TSTP Solution File: NUM410+1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : NUM410+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 12:07:56 EDT 2023
% Result : Theorem 0.22s 0.43s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 10 unt; 0 def)
% Number of atoms : 87 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 94 ( 33 ~; 26 |; 22 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 24 (; 21 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f218,plain,
$false,
inference(subsumption_resolution,[],[f216,f129]) ).
fof(f129,plain,
~ transfinite_sequence_of(sK0,relation_rng(sK0)),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
( ~ transfinite_sequence_of(sK0,relation_rng(sK0))
& ordinal(relation_dom(sK0))
& function(sK0)
& relation(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f59,f89]) ).
fof(f89,plain,
( ? [X0] :
( ~ transfinite_sequence_of(X0,relation_rng(X0))
& ordinal(relation_dom(X0))
& function(X0)
& relation(X0) )
=> ( ~ transfinite_sequence_of(sK0,relation_rng(sK0))
& ordinal(relation_dom(sK0))
& function(sK0)
& relation(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
? [X0] :
( ~ transfinite_sequence_of(X0,relation_rng(X0))
& ordinal(relation_dom(X0))
& function(X0)
& relation(X0) ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
? [X0] :
( ~ transfinite_sequence_of(X0,relation_rng(X0))
& ordinal(relation_dom(X0))
& function(X0)
& relation(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( ordinal(relation_dom(X0))
=> transfinite_sequence_of(X0,relation_rng(X0)) ) ),
inference(negated_conjecture,[],[f40]) ).
fof(f40,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( ordinal(relation_dom(X0))
=> transfinite_sequence_of(X0,relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.azHYmW3pUt/Vampire---4.8_12131',t46_ordinal1) ).
fof(f216,plain,
transfinite_sequence_of(sK0,relation_rng(sK0)),
inference(unit_resulting_resolution,[],[f126,f127,f162,f213,f170]) ).
fof(f170,plain,
! [X0,X1] :
( transfinite_sequence_of(X1,X0)
| ~ subset(relation_rng(X1),X0)
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1] :
( ( ( transfinite_sequence_of(X1,X0)
| ~ subset(relation_rng(X1),X0) )
& ( subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0) ) )
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) )
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) )
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( transfinite_sequence(X1)
& function(X1)
& relation(X1) )
=> ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.azHYmW3pUt/Vampire---4.8_12131',d8_ordinal1) ).
fof(f213,plain,
transfinite_sequence(sK0),
inference(unit_resulting_resolution,[],[f126,f127,f128,f157]) ).
fof(f157,plain,
! [X0] :
( transfinite_sequence(X0)
| ~ ordinal(relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ( ( transfinite_sequence(X0)
| ~ ordinal(relation_dom(X0)) )
& ( ordinal(relation_dom(X0))
| ~ transfinite_sequence(X0) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0] :
( ( transfinite_sequence(X0)
<=> ordinal(relation_dom(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f73]) ).
fof(f73,plain,
! [X0] :
( ( transfinite_sequence(X0)
<=> ordinal(relation_dom(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( transfinite_sequence(X0)
<=> ordinal(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.azHYmW3pUt/Vampire---4.8_12131',d7_ordinal1) ).
fof(f128,plain,
ordinal(relation_dom(sK0)),
inference(cnf_transformation,[],[f90]) ).
fof(f162,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/tmp/tmp.azHYmW3pUt/Vampire---4.8_12131',reflexivity_r1_tarski) ).
fof(f127,plain,
function(sK0),
inference(cnf_transformation,[],[f90]) ).
fof(f126,plain,
relation(sK0),
inference(cnf_transformation,[],[f90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : NUM410+1 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n011.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 25 09:32:08 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.azHYmW3pUt/Vampire---4.8_12131
% 0.15/0.36 % (12259)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42 % (12276)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.22/0.42 % (12268)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.22/0.42 % (12272)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.22/0.42 % (12274)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.22/0.42 % (12267)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.22/0.42 % (12263)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.22/0.42 % (12277)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.22/0.43 % (12272)First to succeed.
% 0.22/0.43 % (12268)Also succeeded, but the first one will report.
% 0.22/0.43 % (12272)Refutation found. Thanks to Tanya!
% 0.22/0.43 % SZS status Theorem for Vampire---4
% 0.22/0.43 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.43 % (12272)------------------------------
% 0.22/0.43 % (12272)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.43 % (12272)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.43 % (12272)Termination reason: Refutation
% 0.22/0.43
% 0.22/0.43 % (12272)Memory used [KB]: 5500
% 0.22/0.43 % (12272)Time elapsed: 0.005 s
% 0.22/0.43 % (12272)------------------------------
% 0.22/0.43 % (12272)------------------------------
% 0.22/0.43 % (12259)Success in time 0.064 s
% 0.22/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------