%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC098-1 : 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 01:02:26 PM UTC 2026
% Result : Unsatisfiable 0.27s 0.79s
% Output : Refutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 23
% Syntax : Number of formulae : 91 ( 12 unt; 8 def)
% Number of atoms : 267 ( 52 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 332 ( 156 ~; 168 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
! [X0] :
( ~ ssItem(X0)
| cons(X0,nil) != sk1
| ssItem(sk5(X0))
| ~ memberP(sk2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
! [X0] :
( ~ ssItem(X0)
| cons(X0,nil) != sk1
| memberP(sk2,sk5(X0))
| ~ memberP(sk2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
! [X0] :
( ~ ssItem(X0)
| cons(X0,nil) != sk1
| leq(X0,sk5(X0))
| ~ memberP(sk2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
! [X0] :
( ~ ssItem(X0)
| cons(X0,nil) != sk1
| X0 != sk5(X0)
| ~ memberP(sk2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f210,plain,
! [X0] :
( ~ ssItem(X0)
| cons(X0,nil) != sk1
| sk5(X0) != X0
| ~ memberP(sk2,X0) ),
inference(reorient_equations,[],[f209]) ).
fof(f211,negated_conjecture,
( nil != sk2
| nil != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f212,negated_conjecture,
( ssItem(sk6)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f213,negated_conjecture,
( ssItem(sk6)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f214,negated_conjecture,
( cons(sk6,nil) = sk3
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f215,plain,
( sk3 = cons(sk6,nil)
| nil = sk4 ),
inference(reorient_equations,[],[f214]) ).
fof(f216,negated_conjecture,
( memberP(sk4,sk6)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f217,negated_conjecture,
! [X0] :
( ~ ssItem(X0)
| sk6 = X0
| ~ memberP(sk4,X0)
| ~ leq(sk6,X0)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f218,negated_conjecture,
( cons(sk6,nil) = sk3
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
fof(f219,plain,
( sk3 = cons(sk6,nil)
| nil = sk3 ),
inference(reorient_equations,[],[f218]) ).
fof(f220,negated_conjecture,
( memberP(sk4,sk6)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
fof(f221,negated_conjecture,
! [X0] :
( ~ ssItem(X0)
| sk6 = X0
| ~ memberP(sk4,X0)
| ~ leq(sk6,X0)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_19) ).
fof(f224,plain,
! [X0] :
( cons(X0,nil) != sk3
| ~ ssItem(X0)
| ssItem(sk5(X0))
| ~ memberP(sk4,X0) ),
inference(definition_unfolding,[],[f206,f205,f204]) ).
fof(f225,plain,
! [X0] :
( cons(X0,nil) != sk3
| ~ ssItem(X0)
| memberP(sk4,sk5(X0))
| ~ memberP(sk4,X0) ),
inference(definition_unfolding,[],[f207,f205,f204,f204]) ).
fof(f226,plain,
! [X0] :
( cons(X0,nil) != sk3
| ~ ssItem(X0)
| leq(X0,sk5(X0))
| ~ memberP(sk4,X0) ),
inference(definition_unfolding,[],[f208,f205,f204]) ).
fof(f227,plain,
! [X0] :
( cons(X0,nil) != sk3
| ~ ssItem(X0)
| sk5(X0) != X0
| ~ memberP(sk4,X0) ),
inference(definition_unfolding,[],[f210,f205,f204]) ).
fof(f228,plain,
( nil != sk4
| nil != sk3 ),
inference(definition_unfolding,[],[f211,f204,f205]) ).
fof(f245,definition,
( spl0_3
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f248,definition,
( spl0_4
<=> ! [X0] :
( ~ ssItem(X0)
| ~ leq(sk6,X0)
| ~ memberP(sk4,X0)
| sk6 = X0 ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f249,plain,
( ! [X0] :
( ~ memberP(sk4,X0)
| ~ leq(sk6,X0)
| ~ ssItem(X0)
| sk6 = X0 )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f250,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f221,f248,f245]) ).
fof(f252,definition,
( spl0_5
<=> memberP(sk4,sk6) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f253,plain,
( memberP(sk4,sk6)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f254,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f220,f252,f245]) ).
fof(f256,definition,
( spl0_6
<=> sk3 = cons(sk6,nil) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f257,plain,
( sk3 = cons(sk6,nil)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f258,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f219,f256,f245]) ).
fof(f260,definition,
( spl0_7
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f262,plain,
( spl0_7
| spl0_4 ),
inference(avatar_split_clause,[],[f217,f248,f260]) ).
fof(f263,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f216,f252,f260]) ).
fof(f264,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f215,f256,f260]) ).
fof(f266,definition,
( spl0_8
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f267,plain,
( ssItem(sk6)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f268,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f213,f266,f245]) ).
fof(f269,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f212,f266,f260]) ).
fof(f272,plain,
( ~ spl0_3
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f228,f260,f245]) ).
fof(f278,plain,
( sk3 != sk3
| ~ ssItem(sk6)
| ssItem(sk5(sk6))
| ~ memberP(sk4,sk6)
| ~ spl0_6 ),
inference(superposition,[],[f224,f257]) ).
fof(f279,plain,
( ~ ssItem(sk6)
| ssItem(sk5(sk6))
| ~ memberP(sk4,sk6)
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f278]) ).
fof(f280,plain,
( ssItem(sk5(sk6))
| ~ memberP(sk4,sk6)
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f279,f267]) ).
fof(f281,plain,
( ssItem(sk5(sk6))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f280,f253]) ).
fof(f282,plain,
( sk3 != sk3
| ~ ssItem(sk6)
| memberP(sk4,sk5(sk6))
| ~ memberP(sk4,sk6)
| ~ spl0_6 ),
inference(superposition,[],[f225,f257]) ).
fof(f283,plain,
( ~ ssItem(sk6)
| memberP(sk4,sk5(sk6))
| ~ memberP(sk4,sk6)
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f282]) ).
fof(f284,plain,
( memberP(sk4,sk5(sk6))
| ~ memberP(sk4,sk6)
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f283,f267]) ).
fof(f285,plain,
( memberP(sk4,sk5(sk6))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f284,f253]) ).
fof(f286,plain,
( ~ leq(sk6,sk5(sk6))
| ~ ssItem(sk5(sk6))
| sk6 = sk5(sk6)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(resolution,[],[f285,f249]) ).
fof(f288,plain,
( ~ leq(sk6,sk5(sk6))
| sk6 = sk5(sk6)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f286,f281]) ).
fof(f290,definition,
( spl0_9
<=> sk6 = sk5(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f291,plain,
( sk6 = sk5(sk6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f293,definition,
( spl0_10
<=> leq(sk6,sk5(sk6)) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f294,plain,
( ~ leq(sk6,sk5(sk6))
| spl0_10 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f295,plain,
( spl0_9
| ~ spl0_10
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f288,f266,f256,f252,f248,f293,f290]) ).
fof(f296,plain,
( sk3 != sk3
| ~ ssItem(sk6)
| leq(sk6,sk5(sk6))
| ~ memberP(sk4,sk6)
| ~ spl0_6 ),
inference(superposition,[],[f226,f257]) ).
fof(f297,plain,
( ~ ssItem(sk6)
| leq(sk6,sk5(sk6))
| ~ memberP(sk4,sk6)
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f296]) ).
fof(f298,plain,
( leq(sk6,sk5(sk6))
| ~ memberP(sk4,sk6)
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f297,f267]) ).
fof(f299,plain,
( leq(sk6,sk5(sk6))
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f298,f253]) ).
fof(f300,plain,
( sk3 != sk3
| ~ ssItem(sk6)
| sk6 != sk5(sk6)
| ~ memberP(sk4,sk6)
| ~ spl0_6 ),
inference(superposition,[],[f227,f257]) ).
fof(f301,plain,
( ~ ssItem(sk6)
| sk6 != sk5(sk6)
| ~ memberP(sk4,sk6)
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f300]) ).
fof(f302,plain,
( sk6 != sk5(sk6)
| ~ memberP(sk4,sk6)
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f301,f267]) ).
fof(f303,plain,
( sk6 != sk5(sk6)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f302,f253]) ).
fof(f309,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| spl0_10 ),
inference(forward_subsumption_resolution,[],[f294,f299]) ).
fof(f310,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| spl0_10 ),
inference(avatar_contradiction_clause,[],[f309]) ).
fof(f311,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f291,f303]) ).
fof(f312,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f311]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f250]) ).
cnf(s3,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f254]) ).
cnf(s4,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f258]) ).
cnf(s5,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f262]) ).
cnf(s6,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f263]) ).
cnf(s7,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f264]) ).
cnf(s8,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f268]) ).
cnf(s9,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f269]) ).
cnf(s10,plain,
( ~ spl0_3
| ~ spl0_7 ),
inference(sat_conversion,[],[f272]) ).
cnf(s11,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f295]) ).
cnf(s13,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f310]) ).
cnf(s14,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f312]) ).
cnf(s15,plain,
spl0_3,
inference(rat,[],[s11,s13,s14,s2,s3,s4,s8]) ).
cnf(s16,plain,
~ spl0_7,
inference(rat,[],[s10,s15]) ).
cnf(s17,plain,
spl0_8,
inference(rat,[],[s9,s16]) ).
cnf(s18,plain,
spl0_6,
inference(rat,[],[s7,s16]) ).
cnf(s19,plain,
spl0_5,
inference(rat,[],[s6,s16]) ).
cnf(s20,plain,
spl0_4,
inference(rat,[],[s5,s16]) ).
cnf(s21,plain,
~ spl0_9,
inference(rat,[],[s14,s18,s17,s19]) ).
cnf(s22,plain,
spl0_10,
inference(rat,[],[s13,s18,s17,s19]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s11,s22,s21,s17,s18,s19,s20]) ).
fof(f313,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC098-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Mon Sep 28 07:51:34 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 0.27/0.79 % (3223373)Input is clausal, will run a generic CNF schedule.
% 0.27/0.79 % (3223382)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1551059423:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.27/0.79 % (3223380)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2219927123:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.27/0.79 % (3223384)dis-21_1_sil=8000:lcm=predicate:random_seed=1609789260: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)
% 0.27/0.79 % (3223383)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1078816877:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.27/0.79 % (3223378)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=122766939:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.27/0.79 % (3223381)lrs+10_1_sil=8000:sp=occurrence:random_seed=1404093768:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.27/0.79 % (3223379)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1877517641:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.27/0.79 % (3223381)Also succeeded, but the first one will report.
% 0.27/0.79 % (3223382)First to succeed.
% 0.27/0.79 % (3223382)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3223373"
% 0.27/0.79 % (3223384)Also succeeded, but the first one will report.
% 0.27/0.79 % (3223383)Also succeeded, but the first one will report.
% 0.27/0.79 % (3223382)Refutation found. Thanks to Tanya!
% 0.27/0.79 % SZS status Unsatisfiable for theBenchmark
% 0.27/0.79 % SZS output start Proof for theBenchmark
% See solution above
% 1.99/0.89 % (3223382)------------------------------
% 1.99/0.89 % (3223382)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.99/0.89 % (3223382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.99/0.89 % (3223382)CaDiCaL version: 2.1.3
% 1.99/0.89 % (3223382)Termination reason: Refutation
% 1.99/0.89 % (3223382)Time elapsed: 0.003 s
% 1.99/0.89 % (3223382)Peak memory usage: 89 MB
% 1.99/0.89 % (3223382)Instructions burned: 5 (million)
% 1.99/0.89 % (3223382)------------------------------
% 1.99/0.89 % (3223382)------------------------------
% 1.99/0.89 % (3223373)Success in time 0.263 s
% 1.99/0.89 % Vampire exiting
%------------------------------------------------------------------------------