%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET063+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 12:39:52 PM UTC 2026
% Result : Theorem 0.16s 1.03s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 6 unt; 0 def)
% Number of atoms : 34 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 33 ( 14 ~; 9 |; 7 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 13 ( 12 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_subset) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f7,conjecture,
! [X0] :
( subset(X0,empty_set)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subset_of_empty_set_is_empty_set) ).
fof(f8,negated_conjecture,
~ ! [X0] :
( subset(X0,empty_set)
=> X0 = empty_set ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f10,plain,
? [X0] :
( empty_set != X0
& subset(X0,empty_set) ),
inference(ennf_transformation,[],[f8]) ).
fof(f14,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f15,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
( empty_set != sK1
& subset(sK1,empty_set) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f10]) ).
fof(f17,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f24,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| X0 = X1
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
subset(sK1,empty_set),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
empty_set != sK1,
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
( empty_set = sK1
| ~ subset(empty_set,sK1) ),
inference(resolution,[],[f24,f26]) ).
fof(f35,plain,
~ subset(empty_set,sK1),
inference(forward_subsumption_resolution,[],[f30,f27]) ).
fof(f36,plain,
$false,
inference(forward_subsumption_resolution,[],[f35,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET063+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 00:29:51 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.16/1.03 % (4045837)Detected formulas, will run a generic FOF schedule.
% 0.16/1.03 % (4045847)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3037770849:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.16/1.03 % (4045847)First to succeed.
% 0.16/1.03 % (4045847)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4045837"
% 0.16/1.03 % (4045845)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3282150851:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.16/1.03 % (4045842)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=912284379:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.16/1.03 % (4045846)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1726699992:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.16/1.03 % (4045844)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=1726344140:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.16/1.03 % (4045843)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=2694880732:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.16/1.03 % (4045848)dis-21_1_sil=8000:lcm=predicate:random_seed=3409191302: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)
% 0.16/1.03 % (4045845)Also succeeded, but the first one will report.
% 0.16/1.03 % (4045846)Also succeeded, but the first one will report.
% 0.16/1.03 % (4045848)Also succeeded, but the first one will report.
% 0.16/1.03 % (4045847)Refutation found. Thanks to Tanya!
% 0.16/1.03 % SZS status Theorem for theBenchmark
% 0.16/1.03 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.03 % (4045847)------------------------------
% 0.16/1.03 % (4045847)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.03 % (4045847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.03 % (4045847)CaDiCaL version: 2.1.3
% 0.16/1.03 % (4045847)Termination reason: Refutation
% 0.16/1.03 % (4045847)Time elapsed: 0.001 s
% 0.16/1.03 % (4045847)Peak memory usage: 88 MB
% 0.16/1.03 % (4045847)Instructions burned: 1 (million)
% 0.16/1.03 % (4045847)------------------------------
% 0.16/1.03 % (4045847)------------------------------
% 0.16/1.03 % (4045837)Success in time 0.328 s
% 0.16/1.03 % Vampire exiting
%------------------------------------------------------------------------------