%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU508^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:32:14 AM UTC 2026
% Result : Theorem 0.23s 0.30s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 7
% Syntax : Number of formulae : 80 ( 32 unt; 0 typ; 4 def)
% Number of atoms : 740 ( 168 equ; 0 cnn)
% Maximal formula atoms : 26 ( 9 avg)
% Number of connectives : 700 ( 54 ~; 53 |; 75 &; 347 @)
% ( 7 <=>; 134 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% Number of symbols : 83 ( 79 usr; 33 con; 0-4 aty)
% ( 30 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 121 ( 0 sgn 57 !; 6 ?; 121 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_36,type,
vAND: $o > $o > $o ).
thf(func_def_37,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_40,type,
vIMP: $o > $o > $o ).
thf(func_def_41,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_43,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_44,type,
vIFF: $o > $o > $o ).
thf(func_def_45,type,
vNOT: $o > $o ).
thf(func_def_46,type,
vOR: $o > $o > $o ).
thf(func_def_47,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
sK1: $i > $o ).
thf(func_def_54,type,
sK3: $i > $i ).
thf(func_def_55,type,
sK4: $i > $i ).
thf(func_def_56,type,
sK5: $i > $i > $i ).
thf(func_def_57,type,
sK6: $i > $i > $i ).
thf(func_def_58,type,
sK7: ( $i > $o ) > $i ).
thf(func_def_59,type,
sK8: ( $i > $o ) > $i > $i ).
thf(func_def_60,type,
sK9: ( $i > $o ) > $i ).
thf(func_def_61,type,
sK10: ( $i > $o ) > $i > $i ).
thf(func_def_62,type,
sK11: ( $i > $o ) > $i > $i ).
thf(func_def_63,type,
sK12: $i > $i ).
thf(func_def_64,type,
sK13: $i > $i > $i > $i ).
thf(func_def_65,type,
sK14: $i > $i > $i ).
thf(func_def_66,type,
sK15: $i > $i > $i ).
thf(func_def_67,type,
sK16: $i > $i > $i ).
thf(func_def_68,type,
sK17: $i > $i ).
thf(func_def_69,type,
sK18: $i > ( $i > $i > $o ) > $i ).
thf(func_def_70,type,
sK19: $i > ( $i > $i > $o ) > $i ).
thf(func_def_71,type,
sK20: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_72,type,
sK21: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_73,type,
sK22: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_74,type,
sK23: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_75,type,
sK24: $i > $i ).
thf(func_def_76,type,
sK25: $i > $i > $i ).
thf(func_def_77,type,
sK26: $i > $i > $i ).
thf(func_def_78,type,
sK27: $i > $i > $i ).
thf(f14,axiom,
( dsetconstrI
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(f16,axiom,
( dsetconstrER
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(f27,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setbeta) ).
thf(f28,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
thf(f53,plain,
( dsetconstrI
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f54,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f57,plain,
( dsetconstrER
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f58,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f79,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f28]) ).
thf(f80,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 )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( X1 @ X2 )
= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f79]) ).
thf(f81,plain,
( ? [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X2 )
!= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
& ( ( in @ X2 @ X0 )
= $true ) )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( 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,[],[f80]) ).
thf(f82,plain,
( ? [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X2 )
!= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
& ( ( in @ X2 @ X0 )
= $true ) )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( 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(flattening,[],[f81]) ).
thf(f83,plain,
( ( ( sK1 @ sK2 )
!= ( in @ sK2
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ) )
& ( $true
= ( in @ sK2 @ sK0 ) )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( 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(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f82]) ).
thf(f97,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f99,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f122,plain,
dsetconstrI = $true,
inference(cnf_transformation,[],[f83]) ).
thf(f124,plain,
dsetconstrER = $true,
inference(cnf_transformation,[],[f83]) ).
thf(f134,plain,
( $true
= ( in @ sK2 @ sK0 ) ),
inference(cnf_transformation,[],[f83]) ).
thf(f135,plain,
( ( sK1 @ sK2 )
!= ( in @ sK2
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f83]) ).
thf(f150,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f97,f122]) ).
thf(f152,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f99,f124]) ).
thf(f162,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( in @ sK2
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ) ) ),
inference(xor_proxy_clausification,[],[f135]) ).
thf(f163,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( in @ sK2
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ) ) ),
inference(xor_proxy_clausification,[],[f135]) ).
thf(f164,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( in @ sK2 @ ( dsetconstr @ sK0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( in @ sK2 @ ( dsetconstr @ sK0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f248,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f152]) ).
thf(f249,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f248]) ).
thf(f250,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f249]) ).
thf(f251,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f250]) ).
thf(f252,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f251]) ).
thf(f253,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
=> ( X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f252]) ).
thf(f254,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) )
| ( $true
= ( X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f253]) ).
thf(f262,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f150]) ).
thf(f263,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( Y0 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f262]) ).
thf(f264,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( Y0 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f263]) ).
thf(f265,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( X2 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f264]) ).
thf(f266,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( X2 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f265]) ).
thf(f267,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ X3 )
=> ( ( X2 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f266]) ).
thf(f268,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( ( X2 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f267]) ).
thf(f269,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) )
| ( $false
= ( X2 @ X1 ) )
| ( $false
= ( in @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f268]) ).
thf(f508,definition,
( spl28_1
<=> ( $false
= ( in @ sK2 @ ( dsetconstr @ sK0 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl28_1])],[avatar_definition]) ).
thf(f510,plain,
( ( $false
= ( in @ sK2 @ ( dsetconstr @ sK0 @ sK1 ) ) )
| ~ spl28_1 ),
inference(avatar_component_clause,[],[f508]) ).
thf(f512,definition,
( spl28_2
<=> ( $false
= ( sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl28_2])],[avatar_definition]) ).
thf(f514,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ~ spl28_2 ),
inference(avatar_component_clause,[],[f512]) ).
thf(f515,plain,
( spl28_1
| spl28_2 ),
inference(avatar_split_clause,[],[f164,f512,f508]) ).
thf(f517,definition,
( spl28_3
<=> ( $true
= ( in @ sK2 @ ( dsetconstr @ sK0 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl28_3])],[avatar_definition]) ).
thf(f519,plain,
( ( $true
= ( in @ sK2 @ ( dsetconstr @ sK0 @ sK1 ) ) )
| ~ spl28_3 ),
inference(avatar_component_clause,[],[f517]) ).
thf(f521,definition,
( spl28_4
<=> ( $true
= ( sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl28_4])],[avatar_definition]) ).
thf(f523,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ~ spl28_4 ),
inference(avatar_component_clause,[],[f521]) ).
thf(f524,plain,
( spl28_3
| spl28_4 ),
inference(avatar_split_clause,[],[f165,f521,f517]) ).
thf(f535,plain,
( ( $false = $true )
| ( $true
= ( sK1 @ sK2 ) )
| ~ spl28_3 ),
inference(constrained_superposition,[],[f254,f519]) ).
thf(f546,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ~ spl28_3 ),
inference(trivial_inequality_removal,[],[f535]) ).
thf(f552,plain,
( ( $false = $true )
| ~ spl28_2
| ~ spl28_3 ),
inference(forward_demodulation,[],[f546,f514]) ).
thf(f553,plain,
( $false
| ~ spl28_2
| ~ spl28_3 ),
inference(trivial_inequality_removal,[],[f552]) ).
thf(f554,plain,
( ~ spl28_2
| ~ spl28_3 ),
inference(avatar_contradiction_clause,[],[f553]) ).
thf(f565,plain,
( ( $false = $true )
| ~ spl28_1
| ~ spl28_3 ),
inference(constrained_superposition,[],[f510,f519]) ).
thf(f569,plain,
( $false
| ~ spl28_1
| ~ spl28_3 ),
inference(trivial_inequality_removal,[],[f565]) ).
thf(f570,plain,
( ~ spl28_1
| ~ spl28_3 ),
inference(avatar_contradiction_clause,[],[f569]) ).
thf(f579,plain,
( ( $false = $true )
| ~ spl28_2
| ~ spl28_4 ),
inference(constrained_superposition,[],[f514,f523]) ).
thf(f583,plain,
( $false
| ~ spl28_2
| ~ spl28_4 ),
inference(trivial_inequality_removal,[],[f579]) ).
thf(f584,plain,
( ~ spl28_2
| ~ spl28_4 ),
inference(avatar_contradiction_clause,[],[f583]) ).
thf(f640,plain,
( ( $false = $true )
| ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( in @ sK2 @ sK0 ) )
| ~ spl28_1 ),
inference(constrained_superposition,[],[f269,f510]) ).
thf(f641,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( in @ sK2 @ sK0 ) )
| ~ spl28_1 ),
inference(trivial_inequality_removal,[],[f640]) ).
thf(f644,plain,
( ( $false = $true )
| ( $false
= ( in @ sK2 @ sK0 ) )
| ~ spl28_1
| ~ spl28_4 ),
inference(forward_demodulation,[],[f641,f523]) ).
thf(f645,plain,
( ( $false
= ( in @ sK2 @ sK0 ) )
| ~ spl28_1
| ~ spl28_4 ),
inference(trivial_inequality_removal,[],[f644]) ).
thf(f659,plain,
( ( $false = $true )
| ~ spl28_1
| ~ spl28_4 ),
inference(constrained_superposition,[],[f645,f134]) ).
thf(f665,plain,
( $false
| ~ spl28_1
| ~ spl28_4 ),
inference(trivial_inequality_removal,[],[f659]) ).
thf(f666,plain,
( ~ spl28_1
| ~ spl28_4 ),
inference(avatar_contradiction_clause,[],[f665]) ).
cnf(s1,plain,
( spl28_1
| spl28_2 ),
inference(sat_conversion,[],[f515]) ).
cnf(s2,plain,
( spl28_3
| spl28_4 ),
inference(sat_conversion,[],[f524]) ).
cnf(s8,plain,
( ~ spl28_2
| ~ spl28_3 ),
inference(sat_conversion,[],[f554]) ).
cnf(s12,plain,
( ~ spl28_1
| ~ spl28_3 ),
inference(sat_conversion,[],[f570]) ).
cnf(s14,plain,
( ~ spl28_2
| ~ spl28_4 ),
inference(sat_conversion,[],[f584]) ).
cnf(s19,plain,
( ~ spl28_1
| ~ spl28_4 ),
inference(sat_conversion,[],[f666]) ).
cnf(s20,plain,
~ spl28_2,
inference(rat,[],[s2,s8,s14]) ).
cnf(s21,plain,
spl28_1,
inference(rat,[],[s1,s20]) ).
cnf(s22,plain,
~ spl28_4,
inference(rat,[],[s19,s21]) ).
cnf(s23,plain,
~ spl28_3,
inference(rat,[],[s12,s21]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s2,s22,s23]) ).
thf(f667,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU508^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.22 % Computer : n010.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 13:47:34 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.25 Running first-order model finding
% 0.11/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.30 % (2878674)Will run a generic schedule for satisfiability detection.
% 0.23/0.30 % (2878682)dis+10_1_sil=32000:sp=arity:random_seed=443643337:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.23/0.30 % (2878680)% WARNING: option uhcvi not known.
% 0.23/0.30 % (2878680)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3469889230:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.23/0.30 % (2878679)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1948376820_2999 on theBenchmark for (2999ds/0Mi)
% 0.23/0.30 % (2878681)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2511637128:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.23/0.30 % (2878683)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2580442370:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.23/0.30 % (2878684)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1710377912:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.23/0.30 % (2878685)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=489641651:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.23/0.30 % (2878682) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2878674-2878682"...
% 0.23/0.30 % (2878680)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.23/0.30 % (2878683)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.23/0.30 % (2878682)...printing done.
% 0.23/0.30 % (2878682)Refutation found. Thanks to Tanya!
% 0.23/0.30 % SZS status Theorem for theBenchmark
% 0.23/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.30 % (2878682)------------------------------
% 0.23/0.30 % (2878682)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (2878682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (2878682)CaDiCaL version: 2.1.3
% 0.23/0.30 % (2878682)Termination reason: Refutation
% 0.23/0.30 % (2878682)Time elapsed: 0.011 s
% 0.23/0.30 % (2878682)Peak memory usage: 13 MB
% 0.23/0.30 % (2878682)Instructions burned: 38 (million)
% 0.23/0.30 % (2878674)Success in time 0.037 s
% 0.23/0.30 % Vampire exiting
%------------------------------------------------------------------------------