%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU160+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 3.41s 1.46s
% Output : Refutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 60 ( 13 unt; 8 def)
% Number of atoms : 136 ( 41 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 134 ( 58 ~; 57 |; 10 &)
% ( 8 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 26 ( 1 sgn 20 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f7,conjecture,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f10,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f3]) ).
fof(f12,plain,
? [X0,X1] :
( subset(X0,singleton(X1))
<~> ( X0 = empty_set
| X0 = singleton(X1) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f13,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,[],[f12]) ).
fof(f14,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,[],[f13]) ).
fof(f15,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)],[f14]) ).
fof(f16,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,[],[f9]) ).
fof(f17,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,[],[f16]) ).
fof(f18,plain,
( empty_set = sK0
| sK0 = singleton(sK1)
| subset(sK0,singleton(sK1)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f19,plain,
( sK0 != singleton(sK1)
| ~ subset(sK0,singleton(sK1)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f20,plain,
( empty_set != sK0
| ~ subset(sK0,singleton(sK1)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f21,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f17]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,singleton(X1))
| empty_set != X0 ),
inference(cnf_transformation,[],[f17]) ).
fof(f24,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f25,definition,
~ sP2(empty_set),
introduced(definition,[new_symbols(definition,[sP2])],[inequality_splitting_name_introduction]) ).
fof(f26,plain,
( sP2(sK0)
| ~ subset(sK0,singleton(sK1)) ),
inference(inequality_splitting,[],[f20,f25]) ).
fof(f27,definition,
~ sP3(sK0),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
fof(f28,plain,
( sP3(singleton(sK1))
| ~ subset(sK0,singleton(sK1)) ),
inference(inequality_splitting,[],[f19,f27]) ).
fof(f29,definition,
~ sP4(empty_set),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f30,plain,
! [X0,X1] :
( subset(X0,singleton(X1))
| sP4(X0) ),
inference(inequality_splitting,[],[f23,f29]) ).
fof(f32,plain,
( empty_set = sK0
| sK0 = singleton(sK1) ),
inference(forward_subsumption_resolution,[],[f18,f21]) ).
fof(f34,definition,
( spl5_1
<=> subset(sK0,singleton(sK1)) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f36,plain,
( ~ subset(sK0,singleton(sK1))
| spl5_1 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f38,definition,
( spl5_2
<=> sP3(singleton(sK1)) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f41,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f28,f38,f34]) ).
fof(f43,definition,
( spl5_3
<=> sP2(sK0) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f46,plain,
( ~ spl5_1
| spl5_3 ),
inference(avatar_split_clause,[],[f26,f43,f34]) ).
fof(f48,definition,
( spl5_4
<=> sK0 = singleton(sK1) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f50,plain,
( sK0 = singleton(sK1)
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f52,definition,
( spl5_5
<=> empty_set = sK0 ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f54,plain,
( empty_set = sK0
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f55,plain,
( spl5_4
| spl5_5 ),
inference(avatar_split_clause,[],[f32,f52,f48]) ).
fof(f56,plain,
( sP4(sK0)
| spl5_1 ),
inference(resolution,[],[f36,f30]) ).
fof(f58,plain,
( ~ subset(singleton(sK1),singleton(sK1))
| spl5_1
| ~ spl5_4 ),
inference(superposition,[],[f36,f50]) ).
fof(f59,plain,
( ~ sP3(singleton(sK1))
| ~ spl5_4 ),
inference(superposition,[],[f27,f50]) ).
fof(f60,plain,
( ~ spl5_2
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f59,f48,f38]) ).
fof(f61,plain,
( $false
| spl5_1
| ~ spl5_4 ),
inference(forward_subsumption_resolution,[],[f58,f24]) ).
fof(f62,plain,
( spl5_1
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f61]) ).
fof(f63,plain,
( ~ sP2(sK0)
| ~ spl5_5 ),
inference(superposition,[],[f25,f54]) ).
fof(f64,plain,
( ~ sP4(sK0)
| ~ spl5_5 ),
inference(superposition,[],[f29,f54]) ).
fof(f65,plain,
( $false
| spl5_1
| ~ spl5_5 ),
inference(forward_subsumption_resolution,[],[f64,f56]) ).
fof(f66,plain,
( spl5_1
| ~ spl5_5 ),
inference(avatar_contradiction_clause,[],[f65]) ).
fof(f67,plain,
( ~ spl5_3
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f63,f52,f43]) ).
cnf(s1,plain,
( ~ spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f41]) ).
cnf(s2,plain,
( ~ spl5_1
| spl5_3 ),
inference(sat_conversion,[],[f46]) ).
cnf(s3,plain,
( spl5_4
| spl5_5 ),
inference(sat_conversion,[],[f55]) ).
cnf(s4,plain,
( ~ spl5_2
| ~ spl5_4 ),
inference(sat_conversion,[],[f60]) ).
cnf(s5,plain,
( spl5_1
| ~ spl5_4 ),
inference(sat_conversion,[],[f62]) ).
cnf(s6,plain,
( spl5_1
| ~ spl5_5 ),
inference(sat_conversion,[],[f66]) ).
cnf(s7,plain,
( ~ spl5_3
| ~ spl5_5 ),
inference(sat_conversion,[],[f67]) ).
cnf(s8,plain,
spl5_1,
inference(rat,[],[s3,s5,s6]) ).
cnf(s9,plain,
spl5_3,
inference(rat,[],[s2,s8]) ).
cnf(s10,plain,
spl5_2,
inference(rat,[],[s1,s8]) ).
cnf(s11,plain,
~ spl5_5,
inference(rat,[],[s7,s9]) ).
cnf(s12,plain,
~ spl5_4,
inference(rat,[],[s4,s10]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s3,s11,s12]) ).
fof(f68,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU160+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n005.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Mon Sep 28 03:48:17 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 3.41/1.46 % (417031)Detected formulas, will run a generic FOF schedule.
% 3.41/1.46 % (417037)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=662723265:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.41/1.46 % (417039)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=681360059:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.41/1.46 % (417040)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1830647145:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.41/1.46 % (417038)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=539788383:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.41/1.46 % (417036)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=2922996591:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.41/1.46 % (417039)First to succeed.
% 3.41/1.46 % (417041)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=906575482:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.41/1.46 % (417039)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-417031"
% 3.41/1.46 % (417040)Also succeeded, but the first one will report.
% 3.41/1.46 % (417041)Also succeeded, but the first one will report.
% 3.41/1.46 % (417042)dis-21_1_sil=8000:lcm=predicate:random_seed=319836025: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)
% 3.41/1.46 % (417042)Refutation not found, incomplete strategy
% 3.41/1.46 % (417042)------------------------------
% 3.41/1.46 % (417042)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.46 % (417042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.46 % (417042)CaDiCaL version: 2.1.3
% 3.41/1.46 % (417042)Termination reason: Refutation not found, incomplete strategy
% 3.41/1.46 % (417042)Time elapsed: 0.001 s
% 3.41/1.46 % (417042)Peak memory usage: 89 MB
% 3.41/1.46 % (417039)Refutation found. Thanks to Tanya!
% 3.41/1.46 % SZS status Theorem for theBenchmark
% 3.41/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.41/1.46 % (417039)------------------------------
% 3.41/1.46 % (417039)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.46 % (417039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.46 % (417039)CaDiCaL version: 2.1.3
% 3.41/1.46 % (417039)Termination reason: Refutation
% 3.41/1.46 % (417039)Time elapsed: 0.003 s
% 3.41/1.46 % (417039)Peak memory usage: 89 MB
% 3.41/1.46 % (417039)Instructions burned: 2 (million)
% 3.41/1.46 % (417039)------------------------------
% 3.41/1.46 % (417039)------------------------------
% 3.41/1.46 % (417031)Success in time 0.397 s
% 3.41/1.46 % Vampire exiting
%------------------------------------------------------------------------------