%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET637+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 : n009.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 12:41:29 PM UTC 2026
% Result : Theorem 2.76s 1.27s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 65 ( 7 unt; 2 def)
% Number of atoms : 187 ( 16 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 203 ( 81 ~; 88 |; 24 &)
% ( 9 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 80 !; 9 ?)
% 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] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f5,axiom,
! [X0,X1] :
( not_equal(X0,X1)
<=> X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_equal_defn) ).
fof(f9,conjecture,
! [X0,X1] :
( intersect(X0,X1)
<=> not_equal(intersection(X0,X1),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th119) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( intersect(X0,X1)
<=> not_equal(intersection(X0,X1),empty_set) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f12,plain,
? [X0,X1] :
( intersect(X0,X1)
<~> not_equal(intersection(X0,X1),empty_set) ),
inference(ennf_transformation,[],[f10]) ).
fof(f13,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(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(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& member(X2,X1) )
| ~ intersect(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f16,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ? [X3] :
( member(X3,X0)
& member(X3,X1) )
| ~ intersect(X0,X1) ) ),
inference(rectify,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ( member(sK0(X0,X1),X0)
& member(sK0(X0,X1),X1) )
| ~ intersect(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X2] :
( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f19,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(rectify,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( X0 = X1
| ( ( ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) )
& ( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( not_equal(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ not_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f22,plain,
? [X0,X1] :
( ( ~ not_equal(intersection(X0,X1),empty_set)
| ~ intersect(X0,X1) )
& ( not_equal(intersection(X0,X1),empty_set)
| intersect(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f23,plain,
( ( ~ not_equal(intersection(sK2,sK3),empty_set)
| ~ intersect(sK2,sK3) )
& ( not_equal(intersection(sK2,sK3),empty_set)
| intersect(sK2,sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f22]) ).
fof(f24,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,intersection(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| intersect(X0,X1)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f30,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f33,plain,
! [X0,X1] :
( member(sK1(X0,X1),X1)
| X0 = X1
| member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f35,plain,
! [X0,X1] :
( X0 != X1
| ~ not_equal(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
! [X0,X1] :
( not_equal(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
( not_equal(intersection(sK2,sK3),empty_set)
| intersect(sK2,sK3) ),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
( ~ not_equal(intersection(sK2,sK3),empty_set)
| ~ intersect(sK2,sK3) ),
inference(cnf_transformation,[],[f23]) ).
fof(f43,plain,
! [X1] : ~ not_equal(X1,X1),
inference(equality_resolution,[],[f35]) ).
fof(f45,definition,
( spl4_1
<=> intersect(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f46,plain,
( ~ intersect(sK2,sK3)
| spl4_1 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f47,plain,
( intersect(sK2,sK3)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f49,definition,
( spl4_2
<=> not_equal(intersection(sK2,sK3),empty_set) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f50,plain,
( ~ not_equal(intersection(sK2,sK3),empty_set)
| spl4_2 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f51,plain,
( not_equal(intersection(sK2,sK3),empty_set)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f52,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f39,f49,f45]) ).
fof(f53,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f40,f49,f45]) ).
fof(f65,plain,
! [X2,X3,X0,X1] :
( ~ member(X2,X1)
| intersect(X0,X1)
| ~ member(X2,intersection(X0,X3)) ),
inference(resolution,[],[f29,f25]) ).
fof(f88,plain,
! [X2,X3,X0,X1,X4] :
( intersect(X0,X1)
| ~ member(X2,intersection(X0,X3))
| ~ member(X2,intersection(X4,X1)) ),
inference(resolution,[],[f65,f24]) ).
fof(f105,plain,
! [X0] :
( member(sK1(X0,empty_set),X0)
| empty_set = X0 ),
inference(resolution,[],[f33,f30]) ).
fof(f246,plain,
( ! [X2,X0,X1] :
( ~ member(X0,intersection(sK2,X1))
| ~ member(X0,intersection(X2,sK3)) )
| spl4_1 ),
inference(resolution,[],[f88,f46]) ).
fof(f254,plain,
( ! [X0] : ~ member(X0,intersection(sK2,sK3))
| spl4_1 ),
inference(factoring,[],[f246]) ).
fof(f265,plain,
( empty_set = intersection(sK2,sK3)
| spl4_1 ),
inference(resolution,[],[f254,f105]) ).
fof(f271,plain,
( not_equal(empty_set,empty_set)
| spl4_1
| ~ spl4_2 ),
inference(superposition,[],[f51,f265]) ).
fof(f279,plain,
( $false
| spl4_1
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f271,f43]) ).
fof(f280,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f279]) ).
fof(f281,plain,
( member(sK0(sK2,sK3),sK2)
| ~ spl4_1 ),
inference(resolution,[],[f47,f28]) ).
fof(f282,plain,
( member(sK0(sK2,sK3),sK3)
| ~ spl4_1 ),
inference(resolution,[],[f47,f27]) ).
fof(f287,plain,
( empty_set = intersection(sK2,sK3)
| spl4_2 ),
inference(resolution,[],[f50,f36]) ).
fof(f288,plain,
( ! [X0] :
( ~ member(sK0(sK2,sK3),X0)
| member(sK0(sK2,sK3),intersection(sK2,X0)) )
| ~ spl4_1 ),
inference(resolution,[],[f281,f26]) ).
fof(f426,plain,
( member(sK0(sK2,sK3),intersection(sK2,sK3))
| ~ spl4_1 ),
inference(resolution,[],[f288,f282]) ).
fof(f427,plain,
( member(sK0(sK2,sK3),empty_set)
| ~ spl4_1
| spl4_2 ),
inference(forward_demodulation,[],[f426,f287]) ).
fof(f428,plain,
( $false
| ~ spl4_1
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f427,f30]) ).
fof(f429,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_contradiction_clause,[],[f428]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f52]) ).
cnf(s2,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f53]) ).
cnf(s3,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f280]) ).
cnf(s4,plain,
( ~ spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f429]) ).
cnf(s5,plain,
spl4_1,
inference(rat,[],[s1,s3]) ).
cnf(s6,plain,
spl4_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6,s5]) ).
fof(f430,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET637+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n009.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 02:23:30 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
% 2.76/1.27 % (2608797)Detected formulas, will run a generic FOF schedule.
% 2.76/1.27 % (2608803)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=365649235:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.76/1.27 % (2608805)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=296688955:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.76/1.27 % (2608804)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=30364144:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.76/1.27 % (2608808)dis-21_1_sil=8000:lcm=predicate:random_seed=1987608964: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)
% 2.76/1.27 % (2608802)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=2376997805:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.76/1.27 % (2608806)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1102169415:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.76/1.27 % (2608807)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3210405924:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.76/1.27 % (2608805)Refutation not found, incomplete strategy
% 2.76/1.27 % (2608805)------------------------------
% 2.76/1.27 % (2608805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.27 % (2608805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.27 % (2608805)CaDiCaL version: 2.1.3
% 2.76/1.27 % (2608805)Termination reason: Refutation not found, incomplete strategy
% 2.76/1.27 % (2608805)Time elapsed: 0.002 s
% 2.76/1.27 % (2608805)Peak memory usage: 88 MB
% 2.76/1.27 % (2608807)First to succeed.
% 2.76/1.27 % (2608807)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2608797"
% 2.76/1.27 % (2608806)Also succeeded, but the first one will report.
% 2.76/1.27 % (2608808)Instruction limit reached!
% 2.76/1.27 % (2608808)------------------------------
% 2.76/1.27 % (2608808)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.27 % (2608808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.27 % (2608808)CaDiCaL version: 2.1.3
% 2.76/1.27 % (2608808)Termination reason: Instruction limit
% 2.76/1.27 % (2608808)Termination phase: Saturation
% 2.76/1.27 % (2608808)Time elapsed: 0.072 s
% 2.76/1.27 % (2608808)Peak memory usage: 89 MB
% 2.76/1.27 % (2608808)Instructions burned: 129 (million)
% 2.76/1.27 % (2608816)lrs+10_1_sil=8000:sp=occurrence:random_seed=4046865425:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.76/1.27 % (2608816)Also succeeded, but the first one will report.
% 2.76/1.27 % (2608805)------------------------------
% 2.76/1.27 % (2608805)------------------------------
% 2.76/1.27 % (2608807)Refutation found. Thanks to Tanya!
% 2.76/1.27 % SZS status Theorem for theBenchmark
% 2.76/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.46/1.37 % (2608807)------------------------------
% 3.46/1.37 % (2608807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.37 % (2608807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.37 % (2608807)CaDiCaL version: 2.1.3
% 3.46/1.37 % (2608807)Termination reason: Refutation
% 3.46/1.37 % (2608807)Time elapsed: 0.013 s
% 3.46/1.37 % (2608807)Peak memory usage: 90 MB
% 3.46/1.37 % (2608807)Instructions burned: 16 (million)
% 3.46/1.37 % (2608807)------------------------------
% 3.46/1.37 % (2608807)------------------------------
% 3.46/1.37 % (2608797)Success in time 0.422 s
% 3.46/1.37 % Vampire exiting
%------------------------------------------------------------------------------