%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU503^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:29:50 AM UTC 2026
% Result : Theorem 0.24s 0.34s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 467 ( 126 equ; 0 cnn)
% Maximal formula atoms : 21 ( 21 avg)
% Number of connectives : 233 ( 21 ~; 7 |; 60 &; 44 @)
% ( 3 <=>; 98 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 88 ( 85 usr; 27 con; 0-4 aty)
% Number of variables : 19 ( 0 ^; 15 !; 4 ?; 19 :)
% 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_32,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vIMP: $o > $o > $o ).
thf(func_def_38,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_41,type,
sP0: $o ).
thf(func_def_42,type,
sP1: $i > $i > $o ).
thf(func_def_43,type,
sP2: $i > $o ).
thf(func_def_44,type,
sP3: $i > $i > $o ).
thf(func_def_45,type,
sP4: $i > $i > $o ).
thf(func_def_46,type,
sK5: $i > $i > $o ).
thf(func_def_48,type,
sK7: $i > $i ).
thf(func_def_49,type,
sK8: $i > $i ).
thf(func_def_50,type,
sK9: $i > ( $i > $i > $o ) > $i ).
thf(func_def_51,type,
sK10: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_52,type,
sK11: $i > ( $i > $i > $o ) > $i ).
thf(func_def_54,type,
sK13: $i > $o ).
thf(func_def_57,type,
sK16: $i > $i > $i ).
thf(func_def_62,type,
sK21: $i > $o ).
thf(func_def_64,type,
sK23: $o ).
thf(func_def_65,type,
sK24: $o ).
thf(func_def_67,type,
sK26: $i > $o ).
thf(func_def_73,type,
sK32: $i > $i > $i ).
thf(func_def_74,type,
sK33: $i > $i ).
thf(func_def_77,type,
sK36: $i > $i ).
thf(func_def_78,type,
sK37: $i > $o ).
thf(func_def_84,type,
sK43: $i > $i ).
thf(func_def_89,type,
sK48: ( $i > $o ) > $i ).
thf(func_def_90,type,
sK49: $i > $o ).
thf(func_def_91,type,
sK50: $i > $i ).
thf(func_def_92,type,
sK51: $i > $i > $i ).
thf(func_def_93,type,
sK52: $i > $i > $i ).
thf(func_def_94,type,
sK53: $i > $i > $i ).
thf(func_def_95,type,
sK54: $i > $i > $i ).
thf(func_def_96,type,
sK55: $i > $i > $i ).
thf(func_def_97,type,
sK56: $i > $i > $i > $i ).
thf(func_def_98,type,
sK57: $i > $i ).
thf(func_def_99,type,
sK58: $i > $i ).
thf(func_def_100,type,
sK59: $i > $i ).
thf(func_def_101,type,
sK60: $i > $i ).
thf(func_def_102,type,
sK61: $i > $i > $i ).
thf(func_def_103,type,
sK62: $i > $i > $i > $i ).
thf(func_def_104,type,
sK63: $i > $i > $i > $i ).
thf(func_def_105,type,
sK64: $i > $i > $i ).
thf(func_def_106,type,
sK65: $i > $i > $i ).
thf(func_def_108,type,
sK67: $i > $i ).
thf(func_def_109,type,
sK68: $i > $i ).
thf(func_def_110,type,
sK69: $i > $i ).
thf(func_def_113,type,
sK72: $i > $i > $i ).
thf(func_def_114,type,
vNOT: $o > $o ).
thf(f21,axiom,
( emptysetimpfalse
= ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(f22,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(f23,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
thf(f44,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f45,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 )
=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f54,plain,
( emptysetimpfalse
= ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> $false ) ) ),
inference(rectify,[],[f21]) ).
thf(f55,plain,
( ( emptysetimpfalse = $true )
<=> ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
=> $false ) ),
inference(fool_elimination,[],[f54]) ).
thf(f67,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 )
=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f45]) ).
thf(f68,plain,
( ( emptysetimpfalse = $true )
<=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ),
inference(true_and_false_elimination,[],[f55]) ).
thf(f69,plain,
( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
<=> ( emptysetimpfalse = $true ) ),
inference(flattening,[],[f68]) ).
thf(f87,plain,
( ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $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,[],[f67]) ).
thf(f88,plain,
( ( emptysetAx = $true )
& ( exuE1 = $true )
& ( setunionAx = $true )
& ( emptysetE = $true )
& ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true )
& ( powersetAx = $true )
& ( omegaSAx = $true )
& ( setextAx = $true )
& ( setadjoinAx = $true )
& ( replAx = $true )
& ( foundationAx = $true )
& ( prop2setE = $true )
& ( wellorderingAx = $true )
& ( descrp = $true )
& ( omega0Ax = $true )
& ( dsetconstrER = $true )
& ( omegaIndAx = $true )
& ( dsetconstrEL = $true )
& ( emptysetimpfalse = $true )
& ( dsetconstrI = $true ) ),
inference(flattening,[],[f87]) ).
thf(f105,plain,
( ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetimpfalse != $true ) )
& ( ( emptysetimpfalse = $true )
| ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true ) ) ),
inference(nnf_transformation,[],[f69]) ).
thf(f106,plain,
( ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetimpfalse != $true ) )
& ( ( emptysetimpfalse = $true )
| ? [X1: $i] :
( ( in @ X1 @ emptyset )
= $true ) ) ),
inference(rectify,[],[f105]) ).
thf(f107,plain,
( ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetimpfalse != $true ) )
& ( ( emptysetimpfalse = $true )
| ( ( in @ sK15 @ emptyset )
= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X1,sK15)],[f106]) ).
thf(f111,plain,
( ( emptysetAx = $true )
& ( exuE1 = $true )
& ( setunionAx = $true )
& ( emptysetE = $true )
& ( ( in @ sK20 @ emptyset )
= $true )
& ( powersetAx = $true )
& ( omegaSAx = $true )
& ( setextAx = $true )
& ( setadjoinAx = $true )
& ( replAx = $true )
& ( foundationAx = $true )
& ( prop2setE = $true )
& ( wellorderingAx = $true )
& ( descrp = $true )
& ( omega0Ax = $true )
& ( dsetconstrER = $true )
& ( omegaIndAx = $true )
& ( dsetconstrEL = $true )
& ( emptysetimpfalse = $true )
& ( dsetconstrI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X0,sK20)],[f88]) ).
thf(f183,plain,
! [X0: $i] :
( ( emptysetimpfalse != $true )
| ( ( in @ X0 @ emptyset )
!= $true ) ),
inference(cnf_transformation,[],[f107]) ).
thf(f191,plain,
emptysetimpfalse = $true,
inference(cnf_transformation,[],[f111]) ).
thf(f205,plain,
( ( in @ sK20 @ emptyset )
= $true ),
inference(cnf_transformation,[],[f111]) ).
thf(f353,plain,
! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ),
inference(forward_subsumption_resolution,[],[f183,f191]) ).
thf(f354,plain,
$true != $true,
inference(superposition,[],[f353,f205]) ).
thf(f355,plain,
$false,
inference(trivial_inequality_removal,[],[f354]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU503^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n020.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 13:47:35 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.27 Running higher-order theorem proving
% 0.24/0.29 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.34 % (1075155)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.34 % (1075164)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3305036278:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.24/0.34 % (1075160)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3589027629:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.34 % (1075166)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.34 % (1075166)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.24/0.34 % (1075164) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1075155-1075164"...
% 0.24/0.34 % (1075164)...printing done.
% 0.24/0.34 % (1075162)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2699801637:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.34 % (1075161)lrs+10_16_si=on:nwc=1.5:random_seed=1441945047:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.34 % (1075163)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1005988539:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.24/0.34 % (1075165)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1802298448:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.34 % (1075164)Refutation found. Thanks to Tanya!
% 0.24/0.34 % SZS status Theorem for theBenchmark
% 0.24/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.34 % (1075164)------------------------------
% 0.24/0.34 % (1075164)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.34 % (1075164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.34 % (1075164)CaDiCaL version: 2.1.3
% 0.24/0.34 % (1075164)Termination reason: Refutation
% 0.24/0.34 % (1075164)Time elapsed: 0.012 s
% 0.24/0.34 % (1075164)Peak memory usage: 12 MB
% 0.24/0.34 % (1075164)Instructions burned: 25 (million)
% 0.24/0.34 % (1075155)Success in time 0.036 s
% 0.24/0.34 % Vampire exiting
%------------------------------------------------------------------------------