%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU580^2 : 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 : n003.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 0.21s 0.26s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 44 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 262 ( 60 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 443 ( 9 ~; 12 |; 6 &; 345 @)
% ( 0 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 6 con; 0-4 aty)
% ( 31 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 118 ( 51 ^; 63 !; 4 ?; 118 :)
% 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,
dsetconstrEL: $o ).
thf(func_def_5,type,
powersetI: $o ).
thf(func_def_6,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
vIMP: $o > $o > $o ).
thf(func_def_8,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK1: $i > $o ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(func_def_17,type,
sK2: $i > $i > $i ).
thf(f1,axiom,
( dsetconstrEL
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(f2,axiom,
( powersetI
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(f3,conjecture,
( dsetconstrEL
=> ( powersetI
=> ! [X0: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(f4,negated_conjecture,
~ ( dsetconstrEL
=> ( powersetI
=> ! [X0: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( dsetconstrEL
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( powersetI
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( powersetI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( in @ Y0 @ ( powerset @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( dsetconstrEL
=> ( powersetI
=> ! [X0: $i,X1: $i > $o] :
( in
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X0 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( dsetconstrEL = $true )
=> ( ( powersetI = $true )
=> ! [X0: $i,X1: $i > $o] :
( $true
= ( in
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( powerset @ X0 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i > $o] :
( $true
!= ( in
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( powerset @ X0 ) ) )
& ( powersetI = $true )
& ( dsetconstrEL = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i > $o] :
( $true
!= ( in
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( powerset @ X0 ) ) )
& ( powersetI = $true )
& ( dsetconstrEL = $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ( $true
!= ( in
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
@ ( powerset @ sK0 ) ) )
& ( powersetI = $true )
& ( dsetconstrEL = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12]) ).
thf(f14,plain,
( dsetconstrEL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f15,plain,
( powersetI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( in @ Y0 @ ( powerset @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f17,plain,
powersetI = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f18,plain,
( $true
!= ( in
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
@ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f21,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y0 @ Y2 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f14,f16]) ).
thf(f22,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( in @ Y0 @ ( powerset @ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f15,f17]) ).
thf(f23,plain,
( $true
!= ( in @ ( dsetconstr @ sK0 @ sK1 ) @ ( powerset @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f24,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( in @ Y0 @ ( powerset @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f22]) ).
thf(f25,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( in @ X1 @ ( powerset @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( in @ X1 @ ( powerset @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) ) )
| ( $true
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) )
@ ( sK2 @ X1 @ X2 ) ) )
| ( $true
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f28]) ).
thf(f30,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ ( sK2 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK2 @ X1 @ X2 ) @ X2 ) ) )
| ( $true
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f29]) ).
thf(f31,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK2 @ X1 @ X2 ) @ X2 ) )
| ( $true
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f30]) ).
thf(f32,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ X1 @ X2 ) @ X1 ) )
| ( $true
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f30]) ).
thf(f33,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( in @ Y0 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f21]) ).
thf(f34,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( dsetconstr @ Y1 @ Y0 ) )
=> ( in @ X1 @ Y1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f34]) ).
thf(f36,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( in @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f37,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ X2 ) )
=> ( in @ X1 @ Y0 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f36]) ).
thf(f38,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
=> ( in @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f37]) ).
thf(f39,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f38]) ).
thf(f58,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( $true = $false )
| ( $true
= ( in @ ( sK2 @ ( dsetconstr @ X0 @ X1 ) @ X2 ) @ X0 ) )
| ( $true
= ( in @ ( dsetconstr @ X0 @ X1 ) @ ( powerset @ X2 ) ) ) ),
inference(constrained_superposition,[],[f39,f32]) ).
thf(f62,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( $true
= ( in @ ( sK2 @ ( dsetconstr @ X0 @ X1 ) @ X2 ) @ X0 ) )
| ( $true
= ( in @ ( dsetconstr @ X0 @ X1 ) @ ( powerset @ X2 ) ) ) ),
inference(trivial_inequality_removal,[],[f58]) ).
thf(f69,plain,
! [X0: $i,X1: $i > $o] :
( ( $true = $false )
| ( $true
= ( in @ ( dsetconstr @ X0 @ X1 ) @ ( powerset @ X0 ) ) )
| ( $true
= ( in @ ( dsetconstr @ X0 @ X1 ) @ ( powerset @ X0 ) ) ) ),
inference(constrained_superposition,[],[f31,f62]) ).
thf(f70,plain,
! [X0: $i,X1: $i > $o] :
( ( $true = $false )
| ( $true
= ( in @ ( dsetconstr @ X0 @ X1 ) @ ( powerset @ X0 ) ) ) ),
inference(duplicate_literal_removal,[],[f69]) ).
thf(f71,plain,
! [X0: $i,X1: $i > $o] :
( $true
= ( in @ ( dsetconstr @ X0 @ X1 ) @ ( powerset @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f70]) ).
thf(f78,plain,
$true != $true,
inference(constrained_superposition,[],[f23,f71]) ).
thf(f79,plain,
$false,
inference(trivial_inequality_removal,[],[f78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU580^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:53:59 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.21/0.26 % (2539417)Will run a generic schedule for satisfiability detection.
% 0.21/0.26 % (2539427)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1970361118:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.26 % (2539427) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2539417-2539427"...
% 0.21/0.26 % (2539423)% WARNING: option uhcvi not known.
% 0.21/0.26 % (2539427)...printing done.
% 0.21/0.26 % (2539422)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4007060398_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.26 % (2539424)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=357277573:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.26 % (2539423)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1913071352:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.26 % (2539425)dis+10_1_sil=32000:sp=arity:random_seed=3377919004:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.26 % (2539427)Refutation found. Thanks to Tanya!
% 0.21/0.26 % SZS status Theorem for theBenchmark
% 0.21/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.26 % (2539427)------------------------------
% 0.21/0.26 % (2539427)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.26 % (2539427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.26 % (2539427)CaDiCaL version: 2.1.3
% 0.21/0.26 % (2539427)Termination reason: Refutation
% 0.21/0.26 % (2539427)Time elapsed: 0.003 s
% 0.21/0.26 % (2539427)Peak memory usage: 12 MB
% 0.21/0.26 % (2539427)Instructions burned: 7 (million)
% 0.21/0.26 % (2539417)Success in time 0.029 s
% 0.21/0.26 % Vampire exiting
%------------------------------------------------------------------------------