%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET923+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:42:19 PM UTC 2026
% Result : Theorem 2.44s 1.21s
% Output : Refutation 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 48 ( 35 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 53 ( 24 ~; 14 |; 13 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 18 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f6,axiom,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f7,conjecture,
! [X0,X1] :
~ ( set_difference(X0,singleton(X1)) = empty_set
& X0 != empty_set
& X0 != singleton(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
~ ( set_difference(X0,singleton(X1)) = empty_set
& X0 != empty_set
& X0 != singleton(X1) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f10,plain,
? [X0,X1] :
( set_difference(X0,singleton(X1)) = empty_set
& X0 != empty_set
& X0 != singleton(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,plain,
( empty_set = set_difference(sK0,singleton(sK1))
& empty_set != sK0
& sK0 != singleton(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( empty_set != X0
& singleton(X1) != X0 ) )
& ( X0 = empty_set
| X0 = singleton(X1)
| ~ subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f13,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( empty_set != X0
& singleton(X1) != X0 ) )
& ( X0 = empty_set
| X0 = singleton(X1)
| ~ subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( set_difference(X0,X1) = empty_set
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f15,plain,
sK0 != singleton(sK1),
inference(cnf_transformation,[],[f11]) ).
fof(f16,plain,
empty_set != sK0,
inference(cnf_transformation,[],[f11]) ).
fof(f17,plain,
empty_set = set_difference(sK0,singleton(sK1)),
inference(cnf_transformation,[],[f11]) ).
fof(f18,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
! [X0,X1] :
( empty_set != set_difference(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f26,plain,
( empty_set != empty_set
| subset(sK0,singleton(sK1)) ),
inference(superposition,[],[f21,f17]) ).
fof(f27,plain,
subset(sK0,singleton(sK1)),
inference(trivial_inequality_removal,[],[f26]) ).
fof(f31,plain,
( sK0 = singleton(sK1)
| empty_set = sK0 ),
inference(resolution,[],[f18,f27]) ).
fof(f32,plain,
empty_set = sK0,
inference(forward_subsumption_resolution,[],[f31,f15]) ).
fof(f33,plain,
$false,
inference(forward_subsumption_resolution,[],[f32,f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET923+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n018.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 03:12:25 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 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
% 2.44/1.21 % (2959385)Detected formulas, will run a generic FOF schedule.
% 2.44/1.21 % (2959394)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3674642370:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.44/1.21 % (2959394)First to succeed.
% 2.44/1.21 % (2959394)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2959385"
% 2.44/1.21 % (2959395)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=122554136:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.44/1.21 % (2959390)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=2171899633:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.44/1.21 % (2959396)dis-21_1_sil=8000:lcm=predicate:random_seed=3944118780: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)
% 2.44/1.21 % (2959393)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=629961755:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.44/1.21 % (2959391)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=2022717453:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.44/1.21 % (2959392)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=2350716694:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.44/1.21 % (2959396)Also succeeded, but the first one will report.
% 2.44/1.21 % (2959395)Also succeeded, but the first one will report.
% 2.44/1.21 % (2959393)Also succeeded, but the first one will report.
% 2.44/1.21 % (2959394)Refutation found. Thanks to Tanya!
% 2.44/1.21 % SZS status Theorem for theBenchmark
% 2.44/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 2.44/1.21 % (2959394)------------------------------
% 2.44/1.21 % (2959394)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.44/1.21 % (2959394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/1.21 % (2959394)CaDiCaL version: 2.1.3
% 2.44/1.21 % (2959394)Termination reason: Refutation
% 2.44/1.21 % (2959394)Time elapsed: 0.001 s
% 2.44/1.21 % (2959394)Peak memory usage: 88 MB
% 2.44/1.21 % (2959394)Instructions burned: 1 (million)
% 2.44/1.21 % (2959394)------------------------------
% 2.44/1.21 % (2959394)------------------------------
% 2.44/1.21 % (2959385)Success in time 0.269 s
% 2.44/1.21 % Vampire exiting
%------------------------------------------------------------------------------