%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET008+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 12:39:28 PM UTC 2026
% Result : Theorem 2.60s 1.37s
% Output : Refutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 14 unt; 0 def)
% Number of atoms : 96 ( 25 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 104 ( 41 ~; 40 |; 19 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 69 ( 65 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( member(X2,X0)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f5,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f9,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f10,conjecture,
! [X0,X1] : intersection(difference(X0,X1),X1) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_difference_empty_set) ).
fof(f11,negated_conjecture,
~ ! [X0,X1] : intersection(difference(X0,X1),X1) = empty_set,
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,plain,
? [X0,X1] : empty_set != intersection(difference(X0,X1),X1),
inference(ennf_transformation,[],[f11]) ).
fof(f13,plain,
empty_set != intersection(difference(sK0,sK1),sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12]) ).
fof(f14,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,[],[f9]) ).
fof(f15,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,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ( X0 = X1
| ( ( ~ member(sK2(X0,X1),X1)
| ~ member(sK2(X0,X1),X0) )
& ( member(sK2(X0,X1),X1)
| member(sK2(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,[sK2]),skolemize(X2,sK2(X0,X1))],[f15]) ).
fof(f17,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(f18,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,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
empty_set != intersection(difference(sK0,sK1),sK1),
inference(cnf_transformation,[],[f13]) ).
fof(f24,plain,
! [X0,X1] :
( member(sK2(X0,X1),X1)
| X0 = X1
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f26,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f33,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f36,plain,
empty_set != intersection(sK1,difference(sK0,sK1)),
inference(superposition,[],[f21,f26]) ).
fof(f48,plain,
! [X0] :
( member(sK2(X0,empty_set),X0)
| empty_set = X0 ),
inference(resolution,[],[f24,f33]) ).
fof(f54,plain,
! [X0,X1] :
( member(sK2(intersection(X0,X1),empty_set),X0)
| intersection(X0,X1) = empty_set ),
inference(resolution,[],[f48,f28]) ).
fof(f55,plain,
! [X0,X1] :
( member(sK2(intersection(X0,X1),empty_set),X1)
| intersection(X0,X1) = empty_set ),
inference(resolution,[],[f48,f27]) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ member(sK2(intersection(difference(X0,X1),X2),empty_set),X1)
| empty_set = intersection(difference(X0,X1),X2) ),
inference(resolution,[],[f54,f30]) ).
fof(f348,plain,
! [X0,X1] :
( empty_set = intersection(difference(X0,X1),X1)
| empty_set = intersection(difference(X0,X1),X1) ),
inference(resolution,[],[f62,f55]) ).
fof(f359,plain,
! [X0,X1] : empty_set = intersection(difference(X0,X1),X1),
inference(duplicate_literal_removal,[],[f348]) ).
fof(f361,plain,
! [X0,X1] : empty_set = intersection(X1,difference(X0,X1)),
inference(forward_demodulation,[],[f359,f26]) ).
fof(f379,plain,
empty_set != empty_set,
inference(superposition,[],[f36,f361]) ).
fof(f380,plain,
$false,
inference(trivial_inequality_removal,[],[f379]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET008+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n016.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 00:07:48 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.60/1.37 % (3134492)Detected formulas, will run a generic FOF schedule.
% 2.60/1.37 % (3134571)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=69070510:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.60/1.37 % (3134571)First to succeed.
% 2.60/1.37 % (3134571)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3134492"
% 2.60/1.37 % (3134574)dis-21_1_sil=8000:lcm=predicate:random_seed=2575150428: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)
% 2.60/1.37 % (3134567)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=158296279:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.60/1.37 % (3134566)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=2933557324:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.60/1.37 % (3134569)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=1095519019:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.60/1.37 % (3134574)Also succeeded, but the first one will report.
% 2.60/1.37 % (3134573)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1424021418:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.60/1.37 % (3134570)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=802252522:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.60/1.37 % (3134570)Refutation not found, incomplete strategy
% 2.60/1.37 % (3134570)------------------------------
% 2.60/1.37 % (3134570)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.37 % (3134570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.37 % (3134570)CaDiCaL version: 2.1.3
% 2.60/1.37 % (3134570)Termination reason: Refutation not found, incomplete strategy
% 2.60/1.37 % (3134570)Time elapsed: 0.002 s
% 2.60/1.37 % (3134570)Peak memory usage: 88 MB
% 2.60/1.37 % (3134573)Instruction limit reached!
% 2.60/1.37 % (3134573)------------------------------
% 2.60/1.37 % (3134573)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.37 % (3134573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.37 % (3134573)CaDiCaL version: 2.1.3
% 2.60/1.37 % (3134573)Termination reason: Instruction limit
% 2.60/1.37 % (3134573)Termination phase: Saturation
% 2.60/1.37 % (3134573)Time elapsed: 0.091 s
% 2.60/1.37 % (3134573)Peak memory usage: 89 MB
% 2.60/1.37 % (3134573)Instructions burned: 139 (million)
% 2.60/1.37 % (3134571)Refutation found. Thanks to Tanya!
% 2.60/1.37 % SZS status Theorem for theBenchmark
% 2.60/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.60/1.37 % (3134571)------------------------------
% 2.60/1.37 % (3134571)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.37 % (3134571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.37 % (3134571)CaDiCaL version: 2.1.3
% 2.60/1.37 % (3134571)Termination reason: Refutation
% 2.60/1.37 % (3134571)Time elapsed: 0.006 s
% 2.60/1.37 % (3134571)Peak memory usage: 88 MB
% 2.60/1.37 % (3134571)Instructions burned: 13 (million)
% 2.60/1.37 % (3134571)------------------------------
% 2.60/1.37 % (3134571)------------------------------
% 2.60/1.37 % (3134492)Success in time 0.298 s
% 2.60/1.37 % Vampire exiting
%------------------------------------------------------------------------------