%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU518^2 : 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 : n011.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 08:32:16 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of formulae : 31 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 225 ( 55 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 296 ( 11 ~; 14 |; 4 &; 223 @)
% ( 2 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 6 con; 0-4 aty)
% ( 17 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 63 ( 20 ^; 41 !; 2 ?; 63 :)
% 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,
powersetAx: $o ).
thf(func_def_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
vIFF: $o > $o > $o ).
thf(func_def_6,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vIMP: $o > $o > $o ).
thf(func_def_9,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_16,type,
sK2: $i > $i > $i ).
thf(f1,axiom,
( powersetAx
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx) ).
thf(f2,conjecture,
( powersetAx
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( in @ X1 @ ( powerset @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI) ).
thf(f3,negated_conjecture,
~ ( powersetAx
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( in @ X1 @ ( powerset @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( powersetAx
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( powersetAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( powersetAx
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( in @ X1 @ ( powerset @ X0 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( powersetAx = $true )
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) )
=> ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ) )
& ( powersetAx = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ( $true
!= ( in @ sK1 @ ( powerset @ sK0 ) ) )
& ! [X2: $i] :
( ( $true
= ( in @ X2 @ sK0 ) )
| ( $true
!= ( in @ X2 @ sK1 ) ) )
& ( powersetAx = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f8]) ).
thf(f10,plain,
( powersetAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f11,plain,
powersetAx = $true,
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK1 ) )
| ( $true
= ( in @ X2 @ sK0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
( $true
!= ( in @ sK1 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f10,f11]) ).
thf(f17,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f16]) ).
thf(f18,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
= ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
= ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f18]) ).
thf(f20,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
! [X2: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X2 ) )
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) ) ),
inference(iff_proxy_clausification,[],[f20]) ).
thf(f22,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) ) ) ),
inference(iff_proxy_clausification,[],[f21]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) )
@ ( sK2 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f22]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( ( in @ ( sK2 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK2 @ X1 @ X2 ) @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK2 @ X1 @ X2 ) @ X2 ) )
| ( $true
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f28]) ).
thf(f30,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ X1 @ X2 ) @ X1 ) )
| ( $true
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f28]) ).
thf(f33,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
= ( in @ ( sK2 @ sK1 @ X0 ) @ sK0 ) )
| ( $true
= ( in @ sK1 @ ( powerset @ X0 ) ) ) ),
inference(constrained_superposition,[],[f12,f30]) ).
thf(f37,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK2 @ sK1 @ X0 ) @ sK0 ) )
| ( $true
= ( in @ sK1 @ ( powerset @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f41,plain,
( ( $true = $false )
| ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
| ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ) ),
inference(constrained_superposition,[],[f29,f37]) ).
thf(f42,plain,
( ( $true = $false )
| ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ) ),
inference(duplicate_literal_removal,[],[f41]) ).
thf(f43,plain,
( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f46,plain,
$true != $true,
inference(constrained_superposition,[],[f13,f43]) ).
thf(f47,plain,
$false,
inference(trivial_inequality_removal,[],[f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU518^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n011.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:47:47 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.24 Running first-order model finding
% 0.08/0.24 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
% 0.22/0.28 % (121588)Will run a generic schedule for satisfiability detection.
% 0.22/0.28 % (121594)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2847088898_3000 on theBenchmark for (3000ds/0Mi)
% 0.22/0.28 % Exception at run slice level
% 0.22/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.28 % (121595)% WARNING: option uhcvi not known.
% 0.22/0.28 % (121596)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2667848754:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.22/0.28 % (121598)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1540472913:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.22/0.28 % (121595)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3750751579:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.22/0.28 % (121597)dis+10_1_sil=32000:sp=arity:random_seed=2219664919:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.22/0.28 % (121600)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2680669734:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.22/0.28 % (121598)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.28 % (121599)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2853856608:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.22/0.28 % (121595)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.28 % (121595)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.28 % (121600) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-121588-121600"...
% 0.22/0.28 % (121605)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3305481396:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.22/0.28 % Exception at run slice level
% 0.22/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.28 % (121596) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-121588-121596"...
% 0.22/0.28 % (121600)...printing done.
% 0.22/0.28 % (121600)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 % (121600)------------------------------
% 0.22/0.28 % (121600)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (121600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (121600)CaDiCaL version: 2.1.3
% 0.22/0.28 % (121600)Termination reason: Refutation
% 0.22/0.28 % (121600)Time elapsed: 0.003 s
% 0.22/0.28 % (121600)Peak memory usage: 12 MB
% 0.22/0.28 % (121600)Instructions burned: 4 (million)
% 0.22/0.28 % (121588)Success in time 0.028 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------