%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU507^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 2
% Syntax : Number of formulae : 26 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 543 ( 160 equ; 0 cnn)
% Maximal formula atoms : 25 ( 20 avg)
% Number of connectives : 310 ( 29 ~; 6 |; 72 &; 67 @)
% ( 0 <=>; 127 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 76 ( 72 usr; 28 con; 0-4 aty)
% ( 9 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 39 ( 12 ^; 25 !; 2 ?; 39 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_35,type,
vAND: $o > $o > $o ).
thf(func_def_36,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_39,type,
vIMP: $o > $o > $o ).
thf(func_def_40,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_42,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_43,type,
vIFF: $o > $o > $o ).
thf(func_def_44,type,
vNOT: $o > $o ).
thf(func_def_45,type,
vOR: $o > $o > $o ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
sK1: $i > $i ).
thf(func_def_52,type,
sK2: $i > $i > $i ).
thf(func_def_53,type,
sK3: $i > $i > $i ).
thf(func_def_54,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_55,type,
sK5: ( $i > $o ) > $i > $i ).
thf(func_def_56,type,
sK6: ( $i > $o ) > $i ).
thf(func_def_57,type,
sK7: ( $i > $o ) > $i > $i ).
thf(func_def_58,type,
sK8: ( $i > $o ) > $i > $i ).
thf(func_def_59,type,
sK9: $i > $i ).
thf(func_def_60,type,
sK10: $i > $i > $i > $i ).
thf(func_def_61,type,
sK11: $i > $i > $i ).
thf(func_def_62,type,
sK12: $i > $i > $i ).
thf(func_def_63,type,
sK13: $i > $i > $i ).
thf(func_def_64,type,
sK14: $i > $i ).
thf(func_def_65,type,
sK15: $i > ( $i > $i > $o ) > $i ).
thf(func_def_66,type,
sK16: $i > ( $i > $i > $o ) > $i ).
thf(func_def_67,type,
sK17: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_68,type,
sK18: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_69,type,
sK19: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_70,type,
sK20: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_71,type,
sK21: $i > $i ).
thf(func_def_72,type,
sK22: $i > $i > $i ).
thf(func_def_73,type,
sK23: $i > $i > $i ).
thf(func_def_74,type,
sK24: $i > $i > $i ).
thf(f25,axiom,
( emptyI
= ( ! [X0: $i] :
( ! [X1: $i] :
~ ( in @ X1 @ X0 )
=> ( X0 = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(f26,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ! [X0: $i] :
( ! [X1: $i] :
~ ( in @ X1 @ X0 )
=> ( X0 = emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(f27,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
=> ! [X0: $i] :
( ! [X1: $i] :
~ ( in @ X1 @ X0 )
=> ( X0 = emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
thf(f74,plain,
( emptyI
= ( ! [X0: $i] :
( ! [X1: $i] :
~ ( in @ X1 @ X0 )
=> ( X0 = emptyset ) ) ) ),
inference(rectify,[],[f25]) ).
thf(f75,plain,
( emptyI
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
~ ( in @ Y1 @ Y0 ) )
=> ( emptyset = Y0 ) ) ) ),
inference(fool_elimination,[],[f74]) ).
thf(f76,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ! [X0: $i] :
( ! [X1: $i] :
~ ( in @ X1 @ X0 )
=> ( X0 = emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f77,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 )
=> ! [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true )
=> ( emptyset = X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f76]) ).
thf(f78,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 )
=> ! [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true )
=> ( emptyset = X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f77]) ).
thf(f79,plain,
( ? [X0: $i] :
( ( emptyset != X0 )
& ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $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,[],[f78]) ).
thf(f80,plain,
( ? [X0: $i] :
( ( emptyset != X0 )
& ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $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,[],[f79]) ).
thf(f81,plain,
( ( emptyset != sK0 )
& ! [X1: $i] :
( $true
!= ( in @ X1 @ sK0 ) )
& ( 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]),skolemize(X0,sK0)],[f80]) ).
thf(f106,plain,
( emptyI
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
~ ( in @ Y1 @ Y0 ) )
=> ( emptyset = Y0 ) ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f129,plain,
emptyI = $true,
inference(cnf_transformation,[],[f81]) ).
thf(f130,plain,
! [X1: $i] :
( $true
!= ( in @ X1 @ sK0 ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f131,plain,
emptyset != sK0,
inference(cnf_transformation,[],[f81]) ).
thf(f156,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
~ ( in @ Y1 @ Y0 ) )
=> ( emptyset = Y0 ) ) )
= $true ),
inference(definition_unfolding,[],[f106,f129]) ).
thf(f157,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
~ ( in @ Y1 @ Y0 ) )
=> ( emptyset = Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( in @ Y0 @ X1 ) )
=> ( emptyset = X1 ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( in @ Y0 @ X1 ) ) )
| ( $true
= ( emptyset = X1 ) ) ),
inference(imp_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
~ ( in @ Y0 @ X1 )
@ ( sK1 @ X1 ) ) )
| ( $true
= ( emptyset = X1 ) ) ),
inference(sigma_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
~ ( in @ Y0 @ X1 )
@ ( sK1 @ X1 ) ) )
| ( emptyset = X1 ) ),
inference(equality_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X1: $i] :
( ( $false
= ( ~ ( in @ ( sK1 @ X1 ) @ X1 ) ) )
| ( emptyset = X1 ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( ( $true
= ( in @ ( sK1 @ X1 ) @ X1 ) )
| ( emptyset = X1 ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f491,plain,
( ( $true != $true )
| ( emptyset = sK0 ) ),
inference(constrained_superposition,[],[f130,f163]) ).
thf(f492,plain,
emptyset = sK0,
inference(trivial_inequality_removal,[],[f491]) ).
thf(f493,plain,
$false,
inference(forward_subsumption_resolution,[],[f492,f131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU507^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n015.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:50:33 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.28 % (3549911)Will run a generic schedule for satisfiability detection.
% 0.21/0.28 % (3549923)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=999363097:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.28 % (3549919)% WARNING: option uhcvi not known.
% 0.21/0.28 % (3549923) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3549911-3549923"...
% 0.21/0.28 % (3549918)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=348625419_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.28 % (3549919)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2870752084:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.28 % (3549920)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3338557877:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.28 % (3549921)dis+10_1_sil=32000:sp=arity:random_seed=1690320670:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.28 % (3549922)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1827848830:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.28 % (3549925)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2389027745:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.28 % (3549923)...printing done.
% 0.21/0.28 % (3549923)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (3549923)------------------------------
% 0.21/0.28 % (3549923)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (3549923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (3549923)CaDiCaL version: 2.1.3
% 0.21/0.28 % (3549923)Termination reason: Refutation
% 0.21/0.28 % (3549923)Time elapsed: 0.008 s
% 0.21/0.28 % (3549923)Peak memory usage: 12 MB
% 0.21/0.28 % (3549923)Instructions burned: 29 (million)
% 0.21/0.28 % (3549911)Success in time 0.033 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------