%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET799+4 : 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 : n019.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 12:41:57 PM UTC 2026
% Result : Theorem 2.67s 1.35s
% Output : Refutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 115 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 118 ( 35 ~; 26 |; 40 &)
% ( 4 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-3 aty)
% Number of variables : 92 ( 78 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f14,axiom,
! [X0,X1,X2] :
( upper_bound(X2,X0,X1)
<=> ! [X3] :
( member(X3,X1)
=> apply(X0,X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upper_bound) ).
fof(f20,axiom,
! [X0,X1,X2,X3] :
( least_upper_bound(X0,X1,X2,X3)
<=> ( member(X0,X1)
& upper_bound(X0,X2,X1)
& ! [X4] :
( ( member(X4,X3)
& upper_bound(X4,X2,X1) )
=> apply(X2,X0,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',least_upper_bound) ).
fof(f22,conjecture,
! [X0,X1] :
( order(X0,X1)
=> ! [X2,X3] :
( ( subset(X2,X1)
& subset(X3,X1)
& subset(X2,X3) )
=> ! [X4,X5] :
( ( least_upper_bound(X4,X2,X0,X1)
& least_upper_bound(X5,X3,X0,X1) )
=> apply(X0,X4,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV11) ).
fof(f23,negated_conjecture,
~ ! [X0,X1] :
( order(X0,X1)
=> ! [X2,X3] :
( ( subset(X2,X1)
& subset(X3,X1)
& subset(X2,X3) )
=> ! [X4,X5] :
( ( least_upper_bound(X4,X2,X0,X1)
& least_upper_bound(X5,X3,X0,X1) )
=> apply(X0,X4,X5) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( least_upper_bound(X0,X1,X2,X3)
=> ( member(X0,X1)
& upper_bound(X0,X2,X1)
& ! [X4] :
( ( member(X4,X3)
& upper_bound(X4,X2,X1) )
=> apply(X2,X0,X4) ) ) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f27,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f28,plain,
? [X0,X1] :
( ? [X2,X3] :
( ? [X4,X5] :
( ~ apply(X0,X4,X5)
& least_upper_bound(X4,X2,X0,X1)
& least_upper_bound(X5,X3,X0,X1) )
& subset(X2,X1)
& subset(X3,X1)
& subset(X2,X3) )
& order(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f29,plain,
? [X0,X1] :
( ? [X2,X3] :
( ? [X4,X5] :
( ~ apply(X0,X4,X5)
& least_upper_bound(X4,X2,X0,X1)
& least_upper_bound(X5,X3,X0,X1) )
& subset(X2,X1)
& subset(X3,X1)
& subset(X2,X3) )
& order(X0,X1) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( ( member(X0,X1)
& upper_bound(X0,X2,X1)
& ! [X4] :
( apply(X2,X0,X4)
| ~ member(X4,X3)
| ~ upper_bound(X4,X2,X1) ) )
| ~ least_upper_bound(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f25]) ).
fof(f34,plain,
! [X0,X1,X2,X3] :
( ( member(X0,X1)
& upper_bound(X0,X2,X1)
& ! [X4] :
( apply(X2,X0,X4)
| ~ member(X4,X3)
| ~ upper_bound(X4,X2,X1) ) )
| ~ least_upper_bound(X0,X1,X2,X3) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( upper_bound(X2,X0,X1)
<=> ! [X3] :
( apply(X0,X3,X2)
| ~ member(X3,X1) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f36,plain,
( ~ apply(sK0,sK4,sK5)
& least_upper_bound(sK4,sK2,sK0,sK1)
& least_upper_bound(sK5,sK3,sK0,sK1)
& subset(sK2,sK1)
& subset(sK3,sK1)
& subset(sK2,sK3)
& order(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f29]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( upper_bound(X2,X0,X1)
| ? [X3] :
( ~ apply(X0,X3,X2)
& member(X3,X1) ) )
& ( ! [X3] :
( apply(X0,X3,X2)
| ~ member(X3,X1) )
| ~ upper_bound(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( upper_bound(X2,X0,X1)
| ? [X3] :
( ~ apply(X0,X3,X2)
& member(X3,X1) ) )
& ( ! [X4] :
( apply(X0,X4,X2)
| ~ member(X4,X1) )
| ~ upper_bound(X2,X0,X1) ) ),
inference(rectify,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( upper_bound(X2,X0,X1)
| ( ~ apply(X0,sK6(X0,X1,X2),X2)
& member(sK6(X0,X1,X2),X1) ) )
& ( ! [X4] :
( apply(X0,X4,X2)
| ~ member(X4,X1) )
| ~ upper_bound(X2,X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X3,sK6(X0,X1,X2))],[f38]) ).
fof(f41,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f36]) ).
fof(f44,plain,
least_upper_bound(sK5,sK3,sK0,sK1),
inference(cnf_transformation,[],[f36]) ).
fof(f45,plain,
least_upper_bound(sK4,sK2,sK0,sK1),
inference(cnf_transformation,[],[f36]) ).
fof(f46,plain,
~ apply(sK0,sK4,sK5),
inference(cnf_transformation,[],[f36]) ).
fof(f47,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f52,plain,
! [X2,X3,X0,X1] :
( ~ least_upper_bound(X0,X1,X2,X3)
| upper_bound(X0,X2,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( ~ least_upper_bound(X0,X1,X2,X3)
| member(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f54,plain,
! [X2,X0,X1,X4] :
( apply(X0,X4,X2)
| ~ member(X4,X1)
| ~ upper_bound(X2,X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f58,plain,
member(sK4,sK2),
inference(resolution,[],[f53,f45]) ).
fof(f59,plain,
upper_bound(sK5,sK0,sK3),
inference(resolution,[],[f52,f44]) ).
fof(f61,plain,
! [X0] :
( ~ upper_bound(sK5,sK0,X0)
| ~ member(sK4,X0) ),
inference(resolution,[],[f54,f46]) ).
fof(f62,plain,
~ member(sK4,sK3),
inference(resolution,[],[f61,f59]) ).
fof(f64,plain,
! [X0] :
( ~ member(sK4,X0)
| ~ subset(X0,sK3) ),
inference(resolution,[],[f62,f47]) ).
fof(f65,plain,
~ subset(sK2,sK3),
inference(resolution,[],[f64,f58]) ).
fof(f67,plain,
$false,
inference(forward_subsumption_resolution,[],[f65,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET799+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 02:50:04 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.67/1.35 % (3616665)Detected formulas, will run a generic FOF schedule.
% 2.67/1.35 % (3616674)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1676525214:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.67/1.35 % (3616674)First to succeed.
% 2.67/1.35 % (3616674)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3616665"
% 2.67/1.35 % (3616670)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=3990651222:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.67/1.35 % (3616671)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=946361164:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.67/1.35 % (3616672)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=4090806354:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.67/1.35 % (3616673)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1876001922:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.67/1.35 % (3616673)Refutation not found, incomplete strategy
% 2.67/1.35 % (3616673)------------------------------
% 2.67/1.35 % (3616673)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.35 % (3616673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.35 % (3616673)CaDiCaL version: 2.1.3
% 2.67/1.35 % (3616673)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.35 % (3616673)Time elapsed: 0.003 s
% 2.67/1.35 % (3616673)Peak memory usage: 88 MB
% 2.67/1.35 % (3616673)Instructions burned: 1 (million)
% 2.67/1.35 % (3616676)dis-21_1_sil=8000:lcm=predicate:random_seed=1136995837: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)
% 2.67/1.35 % (3616675)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3415354492:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.67/1.35 % (3616676)Also succeeded, but the first one will report.
% 2.67/1.35 % (3616675)Also succeeded, but the first one will report.
% 2.67/1.35 % (3616674)Refutation found. Thanks to Tanya!
% 2.67/1.35 % SZS status Theorem for theBenchmark
% 2.67/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.67/1.35 % (3616674)------------------------------
% 2.67/1.35 % (3616674)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.35 % (3616674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.35 % (3616674)CaDiCaL version: 2.1.3
% 2.67/1.35 % (3616674)Termination reason: Refutation
% 2.67/1.35 % (3616674)Time elapsed: 0.002 s
% 2.67/1.35 % (3616674)Peak memory usage: 88 MB
% 2.67/1.35 % (3616674)Instructions burned: 2 (million)
% 2.67/1.35 % (3616674)------------------------------
% 2.67/1.35 % (3616674)------------------------------
% 2.67/1.35 % (3616665)Success in time 0.29 s
% 2.67/1.35 % Vampire exiting
%------------------------------------------------------------------------------