%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM390+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 : Tue Sep 29 12:24:06 PM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 71 ( 15 unt; 2 def)
% Number of atoms : 192 ( 8 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 194 ( 73 ~; 69 |; 30 &)
% ( 6 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 83 ( 0 sgn 75 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_transitive(X0)
& epsilon_connected(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f8,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f9,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( subset(X0,X1)
& X0 != X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f29,axiom,
! [X0] :
( epsilon_transitive(X0)
=> ! [X1] :
( ordinal(X1)
=> ( proper_subset(X0,X1)
=> in(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_ordinal1) ).
fof(f30,conjecture,
! [X0] :
( epsilon_transitive(X0)
=> ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( ( subset(X0,X1)
& in(X1,X2) )
=> in(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_ordinal1) ).
fof(f31,negated_conjecture,
~ ! [X0] :
( epsilon_transitive(X0)
=> ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( ( subset(X0,X1)
& in(X1,X2) )
=> in(X0,X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f32,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f33,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f34,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f37,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f42,plain,
! [X0,X1] :
( ( subset(X0,X1)
& X0 != X1 )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f52,plain,
! [X0] :
( ( epsilon_transitive(X0)
& epsilon_connected(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f58,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f59,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f42]) ).
fof(f60,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f59]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1) )
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1) )
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ in(X0,X2)
& subset(X0,X1)
& in(X1,X2)
& ordinal(X2) )
& ordinal(X1) )
& epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f67,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ in(X0,X2)
& subset(X0,X1)
& in(X1,X2)
& ordinal(X2) )
& ordinal(X1) )
& epsilon_transitive(X0) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f69,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f34]) ).
fof(f71,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f70]) ).
fof(f74,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f77,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f78,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK0(X0),X0)
& in(sK0(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f78]) ).
fof(f92,plain,
( ~ in(sK13,sK15)
& subset(sK13,sK14)
& in(sK14,sK15)
& ordinal(sK15)
& ordinal(sK14)
& epsilon_transitive(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15)],[f67]) ).
fof(f93,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f98,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f103,plain,
! [X2,X0] :
( ~ in(X2,X0)
| subset(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f106,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| proper_subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f60]) ).
fof(f138,plain,
! [X0,X1] :
( ~ proper_subset(X0,X1)
| in(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f139,plain,
epsilon_transitive(sK13),
inference(cnf_transformation,[],[f92]) ).
fof(f140,plain,
ordinal(sK14),
inference(cnf_transformation,[],[f92]) ).
fof(f141,plain,
ordinal(sK15),
inference(cnf_transformation,[],[f92]) ).
fof(f142,plain,
in(sK14,sK15),
inference(cnf_transformation,[],[f92]) ).
fof(f143,plain,
subset(sK13,sK14),
inference(cnf_transformation,[],[f92]) ).
fof(f144,plain,
~ in(sK13,sK15),
inference(cnf_transformation,[],[f92]) ).
fof(f145,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f147,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f71]) ).
fof(f151,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f162,plain,
epsilon_transitive(sK15),
inference(resolution,[],[f98,f141]) ).
fof(f172,plain,
~ empty(sK15),
inference(resolution,[],[f151,f142]) ).
fof(f201,plain,
( subset(sK14,sK15)
| ~ epsilon_transitive(sK15) ),
inference(resolution,[],[f103,f142]) ).
fof(f203,plain,
subset(sK14,sK15),
inference(forward_subsumption_resolution,[],[f201,f162]) ).
fof(f215,plain,
( proper_subset(sK13,sK14)
| sK13 = sK14 ),
inference(resolution,[],[f106,f143]) ).
fof(f228,definition,
( spl16_3
<=> sK13 = sK14 ),
introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition]) ).
fof(f230,plain,
( sK13 = sK14
| ~ spl16_3 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f232,definition,
( spl16_4
<=> proper_subset(sK13,sK14) ),
introduced(definition,[new_symbols(definition,[spl16_4])],[avatar_definition]) ).
fof(f234,plain,
( proper_subset(sK13,sK14)
| ~ spl16_4 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f235,plain,
( spl16_3
| spl16_4 ),
inference(avatar_split_clause,[],[f215,f232,f228]) ).
fof(f237,plain,
( in(sK13,sK15)
| ~ spl16_3 ),
inference(superposition,[],[f142,f230]) ).
fof(f245,plain,
( $false
| ~ spl16_3 ),
inference(forward_subsumption_resolution,[],[f237,f144]) ).
fof(f246,plain,
~ spl16_3,
inference(avatar_contradiction_clause,[],[f245]) ).
fof(f253,plain,
( in(sK13,sK14)
| ~ ordinal(sK14)
| ~ epsilon_transitive(sK13)
| ~ spl16_4 ),
inference(resolution,[],[f138,f234]) ).
fof(f254,plain,
( in(sK13,sK14)
| ~ epsilon_transitive(sK13)
| ~ spl16_4 ),
inference(forward_subsumption_resolution,[],[f253,f140]) ).
fof(f255,plain,
( in(sK13,sK14)
| ~ spl16_4 ),
inference(forward_subsumption_resolution,[],[f254,f139]) ).
fof(f259,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| element(X0,X2)
| ~ in(X0,X1) ),
inference(resolution,[],[f148,f147]) ).
fof(f326,plain,
! [X0] :
( ~ in(X0,sK14)
| element(X0,sK15) ),
inference(resolution,[],[f259,f203]) ).
fof(f376,plain,
( element(sK13,sK15)
| ~ spl16_4 ),
inference(resolution,[],[f326,f255]) ).
fof(f378,plain,
( in(sK13,sK15)
| empty(sK15)
| ~ spl16_4 ),
inference(resolution,[],[f376,f145]) ).
fof(f379,plain,
( empty(sK15)
| ~ spl16_4 ),
inference(forward_subsumption_resolution,[],[f378,f144]) ).
fof(f380,plain,
( $false
| ~ spl16_4 ),
inference(forward_subsumption_resolution,[],[f379,f172]) ).
fof(f381,plain,
~ spl16_4,
inference(avatar_contradiction_clause,[],[f380]) ).
cnf(s2,plain,
( spl16_3
| spl16_4 ),
inference(sat_conversion,[],[f235]) ).
cnf(s3,plain,
~ spl16_3,
inference(sat_conversion,[],[f246]) ).
cnf(s10,plain,
~ spl16_4,
inference(sat_conversion,[],[f381]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s2,s10,s3]) ).
fof(f382,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM390+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 % Computer : n020.cluster.edu
% 0.10/0.40 % Model : x86_64 x86_64
% 0.10/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.40 % Memory : 8046.5625MB
% 0.10/0.40 % OS : Linux 6.8.0-71-generic
% 0.10/0.40 % CPULimit : 300
% 0.10/0.40 % WCLimit : 300
% 0.10/0.40 % DateTime : Sun Sep 27 19:46:49 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.43 Running first-order model finding
% 0.10/0.43 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
% 0.16/0.48 % (3702334)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (3702342)dis+10_1_sil=32000:sp=arity:random_seed=4167148581:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (3702340)% WARNING: option uhcvi not known.
% 0.16/0.48 % (3702342) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3702334-3702342"...
% 0.16/0.48 % (3702342)...printing done.
% 0.16/0.48 % (3702342)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Theorem for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (3702342)------------------------------
% 0.16/0.48 % (3702342)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (3702342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (3702342)CaDiCaL version: 2.1.3
% 0.16/0.48 % (3702342)Termination reason: Refutation
% 0.16/0.48 % (3702342)Time elapsed: 0.004 s
% 0.16/0.48 % (3702342)Peak memory usage: 12 MB
% 0.16/0.48 % (3702342)Instructions burned: 8 (million)
% 0.16/0.48 % (3702334)Success in time 0.041 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------