%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM409+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 : n010.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 12:24:07 PM UTC 2026
% Result : Theorem 0.13s 0.46s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 14 unt; 0 def)
% Number of atoms : 160 ( 5 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 164 ( 60 ~; 56 |; 34 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 48 ( 47 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f4,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f7,axiom,
! [X0] :
( empty(X0)
=> ( epsilon_transitive(X0)
& epsilon_connected(X0)
& ordinal(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(f11,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( transfinite_sequence(X0)
<=> ordinal(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_ordinal1) ).
fof(f12,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1)
& transfinite_sequence(X1) )
=> ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_ordinal1) ).
fof(f16,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(f19,axiom,
( relation(empty_set)
& relation_empty_yielding(empty_set)
& function(empty_set)
& one_to_one(empty_set)
& empty(empty_set)
& epsilon_transitive(empty_set)
& epsilon_connected(empty_set)
& ordinal(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(f24,axiom,
! [X0] :
( empty(X0)
=> ( empty(relation_dom(X0))
& relation(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f25,axiom,
! [X0] :
( empty(X0)
=> ( empty(relation_rng(X0))
& relation(relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f43,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f45,conjecture,
! [X0] : transfinite_sequence_of(empty_set,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_ordinal1) ).
fof(f46,negated_conjecture,
~ ! [X0] : transfinite_sequence_of(empty_set,X0),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f50,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f57,plain,
( empty(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f16]) ).
fof(f59,plain,
( relation(empty_set)
& function(empty_set)
& one_to_one(empty_set)
& empty(empty_set)
& epsilon_transitive(empty_set)
& epsilon_connected(empty_set)
& ordinal(empty_set) ),
inference(pure_predicate_removal,[],[f19]) ).
fof(f63,plain,
( relation(empty_set)
& function(empty_set)
& empty(empty_set)
& epsilon_transitive(empty_set)
& epsilon_connected(empty_set)
& ordinal(empty_set) ),
inference(pure_predicate_removal,[],[f59]) ).
fof(f65,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f67,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f72,plain,
! [X0] :
( ( epsilon_transitive(X0)
& epsilon_connected(X0)
& ordinal(X0) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f74,plain,
! [X0] :
( ( transfinite_sequence(X0)
<=> ordinal(relation_dom(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f75,plain,
! [X0] :
( ( transfinite_sequence(X0)
<=> ordinal(relation_dom(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) )
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f77,plain,
! [X0,X1] :
( ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) )
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(flattening,[],[f76]) ).
fof(f83,plain,
! [X0] :
( ( empty(relation_dom(X0))
& relation(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f84,plain,
! [X0] :
( ( empty(relation_rng(X0))
& relation(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f88,plain,
? [X0] : ~ transfinite_sequence_of(empty_set,X0),
inference(ennf_transformation,[],[f46]) ).
fof(f93,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f99,plain,
! [X0] :
( ( ( transfinite_sequence(X0)
| ~ ordinal(relation_dom(X0)) )
& ( ordinal(relation_dom(X0))
| ~ transfinite_sequence(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f75]) ).
fof(f100,plain,
! [X0,X1] :
( ( ( transfinite_sequence_of(X1,X0)
| ~ subset(relation_rng(X1),X0) )
& ( subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0) ) )
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(nnf_transformation,[],[f77]) ).
fof(f118,plain,
~ transfinite_sequence_of(empty_set,sK19),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X0,sK19)],[f88]) ).
fof(f121,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f124,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f128,plain,
! [X0] :
( ~ empty(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f138,plain,
! [X0] :
( ~ ordinal(relation_dom(X0))
| transfinite_sequence(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f140,plain,
! [X0,X1] :
( ~ subset(relation_rng(X1),X0)
| transfinite_sequence_of(X1,X0)
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f146,plain,
relation(empty_set),
inference(cnf_transformation,[],[f57]) ).
fof(f147,plain,
empty(empty_set),
inference(cnf_transformation,[],[f57]) ).
fof(f154,plain,
function(empty_set),
inference(cnf_transformation,[],[f63]) ).
fof(f161,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f163,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f201,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f43]) ).
fof(f204,plain,
~ transfinite_sequence_of(empty_set,sK19),
inference(cnf_transformation,[],[f118]) ).
fof(f209,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f93]) ).
fof(f263,plain,
! [X0] :
( ordinal(relation_dom(X0))
| ~ empty(X0) ),
inference(resolution,[],[f161,f128]) ).
fof(f272,plain,
! [X0] :
( ~ empty(X0)
| empty_set = relation_rng(X0) ),
inference(resolution,[],[f209,f163]) ).
fof(f336,plain,
! [X0] :
( transfinite_sequence(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ empty(X0) ),
inference(resolution,[],[f138,f263]) ).
fof(f338,plain,
! [X0] :
( transfinite_sequence(X0)
| ~ function(X0)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[],[f336,f124]) ).
fof(f339,plain,
! [X0] :
( ~ empty(X0)
| transfinite_sequence(X0) ),
inference(forward_subsumption_resolution,[],[f338,f121]) ).
fof(f342,plain,
transfinite_sequence(empty_set),
inference(resolution,[],[f339,f147]) ).
fof(f414,plain,
empty_set = relation_rng(empty_set),
inference(resolution,[],[f272,f147]) ).
fof(f434,plain,
! [X0] :
( ~ subset(empty_set,X0)
| transfinite_sequence_of(empty_set,X0)
| ~ relation(empty_set)
| ~ function(empty_set)
| ~ transfinite_sequence(empty_set) ),
inference(superposition,[],[f140,f414]) ).
fof(f446,plain,
! [X0] :
( ~ subset(empty_set,X0)
| transfinite_sequence_of(empty_set,X0)
| ~ function(empty_set)
| ~ transfinite_sequence(empty_set) ),
inference(forward_subsumption_resolution,[],[f434,f146]) ).
fof(f447,plain,
! [X0] :
( ~ subset(empty_set,X0)
| transfinite_sequence_of(empty_set,X0)
| ~ transfinite_sequence(empty_set) ),
inference(forward_subsumption_resolution,[],[f446,f154]) ).
fof(f448,plain,
! [X0] :
( ~ subset(empty_set,X0)
| transfinite_sequence_of(empty_set,X0) ),
inference(forward_subsumption_resolution,[],[f447,f342]) ).
fof(f449,plain,
! [X0] : transfinite_sequence_of(empty_set,X0),
inference(forward_subsumption_resolution,[],[f448,f201]) ).
fof(f453,plain,
$false,
inference(resolution,[],[f449,f204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM409+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.37 % Computer : n010.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sun Sep 27 19:49:01 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.40 Running first-order model finding
% 0.13/0.40 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
% 0.13/0.46 % (1266049)Will run a generic schedule for satisfiability detection.
% 0.13/0.46 % (1266057)dis+10_1_sil=32000:sp=arity:random_seed=3435849177:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.46 % (1266055)% WARNING: option uhcvi not known.
% 0.13/0.46 % (1266057) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1266049-1266057"...
% 0.13/0.46 % (1266057)...printing done.
% 0.13/0.46 % (1266060)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1792097916:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.46 % (1266056)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2834219118:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.46 % (1266055)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4245638788:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.46 % (1266057)Refutation found. Thanks to Tanya!
% 0.13/0.46 % SZS status Theorem for theBenchmark
% 0.13/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.46 % (1266057)------------------------------
% 0.13/0.46 % (1266057)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.46 % (1266057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.46 % (1266057)CaDiCaL version: 2.1.3
% 0.13/0.46 % (1266057)Termination reason: Refutation
% 0.13/0.46 % (1266057)Time elapsed: 0.005 s
% 0.13/0.46 % (1266057)Peak memory usage: 12 MB
% 0.13/0.46 % (1266057)Instructions burned: 10 (million)
% 0.13/0.46 % (1266049)Success in time 0.042 s
% 0.13/0.46 % Vampire exiting
%------------------------------------------------------------------------------