%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET917+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 : n007.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 12:42:19 PM UTC 2026
% Result : Theorem 4.69s 1.83s
% Output : Refutation 4.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 7 unt; 0 def)
% Number of atoms : 29 ( 13 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 11 ~; 7 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f4,axiom,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f5,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_intersection2(X1,singleton(X0)) = singleton(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| set_intersection2(singleton(X0),X1) = singleton(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( disjoint(singleton(X0),X1)
| set_intersection2(singleton(X0),X1) = singleton(X0) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f13,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f14,plain,
! [X0,X1] :
( set_intersection2(X1,singleton(X0)) = singleton(X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f16,plain,
? [X0,X1] :
( ~ disjoint(singleton(X0),X1)
& singleton(X0) != set_intersection2(singleton(X0),X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f19,plain,
( ~ disjoint(singleton(sK2),sK3)
& singleton(sK2) != set_intersection2(singleton(sK2),sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f16]) ).
fof(f21,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f23,plain,
! [X0,X1] :
( in(X0,X1)
| disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f24,plain,
! [X0,X1] :
( ~ in(X0,X1)
| singleton(X0) = set_intersection2(X1,singleton(X0)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f28,plain,
singleton(sK2) != set_intersection2(singleton(sK2),sK3),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
~ disjoint(singleton(sK2),sK3),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
singleton(sK2) != set_intersection2(sK3,singleton(sK2)),
inference(superposition,[],[f28,f21]) ).
fof(f34,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| singleton(X0) = set_intersection2(X1,singleton(X0)) ),
inference(resolution,[],[f24,f23]) ).
fof(f36,plain,
singleton(sK2) = set_intersection2(sK3,singleton(sK2)),
inference(resolution,[],[f34,f29]) ).
fof(f38,plain,
$false,
inference(forward_subsumption_resolution,[],[f36,f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET917+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 % Computer : n007.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 28 03:07:56 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.49 Running first-order theorem proving
% 0.25/0.49 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
% 4.69/1.83 % (1989158)Detected formulas, will run a generic FOF schedule.
% 4.69/1.83 % (1989179)dis-21_1_sil=8000:lcm=predicate:random_seed=2533861412: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)
% 4.69/1.83 % (1989179)Refutation not found, incomplete strategy
% 4.69/1.83 % (1989179)------------------------------
% 4.69/1.83 % (1989179)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.83 % (1989179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.83 % (1989179)CaDiCaL version: 2.1.3
% 4.69/1.83 % (1989179)Termination reason: Refutation not found, incomplete strategy
% 4.69/1.83 % (1989179)Time elapsed: 0.001 s
% 4.69/1.83 % (1989179)Peak memory usage: 88 MB
% 4.69/1.83 % (1989178)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=710616150:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.69/1.83 % (1989178)First to succeed.
% 4.69/1.83 % (1989178)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1989158"
% 4.69/1.83 % (1989176)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1416396943:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.69/1.83 % (1989176)Refutation not found, incomplete strategy
% 4.69/1.83 % (1989176)------------------------------
% 4.69/1.83 % (1989176)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.83 % (1989176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.83 % (1989176)CaDiCaL version: 2.1.3
% 4.69/1.83 % (1989176)Termination reason: Refutation not found, incomplete strategy
% 4.69/1.83 % (1989176)Time elapsed: 0.002 s
% 4.69/1.83 % (1989176)Peak memory usage: 88 MB
% 4.69/1.83 % (1989175)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=3060652001:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.69/1.83 % (1989173)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=3066288576:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.69/1.83 % (1989174)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=819154358:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.69/1.83 % (1989177)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1908158277:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.69/1.83 % (1989177)Also succeeded, but the first one will report.
% 4.69/1.83 % (1989179)------------------------------
% 4.69/1.83 % (1989179)------------------------------
% 4.69/1.83 % (1989178)Refutation found. Thanks to Tanya!
% 4.69/1.83 % SZS status Theorem for theBenchmark
% 4.69/1.83 % SZS output start Proof for theBenchmark
% See solution above
% 4.69/1.83 % (1989178)------------------------------
% 4.69/1.83 % (1989178)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.83 % (1989178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.83 % (1989178)CaDiCaL version: 2.1.3
% 4.69/1.83 % (1989178)Termination reason: Refutation
% 4.69/1.83 % (1989178)Time elapsed: 0.003 s
% 4.69/1.83 % (1989178)Peak memory usage: 89 MB
% 4.69/1.83 % (1989178)Instructions burned: 1 (million)
% 4.69/1.83 % (1989178)------------------------------
% 4.69/1.83 % (1989178)------------------------------
% 4.69/1.83 % (1989158)Success in time 0.54 s
% 4.69/1.83 % Vampire exiting
%------------------------------------------------------------------------------