%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC218-1 : 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 : 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 01:02:59 PM UTC 2026
% Result : Unsatisfiable 0.19s 1.13s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 63 ( 20 unt; 4 def)
% Number of atoms : 140 ( 31 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 157 ( 80 ~; 73 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause85) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause86) ).
fof(f98,axiom,
! [X0,X1] :
( cons(X0,X1) != nil
| ~ ssItem(X0)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause98) ).
fof(f99,plain,
! [X0,X1] :
( nil != cons(X0,X1)
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(reorient_equations,[],[f98]) ).
fof(f101,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| neq(X1,X0)
| X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause100) ).
fof(f102,plain,
! [X0,X1] :
( neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1 ),
inference(reorient_equations,[],[f101]) ).
fof(f121,axiom,
! [X0,X1] :
( app(X0,X1) != nil
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause118) ).
fof(f122,plain,
! [X0,X1] :
( nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X0 ),
inference(reorient_equations,[],[f121]) ).
fof(f123,axiom,
! [X0,X1] :
( app(X0,X1) != nil
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause119) ).
fof(f124,plain,
! [X0,X1] :
( nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X1 ),
inference(reorient_equations,[],[f123]) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
ssList(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f210,negated_conjecture,
ssItem(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f211,negated_conjecture,
app(app(sk5,cons(sk7,nil)),sk6) = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f212,plain,
sk3 = app(app(sk5,cons(sk7,nil)),sk6),
inference(reorient_equations,[],[f211]) ).
fof(f213,negated_conjecture,
~ neq(sk1,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f216,plain,
~ neq(sk3,nil),
inference(definition_unfolding,[],[f213,f205]) ).
fof(f241,plain,
( ~ ssList(sk3)
| ~ ssList(nil)
| nil = sk3 ),
inference(resolution,[],[f102,f216]) ).
fof(f246,plain,
( ~ ssList(nil)
| nil = sk3 ),
inference(forward_subsumption_resolution,[],[f241,f202]) ).
fof(f247,plain,
nil = sk3,
inference(forward_subsumption_resolution,[],[f246,f8]) ).
fof(f260,plain,
( nil != sk3
| ~ ssList(sk6)
| ~ ssList(app(sk5,cons(sk7,nil)))
| nil = app(sk5,cons(sk7,nil)) ),
inference(superposition,[],[f122,f212]) ).
fof(f263,plain,
( ~ ssList(sk6)
| ~ ssList(app(sk5,cons(sk7,nil)))
| nil = app(sk5,cons(sk7,nil)) ),
inference(forward_subsumption_resolution,[],[f260,f247]) ).
fof(f265,plain,
( ~ ssList(app(sk5,cons(sk7,nil)))
| nil = app(sk5,cons(sk7,nil)) ),
inference(forward_subsumption_resolution,[],[f263,f207]) ).
fof(f268,definition,
( spl0_3
<=> nil = app(sk5,cons(sk7,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f269,plain,
( nil = app(sk5,cons(sk7,nil))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f271,definition,
( spl0_4
<=> ssList(app(sk5,cons(sk7,nil))) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f272,plain,
( ~ ssList(app(sk5,cons(sk7,nil)))
| spl0_4 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f273,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f265,f271,f268]) ).
fof(f291,plain,
( ~ ssList(sk5)
| ~ ssList(cons(sk7,nil))
| spl0_4 ),
inference(resolution,[],[f272,f85]) ).
fof(f292,plain,
( ~ ssList(cons(sk7,nil))
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f291,f206]) ).
fof(f305,plain,
( ~ ssList(nil)
| ~ ssItem(sk7)
| spl0_4 ),
inference(resolution,[],[f292,f86]) ).
fof(f306,plain,
( ~ ssItem(sk7)
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f305,f8]) ).
fof(f307,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f306,f210]) ).
fof(f308,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f307]) ).
fof(f471,definition,
( spl0_11
<=> ssList(cons(sk7,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f472,plain,
( ~ ssList(cons(sk7,nil))
| spl0_11 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f537,plain,
( ~ ssList(nil)
| ~ ssItem(sk7)
| spl0_11 ),
inference(resolution,[],[f472,f86]) ).
fof(f538,plain,
( ~ ssItem(sk7)
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f537,f8]) ).
fof(f539,plain,
( $false
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f538,f210]) ).
fof(f540,plain,
spl0_11,
inference(avatar_contradiction_clause,[],[f539]) ).
fof(f577,plain,
( nil != nil
| ~ ssList(cons(sk7,nil))
| ~ ssList(sk5)
| nil = cons(sk7,nil)
| ~ spl0_3 ),
inference(superposition,[],[f124,f269]) ).
fof(f584,plain,
( ~ ssList(cons(sk7,nil))
| ~ ssList(sk5)
| nil = cons(sk7,nil)
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f577]) ).
fof(f592,plain,
( ~ ssList(cons(sk7,nil))
| nil = cons(sk7,nil)
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f584,f206]) ).
fof(f610,definition,
( spl0_17
<=> nil = cons(sk7,nil) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f611,plain,
( nil = cons(sk7,nil)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f610]) ).
fof(f612,plain,
( spl0_17
| ~ spl0_11
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f592,f268,f471,f610]) ).
fof(f799,plain,
( nil != nil
| ~ ssItem(sk7)
| ~ ssList(nil)
| ~ spl0_17 ),
inference(superposition,[],[f99,f611]) ).
fof(f807,plain,
( ~ ssItem(sk7)
| ~ ssList(nil)
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f799]) ).
fof(f809,plain,
( ~ ssList(nil)
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f807,f210]) ).
fof(f813,plain,
( $false
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f809,f8]) ).
fof(f814,plain,
~ spl0_17,
inference(avatar_contradiction_clause,[],[f813]) ).
cnf(s3,plain,
( spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f273]) ).
cnf(s6,plain,
spl0_4,
inference(sat_conversion,[],[f308]) ).
cnf(s15,plain,
spl0_11,
inference(sat_conversion,[],[f540]) ).
cnf(s21,plain,
( ~ spl0_3
| ~ spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f612]) ).
cnf(s38,plain,
~ spl0_17,
inference(sat_conversion,[],[f814]) ).
cnf(s39,plain,
( ~ spl0_3
| ~ spl0_11 ),
inference(rat,[],[s21,s38]) ).
cnf(s40,plain,
~ spl0_3,
inference(rat,[],[s39,s15]) ).
cnf(s47,plain,
$false,
inference(rat,[],[s3,s6,s40]) ).
fof(f816,plain,
$false,
inference(avatar_sat_refutation,[],[s47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC218-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n002.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 08:34:52 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 0.19/1.13 % (212866)Input is clausal, will run a generic CNF schedule.
% 0.19/1.13 % (212875)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3457059262:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.19/1.13 % (212875)First to succeed.
% 0.19/1.13 % (212875)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-212866"
% 0.19/1.13 % (212872)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1244273220:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.19/1.13 % (212873)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1967820653:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.19/1.13 % (212871)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=2484024330:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.19/1.13 % (212874)lrs+10_1_sil=8000:sp=occurrence:random_seed=2592667914:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.19/1.13 % (212876)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3689179829:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.19/1.13 % (212877)dis-21_1_sil=8000:lcm=predicate:random_seed=2700923204: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)
% 0.19/1.13 % (212874)Also succeeded, but the first one will report.
% 0.19/1.13 % (212876)Also succeeded, but the first one will report.
% 0.19/1.13 % (212877)Instruction limit reached!
% 0.19/1.13 % (212877)------------------------------
% 0.19/1.13 % (212877)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.13 % (212877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.13 % (212877)CaDiCaL version: 2.1.3
% 0.19/1.13 % (212877)Termination reason: Instruction limit
% 0.19/1.13 % (212877)Termination phase: Saturation
% 0.19/1.13 % (212877)Time elapsed: 0.062 s
% 0.19/1.13 % (212877)Peak memory usage: 89 MB
% 0.19/1.13 % (212877)Instructions burned: 119 (million)
% 0.19/1.13 % (212875)Refutation found. Thanks to Tanya!
% 0.19/1.13 % SZS status Unsatisfiable for theBenchmark
% 0.19/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.13 % (212875)------------------------------
% 0.19/1.13 % (212875)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.13 % (212875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.13 % (212875)CaDiCaL version: 2.1.3
% 0.19/1.13 % (212875)Termination reason: Refutation
% 0.19/1.13 % (212875)Time elapsed: 0.010 s
% 0.19/1.13 % (212875)Peak memory usage: 90 MB
% 0.19/1.13 % (212875)Instructions burned: 24 (million)
% 0.19/1.13 % (212875)------------------------------
% 0.19/1.13 % (212875)------------------------------
% 0.19/1.13 % (212866)Success in time 0.279 s
% 0.19/1.13 % Vampire exiting
%------------------------------------------------------------------------------