%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC241-1 : 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 01:03:05 PM UTC 2026
% Result : Unsatisfiable 3.49s 1.26s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 71 ( 12 unt; 6 def)
% Number of atoms : 239 ( 25 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 331 ( 163 ~; 162 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 29 ( 0 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f106,axiom,
! [X0,X1] :
( ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0)
| leq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause103) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
nil != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,cons(X0,nil)),X2) != sk1
| ssItem(sk5(X2,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| sk1 != app(app(X1,cons(X0,nil)),X2)
| ssItem(sk5(X2,X1,X0)) ),
inference(reorient_equations,[],[f207]) ).
fof(f213,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,cons(X0,nil)),X2) != sk1
| lt(X0,sk5(X2,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f214,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| sk1 != app(app(X1,cons(X0,nil)),X2)
| lt(X0,sk5(X2,X1,X0)) ),
inference(reorient_equations,[],[f213]) ).
fof(f215,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ leq(X0,sk5(X2,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f216,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| sk1 != app(app(X1,cons(X0,nil)),X2)
| ~ leq(X0,sk5(X2,X1,X0)) ),
inference(reorient_equations,[],[f215]) ).
fof(f217,negated_conjecture,
( nil = sk3
| ssItem(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f218,negated_conjecture,
( nil = sk3
| ssList(sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f219,negated_conjecture,
( nil = sk3
| ssList(sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f220,negated_conjecture,
( nil = sk3
| app(app(sk7,cons(sk6,nil)),sk8) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f221,plain,
( nil = sk3
| sk3 = app(app(sk7,cons(sk6,nil)),sk8) ),
inference(reorient_equations,[],[f220]) ).
fof(f225,plain,
nil != sk3,
inference(definition_unfolding,[],[f206,f205]) ).
fof(f226,plain,
! [X2,X0,X1] :
( sk3 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X0)
| ssItem(sk5(X2,X1,X0)) ),
inference(definition_unfolding,[],[f208,f205]) ).
fof(f229,plain,
! [X2,X0,X1] :
( sk3 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X0)
| lt(X0,sk5(X2,X1,X0)) ),
inference(definition_unfolding,[],[f214,f205]) ).
fof(f230,plain,
! [X2,X0,X1] :
( sk3 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X0)
| ~ leq(X0,sk5(X2,X1,X0)) ),
inference(definition_unfolding,[],[f216,f205]) ).
fof(f243,definition,
( spl0_2
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f248,definition,
( spl0_3
<=> sk3 = app(app(sk7,cons(sk6,nil)),sk8) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f250,plain,
( sk3 = app(app(sk7,cons(sk6,nil)),sk8)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f251,plain,
( spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f221,f243,f248]) ).
fof(f253,definition,
( spl0_4
<=> ssList(sk8) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f255,plain,
( ssList(sk8)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f256,plain,
( spl0_4
| spl0_2 ),
inference(avatar_split_clause,[],[f219,f243,f253]) ).
fof(f258,definition,
( spl0_5
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f260,plain,
( ssList(sk7)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f261,plain,
( spl0_5
| spl0_2 ),
inference(avatar_split_clause,[],[f218,f243,f258]) ).
fof(f263,definition,
( spl0_6
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f265,plain,
( ssItem(sk6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f266,plain,
( spl0_6
| spl0_2 ),
inference(avatar_split_clause,[],[f217,f243,f263]) ).
fof(f267,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f225,f243]) ).
fof(f268,plain,
( sk3 != sk3
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ssItem(sk5(sk8,sk7,sk6))
| ~ spl0_3 ),
inference(superposition,[],[f226,f250]) ).
fof(f269,plain,
( ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ssItem(sk5(sk8,sk7,sk6))
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f268]) ).
fof(f270,plain,
( ~ ssList(sk8)
| ~ ssItem(sk6)
| ssItem(sk5(sk8,sk7,sk6))
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f269,f260]) ).
fof(f271,plain,
( ~ ssItem(sk6)
| ssItem(sk5(sk8,sk7,sk6))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f270,f255]) ).
fof(f272,plain,
( ssItem(sk5(sk8,sk7,sk6))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f271,f265]) ).
fof(f291,definition,
( spl0_8
<=> leq(sk6,sk5(sk8,sk7,sk6)) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f292,plain,
( leq(sk6,sk5(sk8,sk7,sk6))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f293,plain,
( ~ leq(sk6,sk5(sk8,sk7,sk6))
| spl0_8 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f295,plain,
( sk3 != sk3
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| lt(sk6,sk5(sk8,sk7,sk6))
| ~ spl0_3 ),
inference(superposition,[],[f229,f250]) ).
fof(f296,plain,
( ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| lt(sk6,sk5(sk8,sk7,sk6))
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f295]) ).
fof(f297,plain,
( ~ ssList(sk8)
| ~ ssItem(sk6)
| lt(sk6,sk5(sk8,sk7,sk6))
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f296,f260]) ).
fof(f298,plain,
( ~ ssItem(sk6)
| lt(sk6,sk5(sk8,sk7,sk6))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f297,f255]) ).
fof(f299,plain,
( lt(sk6,sk5(sk8,sk7,sk6))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f298,f265]) ).
fof(f300,plain,
( sk3 != sk3
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ spl0_3 ),
inference(superposition,[],[f230,f250]) ).
fof(f301,plain,
( ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f300]) ).
fof(f323,plain,
( ~ ssItem(sk5(sk8,sk7,sk6))
| ~ ssItem(sk6)
| leq(sk6,sk5(sk8,sk7,sk6))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(resolution,[],[f106,f299]) ).
fof(f324,plain,
( ~ ssItem(sk6)
| leq(sk6,sk5(sk8,sk7,sk6))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f323,f272]) ).
fof(f325,plain,
( leq(sk6,sk5(sk8,sk7,sk6))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f324,f265]) ).
fof(f326,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f325,f293]) ).
fof(f327,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f326]) ).
fof(f328,plain,
( ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f301,f260]) ).
fof(f329,plain,
( ~ ssItem(sk6)
| ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f328,f255]) ).
fof(f330,plain,
( ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f329,f265]) ).
fof(f331,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f330,f292]) ).
fof(f332,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f331]) ).
cnf(s2,plain,
( spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f251]) ).
cnf(s3,plain,
( spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f256]) ).
cnf(s4,plain,
( spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f261]) ).
cnf(s5,plain,
( spl0_2
| spl0_6 ),
inference(sat_conversion,[],[f266]) ).
cnf(s6,plain,
~ spl0_2,
inference(sat_conversion,[],[f267]) ).
cnf(s8,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f327]) ).
cnf(s9,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f332]) ).
cnf(s10,plain,
spl0_6,
inference(rat,[],[s5,s6]) ).
cnf(s11,plain,
spl0_5,
inference(rat,[],[s4,s6]) ).
cnf(s12,plain,
spl0_4,
inference(rat,[],[s3,s6]) ).
cnf(s13,plain,
spl0_3,
inference(rat,[],[s2,s6]) ).
cnf(s14,plain,
~ spl0_8,
inference(rat,[],[s9,s12,s10,s11,s13]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s8,s12,s10,s11,s14,s13]) ).
fof(f333,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC241-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n020.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 08:39:35 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 3.49/1.26 % (36302)Input is clausal, will run a generic CNF schedule.
% 3.49/1.26 % (36309)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3130095169:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.49/1.26 % (36310)lrs+10_1_sil=8000:sp=occurrence:random_seed=2000269595:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.49/1.26 % (36308)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=253404558:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.49/1.26 % (36311)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2612667669:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.49/1.26 % (36312)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=526023593:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.49/1.26 % (36307)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=3247960711:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.49/1.26 % (36310)First to succeed.
% 3.49/1.26 % (36311)Also succeeded, but the first one will report.
% 3.49/1.26 % (36310)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-36302"
% 3.49/1.26 % (36313)dis-21_1_sil=8000:lcm=predicate:random_seed=2851606000:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.49/1.26 % (36312)Also succeeded, but the first one will report.
% 3.49/1.26 % (36313)Also succeeded, but the first one will report.
% 3.49/1.26 % (36310)Refutation found. Thanks to Tanya!
% 3.49/1.26 % SZS status Unsatisfiable for theBenchmark
% 3.49/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.26 % (36310)------------------------------
% 3.49/1.26 % (36310)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.26 % (36310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.26 % (36310)CaDiCaL version: 2.1.3
% 3.49/1.26 % (36310)Termination reason: Refutation
% 3.49/1.26 % (36310)Time elapsed: 0.006 s
% 3.49/1.26 % (36310)Peak memory usage: 90 MB
% 3.49/1.26 % (36310)Instructions burned: 7 (million)
% 3.49/1.26 % (36310)------------------------------
% 3.49/1.26 % (36310)------------------------------
% 3.49/1.26 % (36302)Success in time 0.411 s
% 3.49/1.26 % Vampire exiting
%------------------------------------------------------------------------------