%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET797+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 : n008.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 3.79s 1.58s
% Output : Refutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 5 unt; 0 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 101 ( 34 ~; 29 |; 25 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-3 aty)
% Number of variables : 82 ( 70 !; 12 ?)
% 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(f22,conjecture,
! [X0,X1] :
( order(X0,X1)
=> ! [X2,X3] :
( ( subset(X2,X1)
& subset(X3,X1)
& subset(X2,X3) )
=> ! [X4] :
( upper_bound(X4,X0,X3)
=> upper_bound(X4,X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV9) ).
fof(f23,negated_conjecture,
~ ! [X0,X1] :
( order(X0,X1)
=> ! [X2,X3] :
( ( subset(X2,X1)
& subset(X3,X1)
& subset(X2,X3) )
=> ! [X4] :
( upper_bound(X4,X0,X3)
=> upper_bound(X4,X0,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f26,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f27,plain,
? [X0,X1] :
( ? [X2,X3] :
( ? [X4] :
( ~ upper_bound(X4,X0,X2)
& upper_bound(X4,X0,X3) )
& subset(X2,X1)
& subset(X3,X1)
& subset(X2,X3) )
& order(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f28,plain,
? [X0,X1] :
( ? [X2,X3] :
( ? [X4] :
( ~ upper_bound(X4,X0,X2)
& upper_bound(X4,X0,X3) )
& subset(X2,X1)
& subset(X3,X1)
& subset(X2,X3) )
& order(X0,X1) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f26]) ).
fof(f32,plain,
! [X0,X1,X2] :
( upper_bound(X2,X0,X1)
<=> ! [X3] :
( apply(X0,X3,X2)
| ~ member(X3,X1) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f33,plain,
( ~ upper_bound(sK4,sK0,sK2)
& upper_bound(sK4,sK0,sK3)
& subset(sK2,sK1)
& subset(sK3,sK1)
& subset(sK2,sK3)
& order(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f28]) ).
fof(f34,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,[],[f32]) ).
fof(f35,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,[],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( upper_bound(X2,X0,X1)
| ( ~ apply(X0,sK5(X0,X1,X2),X2)
& member(sK5(X0,X1,X2),X1) ) )
& ( ! [X4] :
( apply(X0,X4,X2)
| ~ member(X4,X1) )
| ~ upper_bound(X2,X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f35]) ).
fof(f38,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f33]) ).
fof(f41,plain,
upper_bound(sK4,sK0,sK3),
inference(cnf_transformation,[],[f33]) ).
fof(f42,plain,
~ upper_bound(sK4,sK0,sK2),
inference(cnf_transformation,[],[f33]) ).
fof(f43,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f47,plain,
! [X2,X0,X1,X4] :
( apply(X0,X4,X2)
| ~ member(X4,X1)
| ~ upper_bound(X2,X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f48,plain,
! [X2,X0,X1] :
( member(sK5(X0,X1,X2),X1)
| upper_bound(X2,X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ apply(X0,sK5(X0,X1,X2),X2)
| upper_bound(X2,X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f50,plain,
! [X2,X3,X0,X1] :
( ~ member(sK5(X1,X2,X0),X3)
| upper_bound(X0,X1,X2)
| ~ upper_bound(X0,X1,X3) ),
inference(resolution,[],[f49,f47]) ).
fof(f57,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(sK5(X1,X2,X0),X4)
| ~ upper_bound(X0,X1,X3)
| upper_bound(X0,X1,X2)
| ~ subset(X4,X3) ),
inference(resolution,[],[f50,f43]) ).
fof(f61,plain,
! [X2,X3,X0,X1] :
( ~ upper_bound(X0,X1,X2)
| upper_bound(X0,X1,X3)
| ~ subset(X3,X2)
| upper_bound(X0,X1,X3) ),
inference(resolution,[],[f57,f48]) ).
fof(f63,plain,
! [X2,X3,X0,X1] :
( upper_bound(X0,X1,X3)
| ~ upper_bound(X0,X1,X2)
| ~ subset(X3,X2) ),
inference(duplicate_literal_removal,[],[f61]) ).
fof(f64,plain,
! [X0] :
( ~ upper_bound(sK4,sK0,X0)
| ~ subset(sK2,X0) ),
inference(resolution,[],[f63,f42]) ).
fof(f67,plain,
~ subset(sK2,sK3),
inference(resolution,[],[f64,f41]) ).
fof(f69,plain,
$false,
inference(forward_subsumption_resolution,[],[f67,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET797+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.45 % Computer : n008.cluster.edu
% 0.12/0.45 % Model : x86_64 x86_64
% 0.12/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.45 % Memory : 8046.5625MB
% 0.12/0.45 % OS : Linux 6.8.0-71-generic
% 0.12/0.45 % CPULimit : 300
% 0.12/0.45 % WCLimit : 300
% 0.12/0.45 % DateTime : Mon Sep 28 02:50:55 UTC 2026
% 0.12/0.46 % CPUTime :
% 0.12/0.46 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.49 Running first-order theorem proving
% 0.16/0.49 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
% 3.79/1.58 % (1819146)Detected formulas, will run a generic FOF schedule.
% 3.79/1.58 % (1819154)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1467538691:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.79/1.58 % (1819154)Refutation not found, incomplete strategy
% 3.79/1.58 % (1819154)------------------------------
% 3.79/1.58 % (1819154)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.58 % (1819154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.58 % (1819154)CaDiCaL version: 2.1.3
% 3.79/1.58 % (1819154)Termination reason: Refutation not found, incomplete strategy
% 3.79/1.58 % (1819154)Time elapsed: 0.001 s
% 3.79/1.58 % (1819154)Peak memory usage: 88 MB
% 3.79/1.58 % (1819154)Instructions burned: 1 (million)
% 3.79/1.58 % (1819152)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=2171656470:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.79/1.58 % (1819153)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=656477497:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.79/1.58 % (1819151)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=2158275192:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.79/1.58 % (1819157)dis-21_1_sil=8000:lcm=predicate:random_seed=3496327874: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)
% 3.79/1.58 % (1819156)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2774457086:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.79/1.58 % (1819155)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1611396061:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.79/1.58 % (1819155)First to succeed.
% 3.79/1.58 % (1819157)Also succeeded, but the first one will report.
% 3.79/1.58 % (1819155)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1819146"
% 3.79/1.58 % (1819156)Also succeeded, but the first one will report.
% 3.79/1.58 % (1819154)------------------------------
% 3.79/1.58 % (1819154)------------------------------
% 3.79/1.58 % (1819165)lrs+10_1_sil=8000:sp=occurrence:random_seed=4278075229:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.79/1.58 % (1819165)Also succeeded, but the first one will report.
% 3.79/1.58 % (1819155)Refutation found. Thanks to Tanya!
% 3.79/1.58 % SZS status Theorem for theBenchmark
% 3.79/1.58 % SZS output start Proof for theBenchmark
% See solution above
% 3.79/1.58 % (1819155)------------------------------
% 3.79/1.58 % (1819155)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.58 % (1819155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.58 % (1819155)CaDiCaL version: 2.1.3
% 3.79/1.58 % (1819155)Termination reason: Refutation
% 3.79/1.58 % (1819155)Time elapsed: 0.003 s
% 3.79/1.58 % (1819155)Peak memory usage: 88 MB
% 3.79/1.58 % (1819155)Instructions burned: 2 (million)
% 3.79/1.58 % (1819155)------------------------------
% 3.79/1.58 % (1819155)------------------------------
% 3.79/1.58 % (1819146)Success in time 0.452 s
% 3.79/1.58 % Vampire exiting
%------------------------------------------------------------------------------