%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET604+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 : 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 12:41:19 PM UTC 2026
% Result : Theorem 2.60s 1.23s
% Output : Refutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 10 unt; 1 def)
% Number of atoms : 22 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 4 |; 1 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 15 ( 14 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_subset) ).
fof(f2,axiom,
! [X0,X1] :
( difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_empty_set) ).
fof(f9,conjecture,
! [X0] : difference(empty_set,X0) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_no_difference_with_empty_set) ).
fof(f10,negated_conjecture,
~ ! [X0] : difference(empty_set,X0) = empty_set,
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f12,plain,
? [X0] : empty_set != difference(empty_set,X0),
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
! [X0,X1] :
( ( difference(X0,X1) = empty_set
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != difference(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f21,plain,
empty_set != difference(empty_set,sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f12]) ).
fof(f22,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f24,plain,
! [X0,X1] :
( empty_set = difference(X0,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f36,plain,
empty_set != difference(empty_set,sK1),
inference(cnf_transformation,[],[f21]) ).
fof(f39,definition,
! [X0,X1] :
( sQ2_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ2_eqProxy])],[equality_proxy_definition]) ).
fof(f40,plain,
! [X0,X1] :
( sQ2_eqProxy(empty_set,difference(X0,X1))
| ~ subset(X0,X1) ),
inference(equality_proxy_replacement,[],[f24,f39]) ).
fof(f43,plain,
~ sQ2_eqProxy(empty_set,difference(empty_set,sK1)),
inference(equality_proxy_replacement,[],[f36,f39]) ).
fof(f48,plain,
~ subset(empty_set,sK1),
inference(resolution,[],[f40,f43]) ).
fof(f49,plain,
$false,
inference(resolution,[],[f48,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET604+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.35 % Computer : n002.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Mon Sep 28 02:20:38 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 2.60/1.23 % (4093415)Detected formulas, will run a generic FOF schedule.
% 2.60/1.23 % (4093426)dis-21_1_sil=8000:lcm=predicate:random_seed=2959037250: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)
% 2.60/1.23 % (4093426)First to succeed.
% 2.60/1.23 % (4093426)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4093415"
% 2.60/1.23 % (4093424)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2830862417:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.60/1.23 % (4093421)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=2580482708:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.60/1.23 % (4093423)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=54187518:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.60/1.23 % (4093420)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=891890872:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.60/1.23 % (4093422)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=198605937:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.60/1.23 % (4093425)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4119184935:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.60/1.23 % (4093424)Also succeeded, but the first one will report.
% 2.60/1.23 % (4093423)Also succeeded, but the first one will report.
% 2.60/1.23 % (4093425)Also succeeded, but the first one will report.
% 2.60/1.23 % (4093426)Refutation found. Thanks to Tanya!
% 2.60/1.23 % SZS status Theorem for theBenchmark
% 2.60/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 2.60/1.23 % (4093426)------------------------------
% 2.60/1.23 % (4093426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.23 % (4093426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.23 % (4093426)CaDiCaL version: 2.1.3
% 2.60/1.23 % (4093426)Termination reason: Refutation
% 2.60/1.23 % (4093426)Time elapsed: 0.001 s
% 2.60/1.23 % (4093426)Peak memory usage: 88 MB
% 2.60/1.23 % (4093426)Instructions burned: 1 (million)
% 2.60/1.23 % (4093426)------------------------------
% 2.60/1.23 % (4093426)------------------------------
% 2.60/1.23 % (4093415)Success in time 0.297 s
% 2.60/1.23 % Vampire exiting
%------------------------------------------------------------------------------