%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU500^1 : 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 : 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 08:32:12 AM UTC 2026
% Result : Theorem 0.25s 0.33s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 365 ( 98 equ; 0 cnn)
% Maximal formula atoms : 18 ( 11 avg)
% Number of connectives : 302 ( 7 ~; 2 |; 51 &; 148 @)
% ( 0 <=>; 79 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 61 usr; 22 con; 0-4 aty)
% ( 15 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 70 ( 37 ^; 29 !; 4 ?; 70 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_28,type,
vAND: $o > $o > $o ).
thf(func_def_29,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_32,type,
vIMP: $o > $o > $o ).
thf(func_def_33,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_35,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_36,type,
vIFF: $o > $o > $o ).
thf(func_def_37,type,
vNOT: $o > $o ).
thf(func_def_38,type,
vOR: $o > $o > $o ).
thf(func_def_39,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
sK0: $o ).
thf(func_def_45,type,
sK2: ( $i > $o ) > $i ).
thf(func_def_46,type,
sK3: ( $i > $o ) > $i > $i ).
thf(func_def_47,type,
sK4: ( $i > $o ) > $i > $i ).
thf(func_def_48,type,
sK5: $i > $i ).
thf(func_def_49,type,
sK6: $i > $i > $i > $i ).
thf(func_def_50,type,
sK7: $i > $i > $i ).
thf(func_def_51,type,
sK8: $i > $i > $i ).
thf(func_def_52,type,
sK9: $i > $i > $i ).
thf(func_def_53,type,
sK10: $i > $i ).
thf(func_def_54,type,
sK11: $i > ( $i > $i > $o ) > $i ).
thf(func_def_55,type,
sK12: $i > ( $i > $i > $o ) > $i ).
thf(func_def_56,type,
sK13: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_57,type,
sK14: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_58,type,
sK15: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_59,type,
sK16: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_60,type,
sK17: $i > $i ).
thf(func_def_61,type,
sK18: $i > $i > $i ).
thf(func_def_62,type,
sK19: $i > $i > $i ).
thf(func_def_63,type,
sK20: $i > $i > $i ).
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(f18,axiom,
( prop2set
= ( ^ [X0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [X1: $i] : X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2set) ).
thf(f19,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ! [X0: $o,X1: $i] :
( ( in @ X1 @ ( prop2set @ X0 ) )
=> X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
thf(f20,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ! [X0: $o,X1: $i] :
( ( in @ X1 @ ( prop2set @ X0 ) )
=> X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
thf(f49,plain,
( dsetconstrER
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f50,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,[],[f49]) ).
thf(f53,plain,
( prop2set
= ( ^ [X0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [X1: $i] : X0 ) ) ),
inference(rectify,[],[f18]) ).
thf(f54,plain,
( prop2set
= ( ^ [Y0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y1: $i] : Y0 ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f55,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ! [X0: $o,X1: $i] :
( ( in @ X1 @ ( prop2set @ X0 ) )
=> X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f56,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 )
=> ! [X0: $o,X1: $i] :
( ( ( in @ X1 @ ( prop2set @ X0 ) )
= $true )
=> ( $true = X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f57,plain,
( ? [X0: $o,X1: $i] :
( ( $true != X0 )
& ( ( in @ X1 @ ( prop2set @ X0 ) )
= $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,[],[f56]) ).
thf(f58,plain,
( ? [X0: $o,X1: $i] :
( ( $true != X0 )
& ( ( in @ X1 @ ( prop2set @ X0 ) )
= $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,[],[f57]) ).
thf(f59,plain,
( ( $true != sK0 )
& ( $true
= ( in @ sK1 @ ( prop2set @ sK0 ) ) )
& ( 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)],[f58]) ).
thf(f75,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,[],[f50]) ).
thf(f77,plain,
( prop2set
= ( ^ [Y0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y1: $i] : Y0 ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f92,plain,
dsetconstrER = $true,
inference(cnf_transformation,[],[f59]) ).
thf(f94,plain,
( $true
= ( in @ sK1 @ ( prop2set @ sK0 ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f95,plain,
$true != sK0,
inference(cnf_transformation,[],[f59]) ).
thf(f112,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,[],[f75,f92]) ).
thf(f114,plain,
( $true
= ( in @ sK1
@ ( ^ [Y0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y1: $i] : Y0 )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f94,f77]) ).
thf(f115,plain,
( $true
= ( in @ sK1
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y0: $i] : sK0 ) ) ),
inference(beta-eta_normalization,[],[f114]) ).
thf(f139,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,[],[f112]) ).
thf(f140,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,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,[],[f140]) ).
thf(f142,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( X2 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f142]) ).
thf(f144,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
=> ( X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f145,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) )
| ( $true
= ( X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f144]) ).
thf(f410,plain,
( ( $true = $false )
| ( $true
= ( ^ [Y0: $i] : sK0
@ sK1 ) ) ),
inference(constrained_superposition,[],[f115,f145]) ).
thf(f415,plain,
( $true
= ( ^ [Y0: $i] : sK0
@ sK1 ) ),
inference(trivial_inequality_removal,[],[f410]) ).
thf(f416,plain,
$true = sK0,
inference(beta-eta_normalization,[],[f415]) ).
thf(f421,plain,
$false,
inference(forward_subsumption_resolution,[],[f416,f95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU500^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 % Computer : n020.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 13:47:19 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.25/0.28 Running first-order model finding
% 0.25/0.28 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
% 0.25/0.33 % (1074652)Will run a generic schedule for satisfiability detection.
% 0.25/0.33 % (1074660)dis+10_1_sil=32000:sp=arity:random_seed=237927757:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.25/0.33 % (1074657)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2684770637_2999 on theBenchmark for (2999ds/0Mi)
% 0.25/0.33 % (1074658)% WARNING: option uhcvi not known.
% 0.25/0.33 % Exception at run slice level
% 0.25/0.33 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.25/0.33 % (1074660) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1074652-1074660"...
% 0.25/0.33 % (1074660)...printing done.
% 0.25/0.33 % (1074659)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2477030405:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.25/0.33 % (1074660)Refutation found. Thanks to Tanya!
% 0.25/0.33 % SZS status Theorem for theBenchmark
% 0.25/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.33 % (1074660)------------------------------
% 0.25/0.33 % (1074660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.33 % (1074660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.33 % (1074660)CaDiCaL version: 2.1.3
% 0.25/0.33 % (1074660)Termination reason: Refutation
% 0.25/0.33 % (1074660)Time elapsed: 0.012 s
% 0.25/0.33 % (1074660)Peak memory usage: 12 MB
% 0.25/0.33 % (1074660)Instructions burned: 24 (million)
% 0.25/0.33 % (1074652)Success in time 0.035 s
% 0.25/0.33 % Vampire exiting
%------------------------------------------------------------------------------