%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU511^1 : 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 : n016.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 0.10s 0.26s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 524 ( 142 equ; 0 cnn)
% Maximal formula atoms : 29 ( 18 avg)
% Number of connectives : 270 ( 21 ~; 0 |; 84 &; 50 @)
% ( 0 <=>; 112 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 84 ( 80 usr; 33 con; 0-4 aty)
% ( 3 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 25 ( 8 ^; 9 !; 8 ?; 25 :)
% 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,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_40,type,
vAND: $o > $o > $o ).
thf(func_def_41,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
vIMP: $o > $o > $o ).
thf(func_def_45,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_47,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_48,type,
vIFF: $o > $o > $o ).
thf(func_def_49,type,
vNOT: $o > $o ).
thf(func_def_50,type,
vOR: $o > $o > $o ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_57,type,
sK2: $i > $i ).
thf(func_def_58,type,
sK3: $i > $i ).
thf(func_def_59,type,
sK4: $i > $i ).
thf(func_def_60,type,
sK5: $i > $i > $i ).
thf(func_def_61,type,
sK6: $i > $i > $i ).
thf(func_def_62,type,
sK7: ( $i > $o ) > $i ).
thf(func_def_63,type,
sK8: ( $i > $o ) > $i > $i ).
thf(func_def_64,type,
sK9: ( $i > $o ) > $i ).
thf(func_def_65,type,
sK10: ( $i > $o ) > $i > $i ).
thf(func_def_66,type,
sK11: ( $i > $o ) > $i > $i ).
thf(func_def_67,type,
sK12: $i > $i ).
thf(func_def_68,type,
sK13: $i > $i > $i > $i ).
thf(func_def_69,type,
sK14: $i > $i > $i ).
thf(func_def_70,type,
sK15: $i > $i > $i ).
thf(func_def_71,type,
sK16: $i > $i > $i ).
thf(func_def_72,type,
sK17: $i > $i ).
thf(func_def_73,type,
sK18: $i > ( $i > $i > $o ) > $i ).
thf(func_def_74,type,
sK19: $i > ( $i > $i > $o ) > $i ).
thf(func_def_75,type,
sK20: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_76,type,
sK21: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_77,type,
sK22: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_78,type,
sK23: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_79,type,
sK24: $i > $i ).
thf(func_def_80,type,
sK25: $i > $i > $i ).
thf(func_def_81,type,
sK26: $i > $i > $i ).
thf(func_def_82,type,
sK27: $i > $i > $i ).
thf(f22,axiom,
( notinemptyset
= ( ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(f28,axiom,
( nonempty
= ( ^ [X0: $i] : ( X0 != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).
thf(f31,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
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ! [X0: $i] :
( ? [X1: $i] : ( in @ X1 @ X0 )
=> ( nonempty @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(f32,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
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ! [X0: $i] :
( ? [X1: $i] : ( in @ X1 @ X0 )
=> ( nonempty @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
thf(f73,plain,
( notinemptyset
= ( ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ) ),
inference(rectify,[],[f22]) ).
thf(f74,plain,
( notinemptyset
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( in @ Y0 @ emptyset ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f85,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f90,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
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ! [X0: $i] :
( ? [X1: $i] : ( in @ X1 @ X0 )
=> ( nonempty @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f91,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 )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ! [X0: $i] :
( ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true )
=> ( ( nonempty @ X0 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f90]) ).
thf(f92,plain,
( ? [X0: $i] :
( ( ( nonempty @ X0 )
!= $true )
& ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true ) )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $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,[],[f91]) ).
thf(f93,plain,
( ? [X0: $i] :
( ( ( nonempty @ X0 )
!= $true )
& ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true ) )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $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,[],[f92]) ).
thf(f94,plain,
( ( $true
!= ( nonempty @ sK0 ) )
& ( $true
= ( in @ sK1 @ sK0 ) )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $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(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f93]) ).
thf(f116,plain,
( notinemptyset
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( in @ Y0 @ emptyset ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f122,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(cnf_transformation,[],[f85]) ).
thf(f144,plain,
notinemptyset = $true,
inference(cnf_transformation,[],[f94]) ).
thf(f152,plain,
( $true
= ( in @ sK1 @ sK0 ) ),
inference(cnf_transformation,[],[f94]) ).
thf(f153,plain,
( $true
!= ( nonempty @ sK0 ) ),
inference(cnf_transformation,[],[f94]) ).
thf(f175,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
~ ( in @ Y0 @ emptyset ) )
= $true ),
inference(definition_unfolding,[],[f116,f144]) ).
thf(f183,plain,
( $true
!= ( ^ [Y0: $i] : ( emptyset != Y0 )
@ sK0 ) ),
inference(definition_unfolding,[],[f153,f122]) ).
thf(f184,plain,
( $true
!= ( emptyset != sK0 ) ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f185,plain,
( $true
= ( emptyset = sK0 ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f186,plain,
emptyset = sK0,
inference(equality_proxy_clausification,[],[f185]) ).
thf(f256,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
~ ( in @ Y0 @ emptyset )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f175]) ).
thf(f257,plain,
! [X1: $i] :
( $true
= ( ~ ( in @ X1 @ emptyset ) ) ),
inference(beta-eta_normalization,[],[f256]) ).
thf(f258,plain,
! [X1: $i] :
( $false
= ( in @ X1 @ emptyset ) ),
inference(not_proxy_clausification,[],[f257]) ).
thf(f555,plain,
( $true
= ( in @ sK1 @ emptyset ) ),
inference(constrained_superposition,[],[f152,f186]) ).
thf(f556,plain,
$false = $true,
inference(forward_demodulation,[],[f555,f258]) ).
thf(f557,plain,
$false,
inference(trivial_inequality_removal,[],[f556]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU511^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n016.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 13:52:20 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 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
% 0.10/0.26 % (379225)Will run a generic schedule for satisfiability detection.
% 0.10/0.26 % (379234)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2045429549:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.26 % (379234)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.26 % (379231)% WARNING: option uhcvi not known.
% 0.10/0.26 % (379230)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2426110550_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.26 % (379231)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=193977578:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.26 % (379232)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=301224418:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.26 % (379233)dis+10_1_sil=32000:sp=arity:random_seed=280895253:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.26 % (379236)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1981798537:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.26 % (379234) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-379225-379234"...
% 0.10/0.26 % (379235)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1867461295:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.26 % (379234)...printing done.
% 0.10/0.26 % (379234)Refutation found. Thanks to Tanya!
% 0.10/0.26 % SZS status Theorem for theBenchmark
% 0.10/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.26 % (379234)------------------------------
% 0.10/0.26 % (379234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.26 % (379234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.26 % (379234)CaDiCaL version: 2.1.3
% 0.10/0.26 % (379234)Termination reason: Refutation
% 0.10/0.26 % (379234)Time elapsed: 0.009 s
% 0.10/0.26 % (379234)Peak memory usage: 12 MB
% 0.10/0.26 % (379234)Instructions burned: 31 (million)
% 0.10/0.26 % (379225)Success in time 0.026 s
% 0.10/0.26 % Vampire exiting
%------------------------------------------------------------------------------