%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU505^1 : 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 09:34:58 AM UTC 2026
% Result : Theorem 1.88s 1.85s
% Output : Refutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 3
% Syntax : Number of formulae : 41 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 729 ( 218 equ; 0 cnn)
% Maximal formula atoms : 26 ( 17 avg)
% Number of connectives : 543 ( 28 ~; 35 |; 96 &; 255 @)
% ( 2 <=>; 110 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 52 usr; 26 con; 0-3 aty)
% ( 17 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 86 ( 20 ^; 58 !; 8 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_51,type,
sK3: ( $i > $o ) > $i > $i ).
thf(func_def_53,type,
sK4: ( $i > $i > $o ) > $i > $i ).
thf(func_def_54,type,
sK5: ( $i > $i > $o ) > $i > $i ).
thf(func_def_55,type,
sK6: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_56,type,
sK7: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_57,type,
sK8: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_58,type,
sK9: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_59,type,
sK10: $i > $i > $i ).
thf(func_def_60,type,
sK11: $i > $i ).
thf(func_def_61,type,
sK12: $i > $i > $i > $i ).
thf(func_def_62,type,
sK13: $i > $i > $i ).
thf(func_def_63,type,
sK14: $i > $i > $i ).
thf(func_def_64,type,
sK15: $i > $i > $i ).
thf(func_def_65,type,
sK16: $i > $i > $i ).
thf(func_def_66,type,
sK17: $i > $i ).
thf(func_def_67,type,
sK18: $i > $i ).
thf(func_def_68,type,
sK19: ( $i > $o ) > $i > $i ).
thf(func_def_69,type,
sK20: ( $i > $o ) > $i ).
thf(func_def_70,type,
sK21: ( $i > $o ) > $i ).
thf(func_def_71,type,
sK22: $i > $i > $i ).
thf(func_def_72,type,
ph23:
!>[X0: $tType] : X0 ).
thf(f3080,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f3079]) ).
thf(f3079,plain,
$true = $false,
inference(forward_demodulation,[status(thm)],[f3074,f3078]) ).
thf(f3078,plain,
( ( in @ ( sK10 @ sK0 @ sK1 ) @ sK1 )
= $false ),
inference(subsumption_resolution,[status(thm)],[f3077,f121]) ).
thf(f121,plain,
sK1 != sK0,
inference(cnf_transformation,[status(thm)],[f76]) ).
thf(f76,plain,
( ( sK1 != sK0 )
& ! [X2: $i] :
( ( $true
= ( in @ X2 @ sK1 ) )
| ( $true
!= ( in @ X2 @ sK0 ) ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK1 ) )
| ( $true
= ( in @ X3 @ sK0 ) ) )
& ( foundationAx = $true )
& ( dsetconstrER = $true )
& ( omegaSAx = $true )
& ( descrp = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( prop2setE = $true )
& ( dsetconstrEL = $true )
& ( emptysetE = $true )
& ( exuE1 = $true )
& ( dsetconstrI = $true )
& ( replAx = $true )
& ( wellorderingAx = $true )
& ( omega0Ax = $true )
& ( omegaIndAx = $true )
& ( emptysetimpfalse = $true )
& ( notinemptyset = $true )
& ( exuE3e = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f74,f75]) ).
thf(f75,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ! [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
| ( $true
!= ( in @ X2 @ X0 ) ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ X3 @ X0 ) ) ) )
=> ( ( sK1 != sK0 )
& ! [X2: $i] :
( ( $true
= ( in @ X2 @ sK1 ) )
| ( $true
!= ( in @ X2 @ sK0 ) ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK1 ) )
| ( $true
= ( in @ X3 @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f74,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ! [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
| ( $true
!= ( in @ X2 @ X0 ) ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ X3 @ X0 ) ) ) )
& ( foundationAx = $true )
& ( dsetconstrER = $true )
& ( omegaSAx = $true )
& ( descrp = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( prop2setE = $true )
& ( dsetconstrEL = $true )
& ( emptysetE = $true )
& ( exuE1 = $true )
& ( dsetconstrI = $true )
& ( replAx = $true )
& ( wellorderingAx = $true )
& ( omega0Ax = $true )
& ( omegaIndAx = $true )
& ( emptysetimpfalse = $true )
& ( notinemptyset = $true )
& ( exuE3e = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(rectify,[status(thm)],[f73]) ).
thf(f73,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
| ( $true
!= ( in @ X3 @ X0 ) ) )
& ! [X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
= ( in @ X2 @ X0 ) ) ) )
& ( foundationAx = $true )
& ( dsetconstrER = $true )
& ( omegaSAx = $true )
& ( descrp = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( prop2setE = $true )
& ( dsetconstrEL = $true )
& ( emptysetE = $true )
& ( exuE1 = $true )
& ( dsetconstrI = $true )
& ( replAx = $true )
& ( wellorderingAx = $true )
& ( omega0Ax = $true )
& ( omegaIndAx = $true )
& ( emptysetimpfalse = $true )
& ( notinemptyset = $true )
& ( exuE3e = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(flattening,[status(thm)],[f72]) ).
thf(f72,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
| ( $true
!= ( in @ X3 @ X0 ) ) )
& ! [X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
= ( in @ X2 @ X0 ) ) ) )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
=> ( $true
= ( in @ X2 @ X0 ) ) )
=> ( ! [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ( $true
= ( in @ X3 @ X1 ) ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f33]) ).
thf(f33,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ X3 @ X1 ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ! [X4: $i,X3: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ X1 @ X4 ) )
=> ( ! [X1: $i] :
( ( in @ X1 @ X4 )
=> ( in @ X1 @ X3 ) )
=> ( X3 = X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
thf(f24,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ! [X4: $i,X3: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ X1 @ X4 ) )
=> ( ! [X1: $i] :
( ( in @ X1 @ X4 )
=> ( in @ X1 @ X3 ) )
=> ( X3 = X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TAQz0c6eb3/DTF2THF_27688.p',setext) ).
thf(f3077,plain,
( ( sK1 = sK0 )
| ( ( in @ ( sK10 @ sK0 @ sK1 ) @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f3067]) ).
thf(f3067,plain,
( ( ( in @ ( sK10 @ sK0 @ sK1 ) @ sK1 )
= $false )
| ( $true = $false )
| ( sK1 = sK0 ) ),
inference(superposition,[status(thm)],[f238,f1760]) ).
thf(f1760,plain,
( $true
= ( in @ ( sK10 @ sK0 @ sK1 ) @ sK0 ) ),
inference(subsumption_resolution,[status(thm)],[f1752,f121]) ).
thf(f1752,plain,
( ( $true
= ( in @ ( sK10 @ sK0 @ sK1 ) @ sK0 ) )
| ( sK1 = sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f1735]) ).
thf(f1735,plain,
( ( sK1 = sK0 )
| ( $true
= ( in @ ( sK10 @ sK0 @ sK1 ) @ sK0 ) )
| ( $true != $true ) ),
inference(equality_factoring,[status(thm)],[f830]) ).
thf(f830,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK10 @ X0 @ sK1 ) @ X0 ) )
| ( ( in @ ( sK10 @ X0 @ sK1 ) @ sK0 )
= $true )
| ( sK1 = X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f825]) ).
thf(f825,plain,
! [X0: $i] :
( ( ( in @ ( sK10 @ X0 @ sK1 ) @ sK0 )
= $true )
| ( $true
= ( in @ ( sK10 @ X0 @ sK1 ) @ X0 ) )
| ( $true != $true )
| ( sK1 = X0 ) ),
inference(superposition,[status(thm)],[f119,f237]) ).
thf(f237,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK10 @ X1 @ X2 ) @ X2 ) )
| ( X1 = X2 )
| ( $true
= ( in @ ( sK10 @ X1 @ X2 ) @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f236]) ).
thf(f236,plain,
! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( ( in @ ( sK10 @ X1 @ X2 ) @ X2 )
!= ( in @ ( sK10 @ X1 @ X2 ) @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f235]) ).
thf(f235,plain,
! [X2: $i,X1: $i] :
( ( ( ( in @ ( sK10 @ X1 @ X2 ) @ X2 )
= ( in @ ( sK10 @ X1 @ X2 ) @ X1 ) )
= $false )
| ( X1 = X2 ) ),
inference(beta_eta_normalization,[status(thm)],[f234]) ).
thf(f234,plain,
! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
= ( in @ Y0 @ X1 ) )
@ ( sK10 @ X1 @ X2 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f233]) ).
thf(f233,plain,
! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
= ( in @ Y0 @ X1 ) ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f232]) ).
thf(f232,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( X2 = X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
= ( in @ Y0 @ X1 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f231]) ).
thf(f231,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
= ( in @ Y0 @ X1 ) ) )
=> ( X2 = X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f230]) ).
thf(f230,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
= ( in @ Y1 @ X1 ) ) )
=> ( Y0 = X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f229]) ).
thf(f229,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
= ( in @ Y1 @ X1 ) ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f228]) ).
thf(f228,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
= ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f147]) ).
thf(f147,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
= ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f98,f77]) ).
thf(f77,plain,
( setextAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
= ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
( setextAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
= ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f37]) ).
thf(f37,plain,
( setextAx
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
<=> ( in @ X2 @ X1 ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( setextAx
= ( ! [X3: $i,X4: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
<=> ( in @ X1 @ X4 ) )
=> ( X3 = X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TAQz0c6eb3/DTF2THF_27688.p',setextAx) ).
thf(f98,plain,
setextAx = $true,
inference(cnf_transformation,[status(thm)],[f76]) ).
thf(f119,plain,
! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK1 ) )
| ( $true
= ( in @ X3 @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
thf(f238,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK10 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X2 )
| ( ( in @ ( sK10 @ X1 @ X2 ) @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f236]) ).
thf(f3074,plain,
( $true
= ( in @ ( sK10 @ sK0 @ sK1 ) @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f3068]) ).
thf(f3068,plain,
( ( $true
= ( in @ ( sK10 @ sK0 @ sK1 ) @ sK1 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f120,f1760]) ).
thf(f120,plain,
! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK0 ) )
| ( $true
= ( in @ X2 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU505^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.29 % Computer : n011.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Feb 24 12:24:32 EST 2026
% 0.10/0.29 % CPUTime :
% 0.10/0.29 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SEU505^1 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.39 % Domain : Set Theory
% 0.16/0.39 % Problem : Preliminary Notions - Basic Laws of Logic
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English : (!A:i.!B:i.(!x:i.in x A -> in x B)->(!x:i.in x B -> in x A)-> A=B)
% 0.16/0.39
% 0.16/0.39 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.39 % Source : [Bro08]
% 0.16/0.39 % Names : ZFC007g [Bro08]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.18 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.2.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.67 v4.0.1, 1.00 v3.7.0
% 0.16/0.39 % Syntax : Number of formulae : 55 ( 23 unt; 31 typ; 23 def)
% 0.16/0.39 % Number of atoms : 142 ( 29 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 26 ( 5 avg)
% 0.16/0.39 % Number of connectives : 261 ( 4 ~; 3 |; 18 &; 172 @)
% 0.16/0.39 % ( 6 <=>; 58 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 30 ( 2 avg)
% 0.16/0.39 % Number of types : 2 ( 0 usr)
% 0.16/0.39 % Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 33 ( 31 usr; 24 con; 0-2 aty)
% 0.16/0.39 % Number of variables : 84 ( 11 ^; 59 !; 14 ?; 84 :)
% 0.16/0.39 % SPC : TH0_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : http://mathgate.info/detsetitem.php?id=78
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(in_type,type,
% 0.16/0.39 in: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(exu_type,type,
% 0.16/0.39 exu: ( $i > $o ) > $o ).
% 0.16/0.39
% 0.16/0.39 thf(exu,definition,
% 0.16/0.39 ( exu
% 0.16/0.39 = ( ^ [Xphi: $i > $o] :
% 0.16/0.39 ? [Xx: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 & ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setextAx_type,type,
% 0.16/0.39 setextAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setextAx,definition,
% 0.16/0.39 ( setextAx
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 <=> ( in @ Xx @ B ) )
% 0.16/0.39 => ( A = B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptyset_type,type,
% 0.16/0.39 emptyset: $i ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetAx_type,type,
% 0.16/0.39 emptysetAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetAx,definition,
% 0.16/0.39 ( emptysetAx
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoin_type,type,
% 0.16/0.39 setadjoin: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinAx_type,type,
% 0.16/0.39 setadjoinAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setadjoinAx,definition,
% 0.16/0.39 ( setadjoinAx
% 0.16/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.39 <=> ( ( Xy = Xx )
% 0.16/0.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(powerset_type,type,
% 0.16/0.39 powerset: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(powersetAx_type,type,
% 0.16/0.39 powersetAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(powersetAx,definition,
% 0.16/0.39 ( powersetAx
% 0.16/0.39 = ( ! [A: $i,B: $i] :
% 0.16/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.39 <=> ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunion_type,type,
% 0.16/0.39 setunion: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(setunionAx_type,type,
% 0.16/0.39 setunionAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionAx,definition,
% 0.16/0.39 ( setunionAx
% 0.16/0.39 = ( ! [A: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.16/0.39 <=> ? [B: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 & ( in @ B @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omega_type,type,
% 0.16/0.39 omega: $i ).
% 0.16/0.39
% 0.16/0.39 thf(omega0Ax_type,type,
% 0.16/0.39 omega0Ax: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omega0Ax,definition,
% 0.16/0.39 ( omega0Ax
% 0.16/0.39 = ( in @ emptyset @ omega ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omegaSAx_type,type,
% 0.16/0.39 omegaSAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omegaSAx,definition,
% 0.16/0.39 ( omegaSAx
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ omega )
% 0.16/0.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(omegaIndAx_type,type,
% 0.16/0.39 omegaIndAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(omegaIndAx,definition,
% 0.16/0.39 ( omegaIndAx
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ( ( in @ emptyset @ A )
% 0.16/0.39 & ! [Xx: $i] :
% 0.16/0.39 ( ( ( in @ Xx @ omega )
% 0.16/0.39 & ( in @ Xx @ A ) )
% 0.16/0.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ omega )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(replAx_type,type,
% 0.16/0.39 replAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(replAx,definition,
% 0.16/0.39 ( replAx
% 0.16/0.39 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( exu
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.16/0.39 => ? [B: $i] :
% 0.16/0.39 ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 <=> ? [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ A )
% 0.16/0.39 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(foundationAx_type,type,
% 0.16/0.39 foundationAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(foundationAx,definition,
% 0.16/0.39 ( foundationAx
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.16/0.39 => ? [B: $i] :
% 0.16/0.39 ( ( in @ B @ A )
% 0.16/0.39 & ~ ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(wellorderingAx_type,type,
% 0.16/0.39 wellorderingAx: $o ).
% 0.16/0.39
% 0.16/0.39 thf(wellorderingAx,definition,
% 0.16/0.39 ( wellorderingAx
% 0.16/0.39 = ( ! [A: $i] :
% 0.16/0.39 ? [B: $i] :
% 0.16/0.39 ( ! [C: $i] :
% 0.16/0.39 ( ( in @ C @ B )
% 0.16/0.39 => ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ C )
% 0.16/0.39 => ( in @ Xx @ A ) ) )
% 0.16/0.39 & ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( ( in @ Xx @ A )
% 0.16/0.39 & ( in @ Xy @ A ) )
% 0.16/0.39 => ( ! [C: $i] :
% 0.16/0.39 ( ( in @ C @ B )
% 0.16/0.39 => ( ( in @ Xx @ C )
% 0.16/0.39 <=> ( in @ Xy @ C ) ) )
% 0.16/0.39 => ( Xx = Xy ) ) )
% 0.16/0.39 & ! [C: $i,D: $i] :
% 0.16/0.39 ( ( ( in @ C @ B )
% 0.16/0.39 & ( in @ D @ B ) )
% 0.16/0.39 => ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ C )
% 0.16/0.39 => ( in @ Xx @ D ) )
% 0.16/0.39 | ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ D )
% 0.16/0.39 => ( in @ Xx @ C ) ) ) )
% 0.16/0.39 & ! [C: $i] :
% 0.16/0.39 ( ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ C )
% 0.16/0.39 => ( in @ Xx @ A ) )
% 0.16/0.39 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.16/0.39 => ? [D: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ D @ B )
% 0.16/0.39 & ( in @ Xx @ C )
% 0.16/0.39 & ~ ? [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ D )
% 0.16/0.39 & ( in @ Xy @ C ) )
% 0.16/0.39 & ! [E: $i] :
% 0.16/0.39 ( ( in @ E @ B )
% 0.16/0.39 => ( ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ E )
% 0.16/0.39 => ( in @ Xy @ D ) )
% 0.16/0.39 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(descr_type,type,
% 0.16/0.39 descr: ( $i > $o ) > $i ).
% 0.16/0.39
% 0.16/0.39 thf(descrp_type,type,
% 0.16/0.39 descrp: $o ).
% 0.16/0.39
% 0.16/0.39 thf(descrp,definition,
% 0.16/0.39 ( descrp
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ( Xphi
% 0.16/0.39 @ ( descr
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstr_type,type,
% 0.16/0.39 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrI_type,type,
% 0.16/0.39 dsetconstrI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrI,definition,
% 0.16/0.39 ( dsetconstrI
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 => ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrEL_type,type,
% 0.16/0.39 dsetconstrEL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrEL,definition,
% 0.16/0.39 ( dsetconstrEL
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrER_type,type,
% 0.16/0.39 dsetconstrER: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrER,definition,
% 0.16/0.39 ( dsetconstrER
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.39 => ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuE1_type,type,
% 0.16/0.39 exuE1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuE1,definition,
% 0.16/0.39 ( exuE1
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( Xphi @ Xx )
% 0.16/0.39 & ! [Xy: $i] :
% 0.16/0.39 ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(prop2set_type,type,
% 0.16/0.39 prop2set: $o > $i ).
% 0.16/0.39
% 0.16/0.39 thf(prop2set,definition,
% 0.16/0.39 ( prop2set
% 0.16/0.39 = ( ^ [Xphi: $o] :
% 0.16/0.39 ( dsetconstr @ ( powerset @ emptyset )
% 0.16/0.39 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(prop2setE_type,type,
% 0.16/0.39 prop2setE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(prop2setE,definition,
% 0.16/0.39 ( prop2setE
% 0.16/0.39 = ( ! [Xphi: $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.16/0.39 => Xphi ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetE_type,type,
% 0.16/0.39 emptysetE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetE,definition,
% 0.16/0.39 ( emptysetE
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ emptyset )
% 0.16/0.39 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetimpfalse_type,type,
% 0.16/0.39 emptysetimpfalse: $o ).
% 0.16/0.39
% 0.16/0.39 thf(emptysetimpfalse,definition,
% 0.16/0.39 ( emptysetimpfalse
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ emptyset )
% 0.16/0.39 => $false ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(notinemptyset_type,type,
% 0.16/0.39 notinemptyset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(notinemptyset,definition,
% 0.16/0.39 ( notinemptyset
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(exuE3e_type,type,
% 0.16/0.39 exuE3e: $o ).
% 0.16/0.39
% 0.16/0.39 thf(exuE3e,definition,
% 0.16/0.39 ( exuE3e
% 0.16/0.39 = ( ! [Xphi: $i > $o] :
% 0.16/0.39 ( ( exu
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setext,conjecture,
% 0.16/0.39 ( setextAx
% 0.16/0.39 => ( emptysetAx
% 0.16/0.39 => ( setadjoinAx
% 0.16/0.39 => ( powersetAx
% 0.16/0.39 => ( setunionAx
% 0.16/0.39 => ( omega0Ax
% 0.16/0.39 => ( omegaSAx
% 0.16/0.39 => ( omegaIndAx
% 0.16/0.39 => ( replAx
% 0.16/0.39 => ( foundationAx
% 0.16/0.39 => ( wellorderingAx
% 0.16/0.39 => ( descrp
% 0.16/0.39 => ( dsetconstrI
% 0.16/0.39 => ( dsetconstrEL
% 0.16/0.39 => ( dsetconstrER
% 0.16/0.39 => ( exuE1
% 0.16/0.39 => ( prop2setE
% 0.16/0.39 => ( emptysetE
% 0.16/0.39 => ( emptysetimpfalse
% 0.16/0.39 => ( notinemptyset
% 0.16/0.39 => ( exuE3e
% 0.16/0.39 => ! [A: $i,B: $i] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ Xx @ B ) )
% 0.16/0.39 => ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ A ) )
% 0.16/0.39 => ( A = B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.70/1.37 ---- Embedded in THF ---
% 1.70/1.37 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.70/1.37 %%% Generated on Tue Feb 24 12:24:33 EST 2026
% 1.70/1.37 %%% using '$$dhol' embedding, version 1.3.0.
% 1.70/1.37 %%% Logic specification used:
% 1.70/1.37 %%% thf(spec, logic, $$dhol).
% 1.70/1.37
% 1.70/1.37 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.TAQz0c6eb3/DTF2DTF27688.p
% See solution above
% 1.70/1.37 ------------------------
% 1.70/1.39 ---- Cleaned THF ---
% 1.70/1.39 thf(in_type,type,
% 1.70/1.39 in: $i > $i > $o ).
% 1.70/1.39
% 1.70/1.39 thf(exu_type,type,
% 1.70/1.39 exu: ( $i > $o ) > $o ).
% 1.70/1.39
% 1.70/1.39 thf(exu,definition,
% 1.70/1.39 ( exu
% 1.70/1.39 = ( ^ [Xphi: $i > $o] :
% 1.70/1.39 ? [Xx: $i] :
% 1.70/1.39 ( ( Xphi @ Xx )
% 1.70/1.39 & ! [Xy: $i] :
% 1.70/1.39 ( ( Xphi @ Xy )
% 1.70/1.39 => ( Xx = Xy ) ) ) ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(setextAx_type,type,
% 1.70/1.39 setextAx: $o ).
% 1.70/1.39
% 1.70/1.39 thf(setextAx,definition,
% 1.70/1.39 ( setextAx
% 1.70/1.39 = ( ! [A: $i,B: $i] :
% 1.70/1.39 ( ! [Xx: $i] :
% 1.70/1.39 ( ( in @ Xx @ A )
% 1.70/1.39 <=> ( in @ Xx @ B ) )
% 1.70/1.39 => ( A = B ) ) ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(emptyset_type,type,
% 1.70/1.39 emptyset: $i ).
% 1.70/1.39
% 1.70/1.39 thf(emptysetAx_type,type,
% 1.70/1.39 emptysetAx: $o ).
% 1.70/1.39
% 1.70/1.39 thf(emptysetAx,definition,
% 1.70/1.39 ( emptysetAx
% 1.70/1.39 = ( ! [Xx: $i] :
% 1.70/1.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(setadjoin_type,type,
% 1.70/1.39 setadjoin: $i > $i > $i ).
% 1.70/1.39
% 1.70/1.39 thf(setadjoinAx_type,type,
% 1.70/1.39 setadjoinAx: $o ).
% 1.70/1.39
% 1.70/1.39 thf(setadjoinAx,definition,
% 1.70/1.39 ( setadjoinAx
% 1.70/1.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.70/1.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.70/1.39 <=> ( ( Xy = Xx )
% 1.70/1.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(powerset_type,type,
% 1.70/1.39 powerset: $i > $i ).
% 1.70/1.39
% 1.70/1.39 thf(powersetAx_type,type,
% 1.70/1.39 powersetAx: $o ).
% 1.70/1.39
% 1.70/1.39 thf(powersetAx,definition,
% 1.70/1.39 ( powersetAx
% 1.70/1.39 = ( ! [A: $i,B: $i] :
% 1.70/1.39 ( ( in @ B @ ( powerset @ A ) )
% 1.70/1.39 <=> ! [Xx: $i] :
% 1.70/1.39 ( ( in @ Xx @ B )
% 1.70/1.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(setunion_type,type,
% 1.70/1.39 setunion: $i > $i ).
% 1.70/1.39
% 1.70/1.39 thf(setunionAx_type,type,
% 1.70/1.39 setunionAx: $o ).
% 1.70/1.39
% 1.70/1.39 thf(setunionAx,definition,
% 1.70/1.39 ( setunionAx
% 1.70/1.39 = ( ! [A: $i,Xx: $i] :
% 1.70/1.39 ( ( in @ Xx @ ( setunion @ A ) )
% 1.70/1.39 <=> ? [B: $i] :
% 1.70/1.39 ( ( in @ Xx @ B )
% 1.70/1.39 & ( in @ B @ A ) ) ) ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(omega_type,type,
% 1.70/1.39 omega: $i ).
% 1.70/1.39
% 1.70/1.39 thf(omega0Ax_type,type,
% 1.70/1.39 omega0Ax: $o ).
% 1.70/1.39
% 1.70/1.39 thf(omega0Ax,definition,
% 1.70/1.39 ( omega0Ax
% 1.70/1.39 = ( in @ emptyset @ omega ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(omegaSAx_type,type,
% 1.70/1.39 omegaSAx: $o ).
% 1.70/1.39
% 1.70/1.39 thf(omegaSAx,definition,
% 1.70/1.39 ( omegaSAx
% 1.70/1.39 = ( ! [Xx: $i] :
% 1.70/1.39 ( ( in @ Xx @ omega )
% 1.70/1.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(omegaIndAx_type,type,
% 1.70/1.39 omegaIndAx: $o ).
% 1.70/1.39
% 1.70/1.39 thf(omegaIndAx,definition,
% 1.70/1.39 ( omegaIndAx
% 1.70/1.39 = ( ! [A: $i] :
% 1.70/1.39 ( ( ( in @ emptyset @ A )
% 1.70/1.39 & ! [Xx: $i] :
% 1.70/1.39 ( ( ( in @ Xx @ omega )
% 1.70/1.39 & ( in @ Xx @ A ) )
% 1.70/1.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 1.70/1.39 => ! [Xx: $i] :
% 1.70/1.39 ( ( in @ Xx @ omega )
% 1.70/1.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(replAx_type,type,
% 1.70/1.39 replAx: $o ).
% 1.70/1.39
% 1.70/1.39 thf(replAx,definition,
% 1.70/1.39 ( replAx
% 1.70/1.39 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 1.70/1.39 ( ! [Xx: $i] :
% 1.70/1.39 ( ( in @ Xx @ A )
% 1.70/1.39 => ( exu
% 1.70/1.39 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 1.70/1.39 => ? [B: $i] :
% 1.70/1.39 ! [Xx: $i] :
% 1.70/1.39 ( ( in @ Xx @ B )
% 1.70/1.39 <=> ? [Xy: $i] :
% 1.70/1.39 ( ( in @ Xy @ A )
% 1.70/1.39 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(foundationAx_type,type,
% 1.70/1.39 foundationAx: $o ).
% 1.70/1.39
% 1.70/1.39 thf(foundationAx,definition,
% 1.70/1.39 ( foundationAx
% 1.70/1.39 = ( ! [A: $i] :
% 1.70/1.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.70/1.39 => ? [B: $i] :
% 1.70/1.39 ( ( in @ B @ A )
% 1.70/1.39 & ~ ? [Xx: $i] :
% 1.70/1.39 ( ( in @ Xx @ B )
% 1.70/1.39 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(wellorderingAx_type,type,
% 1.70/1.39 wellorderingAx: $o ).
% 1.70/1.39
% 1.70/1.39 thf(wellorderingAx,definition,
% 1.70/1.39 ( wellorderingAx
% 1.70/1.39 = ( ! [A: $i] :
% 1.70/1.39 ? [B: $i] :
% 1.70/1.39 ( ! [C: $i] :
% 1.70/1.39 ( ( in @ C @ B )
% 1.70/1.39 => ! [Xx: $i] :
% 1.70/1.39 ( ( in @ Xx @ C )
% 1.70/1.39 => ( in @ Xx @ A ) ) )
% 1.70/1.39 & ! [Xx: $i,Xy: $i] :
% 1.70/1.39 ( ( ( in @ Xx @ A )
% 1.70/1.39 & ( in @ Xy @ A ) )
% 1.70/1.39 => ( ! [C: $i] :
% 1.70/1.39 ( ( in @ C @ B )
% 1.70/1.39 => ( ( in @ Xx @ C )
% 1.70/1.39 <=> ( in @ Xy @ C ) ) )
% 1.70/1.39 => ( Xx = Xy ) ) )
% 1.70/1.39 & ! [C: $i,D: $i] :
% 1.70/1.39 ( ( ( in @ C @ B )
% 1.70/1.39 & ( in @ D @ B ) )
% 1.70/1.39 => ( ! [Xx: $i] :
% 1.70/1.39 ( ( in @ Xx @ C )
% 1.70/1.39 => ( in @ Xx @ D ) )
% 1.70/1.39 | ! [Xx: $i] :
% 1.70/1.39 ( ( in @ Xx @ D )
% 1.70/1.39 => ( in @ Xx @ C ) ) ) )
% 1.70/1.39 & ! [C: $i] :
% 1.70/1.39 ( ( ! [Xx: $i] :
% 1.70/1.39 ( ( in @ Xx @ C )
% 1.70/1.39 => ( in @ Xx @ A ) )
% 1.70/1.39 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 1.70/1.39 => ? [D: $i,Xx: $i] :
% 1.70/1.39 ( ( in @ D @ B )
% 1.70/1.39 & ( in @ Xx @ C )
% 1.70/1.39 & ~ ? [Xy: $i] :
% 1.70/1.39 ( ( in @ Xy @ D )
% 1.70/1.39 & ( in @ Xy @ C ) )
% 1.70/1.39 & ! [E: $i] :
% 1.70/1.39 ( ( in @ E @ B )
% 1.70/1.39 => ( ! [Xy: $i] :
% 1.70/1.39 ( ( in @ Xy @ E )
% 1.70/1.39 => ( in @ Xy @ D ) )
% 1.70/1.39 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(descr_type,type,
% 1.70/1.39 descr: ( $i > $o ) > $i ).
% 1.70/1.39
% 1.70/1.39 thf(descrp_type,type,
% 1.70/1.39 descrp: $o ).
% 1.70/1.39
% 1.70/1.39 thf(descrp,definition,
% 1.70/1.39 ( descrp
% 1.70/1.39 = ( ! [Xphi: $i > $o] :
% 1.70/1.39 ( ( exu
% 1.70/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.70/1.39 => ( Xphi
% 1.70/1.39 @ ( descr
% 1.70/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(dsetconstr_type,type,
% 1.70/1.39 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.70/1.39
% 1.70/1.39 thf(dsetconstrI_type,type,
% 1.70/1.39 dsetconstrI: $o ).
% 1.70/1.39
% 1.70/1.39 thf(dsetconstrI,definition,
% 1.70/1.39 ( dsetconstrI
% 1.70/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.70/1.39 ( ( in @ Xx @ A )
% 1.70/1.39 => ( ( Xphi @ Xx )
% 1.70/1.39 => ( in @ Xx
% 1.70/1.39 @ ( dsetconstr @ A
% 1.70/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(dsetconstrEL_type,type,
% 1.70/1.39 dsetconstrEL: $o ).
% 1.70/1.39
% 1.70/1.39 thf(dsetconstrEL,definition,
% 1.70/1.39 ( dsetconstrEL
% 1.70/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.70/1.39 ( ( in @ Xx
% 1.70/1.39 @ ( dsetconstr @ A
% 1.70/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.70/1.39 => ( in @ Xx @ A ) ) ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(dsetconstrER_type,type,
% 1.70/1.39 dsetconstrER: $o ).
% 1.70/1.39
% 1.70/1.39 thf(dsetconstrER,definition,
% 1.70/1.39 ( dsetconstrER
% 1.70/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.70/1.39 ( ( in @ Xx
% 1.70/1.39 @ ( dsetconstr @ A
% 1.70/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.70/1.39 => ( Xphi @ Xx ) ) ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(exuE1_type,type,
% 1.70/1.39 exuE1: $o ).
% 1.70/1.39
% 1.70/1.39 thf(exuE1,definition,
% 1.70/1.39 ( exuE1
% 1.70/1.39 = ( ! [Xphi: $i > $o] :
% 1.70/1.39 ( ( exu
% 1.70/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.70/1.39 => ? [Xx: $i] :
% 1.70/1.39 ( ( Xphi @ Xx )
% 1.70/1.39 & ! [Xy: $i] :
% 1.70/1.39 ( ( Xphi @ Xy )
% 1.70/1.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(prop2set_type,type,
% 1.70/1.39 prop2set: $o > $i ).
% 1.70/1.39
% 1.70/1.39 thf(prop2set,definition,
% 1.70/1.39 ( prop2set
% 1.70/1.39 = ( ^ [Xphi: $o] :
% 1.70/1.39 ( dsetconstr @ ( powerset @ emptyset )
% 1.70/1.39 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(prop2setE_type,type,
% 1.70/1.39 prop2setE: $o ).
% 1.70/1.39
% 1.70/1.39 thf(prop2setE,definition,
% 1.70/1.39 ( prop2setE
% 1.70/1.39 = ( ! [Xphi: $o,Xx: $i] :
% 1.70/1.39 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 1.70/1.39 => Xphi ) ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(emptysetE_type,type,
% 1.70/1.39 emptysetE: $o ).
% 1.70/1.39
% 1.70/1.39 thf(emptysetE,definition,
% 1.70/1.39 ( emptysetE
% 1.70/1.39 = ( ! [Xx: $i] :
% 1.70/1.39 ( ( in @ Xx @ emptyset )
% 1.70/1.39 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(emptysetimpfalse_type,type,
% 1.70/1.39 emptysetimpfalse: $o ).
% 1.70/1.39
% 1.70/1.39 thf(emptysetimpfalse,definition,
% 1.70/1.39 ( emptysetimpfalse
% 1.70/1.39 = ( ! [Xx: $i] :
% 1.70/1.39 ( ( in @ Xx @ emptyset )
% 1.70/1.39 => $false ) ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(notinemptyset_type,type,
% 1.70/1.39 notinemptyset: $o ).
% 1.70/1.39
% 1.70/1.39 thf(notinemptyset,definition,
% 1.70/1.39 ( notinemptyset
% 1.70/1.39 = ( ! [Xx: $i] :
% 1.70/1.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(exuE3e_type,type,
% 1.70/1.39 exuE3e: $o ).
% 1.70/1.39
% 1.70/1.39 thf(exuE3e,definition,
% 1.70/1.39 ( exuE3e
% 1.70/1.39 = ( ! [Xphi: $i > $o] :
% 1.70/1.39 ( ( exu
% 1.70/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.70/1.39 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 1.70/1.39
% 1.70/1.39 thf(setext,conjecture,
% 1.70/1.39 ( setextAx
% 1.70/1.39 => ( emptysetAx
% 1.70/1.39 => ( setadjoinAx
% 1.70/1.39 => ( powersetAx
% 1.70/1.39 => ( setunionAx
% 1.70/1.39 => ( omega0Ax
% 1.70/1.39 => ( omegaSAx
% 1.70/1.39 => ( omegaIndAx
% 1.70/1.39 => ( replAx
% 1.70/1.39 => ( foundationAx
% 1.70/1.39 => ( wellorderingAx
% 1.70/1.39 => ( descrp
% 1.70/1.39 => ( dsetconstrI
% 1.70/1.39 => ( dsetconstrEL
% 1.70/1.39 => ( dsetconstrER
% 1.70/1.39 => ( exuE1
% 1.70/1.39 => ( prop2setE
% 1.70/1.39 => ( emptysetE
% 1.70/1.39 => ( emptysetimpfalse
% 1.70/1.39 => ( notinemptyset
% 1.70/1.39 => ( exuE3e
% 1.70/1.39 => ! [A: $i,B: $i] :
% 1.70/1.39 ( ! [Xx: $i] :
% 1.70/1.39 ( ( in @ Xx @ A )
% 1.70/1.39 => ( in @ Xx @ B ) )
% 1.70/1.39 => ( ! [Xx: $i] :
% 1.70/1.39 ( ( in @ Xx @ B )
% 1.70/1.39 => ( in @ Xx @ A ) )
% 1.70/1.39 => ( A = B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.70/1.39 ------------------------
% 1.88/1.41 % (27791)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27688 for (2999ds/2Mi)
% 1.88/1.41 % (27793)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_27688 for (2999ds/275Mi)
% 1.88/1.41 % (27794)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27688 for (2999ds/18Mi)
% 1.88/1.41 % (27792)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_27688 for (2999ds/2Mi)
% 1.88/1.41 % (27789)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_27688 for (2999ds/4Mi)
% 1.88/1.41 % (27790)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_27688 for (2999ds/27Mi)
% 1.88/1.41 % (27788)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27688 for (2999ds/183Mi)
% 1.88/1.41 % (27791)Instruction limit reached!
% 1.88/1.41 % (27791)------------------------------
% 1.88/1.41 % (27791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.41 % (27791)Termination reason: Unknown
% 1.88/1.41 % (27791)Termination phase: shuffling
% 1.88/1.41 % (27792)Instruction limit reached!
% 1.88/1.41 % (27792)------------------------------
% 1.88/1.41 % (27792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.41 % (27792)Termination reason: Unknown
% 1.88/1.41 % (27792)Termination phase: shuffling
% 1.88/1.41
% 1.88/1.41 % (27792)Memory used [KB]: 1023
% 1.88/1.41 % (27792)Time elapsed: 0.003 s
% 1.88/1.41 % (27792)Instructions burned: 3 (million)
% 1.88/1.41 % (27792)------------------------------
% 1.88/1.41 % (27792)------------------------------
% 1.88/1.41
% 1.88/1.41 % (27791)Memory used [KB]: 1023
% 1.88/1.41 % (27791)Time elapsed: 0.003 s
% 1.88/1.41 % (27791)Instructions burned: 3 (million)
% 1.88/1.41 % (27791)------------------------------
% 1.88/1.41 % (27791)------------------------------
% 1.88/1.41 % (27789)Instruction limit reached!
% 1.88/1.41 % (27789)------------------------------
% 1.88/1.41 % (27789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.41 % (27789)Termination reason: Unknown
% 1.88/1.41 % (27789)Termination phase: shuffling
% 1.88/1.41
% 1.88/1.41 % (27789)Memory used [KB]: 1023
% 1.88/1.41 % (27789)Time elapsed: 0.004 s
% 1.88/1.41 % (27789)Instructions burned: 5 (million)
% 1.88/1.41 % (27789)------------------------------
% 1.88/1.41 % (27789)------------------------------
% 1.88/1.42 % (27794)Instruction limit reached!
% 1.88/1.42 % (27794)------------------------------
% 1.88/1.42 % (27794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.42 % (27794)Termination reason: Unknown
% 1.88/1.42 % (27794)Termination phase: Property scanning
% 1.88/1.42
% 1.88/1.42 % (27794)Memory used [KB]: 1407
% 1.88/1.42 % (27794)Time elapsed: 0.011 s
% 1.88/1.42 % (27794)Instructions burned: 20 (million)
% 1.88/1.42 % (27794)------------------------------
% 1.88/1.42 % (27794)------------------------------
% 1.88/1.42 % (27790)Instruction limit reached!
% 1.88/1.42 % (27790)------------------------------
% 1.88/1.42 % (27790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.42 % (27790)Termination reason: Unknown
% 1.88/1.42 % (27790)Termination phase: Saturation
% 1.88/1.42
% 1.88/1.42 % (27790)Memory used [KB]: 5756
% 1.88/1.42 % (27790)Time elapsed: 0.015 s
% 1.88/1.42 % (27790)Instructions burned: 28 (million)
% 1.88/1.42 % (27790)------------------------------
% 1.88/1.42 % (27790)------------------------------
% 1.88/1.43 % (27795)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27688 for (2999ds/3Mi)
% 1.88/1.43 % (27796)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_27688 for (2999ds/37Mi)
% 1.88/1.43 % (27797)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_27688 for (2999ds/15Mi)
% 1.88/1.43 % (27795)Instruction limit reached!
% 1.88/1.43 % (27795)------------------------------
% 1.88/1.43 % (27795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.43 % (27795)Termination reason: Unknown
% 1.88/1.43 % (27795)Termination phase: shuffling
% 1.88/1.43
% 1.88/1.43 % (27795)Memory used [KB]: 1023
% 1.88/1.43 % (27795)Time elapsed: 0.003 s
% 1.88/1.43 % (27795)Instructions burned: 3 (million)
% 1.88/1.43 % (27795)------------------------------
% 1.88/1.43 % (27795)------------------------------
% 1.88/1.43 % (27798)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_27688 for (2999ds/3Mi)
% 1.88/1.43 % (27797)Instruction limit reached!
% 1.88/1.43 % (27797)------------------------------
% 1.88/1.43 % (27797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.43 % (27797)Termination reason: Unknown
% 1.88/1.43 % (27797)Termination phase: Property scanning
% 1.88/1.43
% 1.88/1.43 % (27797)Memory used [KB]: 1407
% 1.88/1.43 % (27797)Time elapsed: 0.009 s
% 1.88/1.43 % (27797)Instructions burned: 16 (million)
% 1.88/1.43 % (27797)------------------------------
% 1.88/1.43 % (27797)------------------------------
% 1.88/1.43 % (27798)Instruction limit reached!
% 1.88/1.43 % (27798)------------------------------
% 1.88/1.43 % (27798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.43 % (27798)Termination reason: Unknown
% 1.88/1.43 % (27798)Termination phase: shuffling
% 1.88/1.43
% 1.88/1.43 % (27798)Memory used [KB]: 1023
% 1.88/1.43 % (27798)Time elapsed: 0.003 s
% 1.88/1.43 % (27798)Instructions burned: 3 (million)
% 1.88/1.43 % (27798)------------------------------
% 1.88/1.43 % (27798)------------------------------
% 1.88/1.44 % (27799)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_27688 for (2999ds/1041Mi)
% 1.88/1.44 % (27796)Instruction limit reached!
% 1.88/1.44 % (27796)------------------------------
% 1.88/1.44 % (27796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.44 % (27796)Termination reason: Unknown
% 1.88/1.44 % (27796)Termination phase: Saturation
% 1.88/1.44
% 1.88/1.44 % (27796)Memory used [KB]: 5756
% 1.88/1.44 % (27796)Time elapsed: 0.018 s
% 1.88/1.44 % (27796)Instructions burned: 38 (million)
% 1.88/1.44 % (27796)------------------------------
% 1.88/1.44 % (27796)------------------------------
% 1.88/1.44 % (27800)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_27688 for (2999ds/7Mi)
% 1.88/1.45 % (27800)Instruction limit reached!
% 1.88/1.45 % (27800)------------------------------
% 1.88/1.45 % (27800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.45 % (27800)Termination reason: Unknown
% 1.88/1.45 % (27800)Termination phase: SInE selection
% 1.88/1.45
% 1.88/1.45 % (27800)Memory used [KB]: 1151
% 1.88/1.45 % (27800)Time elapsed: 0.005 s
% 1.88/1.45 % (27800)Instructions burned: 8 (million)
% 1.88/1.45 % (27800)------------------------------
% 1.88/1.45 % (27800)------------------------------
% 1.88/1.45 % (27801)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_27688 for (2999ds/16Mi)
% 1.88/1.45 % (27802)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_27688 for (2999ds/3Mi)
% 1.88/1.45 % (27802)Instruction limit reached!
% 1.88/1.45 % (27802)------------------------------
% 1.88/1.45 % (27802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.45 % (27802)Termination reason: Unknown
% 1.88/1.45 % (27802)Termination phase: shuffling
% 1.88/1.45
% 1.88/1.45 % (27802)Memory used [KB]: 1023
% 1.88/1.45 % (27802)Time elapsed: 0.003 s
% 1.88/1.45 % (27802)Instructions burned: 4 (million)
% 1.88/1.45 % (27802)------------------------------
% 1.88/1.45 % (27802)------------------------------
% 1.88/1.46 % (27801)Instruction limit reached!
% 1.88/1.46 % (27801)------------------------------
% 1.88/1.46 % (27801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.46 % (27801)Termination reason: Unknown
% 1.88/1.46 % (27801)Termination phase: Saturation
% 1.88/1.46
% 1.88/1.46 % (27801)Memory used [KB]: 5628
% 1.88/1.46 % (27801)Time elapsed: 0.009 s
% 1.88/1.46 % (27801)Instructions burned: 16 (million)
% 1.88/1.46 % (27801)------------------------------
% 1.88/1.46 % (27801)------------------------------
% 1.88/1.46 % (27803)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_27688 for (2999ds/3Mi)
% 1.88/1.46 % (27803)Instruction limit reached!
% 1.88/1.46 % (27803)------------------------------
% 1.88/1.46 % (27803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.46 % (27803)Termination reason: Unknown
% 1.88/1.46 % (27803)Termination phase: shuffling
% 1.88/1.46
% 1.88/1.46 % (27803)Memory used [KB]: 1023
% 1.88/1.46 % (27803)Time elapsed: 0.003 s
% 1.88/1.46 % (27803)Instructions burned: 4 (million)
% 1.88/1.46 % (27803)------------------------------
% 1.88/1.46 % (27803)------------------------------
% 1.88/1.46 % (27804)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_27688 for (2999ds/7Mi)
% 1.88/1.47 % (27804)Instruction limit reached!
% 1.88/1.47 % (27804)------------------------------
% 1.88/1.47 % (27804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.47 % (27804)Termination reason: Unknown
% 1.88/1.47 % (27804)Termination phase: Preprocessing 3
% 1.88/1.47
% 1.88/1.47 % (27804)Memory used [KB]: 1151
% 1.88/1.47 % (27804)Time elapsed: 0.005 s
% 1.88/1.47 % (27804)Instructions burned: 8 (million)
% 1.88/1.47 % (27804)------------------------------
% 1.88/1.47 % (27804)------------------------------
% 1.88/1.47 % (27805)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_27688 for (2999ds/3Mi)
% 1.88/1.47 % (27805)Instruction limit reached!
% 1.88/1.47 % (27805)------------------------------
% 1.88/1.47 % (27805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.47 % (27805)Termination reason: Unknown
% 1.88/1.47 % (27805)Termination phase: shuffling
% 1.88/1.47
% 1.88/1.47 % (27805)Memory used [KB]: 1023
% 1.88/1.47 % (27805)Time elapsed: 0.003 s
% 1.88/1.47 % (27805)Instructions burned: 4 (million)
% 1.88/1.47 % (27805)------------------------------
% 1.88/1.47 % (27805)------------------------------
% 1.88/1.47 % (27806)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_27688 for (2999ds/4Mi)
% 1.88/1.47 % (27806)Instruction limit reached!
% 1.88/1.47 % (27806)------------------------------
% 1.88/1.47 % (27806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.47 % (27806)Termination reason: Unknown
% 1.88/1.47 % (27806)Termination phase: shuffling
% 1.88/1.47
% 1.88/1.47 % (27806)Memory used [KB]: 1023
% 1.88/1.47 % (27806)Time elapsed: 0.003 s
% 1.88/1.47 % (27806)Instructions burned: 4 (million)
% 1.88/1.47 % (27806)------------------------------
% 1.88/1.47 % (27806)------------------------------
% 1.88/1.48 % (27807)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_27688 for (2999ds/18Mi)
% 1.88/1.48 % (27808)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_27688 for (2999ds/710Mi)
% 1.88/1.48 % (27807)Instruction limit reached!
% 1.88/1.48 % (27807)------------------------------
% 1.88/1.48 % (27807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.48 % (27807)Termination reason: Unknown
% 1.88/1.48 % (27807)Termination phase: Saturation
% 1.88/1.48
% 1.88/1.48 % (27807)Memory used [KB]: 5756
% 1.88/1.48 % (27807)Time elapsed: 0.010 s
% 1.88/1.48 % (27807)Instructions burned: 18 (million)
% 1.88/1.48 % (27807)------------------------------
% 1.88/1.48 % (27807)------------------------------
% 1.88/1.49 % (27809)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27688 for (2999ds/6Mi)
% 1.88/1.49 % (27809)Instruction limit reached!
% 1.88/1.49 % (27809)------------------------------
% 1.88/1.49 % (27809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.49 % (27809)Termination reason: Unknown
% 1.88/1.49 % (27809)Termination phase: Property scanning
% 1.88/1.49
% 1.88/1.49 % (27809)Memory used [KB]: 1023
% 1.88/1.49 % (27809)Time elapsed: 0.004 s
% 1.88/1.49 % (27809)Instructions burned: 6 (million)
% 1.88/1.49 % (27809)------------------------------
% 1.88/1.49 % (27809)------------------------------
% 1.88/1.49 % (27810)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_27688 for (2999ds/902Mi)
% 1.88/1.50 % (27788)Instruction limit reached!
% 1.88/1.50 % (27788)------------------------------
% 1.88/1.50 % (27788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.50 % (27788)Termination reason: Unknown
% 1.88/1.50 % (27788)Termination phase: Saturation
% 1.88/1.50
% 1.88/1.50 % (27788)Memory used [KB]: 6780
% 1.88/1.50 % (27788)Time elapsed: 0.092 s
% 1.88/1.50 % (27788)Instructions burned: 183 (million)
% 1.88/1.50 % (27788)------------------------------
% 1.88/1.50 % (27788)------------------------------
% 1.88/1.50 % (27811)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_27688 for (2999ds/21Mi)
% 1.88/1.50 % (27812)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_27688 for (2999ds/5Mi)
% 1.88/1.51 % (27812)Instruction limit reached!
% 1.88/1.51 % (27812)------------------------------
% 1.88/1.51 % (27812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.51 % (27812)Termination reason: Unknown
% 1.88/1.51 % (27812)Termination phase: Property scanning
% 1.88/1.51
% 1.88/1.51 % (27812)Memory used [KB]: 1023
% 1.88/1.51 % (27812)Time elapsed: 0.004 s
% 1.88/1.51 % (27812)Instructions burned: 6 (million)
% 1.88/1.51 % (27812)------------------------------
% 1.88/1.51 % (27812)------------------------------
% 1.88/1.51 % (27811)Instruction limit reached!
% 1.88/1.51 % (27811)------------------------------
% 1.88/1.51 % (27811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.51 % (27811)Termination reason: Unknown
% 1.88/1.51 % (27811)Termination phase: Saturation
% 1.88/1.51
% 1.88/1.51 % (27811)Memory used [KB]: 5628
% 1.88/1.51 % (27811)Time elapsed: 0.012 s
% 1.88/1.51 % (27811)Instructions burned: 22 (million)
% 1.88/1.51 % (27811)------------------------------
% 1.88/1.51 % (27811)------------------------------
% 1.88/1.51 % (27813)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_27688 for (2999ds/6Mi)
% 1.88/1.52 % (27813)Instruction limit reached!
% 1.88/1.52 % (27813)------------------------------
% 1.88/1.52 % (27813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.52 % (27813)Termination reason: Unknown
% 1.88/1.52 % (27813)Termination phase: Property scanning
% 1.88/1.52
% 1.88/1.52 % (27813)Memory used [KB]: 1023
% 1.88/1.52 % (27813)Time elapsed: 0.005 s
% 1.88/1.52 % (27813)Instructions burned: 7 (million)
% 1.88/1.52 % (27813)------------------------------
% 1.88/1.52 % (27813)------------------------------
% 1.88/1.52 % (27814)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_27688 for (2998ds/377Mi)
% 1.88/1.53 % (27815)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_27688 for (2998ds/779Mi)
% 1.88/1.53 % (27816)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_27688 for (2998ds/19Mi)
% 1.88/1.54 % (27816)Instruction limit reached!
% 1.88/1.54 % (27816)------------------------------
% 1.88/1.54 % (27816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.54 % (27816)Termination reason: Unknown
% 1.88/1.54 % (27816)Termination phase: Saturation
% 1.88/1.54
% 1.88/1.54 % (27816)Memory used [KB]: 5628
% 1.88/1.54 % (27816)Time elapsed: 0.010 s
% 1.88/1.54 % (27816)Instructions burned: 19 (million)
% 1.88/1.54 % (27816)------------------------------
% 1.88/1.54 % (27816)------------------------------
% 1.88/1.54 % (27793)Instruction limit reached!
% 1.88/1.54 % (27793)------------------------------
% 1.88/1.54 % (27793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.54 % (27793)Termination reason: Unknown
% 1.88/1.54 % (27793)Termination phase: Saturation
% 1.88/1.54
% 1.88/1.54 % (27793)Memory used [KB]: 6780
% 1.88/1.54 % (27793)Time elapsed: 0.138 s
% 1.88/1.54 % (27793)Instructions burned: 275 (million)
% 1.88/1.54 % (27793)------------------------------
% 1.88/1.54 % (27793)------------------------------
% 1.88/1.56 % (27817)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_27688 for (2998ds/879Mi)
% 1.88/1.56 % (27818)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_27688 for (2998ds/17Mi)
% 1.88/1.57 % (27818)Instruction limit reached!
% 1.88/1.57 % (27818)------------------------------
% 1.88/1.57 % (27818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.57 % (27818)Termination reason: Unknown
% 1.88/1.57 % (27818)Termination phase: Saturation
% 1.88/1.57
% 1.88/1.57 % (27818)Memory used [KB]: 5628
% 1.88/1.57 % (27818)Time elapsed: 0.009 s
% 1.88/1.57 % (27818)Instructions burned: 17 (million)
% 1.88/1.57 % (27818)------------------------------
% 1.88/1.57 % (27818)------------------------------
% 1.88/1.58 % (27819)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_27688 for (2998ds/3Mi)
% 1.88/1.59 % (27819)Instruction limit reached!
% 1.88/1.59 % (27819)------------------------------
% 1.88/1.59 % (27819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.59 % (27819)Termination reason: Unknown
% 1.88/1.59 % (27819)Termination phase: shuffling
% 1.88/1.59
% 1.88/1.59 % (27819)Memory used [KB]: 1023
% 1.88/1.59 % (27819)Time elapsed: 0.003 s
% 1.88/1.59 % (27819)Instructions burned: 3 (million)
% 1.88/1.59 % (27819)------------------------------
% 1.88/1.59 % (27819)------------------------------
% 1.88/1.60 % (27820)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_27688 for (2998ds/30Mi)
% 1.88/1.62 % (27820)Instruction limit reached!
% 1.88/1.62 % (27820)------------------------------
% 1.88/1.62 % (27820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.62 % (27820)Termination reason: Unknown
% 1.88/1.62 % (27820)Termination phase: Saturation
% 1.88/1.62
% 1.88/1.62 % (27820)Memory used [KB]: 5628
% 1.88/1.62 % (27820)Time elapsed: 0.016 s
% 1.88/1.62 % (27820)Instructions burned: 30 (million)
% 1.88/1.62 % (27820)------------------------------
% 1.88/1.62 % (27820)------------------------------
% 1.88/1.63 % (27821)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_27688 for (2997ds/127Mi)
% 1.88/1.70 % (27821)Instruction limit reached!
% 1.88/1.70 % (27821)------------------------------
% 1.88/1.70 % (27821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.70 % (27821)Termination reason: Unknown
% 1.88/1.70 % (27821)Termination phase: Saturation
% 1.88/1.70
% 1.88/1.70 % (27821)Memory used [KB]: 6268
% 1.88/1.70 % (27821)Time elapsed: 0.066 s
% 1.88/1.70 % (27821)Instructions burned: 128 (million)
% 1.88/1.70 % (27821)------------------------------
% 1.88/1.70 % (27821)------------------------------
% 1.88/1.71 % (27814)Instruction limit reached!
% 1.88/1.71 % (27814)------------------------------
% 1.88/1.71 % (27814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.71 % (27814)Termination reason: Unknown
% 1.88/1.71 % (27814)Termination phase: Saturation
% 1.88/1.71
% 1.88/1.71 % (27814)Memory used [KB]: 6396
% 1.88/1.71 % (27814)Time elapsed: 0.184 s
% 1.88/1.71 % (27814)Instructions burned: 378 (million)
% 1.88/1.71 % (27814)------------------------------
% 1.88/1.71 % (27814)------------------------------
% 1.88/1.71 % (27822)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_27688 for (2997ds/100Mi)
% 1.88/1.72 % (27823)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_27688 for (2997ds/3Mi)
% 1.88/1.72 % (27823)Instruction limit reached!
% 1.88/1.72 % (27823)------------------------------
% 1.88/1.72 % (27823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.72 % (27823)Termination reason: Unknown
% 1.88/1.72 % (27823)Termination phase: shuffling
% 1.88/1.72
% 1.88/1.72 % (27823)Memory used [KB]: 1023
% 1.88/1.72 % (27823)Time elapsed: 0.003 s
% 1.88/1.72 % (27823)Instructions burned: 3 (million)
% 1.88/1.72 % (27823)------------------------------
% 1.88/1.72 % (27823)------------------------------
% 1.88/1.74 % (27824)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_27688 for (2996ds/20Mi)
% 1.88/1.75 % (27824)Instruction limit reached!
% 1.88/1.75 % (27824)------------------------------
% 1.88/1.75 % (27824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.75 % (27824)Termination reason: Unknown
% 1.88/1.75 % (27824)Termination phase: Property scanning
% 1.88/1.75
% 1.88/1.75 % (27824)Memory used [KB]: 1279
% 1.88/1.75 % (27824)Time elapsed: 0.011 s
% 1.88/1.75 % (27824)Instructions burned: 20 (million)
% 1.88/1.75 % (27824)------------------------------
% 1.88/1.75 % (27824)------------------------------
% 1.88/1.76 % (27822)Instruction limit reached!
% 1.88/1.76 % (27822)------------------------------
% 1.88/1.76 % (27822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.76 % (27822)Termination reason: Unknown
% 1.88/1.76 % (27822)Termination phase: Saturation
% 1.88/1.76
% 1.88/1.76 % (27822)Memory used [KB]: 6012
% 1.88/1.76 % (27822)Time elapsed: 0.051 s
% 1.88/1.76 % (27822)Instructions burned: 100 (million)
% 1.88/1.76 % (27822)------------------------------
% 1.88/1.76 % (27822)------------------------------
% 1.88/1.76 % (27825)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_27688 for (2996ds/86Mi)
% 1.88/1.78 % (27826)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_27688 for (2996ds/107Mi)
% 1.88/1.81 % (27825)Instruction limit reached!
% 1.88/1.81 % (27825)------------------------------
% 1.88/1.81 % (27825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.81 % (27825)Termination reason: Unknown
% 1.88/1.81 % (27825)Termination phase: Saturation
% 1.88/1.81
% 1.88/1.81 % (27825)Memory used [KB]: 6268
% 1.88/1.81 % (27825)Time elapsed: 0.065 s
% 1.88/1.81 % (27825)Instructions burned: 86 (million)
% 1.88/1.81 % (27825)------------------------------
% 1.88/1.81 % (27825)------------------------------
% 1.88/1.82 % (27827)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_27688 for (2995ds/39Mi)
% 1.88/1.83 % (27826)Instruction limit reached!
% 1.88/1.83 % (27826)------------------------------
% 1.88/1.83 % (27826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.83 % (27826)Termination reason: Unknown
% 1.88/1.83 % (27826)Termination phase: Saturation
% 1.88/1.83
% 1.88/1.83 % (27826)Memory used [KB]: 6140
% 1.88/1.83 % (27826)Time elapsed: 0.076 s
% 1.88/1.83 % (27826)Instructions burned: 107 (million)
% 1.88/1.83 % (27826)------------------------------
% 1.88/1.83 % (27826)------------------------------
% 1.88/1.84 % (27808)Instruction limit reached!
% 1.88/1.84 % (27808)------------------------------
% 1.88/1.84 % (27808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.84 % (27808)Termination reason: Unknown
% 1.88/1.84 % (27808)Termination phase: Saturation
% 1.88/1.84
% 1.88/1.84 % (27808)Memory used [KB]: 7931
% 1.88/1.84 % (27808)Time elapsed: 0.359 s
% 1.88/1.84 % (27808)Instructions burned: 710 (million)
% 1.88/1.84 % (27808)------------------------------
% 1.88/1.84 % (27808)------------------------------
% 1.88/1.84 % (27827)Instruction limit reached!
% 1.88/1.84 % (27827)------------------------------
% 1.88/1.84 % (27827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.84 % (27827)Termination reason: Unknown
% 1.88/1.84 % (27827)Termination phase: Saturation
% 1.88/1.84
% 1.88/1.84 % (27827)Memory used [KB]: 5884
% 1.88/1.84 % (27827)Time elapsed: 0.019 s
% 1.88/1.84 % (27827)Instructions burned: 40 (million)
% 1.88/1.84 % (27827)------------------------------
% 1.88/1.84 % (27827)------------------------------
% 1.88/1.85 % (27828)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_27688 for (2995ds/448Mi)
% 1.88/1.85 % (27817)First to succeed.
% 1.88/1.85 % (27817)Refutation found. Thanks to Tanya!
% 1.88/1.85 % SZS status Theorem for DTF2THF_27688
% 1.88/1.85 % SZS output start Proof for DTF2THF_27688
% 1.88/1.85 thf(func_def_0, type, in: $i > $i > $o).
% 1.88/1.85 thf(func_def_1, type, exu: ($i > $o) > $o).
% 1.88/1.85 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 1.88/1.85 thf(func_def_8, type, powerset: $i > $i).
% 1.88/1.85 thf(func_def_10, type, setunion: $i > $i).
% 1.88/1.85 thf(func_def_19, type, descr: ($i > $o) > $i).
% 1.88/1.85 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 1.88/1.85 thf(func_def_26, type, prop2set: $o > $i).
% 1.88/1.85 thf(func_def_51, type, sK3: ($i > $o) > $i > $i).
% 1.88/1.85 thf(func_def_53, type, sK4: ($i > $i > $o) > $i > $i).
% 1.88/1.85 thf(func_def_54, type, sK5: ($i > $i > $o) > $i > $i).
% 1.88/1.85 thf(func_def_55, type, sK6: ($i > $i > $o) > $i > $i > $i).
% 1.88/1.85 thf(func_def_56, type, sK7: $i > ($i > $i > $o) > $i > $i).
% 1.88/1.85 thf(func_def_57, type, sK8: $i > ($i > $i > $o) > $i > $i).
% 1.88/1.85 thf(func_def_58, type, sK9: $i > ($i > $i > $o) > $i > $i).
% 1.88/1.85 thf(func_def_59, type, sK10: $i > $i > $i).
% 1.88/1.85 thf(func_def_60, type, sK11: $i > $i).
% 1.88/1.85 thf(func_def_61, type, sK12: $i > $i > $i > $i).
% 1.88/1.85 thf(func_def_62, type, sK13: $i > $i > $i).
% 1.88/1.85 thf(func_def_63, type, sK14: $i > $i > $i).
% 1.88/1.85 thf(func_def_64, type, sK15: $i > $i > $i).
% 1.88/1.85 thf(func_def_65, type, sK16: $i > $i > $i).
% 1.88/1.85 thf(func_def_66, type, sK17: $i > $i).
% 1.88/1.85 thf(func_def_67, type, sK18: $i > $i).
% 1.88/1.85 thf(func_def_68, type, sK19: ($i > $o) > $i > $i).
% 1.88/1.85 thf(func_def_69, type, sK20: ($i > $o) > $i).
% 1.88/1.85 thf(func_def_70, type, sK21: ($i > $o) > $i).
% 1.88/1.85 thf(func_def_71, type, sK22: $i > $i > $i).
% 1.88/1.85 thf(func_def_72, type, ph23: !>[X0: $tType]:(X0)).
% 1.88/1.85 thf(f3080,plain,(
% 1.88/1.85 $false),
% 1.88/1.85 inference(trivial_inequality_removal,[status(thm)],[f3079])).
% 1.88/1.85 thf(f3079,plain,(
% 1.88/1.85 ($true = $false)),
% 1.88/1.85 inference(forward_demodulation,[status(thm)],[f3074,f3078])).
% 1.88/1.85 thf(f3078,plain,(
% 1.88/1.85 ((in @ (sK10 @ sK0 @ sK1) @ sK1) = $false)),
% 1.88/1.85 inference(subsumption_resolution,[status(thm)],[f3077,f121])).
% 1.88/1.85 thf(f121,plain,(
% 1.88/1.85 (sK1 != sK0)),
% 1.88/1.85 inference(cnf_transformation,[status(thm)],[f76])).
% 1.88/1.85 thf(f76,plain,(
% 1.88/1.85 ((sK1 != sK0) & ! [X2 : $i] : (($true = (in @ X2 @ sK1)) | ($true != (in @ X2 @ sK0))) & ! [X3 : $i] : (($true != (in @ X3 @ sK1)) | ($true = (in @ X3 @ sK0)))) & (foundationAx = $true) & (dsetconstrER = $true) & (omegaSAx = $true) & (descrp = $true) & (setunionAx = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (prop2setE = $true) & (dsetconstrEL = $true) & (emptysetE = $true) & (exuE1 = $true) & (dsetconstrI = $true) & (replAx = $true) & (wellorderingAx = $true) & (omega0Ax = $true) & (omegaIndAx = $true) & (emptysetimpfalse = $true) & (notinemptyset = $true) & (exuE3e = $true) & (emptysetAx = $true) & (setextAx = $true)),
% 1.88/1.85 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f74,f75])).
% 1.88/1.85 thf(f75,plain,(
% 1.88/1.85 ? [X0 : $i,X1 : $i] : ((X0 != X1) & ! [X2 : $i] : (($true = (in @ X2 @ X1)) | ($true != (in @ X2 @ X0))) & ! [X3 : $i] : (($true != (in @ X3 @ X1)) | ($true = (in @ X3 @ X0)))) => ((sK1 != sK0) & ! [X2 : $i] : (($true = (in @ X2 @ sK1)) | ($true != (in @ X2 @ sK0))) & ! [X3 : $i] : (($true != (in @ X3 @ sK1)) | ($true = (in @ X3 @ sK0))))),
% 1.88/1.85 introduced(definition,[],[choice_axiom])).
% 1.88/1.85 thf(f74,plain,(
% 1.88/1.85 ? [X0 : $i,X1 : $i] : ((X0 != X1) & ! [X2 : $i] : (($true = (in @ X2 @ X1)) | ($true != (in @ X2 @ X0))) & ! [X3 : $i] : (($true != (in @ X3 @ X1)) | ($true = (in @ X3 @ X0)))) & (foundationAx = $true) & (dsetconstrER = $true) & (omegaSAx = $true) & (descrp = $true) & (setunionAx = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (prop2setE = $true) & (dsetconstrEL = $true) & (emptysetE = $true) & (exuE1 = $true) & (dsetconstrI = $true) & (replAx = $true) & (wellorderingAx = $true) & (omega0Ax = $true) & (omegaIndAx = $true) & (emptysetimpfalse = $true) & (notinemptyset = $true) & (exuE3e = $true) & (emptysetAx = $true) & (setextAx = $true)),
% 1.88/1.85 inference(rectify,[status(thm)],[f73])).
% 1.88/1.85 thf(f73,plain,(
% 1.88/1.85 ? [X0 : $i,X1 : $i] : ((X0 != X1) & ! [X3 : $i] : (($true = (in @ X3 @ X1)) | ($true != (in @ X3 @ X0))) & ! [X2 : $i] : (($true != (in @ X2 @ X1)) | ($true = (in @ X2 @ X0)))) & (foundationAx = $true) & (dsetconstrER = $true) & (omegaSAx = $true) & (descrp = $true) & (setunionAx = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (prop2setE = $true) & (dsetconstrEL = $true) & (emptysetE = $true) & (exuE1 = $true) & (dsetconstrI = $true) & (replAx = $true) & (wellorderingAx = $true) & (omega0Ax = $true) & (omegaIndAx = $true) & (emptysetimpfalse = $true) & (notinemptyset = $true) & (exuE3e = $true) & (emptysetAx = $true) & (setextAx = $true)),
% 1.88/1.85 inference(flattening,[status(thm)],[f72])).
% 1.88/1.85 thf(f72,plain,(
% 1.88/1.85 ((((((((((((((((((((? [X0 : $i,X1 : $i] : (((X0 != X1) & ! [X3 : $i] : (($true = (in @ X3 @ X1)) | ($true != (in @ X3 @ X0)))) & ! [X2 : $i] : (($true != (in @ X2 @ X1)) | ($true = (in @ X2 @ X0)))) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 1.88/1.85 inference(ennf_transformation,[status(thm)],[f34])).
% 1.88/1.85 thf(f34,plain,(
% 1.88/1.85 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true = (in @ X2 @ X1)) => ($true = (in @ X2 @ X0))) => (! [X3 : $i] : (($true = (in @ X3 @ X0)) => ($true = (in @ X3 @ X1))) => (X0 = X1))))))))))))))))))))))))),
% 1.88/1.85 inference(fool_elimination,[status(thm)],[f33])).
% 1.88/1.85 thf(f33,plain,(
% 1.88/1.85 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => (in @ X3 @ X1)) => (X0 = X1))))))))))))))))))))))))),
% 1.88/1.85 inference(rectify,[status(thm)],[f25])).
% 1.88/1.85 thf(f25,negated_conjecture,(
% 1.88/1.85 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => ! [X4 : $i,X3 : $i] : (! [X1 : $i] : ((in @ X1 @ X3) => (in @ X1 @ X4)) => (! [X1 : $i] : ((in @ X1 @ X4) => (in @ X1 @ X3)) => (X3 = X4))))))))))))))))))))))))),
% 1.88/1.85 inference(negated_conjecture,[status(cth)],[f24])).
% 1.88/1.85 thf(f24,conjecture,(
% 1.88/1.85 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => ! [X4 : $i,X3 : $i] : (! [X1 : $i] : ((in @ X1 @ X3) => (in @ X1 @ X4)) => (! [X1 : $i] : ((in @ X1 @ X4) => (in @ X1 @ X3)) => (X3 = X4)))))))))))))))))))))))),
% 1.88/1.85 file('/export/starexec/sandbox2/tmp/tmp.TAQz0c6eb3/DTF2THF_27688.p',setext)).
% 1.88/1.85 thf(f3077,plain,(
% 1.88/1.85 (sK1 = sK0) | ((in @ (sK10 @ sK0 @ sK1) @ sK1) = $false)),
% 1.88/1.85 inference(trivial_inequality_removal,[status(thm)],[f3067])).
% 1.88/1.85 thf(f3067,plain,(
% 1.88/1.85 ((in @ (sK10 @ sK0 @ sK1) @ sK1) = $false) | ($true = $false) | (sK1 = sK0)),
% 1.88/1.85 inference(superposition,[status(thm)],[f238,f1760])).
% 1.88/1.85 thf(f1760,plain,(
% 1.88/1.85 ($true = (in @ (sK10 @ sK0 @ sK1) @ sK0))),
% 1.88/1.85 inference(subsumption_resolution,[status(thm)],[f1752,f121])).
% 1.88/1.85 thf(f1752,plain,(
% 1.88/1.85 ($true = (in @ (sK10 @ sK0 @ sK1) @ sK0)) | (sK1 = sK0)),
% 1.88/1.85 inference(trivial_inequality_removal,[status(thm)],[f1735])).
% 1.88/1.85 thf(f1735,plain,(
% 1.88/1.85 (sK1 = sK0) | ($true = (in @ (sK10 @ sK0 @ sK1) @ sK0)) | ($true != $true)),
% 1.88/1.85 inference(equality_factoring,[status(thm)],[f830])).
% 1.88/1.85 thf(f830,plain,(
% 1.88/1.85 ( ! [X0 : $i] : (($true = (in @ (sK10 @ X0 @ sK1) @ X0)) | ((in @ (sK10 @ X0 @ sK1) @ sK0) = $true) | (sK1 = X0)) )),
% 1.88/1.85 inference(trivial_inequality_removal,[status(thm)],[f825])).
% 1.88/1.85 thf(f825,plain,(
% 1.88/1.85 ( ! [X0 : $i] : (((in @ (sK10 @ X0 @ sK1) @ sK0) = $true) | ($true = (in @ (sK10 @ X0 @ sK1) @ X0)) | ($true != $true) | (sK1 = X0)) )),
% 1.88/1.85 inference(superposition,[status(thm)],[f119,f237])).
% 1.88/1.85 thf(f237,plain,(
% 1.88/1.85 ( ! [X2 : $i,X1 : $i] : (($true = (in @ (sK10 @ X1 @ X2) @ X2)) | (X1 = X2) | ($true = (in @ (sK10 @ X1 @ X2) @ X1))) )),
% 1.88/1.85 inference(binary_proxy_clausification,[status(thm)],[f236])).
% 1.88/1.85 thf(f236,plain,(
% 1.88/1.85 ( ! [X2 : $i,X1 : $i] : ((X1 = X2) | ((in @ (sK10 @ X1 @ X2) @ X2) != (in @ (sK10 @ X1 @ X2) @ X1))) )),
% 1.88/1.85 inference(binary_proxy_clausification,[status(thm)],[f235])).
% 1.88/1.85 thf(f235,plain,(
% 1.88/1.85 ( ! [X2 : $i,X1 : $i] : ((((in @ (sK10 @ X1 @ X2) @ X2) = (in @ (sK10 @ X1 @ X2) @ X1)) = $false) | (X1 = X2)) )),
% 1.88/1.85 inference(beta_eta_normalization,[status(thm)],[f234])).
% 1.88/1.85 thf(f234,plain,(
% 1.88/1.85 ( ! [X2 : $i,X1 : $i] : ((X1 = X2) | (((^[Y0 : $i]: ((in @ Y0 @ X2) = (in @ Y0 @ X1))) @ (sK10 @ X1 @ X2)) = $false)) )),
% 1.88/1.85 inference(sigma_clausification,[status(thm)],[f233])).
% 1.88/1.85 thf(f233,plain,(
% 1.88/1.85 ( ! [X2 : $i,X1 : $i] : ((X1 = X2) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) = (in @ Y0 @ X1)))) = $false)) )),
% 1.88/1.85 inference(equality_proxy_clausification,[status(thm)],[f232])).
% 1.88/1.85 thf(f232,plain,(
% 1.88/1.85 ( ! [X2 : $i,X1 : $i] : (($true = (X2 = X1)) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) = (in @ Y0 @ X1)))) = $false)) )),
% 1.88/1.85 inference(binary_proxy_clausification,[status(thm)],[f231])).
% 1.88/1.85 thf(f231,plain,(
% 1.88/1.85 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) = (in @ Y0 @ X1)))) => (X2 = X1)))) )),
% 1.88/1.85 inference(beta_eta_normalization,[status(thm)],[f230])).
% 1.88/1.85 thf(f230,plain,(
% 1.88/1.85 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) = (in @ Y1 @ X1)))) => (Y0 = X1))) @ X2))) )),
% 1.88/1.85 inference(pi_clausification,[status(thm)],[f229])).
% 1.88/1.85 thf(f229,plain,(
% 1.88/1.85 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) = (in @ Y1 @ X1)))) => (Y0 = X1)))))) )),
% 1.88/1.85 inference(beta_eta_normalization,[status(thm)],[f228])).
% 1.88/1.85 thf(f228,plain,(
% 1.88/1.85 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0))))) @ X1))) )),
% 1.88/1.85 inference(pi_clausification,[status(thm)],[f147])).
% 1.88/1.85 thf(f147,plain,(
% 1.88/1.85 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))))),
% 1.88/1.85 inference(definition_unfolding,[status(thm)],[f98,f77])).
% 1.88/1.85 thf(f77,plain,(
% 1.88/1.85 (setextAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))))),
% 1.88/1.85 inference(cnf_transformation,[status(thm)],[f38])).
% 1.88/1.85 thf(f38,plain,(
% 1.88/1.85 (setextAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))))),
% 1.88/1.85 inference(fool_elimination,[status(thm)],[f37])).
% 1.88/1.85 thf(f37,plain,(
% 1.88/1.85 (setextAx = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) <=> (in @ X2 @ X1)) => (X0 = X1)))),
% 1.88/1.85 inference(rectify,[status(thm)],[f2])).
% 1.88/1.85 thf(f2,axiom,(
% 1.88/1.85 (setextAx = ! [X3 : $i,X4 : $i] : (! [X1 : $i] : ((in @ X1 @ X3) <=> (in @ X1 @ X4)) => (X3 = X4)))),
% 1.88/1.85 file('/export/starexec/sandbox2/tmp/tmp.TAQz0c6eb3/DTF2THF_27688.p',setextAx)).
% 1.88/1.85 thf(f98,plain,(
% 1.88/1.85 (setextAx = $true)),
% 1.88/1.85 inference(cnf_transformation,[status(thm)],[f76])).
% 1.88/1.85 thf(f119,plain,(
% 1.88/1.85 ( ! [X3 : $i] : (($true != (in @ X3 @ sK1)) | ($true = (in @ X3 @ sK0))) )),
% 1.88/1.85 inference(cnf_transformation,[status(thm)],[f76])).
% 1.88/1.85 thf(f238,plain,(
% 1.88/1.85 ( ! [X2 : $i,X1 : $i] : (($false = (in @ (sK10 @ X1 @ X2) @ X1)) | (X1 = X2) | ((in @ (sK10 @ X1 @ X2) @ X2) = $false)) )),
% 1.88/1.85 inference(binary_proxy_clausification,[status(thm)],[f236])).
% 1.88/1.85 thf(f3074,plain,(
% 1.88/1.85 ($true = (in @ (sK10 @ sK0 @ sK1) @ sK1))),
% 1.88/1.85 inference(trivial_inequality_removal,[status(thm)],[f3068])).
% 1.88/1.85 thf(f3068,plain,(
% 1.88/1.85 ($true = (in @ (sK10 @ sK0 @ sK1) @ sK1)) | ($true != $true)),
% 1.88/1.85 inference(superposition,[status(thm)],[f120,f1760])).
% 1.88/1.85 thf(f120,plain,(
% 1.88/1.85 ( ! [X2 : $i] : (($true != (in @ X2 @ sK0)) | ($true = (in @ X2 @ sK1))) )),
% 1.88/1.85 inference(cnf_transformation,[status(thm)],[f76])).
% 1.88/1.85 % SZS output end Proof for DTF2THF_27688
% 1.88/1.85 % (27817)------------------------------
% 1.88/1.85 % (27817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.85 % (27817)Termination reason: Refutation
% 1.88/1.85
% 1.88/1.85 % (27817)Memory used [KB]: 7164
% 1.88/1.85 % (27817)Time elapsed: 0.295 s
% 1.88/1.85 % (27817)Instructions burned: 585 (million)
% 1.88/1.85 % (27817)------------------------------
% 1.88/1.85 % (27817)------------------------------
% 1.88/1.85 % (27787)Success in time 0.464 s
%------------------------------------------------------------------------------