%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU169+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 : Tue Sep 29 12:52:13 PM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 14 unt; 2 def)
% Number of atoms : 149 ( 8 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 161 ( 61 ~; 59 |; 24 &)
% ( 10 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 60 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f3,axiom,
! [X0,X1] :
( ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) )
& ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f11,conjecture,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_subset_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f22,plain,
! [X0,X1] :
( ( ( element(X1,X0)
<=> in(X1,X0) )
| empty(X0) )
& ( ( element(X1,X0)
<=> empty(X1) )
| ~ empty(X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f24,plain,
? [X0,X1] :
( ? [X2] :
( ~ in(X2,X0)
& in(X2,X1) )
& element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f29,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0) )
& ( subset(X2,X0)
| ~ in(X2,X1) ) )
| powerset(X0) != X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f30,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(rectify,[],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ( ( ~ subset(sK0(X0,X1),X0)
| ~ in(sK0(X0,X1),X1) )
& ( subset(sK0(X0,X1),X0)
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ( ( ( element(X1,X0)
| ~ in(X1,X0) )
& ( in(X1,X0)
| ~ element(X1,X0) ) )
| empty(X0) )
& ( ( ( element(X1,X0)
| ~ empty(X1) )
& ( empty(X1)
| ~ element(X1,X0) ) )
| ~ empty(X0) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f33,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f34,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK1(X0,X1),X1)
& in(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f34]) ).
fof(f37,plain,
( ~ in(sK5,sK3)
& in(sK5,sK4)
& element(sK4,powerset(sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f24]) ).
fof(f42,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f31]) ).
fof(f48,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f50,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f54,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f56,plain,
element(sK4,powerset(sK3)),
inference(cnf_transformation,[],[f37]) ).
fof(f57,plain,
in(sK5,sK4),
inference(cnf_transformation,[],[f37]) ).
fof(f58,plain,
~ in(sK5,sK3),
inference(cnf_transformation,[],[f37]) ).
fof(f68,plain,
! [X3,X0] :
( subset(X3,X0)
| ~ in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f42]) ).
fof(f73,plain,
! [X3,X0] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ),
inference(consistent_polarity_flipping,[],[f68]) ).
fof(f75,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ~ in(X1,X0)
| ~ empty(X0) ),
inference(consistent_polarity_flipping,[],[f48]) ).
fof(f80,plain,
! [X3,X0,X1] :
( subset(X0,X1)
| in(X3,X0)
| ~ in(X3,X1) ),
inference(consistent_polarity_flipping,[],[f50]) ).
fof(f81,plain,
! [X0] : empty(powerset(X0)),
inference(consistent_polarity_flipping,[],[f54]) ).
fof(f83,plain,
in(sK5,sK3),
inference(consistent_polarity_flipping,[],[f58]) ).
fof(f84,plain,
~ in(sK5,sK4),
inference(consistent_polarity_flipping,[],[f57]) ).
fof(f339,plain,
( ~ in(sK4,powerset(sK3))
| ~ empty(powerset(sK3)) ),
inference(resolution,[],[f75,f56]) ).
fof(f348,definition,
( spl9_1
<=> empty(powerset(sK3)) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f350,plain,
( ~ empty(powerset(sK3))
| spl9_1 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f352,definition,
( spl9_2
<=> in(sK4,powerset(sK3)) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f354,plain,
( ~ in(sK4,powerset(sK3))
| spl9_2 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f355,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f339,f352,f348]) ).
fof(f356,plain,
( $false
| spl9_1 ),
inference(resolution,[],[f350,f81]) ).
fof(f365,plain,
spl9_1,
inference(avatar_contradiction_clause,[],[f356]) ).
fof(f366,plain,
( ~ subset(sK4,sK3)
| spl9_2 ),
inference(resolution,[],[f354,f73]) ).
fof(f923,plain,
( ! [X0] :
( in(X0,sK4)
| ~ in(X0,sK3) )
| spl9_2 ),
inference(resolution,[],[f80,f366]) ).
fof(f926,plain,
( ~ in(sK5,sK3)
| spl9_2 ),
inference(resolution,[],[f923,f84]) ).
fof(f946,plain,
( $false
| spl9_2 ),
inference(resolution,[],[f926,f83]) ).
fof(f948,plain,
spl9_2,
inference(avatar_contradiction_clause,[],[f946]) ).
cnf(s1,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(sat_conversion,[],[f355]) ).
cnf(s2,plain,
spl9_1,
inference(sat_conversion,[],[f365]) ).
cnf(s4,plain,
spl9_2,
inference(sat_conversion,[],[f948]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s2]) ).
fof(f949,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU169+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 03:52:02 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.10/0.45 % (418673)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (418684)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2819937033:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.45 % (418679)% WARNING: option uhcvi not known.
% 0.10/0.45 % (418684) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-418673-418684"...
% 0.10/0.45 % (418678)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3905444496_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.45 % (418682)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3943543888:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % (418679)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3727667861:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.45 % (418681)dis+10_1_sil=32000:sp=arity:random_seed=1329168482:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (418680)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3314516226:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.45 % (418683)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1528756115:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.45 % (418684)...printing done.
% 0.10/0.45 % (418684)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (418684)------------------------------
% 0.10/0.45 % (418684)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (418684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (418684)CaDiCaL version: 2.1.3
% 0.10/0.45 % (418684)Termination reason: Refutation
% 0.10/0.45 % (418684)Time elapsed: 0.006 s
% 0.10/0.45 % (418684)Peak memory usage: 12 MB
% 0.10/0.45 % (418684)Instructions burned: 16 (million)
% 0.10/0.45 % (418673)Success in time 0.034 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------