%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU501^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:29:49 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 379 ( 101 equ; 0 cnn)
% Maximal formula atoms : 19 ( 18 avg)
% Number of connectives : 202 ( 21 ~; 8 |; 57 &; 42 @)
% ( 2 <=>; 72 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 93 ( 90 usr; 25 con; 0-4 aty)
% Number of variables : 24 ( 0 ^; 18 !; 6 ?; 24 :)
% 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_30,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_32,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
vAND: $o > $o > $o ).
thf(func_def_34,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_35,type,
vIMP: $o > $o > $o ).
thf(func_def_36,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_39,type,
sP0: $i > $i > $o ).
thf(func_def_40,type,
sP1: $i > $o ).
thf(func_def_41,type,
sP2: $i > $i > $o ).
thf(func_def_42,type,
sP3: $i > $i > $o ).
thf(func_def_43,type,
sP4: $o ).
thf(func_def_44,type,
sK5: $o ).
thf(func_def_47,type,
sK8: $i > $o ).
thf(func_def_49,type,
sK10: $i > $i > $i ).
thf(func_def_50,type,
sK11: $i > $i > $i ).
thf(func_def_51,type,
sK12: $i > $i > $i ).
thf(func_def_52,type,
sK13: $i > $i > $i ).
thf(func_def_53,type,
sK14: $i > $i > $i ).
thf(func_def_54,type,
sK15: $i > $i > $i > $i ).
thf(func_def_55,type,
sK16: $i > $i ).
thf(func_def_56,type,
sK17: $i > $i ).
thf(func_def_57,type,
sK18: $i > $i ).
thf(func_def_58,type,
sK19: $i > $i ).
thf(func_def_59,type,
sK20: $i > $i > $i > $i ).
thf(func_def_60,type,
sK21: $i > $i > $i > $i ).
thf(func_def_61,type,
sK22: $i > $i > $i ).
thf(func_def_62,type,
sK23: $i > $i > $i ).
thf(func_def_63,type,
sK24: $i > $i > $i ).
thf(func_def_64,type,
sK25: $i > $i ).
thf(func_def_66,type,
sK27: $i > $i ).
thf(func_def_67,type,
sK28: $i > $i ).
thf(func_def_69,type,
sK30: $i > $i > $o ).
thf(func_def_71,type,
sK32: $i > $i ).
thf(func_def_72,type,
sK33: $i > $i ).
thf(func_def_73,type,
sK34: $i > ( $i > $i > $o ) > $i ).
thf(func_def_74,type,
sK35: $i > ( $i > $i > $o ) > $i ).
thf(func_def_75,type,
sK36: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_80,type,
sK41: $o ).
thf(func_def_84,type,
sK45: $i > $i > $i ).
thf(func_def_86,type,
sK47: $i > $i ).
thf(func_def_91,type,
sK52: $i > $i > $i ).
thf(func_def_93,type,
sK54: $i > $i ).
thf(func_def_95,type,
sK56: $i > $i ).
thf(func_def_96,type,
sK57: $i > $o ).
thf(func_def_97,type,
sK58: $i > $i > $i ).
thf(func_def_101,type,
sK62: $i > $o ).
thf(func_def_105,type,
sK66: $i > $o ).
thf(func_def_107,type,
sK68: ( $i > $o ) > $i ).
thf(func_def_108,type,
sK69: $i > $o ).
thf(func_def_109,type,
sK70: $i > $i ).
thf(func_def_110,type,
vNOT: $o > $o ).
thf(func_def_111,type,
sK71: $i > ( $i > $o ) > $i ).
thf(func_def_112,type,
sK72: $i > $i ).
thf(func_def_113,type,
sK73: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_114,type,
sK74: $i > ( $i > $o ) > $i ).
thf(func_def_115,type,
sK75: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_116,type,
sK76: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_117,type,
sK77: $i > ( $i > $o ) > $i ).
thf(f3,axiom,
! [X0: $i] :
( ( ~ ( in @ X0 @ emptyset ) )
= emptysetAx ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(f20,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(f21,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
thf(f42,plain,
! [X0: $i] :
( ( ~ ( in @ X0 @ emptyset ) )
= emptysetAx ),
inference(rectify,[],[f3]) ).
thf(f43,plain,
( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
<=> ( emptysetAx = $true ) ),
inference(fool_elimination,[],[f42]) ).
thf(f54,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f55,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 )
=> ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
=> ! [X1: $o] : ( $true = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f62,plain,
( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
<=> ( emptysetAx = $true ) ),
inference(flattening,[],[f43]) ).
thf(f72,plain,
( ? [X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
& ? [X1: $o] : ( $true != X1 ) )
& ( 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,[],[f55]) ).
thf(f73,plain,
( ( wellorderingAx = $true )
& ( prop2setE = $true )
& ( dsetconstrER = $true )
& ( exuE1 = $true )
& ( replAx = $true )
& ( setunionAx = $true )
& ( foundationAx = $true )
& ( dsetconstrI = $true )
& ( omegaIndAx = $true )
& ( emptysetAx = $true )
& ( omegaSAx = $true )
& ( descrp = $true )
& ? [X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
& ? [X1: $o] : ( $true != X1 ) )
& ( dsetconstrEL = $true )
& ( setextAx = $true )
& ( setadjoinAx = $true )
& ( powersetAx = $true )
& ( omega0Ax = $true ) ),
inference(flattening,[],[f72]) ).
thf(f109,plain,
( ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetAx != $true ) )
& ( ( emptysetAx = $true )
| ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true ) ) ),
inference(nnf_transformation,[],[f62]) ).
thf(f110,plain,
( ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetAx != $true ) )
& ( ( emptysetAx = $true )
| ? [X1: $i] :
( ( in @ X1 @ emptyset )
= $true ) ) ),
inference(rectify,[],[f109]) ).
thf(f111,plain,
( ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetAx != $true ) )
& ( ( emptysetAx = $true )
| ( ( in @ sK29 @ emptyset )
= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(X1,sK29)],[f110]) ).
thf(f120,plain,
( ( wellorderingAx = $true )
& ( prop2setE = $true )
& ( dsetconstrER = $true )
& ( exuE1 = $true )
& ( replAx = $true )
& ( setunionAx = $true )
& ( foundationAx = $true )
& ( dsetconstrI = $true )
& ( omegaIndAx = $true )
& ( emptysetAx = $true )
& ( omegaSAx = $true )
& ( descrp = $true )
& ( $true
= ( in @ sK40 @ emptyset ) )
& ( sK41 != $true )
& ( dsetconstrEL = $true )
& ( setextAx = $true )
& ( setadjoinAx = $true )
& ( powersetAx = $true )
& ( omega0Ax = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40,sK41]),skolemize(X0,sK40),skolemize(X1,sK41)],[f73]) ).
thf(f197,plain,
! [X0: $i] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetAx != $true ) ),
inference(cnf_transformation,[],[f111]) ).
thf(f222,plain,
( $true
= ( in @ sK40 @ emptyset ) ),
inference(cnf_transformation,[],[f120]) ).
thf(f225,plain,
emptysetAx = $true,
inference(cnf_transformation,[],[f120]) ).
thf(f297,plain,
! [X0: $i] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f197,f225]) ).
thf(f417,plain,
! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ),
inference(trivial_inequality_removal,[],[f297]) ).
thf(f499,plain,
$false,
inference(forward_subsumption_resolution,[],[f222,f417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU501^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n026.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 13:49:27 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.28 % (615381)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (615386)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4255678713:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (615392)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.28 % (615392)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
% 0.21/0.28 % (615386) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-615381-615386"...
% 0.21/0.28 % (615388)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=17323108:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.28 % (615387)lrs+10_16_si=on:nwc=1.5:random_seed=3003600869:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.28 % (615390)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=271635523:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.28 % (615392)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2614497857:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.28 % (615389)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=1028949074: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)
% 0.21/0.28 % (615391)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2068481681:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.28 % (615386)...printing done.
% 0.21/0.28 % (615386)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 % (615386)------------------------------
% 0.21/0.28 % (615386)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (615386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (615386)CaDiCaL version: 2.1.3
% 0.21/0.28 % (615386)Termination reason: Refutation
% 0.21/0.28 % (615386)Time elapsed: 0.008 s
% 0.21/0.28 % (615386)Peak memory usage: 12 MB
% 0.21/0.28 % (615386)Instructions burned: 30 (million)
% 0.21/0.28 % (615381)Success in time 0.037 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------