4) & ~X0) | ((X1 = X4) & X0)))))))))),
% 1.37/1.25 inference(rectify,[status(thm)],[f1])).
% 1.37/1.25 thf(f1,axiom,(
% 1.37/1.25 (iffalseProp1 = ! [X1 : $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (~X1 => (in @ X3 @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X3 = X4) & ~X1) | ((X2 = X4) & X1)))))))))),
% 1.37/1.25 file('/export/starexec/sandbox2/tmp/tmp.hNHQIJkcF9/DTF2THF_23592.p',iffalseProp1)).
% 1.37/1.25 thf(f79,plain,(
% 1.37/1.25 ( ! [X2 : $i,X3 : $i] : (((in @ X3 @ X2) != $true) | ((setunion @ X2) = X3) | ((singleton @ X2) != $true)) )),
% 1.37/1.25 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.37/1.25 thf(f68,plain,(
% 1.37/1.25 ( ! [X2 : $i,X3 : $i] : (((setunion @ X2) = X3) | ((in @ X3 @ X2) != $true) | ($true != $true) | ((singleton @ X2) != $true)) )),
% 1.37/1.25 inference(definition_unfolding,[status(thm)],[f44,f54])).
% 1.37/1.25 thf(f54,plain,(
% 1.37/1.25 (theeq = $true)),
% 1.37/1.25 inference(cnf_transformation,[status(thm)],[f33])).
% 1.37/1.25 thf(f44,plain,(
% 1.37/1.25 ( ! [X2 : $i,X3 : $i] : (((singleton @ X2) != $true) | ((in @ X3 @ X2) != $true) | ((setunion @ X2) = X3) | (theeq != $true)) )),
% 1.37/1.25 inference(cnf_transformation,[status(thm)],[f30])).
% 1.37/1.25 thf(f30,plain,(
% 1.37/1.25 ((theeq = $true) | (((singleton @ sK0) = $true) & (($true = (in @ sK1 @ sK0)) & ((setunion @ sK0) != sK1)))) & (! [X2 : $i] : (((singleton @ X2) != $true) | ! [X3 : $i] : (((in @ X3 @ X2) != $true) | ((setunion @ X2) = X3))) | (theeq != $true))),
% 1.37/1.25 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f27,f29,f28])).
% 1.37/1.25 thf(f28,plain,(
% 1.37/1.25 ? [X0 : $i] : (($true = (singleton @ X0)) & ? [X1 : $i] : (((in @ X1 @ X0) = $true) & ((setunion @ X0) != X1))) => (((singleton @ sK0) = $true) & ? [X1 : $i] : (($true = (in @ X1 @ sK0)) & ((setunion @ sK0) != X1)))),
% 1.37/1.25 introduced(definition,[],[choice_axiom])).
% 1.37/1.25 thf(f29,plain,(
% 1.37/1.25 ? [X1 : $i] : (($true = (in @ X1 @ sK0)) & ((setunion @ sK0) != X1)) => (($true = (in @ sK1 @ sK0)) & ((setunion @ sK0) != sK1))),
% 1.37/1.25 introduced(definition,[],[choice_axiom])).
% 1.37/1.25 thf(f27,plain,(
% 1.37/1.25 ((theeq = $true) | ? [X0 : $i] : (($true = (singleton @ X0)) & ? [X1 : $i] : (((in @ X1 @ X0) = $true) & ((setunion @ X0) != X1)))) & (! [X2 : $i] : (((singleton @ X2) != $true) | ! [X3 : $i] : (((in @ X3 @ X2) != $true) | ((setunion @ X2) = X3))) | (theeq != $true))),
% 1.37/1.25 inference(rectify,[status(thm)],[f26])).
% 1.37/1.25 thf(f26,plain,(
% 1.37/1.25 ((theeq = $true) | ? [X0 : $i] : (($true = (singleton @ X0)) & ? [X1 : $i] : (((in @ X1 @ X0) = $true) & ((setunion @ X0) != X1)))) & (! [X0 : $i] : (($true != (singleton @ X0)) | ! [X1 : $i] : (((in @ X1 @ X0) != $true) | ((setunion @ X0) = X1))) | (theeq != $true))),
% 1.37/1.25 inference(nnf_transformation,[status(thm)],[f22])).
% 1.37/1.25 thf(f22,plain,(
% 1.37/1.25 (theeq = $true) <=> ! [X0 : $i] : (($true != (singleton @ X0)) | ! [X1 : $i] : (((in @ X1 @ X0) != $true) | ((setunion @ X0) = X1)))),
% 1.37/1.25 inference(ennf_transformation,[status(thm)],[f13])).
% 1.37/1.25 thf(f13,plain,(
% 1.37/1.25 ! [X0 : $i] : (($true = (singleton @ X0)) => ! [X1 : $i] : (((in @ X1 @ X0) = $true) => ((setunion @ X0) = X1))) <=> (theeq = $true)),
% 1.37/1.25 inference(fool_elimination,[status(thm)],[f12])).
% 1.37/1.25 thf(f12,plain,(
% 1.37/1.25 (! [X0 : $i] : ((singleton @ X0) => ! [X1 : $i] : ((in @ X1 @ X0) => ((setunion @ X0) = X1))) = theeq)),
% 1.37/1.25 inference(rectify,[status(thm)],[f4])).
% 1.37/1.25 thf(f4,axiom,(
% 1.37/1.25 (! [X5 : $i] : ((singleton @ X5) => ! [X2 : $i] : ((in @ X2 @ X5) => ((setunion @ X5) = X2))) = theeq)),
% 1.37/1.25 file('/export/starexec/sandbox2/tmp/tmp.hNHQIJkcF9/DTF2THF_23592.p',theeq)).
% 1.37/1.25 thf(f80,plain,(
% 1.37/1.25 ((setunion @ (dsetconstr @ sK4 @ (^[Y0 : $i]: ((sK2 & (sK3 = Y0)) | ((~ sK2) & (sK5 = Y0)))))) != sK5)),
% 1.37/1.25 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.37/1.25 thf(f69,plain,(
% 1.37/1.25 (((^[Y0 : $i]: ((^[Y1 : $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: ((Y1 & (Y2 = Y4)) | ((~ Y1) & (Y3 = Y4))))))))))))) @ sK4 @ sK2 @ sK3 @ sK5) != sK5)),
% 1.37/1.25 inference(definition_unfolding,[status(thm)],[f49,f64])).
% 1.37/1.25 thf(f64,plain,(
% 1.37/1.25 (if = (^[Y0 : $i]: ((^[Y1 : $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: ((Y1 & (Y2 = Y4)) | ((~ Y1) & (Y3 = Y4))))))))))))))),
% 1.37/1.25 inference(cnf_transformation,[status(thm)],[f9])).
% 1.37/1.25 thf(f9,plain,(
% 1.37/1.25 (if = (^[Y0 : $i]: ((^[Y1 : $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: ((Y1 & (Y2 = Y4)) | ((~ Y1) & (Y3 = Y4))))))))))))))),
% 1.37/1.25 inference(fool_elimination,[status(thm)],[f8])).
% 1.37/1.25 thf(f8,plain,(
% 1.37/1.25 ((^[X0 : $i, X1 : $o, X2 : $i, X3 : $i] : (setunion @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X3 = X4) & ~X1) | ((X2 = X4) & X1)))))) = if)),
% 1.37/1.25 inference(rectify,[status(thm)],[f3])).
% 1.37/1.25 thf(f3,axiom,(
% 1.37/1.25 ((^[X0 : $i, X1 : $o, X2 : $i, X3 : $i] : (setunion @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X3 = X4) & ~X1) | ((X2 = X4) & X1)))))) = if)),
% 1.37/1.25 file('/export/starexec/sandbox2/tmp/tmp.hNHQIJkcF9/DTF2THF_23592.p',if)).
% 1.37/1.25 thf(f49,plain,(
% 1.37/1.25 ((if @ sK4 @ sK2 @ sK3 @ sK5) != sK5)),
% 1.37/1.25 inference(cnf_transformation,[status(thm)],[f33])).
% 1.37/1.25 thf(f300,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (($true = X0) | ((sK16 @ X0) != sK5)) )),
% 1.37/1.25 inference(subsumption_resolution,[status(thm)],[f209,f50])).
% 1.37/1.25 thf(f209,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (((sK16 @ X0) != sK5) | ($true = sK2) | ($true = X0)) )),
% 1.37/1.25 inference(equality_proxy_clausification,[status(thm)],[f208])).
% 1.37/1.25 thf(f208,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (($true = X0) | ((sK5 = (sK16 @ X0)) = $false) | ($true = sK2)) )),
% 1.37/1.25 inference(not_proxy_clausification,[status(thm)],[f207])).
% 1.37/1.25 thf(f207,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (($true = X0) | ((~ sK2) = $false) | ((sK5 = (sK16 @ X0)) = $false)) )),
% 1.37/1.25 inference(duplicate_literal_removal,[status(thm)],[f206])).
% 1.37/1.25 thf(f206,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (((sK5 = (sK16 @ X0)) = $false) | ($true = X0) | ((~ sK2) = $false) | ($true = X0)) )),
% 1.37/1.25 inference(not_proxy_clausification,[status(thm)],[f205])).
% 1.37/1.25 thf(f205,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (((~ X0) = $false) | ((sK5 = (sK16 @ X0)) = $false) | ((~ sK2) = $false) | ($true = X0)) )),
% 1.37/1.25 inference(duplicate_literal_removal,[status(thm)],[f204])).
% 1.37/1.25 thf(f204,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (($true = X0) | ((sK5 = (sK16 @ X0)) = $false) | ((~ sK2) = $false) | ((~ X0) = $false) | ((sK5 = (sK16 @ X0)) = $false)) )),
% 1.37/1.25 inference(binary_proxy_clausification,[status(thm)],[f203])).
% 1.37/1.25 thf(f203,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (($false = ((~ sK2) & (sK5 = (sK16 @ X0)))) | ((sK5 = (sK16 @ X0)) = $false) | ((~ X0) = $false) | ($true = X0)) )),
% 1.37/1.25 inference(binary_proxy_clausification,[status(thm)],[f195])).
% 1.37/1.25 thf(f195,plain,(
% 1.37/1.25 ( ! [X0 : $o] : (($false = ((~ X0) & (sK5 = (sK16 @ X0)))) | ($false = ((~ sK2) & (sK5 = (sK16 @ X0)))) | ($true = X0)) )),
% 1.37/1.25 inference(binary_proxy_clausification,[status(thm)],[f183])).
% 1.37/1.25 thf(f183,plain,(
% 1.37/1.25 ( ! [X0 : $o] : ((((sK2 & (sK3 = (sK16 @ X0))) | ((~ sK2) & (sK5 = (sK16 @ X0)))) = $false) | ($true = X0) | ($false = ((~ X0) & (sK5 = (sK16 @ X0))))) )),
% 1.37/1.25 inference(binary_proxy_clausification,[status(thm)],[f182])).
% 1.37/1.25 thf(f182,plain,(
% 1.37/1.25 ( ! [X0 : $o] : ((((X0 & (sK3 = (sK16 @ X0))) | ((~ X0) & (sK5 = (sK16 @ X0)))) = $false) | ($true = X0) | (((sK2 & (sK3 = (sK16 @ X0))) | ((~ sK2) & (sK5 = (sK16 @ X0)))) = $false)) )),
% 1.37/1.25 inference(binary_proxy_clausification,[status(thm)],[f180])).
% 1.37/1.25 thf(f323,plain,(
% 1.37/1.25 ( ! [X2 : $i,X3 : $i] : (((in @ X3 @ X2) != $true) | ((setunion @ X2) = X3)) )),
% 1.37/1.25 inference(trivial_inequality_removal,[status(thm)],[f302])).
% 1.37/1.25 thf(f302,plain,(
% 1.37/1.25 ( ! [X2 : $i,X3 : $i] : (((setunion @ X2) = X3) | ((in @ X3 @ X2) != $true) | ($true != $true)) )),
% 1.37/1.25 inference(backward_demodulation,[status(thm)],[f79,f301])).
% 1.37/1.25 thf(f362,plain,(
% 1.37/1.25 ( ! [X0 : $i] : (((setunion @ X0) != sK5)) )),
% 1.37/1.25 inference(superposition,[status(thm)],[f80,f332])).
% 1.37/1.25 % SZS output end Proof for DTF2THF_23592
% 1.37/1.25 % (23710)------------------------------
% 1.37/1.25 % (23710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.37/1.25 % (23710)Termination reason: Refutation
% 1.37/1.25
% 1.37/1.25 % (23710)Memory used [KB]: 5756
% 1.37/1.25 % (23710)Time elapsed: 0.036 s
% 1.37/1.25 % (23710)Instructions burned: 61 (million)
% 1.37/1.25 % (23710)------------------------------
% 1.37/1.25 % (23710)------------------------------
% 1.37/1.25 % (23689)Success in time 0.097 s
%------------------------------------------------------------------------------