%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC054-1 : 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 : n002.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 01:02:13 PM UTC 2026
% Result : Unsatisfiable 3.56s 1.50s
% Output : Refutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 58 ( 8 unt; 8 def)
% Number of atoms : 145 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 171 ( 84 ~; 79 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 6 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
( nil = sk3
| nil != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
( ssList(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
( neq(sk5,nil)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
( segmentP(sk4,sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f210,negated_conjecture,
( segmentP(sk3,sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f211,negated_conjecture,
( nil = sk2
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f212,negated_conjecture,
! [X0] :
( nil = sk2
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk2,X0)
| ~ segmentP(sk1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f213,negated_conjecture,
( nil != sk1
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
fof(f214,negated_conjecture,
! [X0] :
( nil != sk1
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk2,X0)
| ~ segmentP(sk1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
fof(f217,plain,
( nil = sk4
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f211,f204,f204]) ).
fof(f218,plain,
! [X0] :
( nil = sk4
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(definition_unfolding,[],[f212,f204,f204,f205]) ).
fof(f219,plain,
( nil != sk3
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f213,f205,f204]) ).
fof(f220,plain,
! [X0] :
( nil != sk3
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(definition_unfolding,[],[f214,f205,f204,f205]) ).
fof(f229,definition,
( spl0_1
<=> ! [X0] :
( ~ ssList(X0)
| ~ segmentP(sk3,X0)
| ~ segmentP(sk4,X0)
| ~ neq(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f230,plain,
( ! [X0] :
( ~ neq(X0,nil)
| ~ segmentP(sk3,X0)
| ~ segmentP(sk4,X0)
| ~ ssList(X0) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f232,definition,
( spl0_2
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f235,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f220,f232,f229]) ).
fof(f237,definition,
( spl0_3
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f240,plain,
( spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f219,f232,f237]) ).
fof(f242,definition,
( spl0_4
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f245,plain,
( spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f218,f242,f229]) ).
fof(f246,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f217,f242,f237]) ).
fof(f248,definition,
( spl0_5
<=> segmentP(sk3,sk5) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f250,plain,
( segmentP(sk3,sk5)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f251,plain,
( ~ spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f210,f248,f237]) ).
fof(f253,definition,
( spl0_6
<=> segmentP(sk4,sk5) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f255,plain,
( segmentP(sk4,sk5)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f256,plain,
( ~ spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f209,f253,f237]) ).
fof(f258,definition,
( spl0_7
<=> neq(sk5,nil) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f260,plain,
( neq(sk5,nil)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f261,plain,
( ~ spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f208,f258,f237]) ).
fof(f263,definition,
( spl0_8
<=> ssList(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f265,plain,
( ssList(sk5)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f266,plain,
( ~ spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f207,f263,f237]) ).
fof(f267,plain,
( ~ spl0_4
| spl0_2 ),
inference(avatar_split_clause,[],[f206,f232,f242]) ).
fof(f271,plain,
( ~ segmentP(sk3,sk5)
| ~ segmentP(sk4,sk5)
| ~ ssList(sk5)
| ~ spl0_1
| ~ spl0_7 ),
inference(resolution,[],[f230,f260]) ).
fof(f272,plain,
( ~ segmentP(sk3,sk5)
| ~ ssList(sk5)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f271,f255]) ).
fof(f274,plain,
( ~ segmentP(sk3,sk5)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f272,f265]) ).
fof(f280,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f274,f250]) ).
fof(f281,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f280]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f235]) ).
cnf(s2,plain,
( ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f240]) ).
cnf(s3,plain,
( spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f245]) ).
cnf(s4,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f246]) ).
cnf(s5,plain,
( ~ spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f251]) ).
cnf(s6,plain,
( ~ spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f256]) ).
cnf(s7,plain,
( ~ spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f261]) ).
cnf(s8,plain,
( ~ spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f266]) ).
cnf(s9,plain,
( spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f267]) ).
cnf(s11,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f281]) ).
cnf(s12,plain,
spl0_1,
inference(rat,[],[s9,s1,s3]) ).
cnf(s13,plain,
~ spl0_3,
inference(rat,[],[s11,s5,s6,s7,s8,s12]) ).
cnf(s14,plain,
spl0_4,
inference(rat,[],[s4,s13]) ).
cnf(s15,plain,
~ spl0_2,
inference(rat,[],[s2,s13]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s9,s14,s15]) ).
fof(f282,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC054-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n002.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 07:40:52 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.56/1.50 % (188738)Input is clausal, will run a generic CNF schedule.
% 3.56/1.50 % (188846)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2914642267:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.56/1.50 % (188850)dis-21_1_sil=8000:lcm=predicate:random_seed=1673446950: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)
% 3.56/1.50 % (188844)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=1163960368:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.56/1.50 % (188849)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3835329017:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.56/1.50 % (188847)lrs+10_1_sil=8000:sp=occurrence:random_seed=2396499263:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.56/1.50 % (188845)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2165843321:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.56/1.50 % (188847)First to succeed.
% 3.56/1.50 % (188850)Also succeeded, but the first one will report.
% 3.56/1.50 % (188847)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-188738"
% 3.56/1.50 % (188849)Also succeeded, but the first one will report.
% 3.56/1.50 % (188848)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1432114487:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.56/1.50 % (188848)Also succeeded, but the first one will report.
% 3.56/1.50 % (188847)Refutation found. Thanks to Tanya!
% 3.56/1.50 % SZS status Unsatisfiable for theBenchmark
% 3.56/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 3.56/1.50 % (188847)------------------------------
% 3.56/1.50 % (188847)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.50 % (188847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.50 % (188847)CaDiCaL version: 2.1.3
% 3.56/1.50 % (188847)Termination reason: Refutation
% 3.56/1.50 % (188847)Time elapsed: 0.004 s
% 3.56/1.50 % (188847)Peak memory usage: 89 MB
% 3.56/1.50 % (188847)Instructions burned: 3 (million)
% 3.56/1.50 % (188847)------------------------------
% 3.56/1.50 % (188847)------------------------------
% 3.56/1.50 % (188738)Success in time 0.427 s
% 3.56/1.50 % Vampire exiting
%------------------------------------------------------------------------------