%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC364+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 : n020.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 01:03:38 PM UTC 2026
% Result : Theorem 2.95s 1.11s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 75 ( 18 unt; 6 def)
% Number of atoms : 249 ( 32 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 284 ( 110 ~; 106 |; 45 &)
% ( 8 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 46 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ! [X4] :
( ssItem(X4)
=> app(cons(X4,nil),X2) != X3 )
| segmentP(X1,X0) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
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
| ( ( ~ neq(X1,nil)
| ! [X4] :
( ssItem(X4)
=> app(cons(X4,nil),X2) != X3 )
| segmentP(X1,X0) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ? [X4] :
( app(cons(X4,nil),X2) = X3
& ssItem(X4) )
& ~ segmentP(X1,X0) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ? [X4] :
( app(cons(X4,nil),X2) = X3
& ssItem(X4) )
& ~ segmentP(X1,X0) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f107,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f129,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f130,plain,
( sK1 = sK3
& sK0 = sK2
& ( ( neq(sK1,nil)
& sK3 = app(cons(sK4,nil),sK2)
& ssItem(sK4)
& ~ segmentP(sK1,sK0) )
| ( neq(sK1,nil)
& ~ neq(sK3,nil) ) )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f99]) ).
fof(f138,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f129]) ).
fof(f139,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(app(X4,X1),X5) = X0 ) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f138]) ).
fof(f140,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ( ssList(sK9(X0,X1))
& ssList(sK10(X0,X1))
& app(app(sK9(X0,X1),X1),sK10(X0,X1)) = X0 )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X4,sK9(X0,X1)),skolemize(X5,sK10(X0,X1))],[f139]) ).
fof(f141,plain,
ssList(sK0),
inference(cnf_transformation,[],[f130]) ).
fof(f142,plain,
ssList(sK1),
inference(cnf_transformation,[],[f130]) ).
fof(f145,plain,
( ~ segmentP(sK1,sK0)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f130]) ).
fof(f147,plain,
( ssItem(sK4)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f130]) ).
fof(f149,plain,
( sK3 = app(cons(sK4,nil),sK2)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f130]) ).
fof(f152,plain,
( neq(sK1,nil)
| neq(sK1,nil) ),
inference(cnf_transformation,[],[f130]) ).
fof(f153,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f130]) ).
fof(f154,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f130]) ).
fof(f165,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f166,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f181,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f192,plain,
! [X2,X3,X0,X1] :
( segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,X1),X3) != X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f140]) ).
fof(f193,plain,
( neq(sK3,nil)
| neq(sK3,nil) ),
inference(definition_unfolding,[],[f152,f154,f154]) ).
fof(f198,plain,
( ~ segmentP(sK3,sK2)
| ~ neq(sK3,nil) ),
inference(definition_unfolding,[],[f145,f154,f153]) ).
fof(f199,plain,
ssList(sK3),
inference(definition_unfolding,[],[f142,f154]) ).
fof(f200,plain,
ssList(sK2),
inference(definition_unfolding,[],[f141,f153]) ).
fof(f216,plain,
! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ),
inference(equality_resolution,[],[f192]) ).
fof(f219,plain,
neq(sK3,nil),
inference(duplicate_literal_removal,[],[f193]) ).
fof(f221,definition,
( spl18_1
<=> neq(sK3,nil) ),
introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).
fof(f225,definition,
( spl18_2
<=> segmentP(sK3,sK2) ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
fof(f227,plain,
( ~ segmentP(sK3,sK2)
| spl18_2 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f228,plain,
( ~ spl18_1
| ~ spl18_2 ),
inference(avatar_split_clause,[],[f198,f225,f221]) ).
fof(f231,definition,
( spl18_3
<=> ssItem(sK4) ),
introduced(definition,[new_symbols(definition,[spl18_3])],[avatar_definition]) ).
fof(f233,plain,
( ssItem(sK4)
| ~ spl18_3 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f234,plain,
( ~ spl18_1
| spl18_3 ),
inference(avatar_split_clause,[],[f147,f231,f221]) ).
fof(f237,definition,
( spl18_4
<=> sK3 = app(cons(sK4,nil),sK2) ),
introduced(definition,[new_symbols(definition,[spl18_4])],[avatar_definition]) ).
fof(f239,plain,
( sK3 = app(cons(sK4,nil),sK2)
| ~ spl18_4 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f240,plain,
( ~ spl18_1
| spl18_4 ),
inference(avatar_split_clause,[],[f149,f237,f221]) ).
fof(f242,plain,
spl18_1,
inference(avatar_split_clause,[],[f219,f221]) ).
fof(f257,plain,
( ! [X0] :
( segmentP(app(sK3,X0),sK2)
| ~ ssList(cons(sK4,nil))
| ~ ssList(X0)
| ~ ssList(sK2)
| ~ ssList(app(sK3,X0)) )
| ~ spl18_4 ),
inference(superposition,[],[f216,f239]) ).
fof(f258,plain,
( ! [X0] :
( segmentP(app(sK3,X0),sK2)
| ~ ssList(cons(sK4,nil))
| ~ ssList(X0)
| ~ ssList(app(sK3,X0)) )
| ~ spl18_4 ),
inference(forward_subsumption_resolution,[],[f257,f200]) ).
fof(f271,definition,
( spl18_5
<=> ssList(cons(sK4,nil)) ),
introduced(definition,[new_symbols(definition,[spl18_5])],[avatar_definition]) ).
fof(f273,plain,
( ~ ssList(cons(sK4,nil))
| spl18_5 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f275,definition,
( spl18_6
<=> ! [X0] :
( segmentP(app(sK3,X0),sK2)
| ~ ssList(app(sK3,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[spl18_6])],[avatar_definition]) ).
fof(f276,plain,
( ! [X0] :
( segmentP(app(sK3,X0),sK2)
| ~ ssList(app(sK3,X0))
| ~ ssList(X0) )
| ~ spl18_6 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f277,plain,
( ~ spl18_5
| spl18_6
| ~ spl18_4 ),
inference(avatar_split_clause,[],[f258,f237,f275,f271]) ).
fof(f332,plain,
( ~ ssItem(sK4)
| ~ ssList(nil)
| spl18_5 ),
inference(resolution,[],[f273,f165]) ).
fof(f334,plain,
( ~ ssList(nil)
| ~ spl18_3
| spl18_5 ),
inference(forward_subsumption_resolution,[],[f332,f233]) ).
fof(f335,plain,
( $false
| ~ spl18_3
| spl18_5 ),
inference(forward_subsumption_resolution,[],[f334,f181]) ).
fof(f336,plain,
( ~ spl18_3
| spl18_5 ),
inference(avatar_contradiction_clause,[],[f335]) ).
fof(f354,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK3)
| ~ ssList(nil)
| ~ ssList(sK3)
| ~ spl18_6 ),
inference(superposition,[],[f276,f166]) ).
fof(f357,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK3)
| ~ ssList(nil)
| ~ spl18_6 ),
inference(duplicate_literal_removal,[],[f354]) ).
fof(f361,plain,
( ~ ssList(sK3)
| ~ ssList(nil)
| spl18_2
| ~ spl18_6 ),
inference(forward_subsumption_resolution,[],[f357,f227]) ).
fof(f365,plain,
( ~ ssList(nil)
| spl18_2
| ~ spl18_6 ),
inference(forward_subsumption_resolution,[],[f361,f199]) ).
fof(f378,plain,
( $false
| spl18_2
| ~ spl18_6 ),
inference(forward_subsumption_resolution,[],[f365,f181]) ).
fof(f379,plain,
( spl18_2
| ~ spl18_6 ),
inference(avatar_contradiction_clause,[],[f378]) ).
cnf(s1,plain,
( ~ spl18_1
| ~ spl18_2 ),
inference(sat_conversion,[],[f228]) ).
cnf(s3,plain,
( ~ spl18_1
| spl18_3 ),
inference(sat_conversion,[],[f234]) ).
cnf(s5,plain,
( ~ spl18_1
| spl18_4 ),
inference(sat_conversion,[],[f240]) ).
cnf(s7,plain,
spl18_1,
inference(sat_conversion,[],[f242]) ).
cnf(s8,plain,
( ~ spl18_4
| ~ spl18_5
| spl18_6 ),
inference(sat_conversion,[],[f277]) ).
cnf(s20,plain,
( ~ spl18_3
| spl18_5 ),
inference(sat_conversion,[],[f336]) ).
cnf(s23,plain,
( spl18_2
| ~ spl18_6 ),
inference(sat_conversion,[],[f379]) ).
cnf(s24,plain,
spl18_4,
inference(rat,[],[s5,s7]) ).
cnf(s25,plain,
spl18_3,
inference(rat,[],[s3,s7]) ).
cnf(s26,plain,
spl18_5,
inference(rat,[],[s20,s25]) ).
cnf(s32,plain,
spl18_6,
inference(rat,[],[s8,s24,s26]) ).
cnf(s33,plain,
spl18_2,
inference(rat,[],[s23,s32]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s1,s33,s7]) ).
fof(f380,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC364+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.19 % Computer : n020.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Mon Sep 28 09:18:42 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.23 Running first-order theorem proving
% 0.06/0.23 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
% 2.95/1.11 % (49450)Detected formulas, will run a generic FOF schedule.
% 2.95/1.11 % (49456)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=425330489:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.95/1.11 % (49457)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=1577641927:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.95/1.11 % (49455)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=4272478175:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.95/1.11 % (49458)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=797284082:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.95/1.11 % (49458)First to succeed.
% 2.95/1.11 % (49458)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-49450"
% 2.95/1.11 % (49459)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1293182397:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.95/1.11 % (49460)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4039152108:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.95/1.11 % (49461)dis-21_1_sil=8000:lcm=predicate:random_seed=2492434336: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)
% 2.95/1.11 % (49459)Also succeeded, but the first one will report.
% 2.95/1.11 % (49460)Also succeeded, but the first one will report.
% 2.95/1.11 % (49461)Instruction limit reached!
% 2.95/1.11 % (49461)------------------------------
% 2.95/1.11 % (49461)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.11 % (49461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.11 % (49461)CaDiCaL version: 2.1.3
% 2.95/1.11 % (49461)Termination reason: Instruction limit
% 2.95/1.11 % (49461)Termination phase: Saturation
% 2.95/1.11 % (49461)Time elapsed: 0.075 s
% 2.95/1.11 % (49461)Peak memory usage: 90 MB
% 2.95/1.11 % (49461)Instructions burned: 129 (million)
% 2.95/1.11 % (49458)Refutation found. Thanks to Tanya!
% 2.95/1.11 % SZS status Theorem for theBenchmark
% 2.95/1.11 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.20 % (49458)------------------------------
% 0.19/1.20 % (49458)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.20 % (49458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.20 % (49458)CaDiCaL version: 2.1.3
% 0.19/1.20 % (49458)Termination reason: Refutation
% 0.19/1.20 % (49458)Time elapsed: 0.007 s
% 0.19/1.20 % (49458)Peak memory usage: 89 MB
% 0.19/1.20 % (49458)Instructions burned: 8 (million)
% 0.19/1.20 % (49458)------------------------------
% 0.19/1.20 % (49458)------------------------------
% 0.19/1.20 % (49450)Success in time 0.433 s
% 0.19/1.20 % Vampire exiting
%------------------------------------------------------------------------------