%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC279+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 : n012.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 01:03:15 PM UTC 2026
% Result : Theorem 2.66s 0.74s
% Output : Refutation 3.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 72 ( 17 unt; 8 def)
% Number of atoms : 290 ( 25 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 357 ( 139 ~; 135 |; 61 &)
% ( 6 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 5 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 91 ( 0 sgn 67 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X2
& ? [X7] :
( ssItem(X7)
& ( ( ~ leq(X4,X7)
& memberP(X6,X7) )
| ( ~ leq(X7,X4)
& memberP(X5,X7) ) ) ) ) ) )
| ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( app(app(X9,cons(X8,nil)),X10) != X0
| ! [X11] :
( ssItem(X11)
=> ( ( ~ memberP(X9,X11)
| leq(X11,X8) )
& ( ~ memberP(X10,X11)
| leq(X8,X11) ) ) ) ) ) ) ) ) ) ) ) ),
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)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X2
& ? [X7] :
( ssItem(X7)
& ( ( ~ leq(X4,X7)
& memberP(X6,X7) )
| ( ~ leq(X7,X4)
& memberP(X5,X7) ) ) ) ) ) )
| ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( app(app(X9,cons(X8,nil)),X10) != X0
| ! [X11] :
( ssItem(X11)
=> ( ( ~ memberP(X9,X11)
| leq(X11,X8) )
& ( ~ memberP(X10,X11)
| leq(X8,X11) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X2
| ! [X7] :
( ~ ssItem(X7)
| ( ( leq(X4,X7)
| ~ memberP(X6,X7) )
& ( leq(X7,X4)
| ~ memberP(X5,X7) ) ) ) ) ) )
& ? [X8] :
( ? [X9] :
( ? [X10] :
( app(app(X9,cons(X8,nil)),X10) = X0
& ? [X11] :
( ( ( memberP(X9,X11)
& ~ leq(X11,X8) )
| ( memberP(X10,X11)
& ~ leq(X8,X11) ) )
& ssItem(X11) )
& ssList(X10) )
& ssList(X9) )
& ssItem(X8) )
& 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)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X2
| ! [X7] :
( ~ ssItem(X7)
| ( ( leq(X4,X7)
| ~ memberP(X6,X7) )
& ( leq(X7,X4)
| ~ memberP(X5,X7) ) ) ) ) ) )
& ? [X8] :
( ? [X9] :
( ? [X10] :
( app(app(X9,cons(X8,nil)),X10) = X0
& ? [X11] :
( ( ( memberP(X9,X11)
& ~ leq(X11,X8) )
| ( memberP(X10,X11)
& ~ leq(X8,X11) ) )
& ssItem(X11) )
& ssList(X10) )
& ssList(X9) )
& ssItem(X8) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f127,plain,
( sK1 = sK3
& sK0 = sK2
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK2
| ! [X7] :
( ~ ssItem(X7)
| ( ( leq(X4,X7)
| ~ memberP(X6,X7) )
& ( leq(X7,X4)
| ~ memberP(X5,X7) ) ) ) ) ) )
& sK0 = app(app(sK5,cons(sK4,nil)),sK6)
& ( ( memberP(sK5,sK7)
& ~ leq(sK7,sK4) )
| ( memberP(sK6,sK7)
& ~ leq(sK4,sK7) ) )
& ssItem(sK7)
& ssList(sK6)
& ssList(sK5)
& ssItem(sK4)
& ssList(sK3)
& 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(X8,sK4),skolemize(X9,sK5),skolemize(X10,sK6),skolemize(X11,sK7)],[f99]) ).
fof(f143,plain,
ssItem(sK4),
inference(cnf_transformation,[],[f127]) ).
fof(f144,plain,
ssList(sK5),
inference(cnf_transformation,[],[f127]) ).
fof(f145,plain,
ssList(sK6),
inference(cnf_transformation,[],[f127]) ).
fof(f146,plain,
ssItem(sK7),
inference(cnf_transformation,[],[f127]) ).
fof(f147,plain,
( ~ leq(sK7,sK4)
| ~ leq(sK4,sK7) ),
inference(cnf_transformation,[],[f127]) ).
fof(f148,plain,
( ~ leq(sK7,sK4)
| memberP(sK6,sK7) ),
inference(cnf_transformation,[],[f127]) ).
fof(f149,plain,
( memberP(sK5,sK7)
| ~ leq(sK4,sK7) ),
inference(cnf_transformation,[],[f127]) ).
fof(f150,plain,
( memberP(sK5,sK7)
| memberP(sK6,sK7) ),
inference(cnf_transformation,[],[f127]) ).
fof(f151,plain,
sK0 = app(app(sK5,cons(sK4,nil)),sK6),
inference(cnf_transformation,[],[f127]) ).
fof(f152,plain,
! [X6,X7,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK2
| ~ ssItem(X7)
| leq(X7,X4)
| ~ memberP(X5,X7) ),
inference(cnf_transformation,[],[f127]) ).
fof(f153,plain,
! [X6,X7,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK2
| ~ ssItem(X7)
| leq(X4,X7)
| ~ memberP(X6,X7) ),
inference(cnf_transformation,[],[f127]) ).
fof(f154,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f127]) ).
fof(f193,plain,
sK2 = app(app(sK5,cons(sK4,nil)),sK6),
inference(definition_unfolding,[],[f151,f154]) ).
fof(f196,definition,
~ sP14(sK2),
introduced(definition,[new_symbols(definition,[sP14])],[inequality_splitting_name_introduction]) ).
fof(f197,plain,
! [X6,X7,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| sP14(app(app(X5,cons(X4,nil)),X6))
| ~ ssItem(X7)
| leq(X4,X7)
| ~ memberP(X6,X7) ),
inference(inequality_splitting,[],[f153,f196]) ).
fof(f198,definition,
~ sP15(sK2),
introduced(definition,[new_symbols(definition,[sP15])],[inequality_splitting_name_introduction]) ).
fof(f199,plain,
! [X6,X7,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| sP15(app(app(X5,cons(X4,nil)),X6))
| ~ ssItem(X7)
| leq(X7,X4)
| ~ memberP(X5,X7) ),
inference(inequality_splitting,[],[f152,f198]) ).
fof(f213,plain,
! [X6,X7,X4] :
( ~ memberP(X6,X7)
| leq(X4,X7)
| ~ ssItem(X7)
| sP22(X4,X6) ),
inference(cnf_transformation,[],[f213_D]) ).
fof(f213_D,definition,
! [X6,X4] :
( ! [X7] :
( ~ memberP(X6,X7)
| leq(X4,X7)
| ~ ssItem(X7) )
<=> ~ sP22(X4,X6) ),
introduced(definition,[new_symbols(definition,[sP22])],[general_splitting_component_introduction]) ).
fof(f214,plain,
! [X6,X4,X5] :
( sP14(app(app(X5,cons(X4,nil)),X6))
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| ~ sP22(X4,X6) ),
inference(general_splitting,[],[f197,f213_D]) ).
fof(f215,plain,
! [X6,X4,X5] :
( sP15(app(app(X5,cons(X4,nil)),X6))
| ~ ssList(X6)
| sP23(X5,X4) ),
inference(cnf_transformation,[],[f215_D]) ).
fof(f215_D,definition,
! [X4,X5] :
( ! [X6] :
( sP15(app(app(X5,cons(X4,nil)),X6))
| ~ ssList(X6) )
<=> ~ sP23(X5,X4) ),
introduced(definition,[new_symbols(definition,[sP23])],[general_splitting_component_introduction]) ).
fof(f216,plain,
! [X7,X4,X5] :
( ~ sP23(X5,X4)
| ~ ssList(X5)
| ~ ssItem(X7)
| leq(X7,X4)
| ~ memberP(X5,X7)
| ~ ssItem(X4) ),
inference(general_splitting,[],[f199,f215_D]) ).
fof(f219,definition,
( spl24_1
<=> leq(sK4,sK7) ),
introduced(definition,[new_symbols(definition,[spl24_1])],[avatar_definition]) ).
fof(f221,plain,
( ~ leq(sK4,sK7)
| spl24_1 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f223,definition,
( spl24_2
<=> leq(sK7,sK4) ),
introduced(definition,[new_symbols(definition,[spl24_2])],[avatar_definition]) ).
fof(f225,plain,
( ~ leq(sK7,sK4)
| spl24_2 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f226,plain,
( ~ spl24_1
| ~ spl24_2 ),
inference(avatar_split_clause,[],[f147,f223,f219]) ).
fof(f228,definition,
( spl24_3
<=> memberP(sK6,sK7) ),
introduced(definition,[new_symbols(definition,[spl24_3])],[avatar_definition]) ).
fof(f230,plain,
( memberP(sK6,sK7)
| ~ spl24_3 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f231,plain,
( spl24_3
| ~ spl24_2 ),
inference(avatar_split_clause,[],[f148,f223,f228]) ).
fof(f233,definition,
( spl24_4
<=> memberP(sK5,sK7) ),
introduced(definition,[new_symbols(definition,[spl24_4])],[avatar_definition]) ).
fof(f235,plain,
( memberP(sK5,sK7)
| ~ spl24_4 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f236,plain,
( ~ spl24_1
| spl24_4 ),
inference(avatar_split_clause,[],[f149,f233,f219]) ).
fof(f237,plain,
( spl24_3
| spl24_4 ),
inference(avatar_split_clause,[],[f150,f233,f228]) ).
fof(f385,plain,
( sP15(sK2)
| ~ ssList(sK6)
| sP23(sK5,sK4) ),
inference(superposition,[],[f215,f193]) ).
fof(f402,plain,
( ~ ssList(sK6)
| sP23(sK5,sK4) ),
inference(forward_subsumption_resolution,[],[f385,f198]) ).
fof(f410,plain,
sP23(sK5,sK4),
inference(forward_subsumption_resolution,[],[f402,f145]) ).
fof(f411,plain,
! [X0] :
( ~ ssList(sK5)
| ~ ssItem(X0)
| leq(X0,sK4)
| ~ memberP(sK5,X0)
| ~ ssItem(sK4) ),
inference(resolution,[],[f410,f216]) ).
fof(f412,plain,
! [X0] :
( ~ ssItem(X0)
| leq(X0,sK4)
| ~ memberP(sK5,X0)
| ~ ssItem(sK4) ),
inference(forward_subsumption_resolution,[],[f411,f144]) ).
fof(f413,plain,
! [X0] :
( ~ memberP(sK5,X0)
| leq(X0,sK4)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[],[f412,f143]) ).
fof(f419,plain,
( sP14(sK2)
| ~ ssList(sK5)
| ~ ssList(sK6)
| ~ ssItem(sK4)
| ~ sP22(sK4,sK6) ),
inference(superposition,[],[f214,f193]) ).
fof(f434,plain,
( ~ ssList(sK5)
| ~ ssList(sK6)
| ~ ssItem(sK4)
| ~ sP22(sK4,sK6) ),
inference(forward_subsumption_resolution,[],[f419,f196]) ).
fof(f444,plain,
( ~ ssList(sK6)
| ~ ssItem(sK4)
| ~ sP22(sK4,sK6) ),
inference(forward_subsumption_resolution,[],[f434,f144]) ).
fof(f445,plain,
( ~ ssItem(sK4)
| ~ sP22(sK4,sK6) ),
inference(forward_subsumption_resolution,[],[f444,f145]) ).
fof(f446,plain,
~ sP22(sK4,sK6),
inference(forward_subsumption_resolution,[],[f445,f143]) ).
fof(f705,plain,
( leq(sK7,sK4)
| ~ ssItem(sK7)
| ~ spl24_4 ),
inference(resolution,[],[f413,f235]) ).
fof(f706,plain,
( ~ ssItem(sK7)
| spl24_2
| ~ spl24_4 ),
inference(forward_subsumption_resolution,[],[f705,f225]) ).
fof(f707,plain,
( $false
| spl24_2
| ~ spl24_4 ),
inference(forward_subsumption_resolution,[],[f706,f146]) ).
fof(f708,plain,
( spl24_2
| ~ spl24_4 ),
inference(avatar_contradiction_clause,[],[f707]) ).
fof(f710,plain,
( ! [X0] :
( leq(X0,sK7)
| ~ ssItem(sK7)
| sP22(X0,sK6) )
| ~ spl24_3 ),
inference(resolution,[],[f230,f213]) ).
fof(f711,plain,
( ! [X0] :
( sP22(X0,sK6)
| leq(X0,sK7) )
| ~ spl24_3 ),
inference(forward_subsumption_resolution,[],[f710,f146]) ).
fof(f713,plain,
( leq(sK4,sK7)
| ~ spl24_3 ),
inference(resolution,[],[f711,f446]) ).
fof(f714,plain,
( $false
| spl24_1
| ~ spl24_3 ),
inference(forward_subsumption_resolution,[],[f713,f221]) ).
fof(f715,plain,
( spl24_1
| ~ spl24_3 ),
inference(avatar_contradiction_clause,[],[f714]) ).
cnf(s1,plain,
( ~ spl24_1
| ~ spl24_2 ),
inference(sat_conversion,[],[f226]) ).
cnf(s2,plain,
( ~ spl24_2
| spl24_3 ),
inference(sat_conversion,[],[f231]) ).
cnf(s3,plain,
( ~ spl24_1
| spl24_4 ),
inference(sat_conversion,[],[f236]) ).
cnf(s4,plain,
( spl24_3
| spl24_4 ),
inference(sat_conversion,[],[f237]) ).
cnf(s52,plain,
( spl24_2
| ~ spl24_4 ),
inference(sat_conversion,[],[f708]) ).
cnf(s53,plain,
( spl24_1
| ~ spl24_3 ),
inference(sat_conversion,[],[f715]) ).
cnf(s77,plain,
spl24_3,
inference(rat,[],[s52,s2,s4]) ).
cnf(s78,plain,
spl24_1,
inference(rat,[],[s53,s77]) ).
cnf(s80,plain,
spl24_4,
inference(rat,[],[s3,s78]) ).
cnf(s81,plain,
~ spl24_2,
inference(rat,[],[s1,s78]) ).
cnf(s83,plain,
$false,
inference(rat,[],[s52,s80,s81]) ).
fof(f716,plain,
$false,
inference(avatar_sat_refutation,[],[s83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC279+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Mon Sep 28 08:50:19 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running first-order theorem proving
% 0.08/0.13 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
% 2.66/0.74 % (3241929)Detected formulas, will run a generic FOF schedule.
% 2.66/0.74 % (3241945)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1842169086:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.66/0.74 % (3241942)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=2074624055:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.66/0.74 % (3241944)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=895377558:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.66/0.74 % (3241943)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=1698506127:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.66/0.74 % (3241948)dis-21_1_sil=8000:lcm=predicate:random_seed=232705684: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)
% 2.66/0.74 % (3241947)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1064897792:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.66/0.74 % (3241946)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2176099504:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.66/0.74 % (3241945)First to succeed.
% 2.66/0.74 % (3241946)Also succeeded, but the first one will report.
% 2.66/0.74 % (3241945)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3241929"
% 2.66/0.74 % (3241948)Also succeeded, but the first one will report.
% 2.66/0.74 % (3241947)Also succeeded, but the first one will report.
% 2.66/0.74 % (3241945)Refutation found. Thanks to Tanya!
% 2.66/0.74 % SZS status Theorem for theBenchmark
% 2.66/0.74 % SZS output start Proof for theBenchmark
% See solution above
% 3.05/0.85 % (3241945)------------------------------
% 3.05/0.85 % (3241945)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.05/0.85 % (3241945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.05/0.85 % (3241945)CaDiCaL version: 2.1.3
% 3.05/0.85 % (3241945)Termination reason: Refutation
% 3.05/0.85 % (3241945)Time elapsed: 0.012 s
% 3.05/0.85 % (3241945)Peak memory usage: 90 MB
% 3.05/0.85 % (3241945)Instructions burned: 18 (million)
% 3.05/0.85 % (3241945)------------------------------
% 3.05/0.85 % (3241945)------------------------------
% 3.05/0.85 % (3241929)Success in time 0.4 s
% 3.05/0.85 % Vampire exiting
%------------------------------------------------------------------------------