%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM411+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 12:15:05 PM UTC 2026
% Result : Theorem 3.47s 1.45s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 9 unt; 2 def)
% Number of atoms : 126 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 144 ( 64 ~; 56 |; 12 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 63 ( 0 sgn 60 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1)
& transfinite_sequence(X1) )
=> ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_ordinal1) ).
fof(f9,axiom,
! [X0,X1] :
( transfinite_sequence_of(X1,X0)
=> ( relation(X1)
& function(X1)
& transfinite_sequence(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_ordinal1) ).
fof(f35,axiom,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X1,X2) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f38,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( transfinite_sequence_of(X2,X0)
=> transfinite_sequence_of(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_ordinal1) ).
fof(f39,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( transfinite_sequence_of(X2,X0)
=> transfinite_sequence_of(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f65,plain,
! [X0,X1] :
( ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) )
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f66,plain,
! [X0,X1] :
( ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) )
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ( relation(X1)
& function(X1)
& transfinite_sequence(X1) )
| ~ transfinite_sequence_of(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f72,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(ennf_transformation,[],[f35]) ).
fof(f73,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(flattening,[],[f72]) ).
fof(f76,plain,
? [X0,X1] :
( ? [X2] :
( ~ transfinite_sequence_of(X2,X1)
& transfinite_sequence_of(X2,X0) )
& subset(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f83,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,[],[f66]) ).
fof(f101,plain,
( ~ transfinite_sequence_of(sK18,sK17)
& transfinite_sequence_of(sK18,sK16)
& subset(sK16,sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18]),skolemize(X0,sK16),skolemize(X1,sK17),skolemize(X2,sK18)],[f76]) ).
fof(f113,plain,
! [X0,X1] :
( subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0)
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f114,plain,
! [X0,X1] :
( ~ transfinite_sequence(X1)
| ~ subset(relation_rng(X1),X0)
| ~ relation(X1)
| ~ function(X1)
| transfinite_sequence_of(X1,X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f115,plain,
! [X0,X1] :
( transfinite_sequence(X1)
| ~ transfinite_sequence_of(X1,X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f116,plain,
! [X0,X1] :
( function(X1)
| ~ transfinite_sequence_of(X1,X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f117,plain,
! [X0,X1] :
( relation(X1)
| ~ transfinite_sequence_of(X1,X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f170,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(cnf_transformation,[],[f73]) ).
fof(f174,plain,
subset(sK16,sK17),
inference(cnf_transformation,[],[f101]) ).
fof(f175,plain,
transfinite_sequence_of(sK18,sK16),
inference(cnf_transformation,[],[f101]) ).
fof(f176,plain,
~ transfinite_sequence_of(sK18,sK17),
inference(cnf_transformation,[],[f101]) ).
fof(f183,plain,
! [X0,X1] :
( subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(forward_subsumption_resolution,[],[f113,f117]) ).
fof(f184,plain,
! [X0,X1] :
( subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0)
| ~ transfinite_sequence(X1) ),
inference(forward_subsumption_resolution,[],[f183,f116]) ).
fof(f185,plain,
! [X0,X1] :
( subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0) ),
inference(forward_subsumption_resolution,[],[f184,f115]) ).
fof(f186,plain,
! [X2,X0,X1] :
( ~ subset(relation_rng(X0),X1)
| ~ relation(X0)
| ~ function(X0)
| transfinite_sequence_of(X0,X1)
| ~ transfinite_sequence_of(X0,X2) ),
inference(resolution,[],[f114,f115]) ).
fof(f187,plain,
! [X2,X0,X1] :
( ~ subset(relation_rng(X0),X1)
| ~ function(X0)
| transfinite_sequence_of(X0,X1)
| ~ transfinite_sequence_of(X0,X2) ),
inference(forward_subsumption_resolution,[],[f186,f117]) ).
fof(f188,plain,
! [X2,X0,X1] :
( transfinite_sequence_of(X0,X1)
| ~ subset(relation_rng(X0),X1)
| ~ transfinite_sequence_of(X0,X2) ),
inference(forward_subsumption_resolution,[],[f187,f116]) ).
fof(f209,plain,
! [X0] :
( ~ subset(relation_rng(sK18),sK17)
| ~ transfinite_sequence_of(sK18,X0) ),
inference(resolution,[],[f188,f176]) ).
fof(f211,definition,
( spl19_4
<=> ! [X0] : ~ transfinite_sequence_of(sK18,X0) ),
introduced(definition,[new_symbols(definition,[spl19_4])],[avatar_definition]) ).
fof(f212,plain,
( ! [X0] : ~ transfinite_sequence_of(sK18,X0)
| ~ spl19_4 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f214,definition,
( spl19_5
<=> subset(relation_rng(sK18),sK17) ),
introduced(definition,[new_symbols(definition,[spl19_5])],[avatar_definition]) ).
fof(f216,plain,
( ~ subset(relation_rng(sK18),sK17)
| spl19_5 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f217,plain,
( spl19_4
| ~ spl19_5 ),
inference(avatar_split_clause,[],[f209,f214,f211]) ).
fof(f219,plain,
( ! [X0] :
( ~ subset(relation_rng(sK18),X0)
| ~ subset(X0,sK17) )
| spl19_5 ),
inference(resolution,[],[f216,f170]) ).
fof(f220,plain,
( ! [X0] :
( ~ transfinite_sequence_of(sK18,X0)
| ~ subset(X0,sK17) )
| spl19_5 ),
inference(resolution,[],[f219,f185]) ).
fof(f223,plain,
( ~ subset(sK16,sK17)
| spl19_5 ),
inference(resolution,[],[f220,f175]) ).
fof(f225,plain,
( $false
| spl19_5 ),
inference(forward_subsumption_resolution,[],[f223,f174]) ).
fof(f226,plain,
spl19_5,
inference(avatar_contradiction_clause,[],[f225]) ).
fof(f227,plain,
( $false
| ~ spl19_4 ),
inference(resolution,[],[f212,f175]) ).
fof(f229,plain,
~ spl19_4,
inference(avatar_contradiction_clause,[],[f227]) ).
cnf(s4,plain,
( spl19_4
| ~ spl19_5 ),
inference(sat_conversion,[],[f217]) ).
cnf(s5,plain,
spl19_5,
inference(sat_conversion,[],[f226]) ).
cnf(s6,plain,
~ spl19_4,
inference(sat_conversion,[],[f229]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s4,s5,s6]) ).
fof(f230,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM411+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n010.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 19:49:02 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.47/1.45 % (1266327)Detected formulas, will run a generic FOF schedule.
% 3.47/1.45 % (1266334)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3861615575:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.47/1.45 % (1266336)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4167262321:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.47/1.45 % (1266338)dis-21_1_sil=8000:lcm=predicate:random_seed=1773150337:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.47/1.45 % (1266332)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2646540763:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.47/1.45 % (1266333)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=130505082:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.47/1.45 % (1266335)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1472629813:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.47/1.45 % (1266337)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1722715693:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.47/1.45 % (1266335)Refutation not found, incomplete strategy
% 3.47/1.45 % (1266335)------------------------------
% 3.47/1.45 % (1266335)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.45 % (1266335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.45 % (1266335)CaDiCaL version: 2.1.3
% 3.47/1.45 % (1266335)Termination reason: Refutation not found, incomplete strategy
% 3.47/1.45 % (1266335)Time elapsed: 0.001 s
% 3.47/1.45 % (1266335)Peak memory usage: 87 MB
% 3.47/1.45 % (1266336)Refutation not found, incomplete strategy
% 3.47/1.45 % (1266336)------------------------------
% 3.47/1.45 % (1266336)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.45 % (1266336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.45 % (1266336)CaDiCaL version: 2.1.3
% 3.47/1.45 % (1266336)Termination reason: Refutation not found, incomplete strategy
% 3.47/1.45 % (1266336)Time elapsed: 0.001 s
% 3.47/1.45 % (1266336)Peak memory usage: 87 MB
% 3.47/1.45 % (1266337)First to succeed.
% 3.47/1.45 % (1266337)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1266327"
% 3.47/1.45 % (1266338)Also succeeded, but the first one will report.
% 3.47/1.45 % (1266336)------------------------------
% 3.47/1.45 % (1266336)------------------------------
% 3.47/1.45 % (1266335)------------------------------
% 3.47/1.45 % (1266335)------------------------------
% 3.47/1.45 % (1266337)Refutation found. Thanks to Tanya!
% 3.47/1.45 % SZS status Theorem for theBenchmark
% 3.47/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.45 % (1266337)------------------------------
% 3.47/1.45 % (1266337)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.45 % (1266337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.45 % (1266337)CaDiCaL version: 2.1.3
% 3.47/1.45 % (1266337)Termination reason: Refutation
% 3.47/1.45 % (1266337)Time elapsed: 0.005 s
% 3.47/1.45 % (1266337)Peak memory usage: 89 MB
% 3.47/1.45 % (1266337)Instructions burned: 5 (million)
% 3.47/1.45 % (1266337)------------------------------
% 3.47/1.45 % (1266337)------------------------------
% 3.47/1.45 % (1266327)Success in time 0.407 s
% 3.47/1.45 % Vampire exiting
%------------------------------------------------------------------------------