%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC098+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 01:02:26 PM UTC 2026
% Result : Theorem 2.76s 1.27s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 1
% Syntax : Number of formulae : 71 ( 7 unt; 0 def)
% Number of atoms : 327 ( 150 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 407 ( 151 ~; 183 |; 61 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 44 ( 28 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssItem(X4)
& cons(X4,nil) = X0
& ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X1,X5)
| ~ leq(X4,X5)
| X4 = X5 ) )
& memberP(X1,X4) )
| ( nil = X1
& nil = X0 )
| ( ! [X6] :
( ssItem(X6)
=> ( cons(X6,nil) != X2
| ~ memberP(X3,X6)
| ? [X7] :
( ssItem(X7)
& X6 != X7
& memberP(X3,X7)
& leq(X6,X7) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssItem(X4)
& cons(X4,nil) = X0
& ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X1,X5)
| ~ leq(X4,X5)
| X4 = X5 ) )
& memberP(X1,X4) )
| ( nil = X1
& nil = X0 )
| ( ! [X6] :
( ssItem(X6)
=> ( cons(X6,nil) != X2
| ~ memberP(X3,X6)
| ? [X7] :
( ssItem(X7)
& X6 != X7
& memberP(X3,X7)
& leq(X6,X7) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != X0
| ? [X5] :
( memberP(X1,X5)
& leq(X4,X5)
& X4 != X5
& ssItem(X5) )
| ~ memberP(X1,X4) )
& ( nil != X1
| nil != X0 )
& ( ? [X6] :
( cons(X6,nil) = X2
& memberP(X3,X6)
& ! [X7] :
( ~ ssItem(X7)
| X6 = X7
| ~ memberP(X3,X7)
| ~ leq(X6,X7) )
& ssItem(X6) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != X0
| ? [X5] :
( memberP(X1,X5)
& leq(X4,X5)
& X4 != X5
& ssItem(X5) )
| ~ memberP(X1,X4) )
& ( nil != X1
| nil != X0 )
& ( ? [X6] :
( cons(X6,nil) = X2
& memberP(X3,X6)
& ! [X7] :
( ~ ssItem(X7)
| X6 = X7
| ~ memberP(X3,X7)
| ~ leq(X6,X7) )
& ssItem(X6) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f127,plain,
( sK1 = sK3
& sK0 = sK2
& ! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != sK0
| ( memberP(sK1,sK4(X4))
& leq(X4,sK4(X4))
& sK4(X4) != X4
& ssItem(sK4(X4)) )
| ~ memberP(sK1,X4) )
& ( nil != sK1
| nil != sK0 )
& ( ( sK2 = cons(sK5,nil)
& memberP(sK3,sK5)
& ! [X7] :
( ~ ssItem(X7)
| sK5 = X7
| ~ memberP(sK3,X7)
| ~ leq(sK5,X7) )
& ssItem(sK5) )
| ( nil = sK3
& nil = sK2 ) )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X5,sK4(X4)),skolemize(X6,sK5)],[f99]) ).
fof(f143,plain,
( nil = sK2
| ssItem(sK5) ),
inference(cnf_transformation,[],[f127]) ).
fof(f144,plain,
( nil = sK3
| ssItem(sK5) ),
inference(cnf_transformation,[],[f127]) ).
fof(f145,plain,
! [X7] :
( ~ leq(sK5,X7)
| sK5 = X7
| ~ memberP(sK3,X7)
| ~ ssItem(X7)
| nil = sK2 ),
inference(cnf_transformation,[],[f127]) ).
fof(f146,plain,
! [X7] :
( ~ leq(sK5,X7)
| sK5 = X7
| ~ memberP(sK3,X7)
| ~ ssItem(X7)
| nil = sK3 ),
inference(cnf_transformation,[],[f127]) ).
fof(f147,plain,
( memberP(sK3,sK5)
| nil = sK2 ),
inference(cnf_transformation,[],[f127]) ).
fof(f148,plain,
( memberP(sK3,sK5)
| nil = sK3 ),
inference(cnf_transformation,[],[f127]) ).
fof(f149,plain,
( sK2 = cons(sK5,nil)
| nil = sK2 ),
inference(cnf_transformation,[],[f127]) ).
fof(f150,plain,
( sK2 = cons(sK5,nil)
| nil = sK3 ),
inference(cnf_transformation,[],[f127]) ).
fof(f151,plain,
( nil != sK1
| nil != sK0 ),
inference(cnf_transformation,[],[f127]) ).
fof(f152,plain,
! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != sK0
| ssItem(sK4(X4))
| ~ memberP(sK1,X4) ),
inference(cnf_transformation,[],[f127]) ).
fof(f153,plain,
! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != sK0
| sK4(X4) != X4
| ~ memberP(sK1,X4) ),
inference(cnf_transformation,[],[f127]) ).
fof(f154,plain,
! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != sK0
| leq(X4,sK4(X4))
| ~ memberP(sK1,X4) ),
inference(cnf_transformation,[],[f127]) ).
fof(f155,plain,
! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != sK0
| memberP(sK1,sK4(X4))
| ~ memberP(sK1,X4) ),
inference(cnf_transformation,[],[f127]) ).
fof(f156,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f127]) ).
fof(f157,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f127]) ).
fof(f195,plain,
! [X4] :
( cons(X4,nil) != sK2
| ~ ssItem(X4)
| memberP(sK3,sK4(X4))
| ~ memberP(sK3,X4) ),
inference(definition_unfolding,[],[f155,f156,f157,f157]) ).
fof(f196,plain,
! [X4] :
( cons(X4,nil) != sK2
| ~ ssItem(X4)
| leq(X4,sK4(X4))
| ~ memberP(sK3,X4) ),
inference(definition_unfolding,[],[f154,f156,f157]) ).
fof(f197,plain,
! [X4] :
( cons(X4,nil) != sK2
| ~ ssItem(X4)
| sK4(X4) != X4
| ~ memberP(sK3,X4) ),
inference(definition_unfolding,[],[f153,f156,f157]) ).
fof(f198,plain,
! [X4] :
( cons(X4,nil) != sK2
| ~ ssItem(X4)
| ssItem(sK4(X4))
| ~ memberP(sK3,X4) ),
inference(definition_unfolding,[],[f152,f156,f157]) ).
fof(f199,plain,
( nil != sK3
| nil != sK2 ),
inference(definition_unfolding,[],[f151,f157,f156]) ).
fof(f225,plain,
( sK2 != sK2
| ~ ssItem(sK5)
| ssItem(sK4(sK5))
| ~ memberP(sK3,sK5)
| nil = sK3 ),
inference(superposition,[],[f198,f150]) ).
fof(f226,plain,
( sK2 != sK2
| ~ ssItem(sK5)
| ssItem(sK4(sK5))
| ~ memberP(sK3,sK5)
| nil = sK2 ),
inference(superposition,[],[f198,f149]) ).
fof(f227,plain,
( ~ ssItem(sK5)
| ssItem(sK4(sK5))
| ~ memberP(sK3,sK5)
| nil = sK2 ),
inference(trivial_inequality_removal,[],[f226]) ).
fof(f228,plain,
( ~ ssItem(sK5)
| ssItem(sK4(sK5))
| ~ memberP(sK3,sK5)
| nil = sK3 ),
inference(trivial_inequality_removal,[],[f225]) ).
fof(f229,plain,
( ssItem(sK4(sK5))
| ~ memberP(sK3,sK5)
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f227,f143]) ).
fof(f230,plain,
( ssItem(sK4(sK5))
| ~ memberP(sK3,sK5)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f228,f144]) ).
fof(f231,plain,
( ssItem(sK4(sK5))
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f229,f147]) ).
fof(f232,plain,
( ssItem(sK4(sK5))
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f230,f148]) ).
fof(f235,plain,
( sK2 != sK2
| ~ ssItem(sK5)
| memberP(sK3,sK4(sK5))
| ~ memberP(sK3,sK5)
| nil = sK3 ),
inference(superposition,[],[f195,f150]) ).
fof(f236,plain,
( sK2 != sK2
| ~ ssItem(sK5)
| memberP(sK3,sK4(sK5))
| ~ memberP(sK3,sK5)
| nil = sK2 ),
inference(superposition,[],[f195,f149]) ).
fof(f237,plain,
( ~ ssItem(sK5)
| memberP(sK3,sK4(sK5))
| ~ memberP(sK3,sK5)
| nil = sK2 ),
inference(trivial_inequality_removal,[],[f236]) ).
fof(f238,plain,
( ~ ssItem(sK5)
| memberP(sK3,sK4(sK5))
| ~ memberP(sK3,sK5)
| nil = sK3 ),
inference(trivial_inequality_removal,[],[f235]) ).
fof(f239,plain,
( memberP(sK3,sK4(sK5))
| ~ memberP(sK3,sK5)
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f237,f143]) ).
fof(f240,plain,
( memberP(sK3,sK4(sK5))
| ~ memberP(sK3,sK5)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f238,f144]) ).
fof(f241,plain,
( memberP(sK3,sK4(sK5))
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f239,f147]) ).
fof(f242,plain,
( memberP(sK3,sK4(sK5))
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f240,f148]) ).
fof(f245,plain,
( sK2 != sK2
| ~ ssItem(sK5)
| leq(sK5,sK4(sK5))
| ~ memberP(sK3,sK5)
| nil = sK3 ),
inference(superposition,[],[f196,f150]) ).
fof(f246,plain,
( sK2 != sK2
| ~ ssItem(sK5)
| leq(sK5,sK4(sK5))
| ~ memberP(sK3,sK5)
| nil = sK2 ),
inference(superposition,[],[f196,f149]) ).
fof(f247,plain,
( ~ ssItem(sK5)
| leq(sK5,sK4(sK5))
| ~ memberP(sK3,sK5)
| nil = sK2 ),
inference(trivial_inequality_removal,[],[f246]) ).
fof(f248,plain,
( ~ ssItem(sK5)
| leq(sK5,sK4(sK5))
| ~ memberP(sK3,sK5)
| nil = sK3 ),
inference(trivial_inequality_removal,[],[f245]) ).
fof(f249,plain,
( leq(sK5,sK4(sK5))
| ~ memberP(sK3,sK5)
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f247,f143]) ).
fof(f250,plain,
( leq(sK5,sK4(sK5))
| ~ memberP(sK3,sK5)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f248,f144]) ).
fof(f251,plain,
( leq(sK5,sK4(sK5))
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f249,f147]) ).
fof(f252,plain,
( leq(sK5,sK4(sK5))
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f250,f148]) ).
fof(f256,plain,
( sK2 != sK2
| ~ ssItem(sK5)
| sK5 != sK4(sK5)
| ~ memberP(sK3,sK5)
| nil = sK3 ),
inference(superposition,[],[f197,f150]) ).
fof(f257,plain,
( sK2 != sK2
| ~ ssItem(sK5)
| sK5 != sK4(sK5)
| ~ memberP(sK3,sK5)
| nil = sK2 ),
inference(superposition,[],[f197,f149]) ).
fof(f258,plain,
( ~ ssItem(sK5)
| sK5 != sK4(sK5)
| ~ memberP(sK3,sK5)
| nil = sK2 ),
inference(trivial_inequality_removal,[],[f257]) ).
fof(f259,plain,
( ~ ssItem(sK5)
| sK5 != sK4(sK5)
| ~ memberP(sK3,sK5)
| nil = sK3 ),
inference(trivial_inequality_removal,[],[f256]) ).
fof(f260,plain,
( sK5 != sK4(sK5)
| ~ memberP(sK3,sK5)
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f258,f143]) ).
fof(f261,plain,
( sK5 != sK4(sK5)
| ~ memberP(sK3,sK5)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f259,f144]) ).
fof(f262,plain,
( sK5 != sK4(sK5)
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f260,f147]) ).
fof(f263,plain,
( sK5 != sK4(sK5)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f261,f148]) ).
fof(f266,plain,
( nil = sK2
| sK5 = sK4(sK5)
| ~ memberP(sK3,sK4(sK5))
| ~ ssItem(sK4(sK5))
| nil = sK2 ),
inference(resolution,[],[f251,f145]) ).
fof(f267,plain,
( nil = sK2
| sK5 = sK4(sK5)
| ~ memberP(sK3,sK4(sK5))
| ~ ssItem(sK4(sK5)) ),
inference(duplicate_literal_removal,[],[f266]) ).
fof(f268,plain,
( nil = sK2
| sK5 = sK4(sK5)
| ~ ssItem(sK4(sK5)) ),
inference(forward_subsumption_resolution,[],[f267,f241]) ).
fof(f270,plain,
( nil = sK2
| sK5 = sK4(sK5) ),
inference(forward_subsumption_resolution,[],[f268,f231]) ).
fof(f272,plain,
( nil = sK3
| sK5 = sK4(sK5)
| ~ memberP(sK3,sK4(sK5))
| ~ ssItem(sK4(sK5))
| nil = sK3 ),
inference(resolution,[],[f252,f146]) ).
fof(f274,plain,
( nil = sK3
| sK5 = sK4(sK5)
| ~ memberP(sK3,sK4(sK5))
| ~ ssItem(sK4(sK5)) ),
inference(duplicate_literal_removal,[],[f272]) ).
fof(f276,plain,
( nil = sK3
| sK5 = sK4(sK5)
| ~ ssItem(sK4(sK5)) ),
inference(forward_subsumption_resolution,[],[f274,f242]) ).
fof(f278,plain,
( nil = sK3
| sK5 = sK4(sK5) ),
inference(forward_subsumption_resolution,[],[f276,f232]) ).
fof(f281,plain,
nil = sK2,
inference(forward_subsumption_resolution,[],[f270,f262]) ).
fof(f290,plain,
( sK2 != sK3
| sK2 != sK2 ),
inference(superposition,[],[f199,f281]) ).
fof(f291,plain,
sK2 != sK3,
inference(trivial_inequality_removal,[],[f290]) ).
fof(f299,plain,
nil = sK3,
inference(forward_subsumption_resolution,[],[f278,f263]) ).
fof(f300,plain,
sK2 = sK3,
inference(forward_demodulation,[],[f299,f281]) ).
fof(f301,plain,
$false,
inference(forward_subsumption_resolution,[],[f300,f291]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC098+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n017.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 07:47:21 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 2.76/1.27 % (3382939)Detected formulas, will run a generic FOF schedule.
% 2.76/1.27 % (3382944)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=843733771:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.76/1.27 % (3382945)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=1705828715:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.76/1.27 % (3382949)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1065972731:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.76/1.27 % (3382948)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1147049665:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.76/1.27 % (3382947)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1742385062:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.76/1.27 % (3382946)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=1784264456:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.76/1.27 % (3382948)First to succeed.
% 2.76/1.27 % (3382948)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3382939"
% 2.76/1.27 % (3382949)Also succeeded, but the first one will report.
% 2.76/1.27 % (3382947)Also succeeded, but the first one will report.
% 2.76/1.27 % (3382950)dis-21_1_sil=8000:lcm=predicate:random_seed=3919671502: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)
% 2.76/1.27 % (3382950)Also succeeded, but the first one will report.
% 2.76/1.27 % (3382948)Refutation found. Thanks to Tanya!
% 2.76/1.27 % SZS status Theorem for theBenchmark
% 2.76/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.46 % (3382948)------------------------------
% 3.47/1.46 % (3382948)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.46 % (3382948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.46 % (3382948)CaDiCaL version: 2.1.3
% 3.47/1.46 % (3382948)Termination reason: Refutation
% 3.47/1.46 % (3382948)Time elapsed: 0.006 s
% 3.47/1.46 % (3382948)Peak memory usage: 88 MB
% 3.47/1.46 % (3382948)Instructions burned: 7 (million)
% 3.47/1.46 % (3382948)------------------------------
% 3.47/1.46 % (3382948)------------------------------
% 3.47/1.46 % (3382939)Success in time 0.406 s
% 3.47/1.46 % Vampire exiting
%------------------------------------------------------------------------------