%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU160+3 : 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 : n011.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 12:47:29 PM UTC 2026
% Result : Theorem 2.56s 1.31s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 7 unt; 0 def)
% Number of atoms : 74 ( 46 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 76 ( 28 ~; 34 |; 10 &)
% ( 3 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 25 ( 19 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f5,conjecture,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f6,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f8,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f1]) ).
fof(f9,plain,
? [X0,X1] :
( subset(X0,singleton(X1))
<~> ( X0 = empty_set
| X0 = singleton(X1) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f10,plain,
? [X0,X1] :
( ( ( empty_set != X0
& singleton(X1) != X0 )
| ~ subset(X0,singleton(X1)) )
& ( X0 = empty_set
| X0 = singleton(X1)
| subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f11,plain,
? [X0,X1] :
( ( ( empty_set != X0
& singleton(X1) != X0 )
| ~ subset(X0,singleton(X1)) )
& ( X0 = empty_set
| X0 = singleton(X1)
| subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
( ( ( empty_set != sK0
& sK0 != singleton(sK1) )
| ~ subset(sK0,singleton(sK1)) )
& ( empty_set = sK0
| sK0 = singleton(sK1)
| subset(sK0,singleton(sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f11]) ).
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(nnf_transformation,[],[f7]) ).
fof(f14,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,[],[f13]) ).
fof(f17,plain,
( subset(sK0,singleton(sK1))
| sK0 = singleton(sK1)
| empty_set = sK0 ),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
( sK0 != singleton(sK1)
| ~ subset(sK0,singleton(sK1)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
( empty_set != sK0
| ~ subset(sK0,singleton(sK1)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f20,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
! [X0,X1] :
( subset(X0,singleton(X1))
| empty_set != X0 ),
inference(cnf_transformation,[],[f14]) ).
fof(f24,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f27,plain,
! [X1] : subset(empty_set,singleton(X1)),
inference(equality_resolution,[],[f22]) ).
fof(f29,plain,
( sK0 = singleton(sK1)
| empty_set = sK0
| sK0 = singleton(sK1)
| empty_set = sK0 ),
inference(resolution,[],[f20,f17]) ).
fof(f32,plain,
( sK0 = singleton(sK1)
| empty_set = sK0 ),
inference(duplicate_literal_removal,[],[f29]) ).
fof(f33,plain,
( sK0 != sK0
| ~ subset(sK0,sK0)
| empty_set = sK0 ),
inference(superposition,[],[f18,f32]) ).
fof(f36,plain,
( ~ subset(sK0,sK0)
| empty_set = sK0 ),
inference(trivial_inequality_removal,[],[f33]) ).
fof(f37,plain,
empty_set = sK0,
inference(forward_subsumption_resolution,[],[f36,f24]) ).
fof(f38,plain,
( empty_set != empty_set
| ~ subset(empty_set,singleton(sK1)) ),
inference(superposition,[],[f19,f37]) ).
fof(f39,plain,
~ subset(empty_set,singleton(sK1)),
inference(trivial_inequality_removal,[],[f38]) ).
fof(f40,plain,
$false,
inference(forward_subsumption_resolution,[],[f39,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU160+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 03:49:01 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.56/1.31 % (2999912)Detected formulas, will run a generic FOF schedule.
% 2.56/1.31 % (2999921)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2080444552:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.56/1.31 % (2999921)First to succeed.
% 2.56/1.31 % (2999921)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2999912"
% 2.56/1.31 % (2999918)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=1529908164:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.56/1.31 % (2999917)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=217257201:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.56/1.31 % (2999919)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=654408010:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.56/1.31 % (2999920)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4105091755:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.56/1.31 % (2999920)Also succeeded, but the first one will report.
% 2.56/1.31 % (2999922)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3574858017:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.56/1.31 % (2999923)dis-21_1_sil=8000:lcm=predicate:random_seed=2338685440: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)
% 2.56/1.31 % (2999923)Refutation not found, incomplete strategy
% 2.56/1.31 % (2999923)------------------------------
% 2.56/1.31 % (2999923)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.31 % (2999923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.31 % (2999923)CaDiCaL version: 2.1.3
% 2.56/1.31 % (2999923)Termination reason: Refutation not found, incomplete strategy
% 2.56/1.31 % (2999923)Time elapsed: 0.001 s
% 2.56/1.31 % (2999923)Peak memory usage: 88 MB
% 2.56/1.31 % (2999922)Also succeeded, but the first one will report.
% 2.56/1.31 % (2999921)Refutation found. Thanks to Tanya!
% 2.56/1.31 % SZS status Theorem for theBenchmark
% 2.56/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.31 % (2999921)------------------------------
% 2.56/1.31 % (2999921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.31 % (2999921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.31 % (2999921)CaDiCaL version: 2.1.3
% 2.56/1.31 % (2999921)Termination reason: Refutation
% 2.56/1.31 % (2999921)Time elapsed: 0.001 s
% 2.56/1.31 % (2999921)Peak memory usage: 88 MB
% 2.56/1.31 % (2999921)Instructions burned: 1 (million)
% 2.56/1.31 % (2999921)------------------------------
% 2.56/1.31 % (2999921)------------------------------
% 2.56/1.31 % (2999912)Success in time 0.268 s
% 2.56/1.31 % Vampire exiting
%------------------------------------------------------------------------------