%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET196+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:43:25 PM UTC 2026
% Result : Theorem 0.11s 0.47s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 56 ( 22 ~; 19 |; 11 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 35 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f6,conjecture,
! [X0,X1] : subset(intersection(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_is_subset) ).
fof(f7,negated_conjecture,
~ ! [X0,X1] : subset(intersection(X0,X1),X0),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
? [X0,X1] : ~ subset(intersection(X0,X1),X0),
inference(ennf_transformation,[],[f7]) ).
fof(f10,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) )
& ( ( member(X2,X0)
& member(X2,X1) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) )
& ( ( member(X2,X0)
& member(X2,X1) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f13,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f13]) ).
fof(f18,plain,
~ subset(intersection(sK2,sK3),sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f9]) ).
fof(f20,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f24,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f31,plain,
~ subset(intersection(sK2,sK3),sK2),
inference(cnf_transformation,[],[f18]) ).
fof(f36,plain,
member(sK0(intersection(sK2,sK3),sK2),intersection(sK2,sK3)),
inference(resolution,[],[f23,f31]) ).
fof(f37,plain,
member(sK0(intersection(sK2,sK3),sK2),sK2),
inference(resolution,[],[f36,f20]) ).
fof(f39,plain,
subset(intersection(sK2,sK3),sK2),
inference(resolution,[],[f37,f24]) ).
fof(f40,plain,
$false,
inference(forward_subsumption_resolution,[],[f39,f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET196+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n010.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 01:04:17 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.47 % (1471259)Will run a generic schedule for satisfiability detection.
% 0.11/0.47 % (1471264)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=355736039_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.47 % TRYING [1]
% 0.11/0.47 % TRYING [2]
% 0.11/0.47 % TRYING [3]
% 0.11/0.47 % TRYING [4]
% 0.11/0.47 % TRYING [5]
% 0.11/0.47 % (1471265)% WARNING: option uhcvi not known.
% 0.11/0.47 % TRYING [6]
% 0.11/0.47 % (1471265)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=754500820:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.47 % (1471266)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1442622693:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.47 % (1471267)dis+10_1_sil=32000:sp=arity:random_seed=3375184056:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.47 % (1471269)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2034402948:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.47 % (1471268)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2924064457:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.47 % (1471270)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2252351320:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.47 % TRYING [7]
% 0.11/0.47 % (1471269) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1471259-1471269"...
% 0.11/0.47 % (1471267) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1471259-1471267"...
% 0.11/0.47 % (1471268) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1471259-1471268"...
% 0.11/0.47 % (1471270) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1471259-1471270"...
% 0.11/0.47 % (1471266) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1471259-1471266"...
% 0.11/0.47 % (1471269)...printing done.
% 0.11/0.47 % (1471268)...printing done.
% 0.11/0.47 % (1471267)...printing done.
% 0.11/0.47 % (1471270)...printing done.
% 0.11/0.47 % (1471265) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1471259-1471265"...
% 0.11/0.47 % (1471269)Refutation found. Thanks to Tanya!
% 0.11/0.47 % SZS status Theorem for theBenchmark
% 0.11/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.47 % (1471269)------------------------------
% 0.11/0.47 % (1471269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.47 % (1471269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.47 % (1471269)CaDiCaL version: 2.1.3
% 0.11/0.47 % (1471269)Termination reason: Refutation
% 0.11/0.47 % (1471269)Time elapsed: 0.002 s
% 0.11/0.47 % (1471269)Peak memory usage: 11 MB
% 0.11/0.47 % (1471269)Instructions burned: 1 (million)
% 0.11/0.47 % (1471259)Success in time 0.039 s
% 0.11/0.47 % Vampire exiting
%------------------------------------------------------------------------------