%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU581^2 : 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 : n018.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 08:32:32 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 170 ( 40 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 241 ( 9 ~; 2 |; 6 &; 191 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 6 con; 0-4 aty)
% ( 16 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 68 ( 34 ^; 30 !; 4 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_3,type,
subset: $i > $i > $o ).
thf(func_def_4,type,
powersetE1: $o ).
thf(func_def_6,type,
sepInPowerset: $o ).
thf(func_def_7,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_8,type,
vIMP: $o > $o > $o ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_12,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK1: $i > $o ).
thf(func_def_17,type,
vNOT: $o > $o ).
thf(f1,axiom,
( powersetE1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(f2,axiom,
( sepInPowerset
= ( ! [X0: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(f3,conjecture,
( powersetE1
=> ( sepInPowerset
=> ! [X0: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(f4,negated_conjecture,
~ ( powersetE1
=> ( sepInPowerset
=> ! [X0: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( powersetE1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( powersetE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( sepInPowerset
= ( ! [X0: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X0 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( sepInPowerset
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( in
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) )
@ ( powerset @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( powersetE1
=> ( sepInPowerset
=> ! [X0: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X0 ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( powersetE1 = $true )
=> ( ( sepInPowerset = $true )
=> ! [X0: $i,X1: $i > $o] :
( $true
= ( subset
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ X0 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i > $o] :
( $true
!= ( subset
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ X0 ) )
& ( sepInPowerset = $true )
& ( powersetE1 = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i > $o] :
( $true
!= ( subset
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ X0 ) )
& ( sepInPowerset = $true )
& ( powersetE1 = $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ( $true
!= ( subset
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
@ sK0 ) )
& ( sepInPowerset = $true )
& ( powersetE1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12]) ).
thf(f14,plain,
( powersetE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f15,plain,
( sepInPowerset
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( in
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) )
@ ( powerset @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
powersetE1 = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f17,plain,
sepInPowerset = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f18,plain,
( $true
!= ( subset
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
@ sK0 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f21,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ Y1 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f14,f16]) ).
thf(f22,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( in
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) )
@ ( powerset @ Y1 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f15,f17]) ).
thf(f23,plain,
( $true
!= ( subset @ ( dsetconstr @ sK0 @ sK1 ) @ sK0 ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f24,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( in
@ ( dsetconstr @ Y1
@ ^ [Y2: $i] : ( Y0 @ Y2 ) )
@ ( powerset @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f22]) ).
thf(f25,plain,
! [X1: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ ( dsetconstr @ Y0 @ X1 ) @ ( powerset @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( ^ [Y0: $i] : ( in @ ( dsetconstr @ Y0 @ X1 ) @ ( powerset @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( in @ ( dsetconstr @ X2 @ X1 ) @ ( powerset @ X2 ) ) ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f28,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f21]) ).
thf(f29,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( subset @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( subset @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f29]) ).
thf(f31,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X2 ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f31]) ).
thf(f33,plain,
( ( $true != $true )
| ( $false
= ( in @ ( dsetconstr @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) ) ),
inference(constrained_superposition,[],[f23,f32]) ).
thf(f34,plain,
( $false
= ( in @ ( dsetconstr @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f36,plain,
$true = $false,
inference(constrained_superposition,[],[f27,f34]) ).
thf(f37,plain,
$false,
inference(trivial_inequality_removal,[],[f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU581^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n018.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 13:54:26 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 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
% 0.22/0.28 % (110822)Will run a generic schedule for satisfiability detection.
% 0.22/0.28 % (110828)% WARNING: option uhcvi not known.
% 0.22/0.28 % (110833)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1779329950:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.28 % (110833) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-110822-110833"...
% 0.22/0.28 % (110833)...printing done.
% 0.22/0.28 % (110831)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2825857869:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.28 % (110828)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1695499605:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.28 % (110833)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (110833)------------------------------
% 0.22/0.28 % (110833)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (110833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (110833)CaDiCaL version: 2.1.3
% 0.22/0.28 % (110833)Termination reason: Refutation
% 0.22/0.28 % (110833)Time elapsed: 0.002 s
% 0.22/0.28 % (110833)Peak memory usage: 12 MB
% 0.22/0.28 % (110833)Instructions burned: 3 (million)
% 0.22/0.28 % (110822)Success in time 0.037 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------