%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET581+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:41:12 PM UTC 2026
% Result : Theorem 2.68s 1.31s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 54 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 53 ( 22 ~; 13 |; 13 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 30 !; 6 ?)
% 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] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f4,axiom,
! [X0,X1] :
( not_equal(X0,X1)
<=> X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_equal_defn) ).
fof(f7,conjecture,
! [X0,X1,X2] :
( ( member(X0,X1)
& member(X0,X2) )
=> not_equal(intersection(X1,X2),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th24) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2] :
( ( member(X0,X1)
& member(X0,X2) )
=> not_equal(intersection(X1,X2),empty_set) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( X0 != X1
=> not_equal(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f10,plain,
? [X0,X1,X2] :
( ~ not_equal(intersection(X1,X2),empty_set)
& member(X0,X1)
& member(X0,X2) ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,plain,
? [X0,X1,X2] :
( ~ not_equal(intersection(X1,X2),empty_set)
& member(X0,X1)
& member(X0,X2) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( not_equal(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f9]) ).
fof(f13,plain,
( ~ not_equal(intersection(sK1,sK2),empty_set)
& member(sK0,sK1)
& member(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f11]) ).
fof(f14,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(f15,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,[],[f14]) ).
fof(f19,plain,
member(sK0,sK2),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
member(sK0,sK1),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
~ not_equal(intersection(sK1,sK2),empty_set),
inference(cnf_transformation,[],[f13]) ).
fof(f25,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X0,X1] :
( not_equal(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f12]) ).
fof(f34,plain,
empty_set = intersection(sK1,sK2),
inference(resolution,[],[f27,f21]) ).
fof(f45,plain,
! [X0] :
( member(X0,empty_set)
| ~ member(X0,sK1)
| ~ member(X0,sK2) ),
inference(superposition,[],[f25,f34]) ).
fof(f48,plain,
! [X0] :
( ~ member(X0,sK2)
| ~ member(X0,sK1) ),
inference(forward_subsumption_resolution,[],[f45,f26]) ).
fof(f49,plain,
~ member(sK0,sK1),
inference(resolution,[],[f48,f19]) ).
fof(f50,plain,
$false,
inference(forward_subsumption_resolution,[],[f49,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET581+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 02:12:52 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 Running first-order theorem proving
% 0.11/0.39 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
% 2.68/1.31 % (4079765)Detected formulas, will run a generic FOF schedule.
% 2.68/1.31 % (4079774)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=528770898:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.31 % (4079774)First to succeed.
% 2.68/1.31 % (4079774)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4079765"
% 2.68/1.31 % (4079770)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=470944888:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.31 % (4079776)dis-21_1_sil=8000:lcm=predicate:random_seed=3828671135: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)
% 2.68/1.31 % (4079775)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4093584535:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.31 % (4079771)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=1506762283:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.31 % (4079772)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=4092458157:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.31 % (4079773)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2822526322:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.31 % (4079776)Refutation not found, incomplete strategy
% 2.68/1.31 % (4079776)------------------------------
% 2.68/1.31 % (4079776)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.31 % (4079776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.31 % (4079776)CaDiCaL version: 2.1.3
% 2.68/1.31 % (4079776)Termination reason: Refutation not found, incomplete strategy
% 2.68/1.31 % (4079776)Time elapsed: 0.001 s
% 2.68/1.31 % (4079776)Peak memory usage: 88 MB
% 2.68/1.31 % (4079773)Also succeeded, but the first one will report.
% 2.68/1.31 % (4079775)Also succeeded, but the first one will report.
% 2.68/1.31 % (4079774)Refutation found. Thanks to Tanya!
% 2.68/1.31 % SZS status Theorem for theBenchmark
% 2.68/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.31 % (4079774)------------------------------
% 2.68/1.31 % (4079774)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.31 % (4079774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.31 % (4079774)CaDiCaL version: 2.1.3
% 2.68/1.31 % (4079774)Termination reason: Refutation
% 2.68/1.31 % (4079774)Time elapsed: 0.002 s
% 2.68/1.31 % (4079774)Peak memory usage: 88 MB
% 2.68/1.31 % (4079774)Instructions burned: 1 (million)
% 2.68/1.31 % (4079774)------------------------------
% 2.68/1.31 % (4079774)------------------------------
% 2.68/1.31 % (4079765)Success in time 0.294 s
% 2.68/1.31 % Vampire exiting
%------------------------------------------------------------------------------