%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC242+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 01:03:06 PM UTC 2026
% Result : Theorem 0.64s 0.97s
% Output : Refutation 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 57 ( 14 unt; 0 def)
% Number of atoms : 266 ( 49 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 369 ( 160 ~; 149 |; 50 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 72 ( 56 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| nil = X0
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X0
& ! [X7] :
( ~ ssItem(X7)
| ~ memberP(X5,X7)
| ~ memberP(X6,X7)
| ~ lt(X4,X7)
| leq(X4,X7) ) ) ) )
| ( nil != X2
& ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ~ ssList(X10)
| app(app(X9,cons(X8,nil)),X10) != X2
| ? [X11] :
( ssItem(X11)
& ~ leq(X8,X11)
& memberP(X9,X11)
& memberP(X10,X11)
& lt(X8,X11) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| nil = X0
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X0
& ! [X7] :
( ~ ssItem(X7)
| ~ memberP(X5,X7)
| ~ memberP(X6,X7)
| ~ lt(X4,X7)
| leq(X4,X7) ) ) ) )
| ( nil != X2
& ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ~ ssList(X10)
| app(app(X9,cons(X8,nil)),X10) != X2
| ? [X11] :
( ssItem(X11)
& ~ leq(X8,X11)
& memberP(X9,X11)
& memberP(X10,X11)
& lt(X8,X11) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& nil != X0
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X0
| ? [X7] :
( ssItem(X7)
& memberP(X5,X7)
& memberP(X6,X7)
& lt(X4,X7)
& ~ leq(X4,X7) ) ) ) )
& ( nil = X2
| ? [X8] :
( ? [X9] :
( ? [X10] :
( ssList(X10)
& app(app(X9,cons(X8,nil)),X10) = X2
& ! [X11] :
( ~ ssItem(X11)
| leq(X8,X11)
| ~ memberP(X9,X11)
| ~ memberP(X10,X11)
| ~ lt(X8,X11) ) )
& ssList(X9) )
& ssItem(X8) ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f136,plain,
( ssList(sK3)
& sK1 = sK3
& sK0 = sK2
& nil != sK0
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK0
| ( ssItem(sK4(X4,X5,X6))
& memberP(X5,sK4(X4,X5,X6))
& memberP(X6,sK4(X4,X5,X6))
& lt(X4,sK4(X4,X5,X6))
& ~ leq(X4,sK4(X4,X5,X6)) ) ) ) )
& ( nil = sK2
| ( ssList(sK7)
& sK2 = app(app(sK6,cons(sK5,nil)),sK7)
& ! [X11] :
( ~ ssItem(X11)
| leq(sK5,X11)
| ~ memberP(sK6,X11)
| ~ memberP(sK7,X11)
| ~ lt(sK5,X11) )
& ssList(sK6)
& ssItem(sK5) ) )
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X7,sK4(X4,X5,X6)),skolemize(X8,sK5),skolemize(X9,sK6),skolemize(X10,sK7)],[f98]) ).
fof(f153,plain,
( nil = sK2
| ssItem(sK5) ),
inference(cnf_transformation,[],[f136]) ).
fof(f154,plain,
( nil = sK2
| ssList(sK6) ),
inference(cnf_transformation,[],[f136]) ).
fof(f155,plain,
! [X11] :
( nil = sK2
| ~ ssItem(X11)
| leq(sK5,X11)
| ~ memberP(sK6,X11)
| ~ memberP(sK7,X11)
| ~ lt(sK5,X11) ),
inference(cnf_transformation,[],[f136]) ).
fof(f156,plain,
( nil = sK2
| sK2 = app(app(sK6,cons(sK5,nil)),sK7) ),
inference(cnf_transformation,[],[f136]) ).
fof(f157,plain,
( nil = sK2
| ssList(sK7) ),
inference(cnf_transformation,[],[f136]) ).
fof(f158,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK0
| ~ leq(X4,sK4(X4,X5,X6)) ),
inference(cnf_transformation,[],[f136]) ).
fof(f159,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK0
| lt(X4,sK4(X4,X5,X6)) ),
inference(cnf_transformation,[],[f136]) ).
fof(f160,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK0
| memberP(X6,sK4(X4,X5,X6)) ),
inference(cnf_transformation,[],[f136]) ).
fof(f161,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK0
| memberP(X5,sK4(X4,X5,X6)) ),
inference(cnf_transformation,[],[f136]) ).
fof(f162,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK0
| ssItem(sK4(X4,X5,X6)) ),
inference(cnf_transformation,[],[f136]) ).
fof(f163,plain,
nil != sK0,
inference(cnf_transformation,[],[f136]) ).
fof(f164,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f136]) ).
fof(f212,plain,
nil != sK2,
inference(definition_unfolding,[],[f163,f164]) ).
fof(f213,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK2
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| ssItem(sK4(X4,X5,X6)) ),
inference(definition_unfolding,[],[f162,f164]) ).
fof(f214,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK2
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| memberP(X5,sK4(X4,X5,X6)) ),
inference(definition_unfolding,[],[f161,f164]) ).
fof(f215,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK2
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| memberP(X6,sK4(X4,X5,X6)) ),
inference(definition_unfolding,[],[f160,f164]) ).
fof(f216,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK2
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| lt(X4,sK4(X4,X5,X6)) ),
inference(definition_unfolding,[],[f159,f164]) ).
fof(f217,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK2
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| ~ leq(X4,sK4(X4,X5,X6)) ),
inference(definition_unfolding,[],[f158,f164]) ).
fof(f228,plain,
ssItem(sK5),
inference(forward_subsumption_resolution,[],[f153,f212]) ).
fof(f229,plain,
ssList(sK6),
inference(forward_subsumption_resolution,[],[f154,f212]) ).
fof(f230,plain,
ssList(sK7),
inference(forward_subsumption_resolution,[],[f157,f212]) ).
fof(f231,plain,
sK2 = app(app(sK6,cons(sK5,nil)),sK7),
inference(forward_subsumption_resolution,[],[f156,f212]) ).
fof(f232,plain,
! [X11] :
( leq(sK5,X11)
| ~ ssItem(X11)
| ~ memberP(sK6,X11)
| ~ memberP(sK7,X11)
| ~ lt(sK5,X11) ),
inference(forward_subsumption_resolution,[],[f155,f212]) ).
fof(f233,plain,
( sK2 != sK2
| ~ ssList(sK6)
| ~ ssList(sK7)
| ~ ssItem(sK5)
| ssItem(sK4(sK5,sK6,sK7)) ),
inference(superposition,[],[f213,f231]) ).
fof(f234,plain,
( ~ ssList(sK6)
| ~ ssList(sK7)
| ~ ssItem(sK5)
| ssItem(sK4(sK5,sK6,sK7)) ),
inference(trivial_inequality_removal,[],[f233]) ).
fof(f235,plain,
( ~ ssList(sK7)
| ~ ssItem(sK5)
| ssItem(sK4(sK5,sK6,sK7)) ),
inference(forward_subsumption_resolution,[],[f234,f229]) ).
fof(f236,plain,
( ~ ssItem(sK5)
| ssItem(sK4(sK5,sK6,sK7)) ),
inference(forward_subsumption_resolution,[],[f235,f230]) ).
fof(f237,plain,
ssItem(sK4(sK5,sK6,sK7)),
inference(forward_subsumption_resolution,[],[f236,f228]) ).
fof(f238,plain,
( sK2 != sK2
| ~ ssList(sK6)
| ~ ssList(sK7)
| ~ ssItem(sK5)
| memberP(sK6,sK4(sK5,sK6,sK7)) ),
inference(superposition,[],[f214,f231]) ).
fof(f239,plain,
( ~ ssList(sK6)
| ~ ssList(sK7)
| ~ ssItem(sK5)
| memberP(sK6,sK4(sK5,sK6,sK7)) ),
inference(trivial_inequality_removal,[],[f238]) ).
fof(f240,plain,
( ~ ssList(sK7)
| ~ ssItem(sK5)
| memberP(sK6,sK4(sK5,sK6,sK7)) ),
inference(forward_subsumption_resolution,[],[f239,f229]) ).
fof(f241,plain,
( ~ ssItem(sK5)
| memberP(sK6,sK4(sK5,sK6,sK7)) ),
inference(forward_subsumption_resolution,[],[f240,f230]) ).
fof(f242,plain,
memberP(sK6,sK4(sK5,sK6,sK7)),
inference(forward_subsumption_resolution,[],[f241,f228]) ).
fof(f243,plain,
( sK2 != sK2
| ~ ssList(sK6)
| ~ ssList(sK7)
| ~ ssItem(sK5)
| memberP(sK7,sK4(sK5,sK6,sK7)) ),
inference(superposition,[],[f215,f231]) ).
fof(f244,plain,
( ~ ssList(sK6)
| ~ ssList(sK7)
| ~ ssItem(sK5)
| memberP(sK7,sK4(sK5,sK6,sK7)) ),
inference(trivial_inequality_removal,[],[f243]) ).
fof(f245,plain,
( ~ ssList(sK7)
| ~ ssItem(sK5)
| memberP(sK7,sK4(sK5,sK6,sK7)) ),
inference(forward_subsumption_resolution,[],[f244,f229]) ).
fof(f246,plain,
( ~ ssItem(sK5)
| memberP(sK7,sK4(sK5,sK6,sK7)) ),
inference(forward_subsumption_resolution,[],[f245,f230]) ).
fof(f247,plain,
memberP(sK7,sK4(sK5,sK6,sK7)),
inference(forward_subsumption_resolution,[],[f246,f228]) ).
fof(f248,plain,
( sK2 != sK2
| ~ ssList(sK6)
| ~ ssList(sK7)
| ~ ssItem(sK5)
| lt(sK5,sK4(sK5,sK6,sK7)) ),
inference(superposition,[],[f216,f231]) ).
fof(f249,plain,
( ~ ssList(sK6)
| ~ ssList(sK7)
| ~ ssItem(sK5)
| lt(sK5,sK4(sK5,sK6,sK7)) ),
inference(trivial_inequality_removal,[],[f248]) ).
fof(f250,plain,
( ~ ssList(sK7)
| ~ ssItem(sK5)
| lt(sK5,sK4(sK5,sK6,sK7)) ),
inference(forward_subsumption_resolution,[],[f249,f229]) ).
fof(f251,plain,
( ~ ssItem(sK5)
| lt(sK5,sK4(sK5,sK6,sK7)) ),
inference(forward_subsumption_resolution,[],[f250,f230]) ).
fof(f252,plain,
lt(sK5,sK4(sK5,sK6,sK7)),
inference(forward_subsumption_resolution,[],[f251,f228]) ).
fof(f253,plain,
( sK2 != sK2
| ~ ssList(sK6)
| ~ ssList(sK7)
| ~ ssItem(sK5)
| ~ leq(sK5,sK4(sK5,sK6,sK7)) ),
inference(superposition,[],[f217,f231]) ).
fof(f254,plain,
( ~ ssList(sK6)
| ~ ssList(sK7)
| ~ ssItem(sK5)
| ~ leq(sK5,sK4(sK5,sK6,sK7)) ),
inference(trivial_inequality_removal,[],[f253]) ).
fof(f255,plain,
( ~ ssList(sK7)
| ~ ssItem(sK5)
| ~ leq(sK5,sK4(sK5,sK6,sK7)) ),
inference(forward_subsumption_resolution,[],[f254,f229]) ).
fof(f256,plain,
( ~ ssItem(sK5)
| ~ leq(sK5,sK4(sK5,sK6,sK7)) ),
inference(forward_subsumption_resolution,[],[f255,f230]) ).
fof(f257,plain,
~ leq(sK5,sK4(sK5,sK6,sK7)),
inference(forward_subsumption_resolution,[],[f256,f228]) ).
fof(f258,plain,
( ~ ssItem(sK4(sK5,sK6,sK7))
| ~ memberP(sK6,sK4(sK5,sK6,sK7))
| ~ memberP(sK7,sK4(sK5,sK6,sK7))
| ~ lt(sK5,sK4(sK5,sK6,sK7)) ),
inference(resolution,[],[f257,f232]) ).
fof(f259,plain,
( ~ memberP(sK6,sK4(sK5,sK6,sK7))
| ~ memberP(sK7,sK4(sK5,sK6,sK7))
| ~ lt(sK5,sK4(sK5,sK6,sK7)) ),
inference(forward_subsumption_resolution,[],[f258,f237]) ).
fof(f260,plain,
( ~ memberP(sK7,sK4(sK5,sK6,sK7))
| ~ lt(sK5,sK4(sK5,sK6,sK7)) ),
inference(forward_subsumption_resolution,[],[f259,f242]) ).
fof(f261,plain,
~ lt(sK5,sK4(sK5,sK6,sK7)),
inference(forward_subsumption_resolution,[],[f260,f247]) ).
fof(f262,plain,
$false,
inference(forward_subsumption_resolution,[],[f261,f252]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC242+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n005.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 08:38:31 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.64/0.97 % (644009)Detected formulas, will run a generic FOF schedule.
% 0.64/0.97 % (644018)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1626788754:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.64/0.97 % (644018)First to succeed.
% 0.64/0.97 % (644018)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-644009"
% 0.64/0.97 % (644016)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=3778846571:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.64/0.97 % (644014)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=4200564961:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.64/0.97 % (644017)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2881805694:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.64/0.97 % (644015)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=1808218612:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.64/0.97 % (644020)dis-21_1_sil=8000:lcm=predicate:random_seed=2969290581: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)
% 0.64/0.97 % (644020)Also succeeded, but the first one will report.
% 0.64/0.97 % (644019)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1867070552:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.64/0.97 % (644017)Also succeeded, but the first one will report.
% 0.64/0.97 % (644019)Also succeeded, but the first one will report.
% 0.64/0.97 % (644018)Refutation found. Thanks to Tanya!
% 0.64/0.97 % SZS status Theorem for theBenchmark
% 0.64/0.97 % SZS output start Proof for theBenchmark
% See solution above
% 2.81/1.17 % (644018)------------------------------
% 2.81/1.17 % (644018)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/1.17 % (644018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/1.17 % (644018)CaDiCaL version: 2.1.3
% 2.81/1.17 % (644018)Termination reason: Refutation
% 2.81/1.17 % (644018)Time elapsed: 0.003 s
% 2.81/1.17 % (644018)Peak memory usage: 88 MB
% 2.81/1.17 % (644018)Instructions burned: 6 (million)
% 2.81/1.17 % (644018)------------------------------
% 2.81/1.17 % (644018)------------------------------
% 2.81/1.17 % (644009)Success in time 0.31 s
% 2.81/1.17 % Vampire exiting
%------------------------------------------------------------------------------