%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET638+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 : n002.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 12:41:30 PM UTC 2026
% Result : Theorem 3.42s 1.23s
% Output : Refutation 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 18 unt; 0 def)
% Number of atoms : 39 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 7 ~; 2 |; 8 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 38 ( 32 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : subset(intersection(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_is_subset) ).
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
=> intersection(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_intersection) ).
fof(f3,axiom,
! [X0] : union(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_empty_set) ).
fof(f4,axiom,
! [X0,X1,X2] : intersection(X0,union(X1,X2)) = union(intersection(X0,X1),intersection(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_distributes_over_union) ).
fof(f11,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f15,conjecture,
! [X0,X1,X2] :
( ( subset(X0,union(X1,X2))
& intersection(X0,X2) = empty_set )
=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th120) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X0,union(X1,X2))
& intersection(X0,X2) = empty_set )
=> subset(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( intersection(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f19,plain,
? [X0,X1,X2] :
( ~ subset(X0,X1)
& subset(X0,union(X1,X2))
& intersection(X0,X2) = empty_set ),
inference(ennf_transformation,[],[f16]) ).
fof(f20,plain,
? [X0,X1,X2] :
( ~ subset(X0,X1)
& subset(X0,union(X1,X2))
& intersection(X0,X2) = empty_set ),
inference(flattening,[],[f19]) ).
fof(f33,plain,
( ~ subset(sK2,sK3)
& subset(sK2,union(sK3,sK4))
& empty_set = intersection(sK2,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f20]) ).
fof(f34,plain,
! [X0,X1] : subset(intersection(X0,X1),X0),
inference(cnf_transformation,[],[f1]) ).
fof(f35,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| intersection(X0,X1) = X0 ),
inference(cnf_transformation,[],[f17]) ).
fof(f36,plain,
! [X0] : union(X0,empty_set) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f37,plain,
! [X2,X0,X1] : intersection(X0,union(X1,X2)) = union(intersection(X0,X1),intersection(X0,X2)),
inference(cnf_transformation,[],[f4]) ).
fof(f52,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f58,plain,
empty_set = intersection(sK2,sK4),
inference(cnf_transformation,[],[f33]) ).
fof(f59,plain,
subset(sK2,union(sK3,sK4)),
inference(cnf_transformation,[],[f33]) ).
fof(f60,plain,
~ subset(sK2,sK3),
inference(cnf_transformation,[],[f33]) ).
fof(f70,plain,
! [X0,X1] : subset(intersection(X0,X1),X1),
inference(superposition,[],[f34,f52]) ).
fof(f79,plain,
sK2 = intersection(sK2,union(sK3,sK4)),
inference(resolution,[],[f35,f59]) ).
fof(f156,plain,
! [X0] : intersection(sK2,union(X0,sK4)) = union(intersection(sK2,X0),empty_set),
inference(superposition,[],[f37,f58]) ).
fof(f167,plain,
! [X0] : intersection(sK2,X0) = intersection(sK2,union(X0,sK4)),
inference(forward_demodulation,[],[f156,f36]) ).
fof(f190,plain,
sK2 = intersection(sK2,sK3),
inference(superposition,[],[f167,f79]) ).
fof(f219,plain,
subset(sK2,sK3),
inference(superposition,[],[f70,f190]) ).
fof(f223,plain,
$false,
inference(forward_subsumption_resolution,[],[f219,f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET638+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 02:26:21 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.42/1.23 % (4095797)Detected formulas, will run a generic FOF schedule.
% 3.42/1.23 % (4095804)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=3883032188:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.42/1.23 % (4095807)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4071634618:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.42/1.23 % (4095805)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3915982999:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.42/1.23 % (4095808)dis-21_1_sil=8000:lcm=predicate:random_seed=611084601: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)
% 3.42/1.23 % (4095803)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=1002973155:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.42/1.23 % (4095806)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1546319797:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.42/1.23 % (4095802)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=2241778806:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.42/1.23 % (4095807)First to succeed.
% 3.42/1.23 % (4095807)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4095797"
% 3.42/1.23 % (4095805)Also succeeded, but the first one will report.
% 3.42/1.23 % (4095806)Also succeeded, but the first one will report.
% 3.42/1.23 % (4095808)Instruction limit reached!
% 3.42/1.23 % (4095808)------------------------------
% 3.42/1.23 % (4095808)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.23 % (4095808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.23 % (4095808)CaDiCaL version: 2.1.3
% 3.42/1.23 % (4095808)Termination reason: Instruction limit
% 3.42/1.23 % (4095808)Termination phase: Saturation
% 3.42/1.23 % (4095808)Time elapsed: 0.077 s
% 3.42/1.23 % (4095808)Peak memory usage: 89 MB
% 3.42/1.23 % (4095808)Instructions burned: 130 (million)
% 3.42/1.23 % (4095816)lrs+10_1_sil=8000:sp=occurrence:random_seed=3550335180:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.42/1.23 % (4095816)Also succeeded, but the first one will report.
% 3.42/1.23 % (4095807)Refutation found. Thanks to Tanya!
% 3.42/1.23 % SZS status Theorem for theBenchmark
% 3.42/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 3.42/1.24 % (4095807)------------------------------
% 3.42/1.24 % (4095807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.24 % (4095807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.24 % (4095807)CaDiCaL version: 2.1.3
% 3.42/1.24 % (4095807)Termination reason: Refutation
% 3.42/1.24 % (4095807)Time elapsed: 0.007 s
% 3.42/1.24 % (4095807)Peak memory usage: 89 MB
% 3.42/1.24 % (4095807)Instructions burned: 7 (million)
% 3.42/1.24 % (4095807)------------------------------
% 3.42/1.24 % (4095807)------------------------------
% 3.42/1.24 % (4095797)Success in time 0.427 s
% 3.42/1.24 % Vampire exiting
%------------------------------------------------------------------------------