%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC039-1 : 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 : n011.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 01:02:09 PM UTC 2026
% Result : Unsatisfiable 5.14s 1.62s
% Output : Refutation 5.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 66 ( 16 unt; 6 def)
% Number of atoms : 151 ( 43 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 158 ( 73 ~; 79 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause85) ).
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(f204,negated_conjecture,
nil = sk2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
nil != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f218,negated_conjecture,
( ssList(sk6)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
fof(f219,negated_conjecture,
( ssList(sk7)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
fof(f222,negated_conjecture,
( app(app(sk6,sk3),sk7) = sk4
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_20) ).
fof(f223,plain,
( sk4 = app(app(sk6,sk3),sk7)
| nil = sk3 ),
inference(reorient_equations,[],[f222]) ).
fof(f226,plain,
nil = sk4,
inference(definition_unfolding,[],[f204,f205]) ).
fof(f229,plain,
sk3 != sk4,
inference(definition_unfolding,[],[f207,f226,f206]) ).
fof(f238,plain,
( ssList(sk6)
| sk3 = sk4 ),
inference(definition_unfolding,[],[f218,f226]) ).
fof(f239,plain,
( ssList(sk7)
| sk3 = sk4 ),
inference(definition_unfolding,[],[f219,f226]) ).
fof(f241,plain,
( sk4 = app(app(sk6,sk3),sk7)
| sk3 = sk4 ),
inference(definition_unfolding,[],[f223,f226]) ).
fof(f248,plain,
! [X0,X1] :
( app(X0,X1) != sk4
| ~ ssList(X1)
| ~ ssList(X0)
| sk4 = X1 ),
inference(definition_unfolding,[],[f124,f226,f226]) ).
fof(f249,plain,
! [X0,X1] :
( app(X0,X1) != sk4
| ~ ssList(X1)
| ~ ssList(X0)
| sk4 = X0 ),
inference(definition_unfolding,[],[f122,f226,f226]) ).
fof(f269,definition,
( spl0_3
<=> sk3 = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f270,plain,
( sk3 = sk4
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f280,definition,
( spl0_6
<=> sk4 = app(app(sk6,sk3),sk7) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f281,plain,
( sk4 = app(app(sk6,sk3),sk7)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f282,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f241,f280,f269]) ).
fof(f288,definition,
( spl0_8
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f289,plain,
( ssList(sk7)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f290,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f239,f288,f269]) ).
fof(f292,definition,
( spl0_9
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f293,plain,
( ssList(sk6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f294,plain,
( spl0_3
| spl0_9 ),
inference(avatar_split_clause,[],[f238,f292,f269]) ).
fof(f301,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f270,f229]) ).
fof(f302,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f301]) ).
fof(f313,definition,
( spl0_12
<=> ssList(app(sk6,sk3)) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f314,plain,
( ~ ssList(app(sk6,sk3))
| spl0_12 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f317,plain,
( sk4 != sk4
| ~ ssList(sk7)
| ~ ssList(app(sk6,sk3))
| sk4 = app(sk6,sk3)
| ~ spl0_6 ),
inference(superposition,[],[f249,f281]) ).
fof(f318,plain,
( ~ ssList(sk7)
| ~ ssList(app(sk6,sk3))
| sk4 = app(sk6,sk3)
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f317]) ).
fof(f320,plain,
( ~ ssList(app(sk6,sk3))
| sk4 = app(sk6,sk3)
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f318,f289]) ).
fof(f322,definition,
( spl0_13
<=> sk4 = app(sk6,sk3) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f323,plain,
( sk4 = app(sk6,sk3)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f324,plain,
( spl0_13
| ~ spl0_12
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f320,f288,f280,f313,f322]) ).
fof(f361,plain,
( ~ ssList(sk6)
| ~ ssList(sk3)
| spl0_12 ),
inference(resolution,[],[f85,f314]) ).
fof(f372,plain,
( ~ ssList(sk3)
| ~ spl0_9
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f361,f293]) ).
fof(f373,plain,
( $false
| ~ spl0_9
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f372,f202]) ).
fof(f374,plain,
( ~ spl0_9
| spl0_12 ),
inference(avatar_contradiction_clause,[],[f373]) ).
fof(f387,plain,
( sk4 != sk4
| ~ ssList(sk3)
| ~ ssList(sk6)
| sk3 = sk4
| ~ spl0_13 ),
inference(superposition,[],[f248,f323]) ).
fof(f388,plain,
( ~ ssList(sk3)
| ~ ssList(sk6)
| sk3 = sk4
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f387]) ).
fof(f390,plain,
( ~ ssList(sk6)
| sk3 = sk4
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f388,f202]) ).
fof(f392,plain,
( sk3 = sk4
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f390,f293]) ).
fof(f394,plain,
( $false
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f392,f229]) ).
fof(f395,plain,
( ~ spl0_9
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f394]) ).
cnf(s4,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f282]) ).
cnf(s6,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f290]) ).
cnf(s7,plain,
( spl0_3
| spl0_9 ),
inference(sat_conversion,[],[f294]) ).
cnf(s10,plain,
~ spl0_3,
inference(sat_conversion,[],[f302]) ).
cnf(s12,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f324]) ).
cnf(s13,plain,
( ~ spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f374]) ).
cnf(s14,plain,
( ~ spl0_9
| ~ spl0_13 ),
inference(sat_conversion,[],[f395]) ).
cnf(s16,plain,
spl0_9,
inference(rat,[],[s7,s10]) ).
cnf(s17,plain,
~ spl0_13,
inference(rat,[],[s14,s16]) ).
cnf(s18,plain,
spl0_12,
inference(rat,[],[s13,s16]) ).
cnf(s19,plain,
spl0_8,
inference(rat,[],[s6,s10]) ).
cnf(s20,plain,
~ spl0_6,
inference(rat,[],[s12,s17,s18,s19]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s4,s20,s10]) ).
fof(f396,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC039-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 07:33:46 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 5.14/1.62 % (3229912)Input is clausal, will run a generic CNF schedule.
% 5.14/1.62 % (3229926)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=1454574094:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.14/1.62 % (3229930)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=116297091:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.14/1.62 % (3229927)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3465613438:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.14/1.62 % (3229929)lrs+10_1_sil=8000:sp=occurrence:random_seed=1679087091:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.14/1.62 % (3229931)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1658889414:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.14/1.62 % (3229932)dis-21_1_sil=8000:lcm=predicate:random_seed=4046774958: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)
% 5.14/1.62 % (3229928)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3090833797:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.14/1.62 % (3229930)First to succeed.
% 5.14/1.62 % (3229929)Also succeeded, but the first one will report.
% 5.14/1.62 % (3229930)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3229912"
% 5.14/1.62 % (3229932)Also succeeded, but the first one will report.
% 5.14/1.62 % (3229931)Also succeeded, but the first one will report.
% 5.14/1.62 % (3229930)Refutation found. Thanks to Tanya!
% 5.14/1.62 % SZS status Unsatisfiable for theBenchmark
% 5.14/1.62 % SZS output start Proof for theBenchmark
% See solution above
% 5.14/1.62 % (3229930)------------------------------
% 5.14/1.62 % (3229930)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.14/1.62 % (3229930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.14/1.62 % (3229930)CaDiCaL version: 2.1.3
% 5.14/1.62 % (3229930)Termination reason: Refutation
% 5.14/1.62 % (3229930)Time elapsed: 0.008 s
% 5.14/1.62 % (3229930)Peak memory usage: 90 MB
% 5.14/1.62 % (3229930)Instructions burned: 6 (million)
% 5.14/1.62 % (3229930)------------------------------
% 5.14/1.62 % (3229930)------------------------------
% 5.14/1.62 % (3229912)Success in time 0.665 s
% 5.14/1.62 % Vampire exiting
%------------------------------------------------------------------------------