%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC024-1 : 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 : n005.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 01:02:05 PM UTC 2026
% Result : Unsatisfiable 2.77s 1.34s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 64 ( 18 unt; 4 def)
% Number of atoms : 151 ( 18 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 171 ( 84 ~; 83 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f61,axiom,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause61) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause85) ).
fof(f101,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| neq(X1,X0)
| X1 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause100) ).
fof(f102,plain,
! [X0,X1] :
( neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1 ),
inference(reorient_equations,[],[f101]) ).
fof(f155,axiom,
! [X2,X0,X1] :
( app(X0,X1) != X2
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| frontsegP(X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause144) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
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,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,nil)
| ~ frontsegP(sk2,X0)
| ~ frontsegP(sk1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
app(sk3,sk5) = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f210,plain,
sk4 = app(sk3,sk5),
inference(reorient_equations,[],[f209]) ).
fof(f214,negated_conjecture,
( nil = sk4
| nil != sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f217,plain,
neq(sk4,nil),
inference(definition_unfolding,[],[f206,f204]) ).
fof(f218,plain,
! [X0] :
( ~ neq(X0,nil)
| ~ ssList(X0)
| ~ frontsegP(sk4,X0)
| ~ frontsegP(sk3,X0) ),
inference(definition_unfolding,[],[f207,f204,f205]) ).
fof(f222,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1))
| frontsegP(app(X0,X1),X0) ),
inference(equality_resolution,[],[f155]) ).
fof(f231,plain,
! [X0,X1] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(forward_subsumption_resolution,[],[f222,f85]) ).
fof(f233,definition,
( spl0_1
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f234,plain,
( nil = sk3
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f235,plain,
( nil != sk3
| spl0_1 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f237,definition,
( spl0_2
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f239,plain,
( nil = sk4
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f240,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f214,f237,f233]) ).
fof(f241,plain,
( ~ ssList(sk4)
| ~ frontsegP(sk4,sk4)
| ~ frontsegP(sk3,sk4) ),
inference(resolution,[],[f218,f217]) ).
fof(f242,plain,
( ~ frontsegP(sk4,sk4)
| ~ frontsegP(sk3,sk4) ),
inference(forward_subsumption_resolution,[],[f241,f203]) ).
fof(f244,definition,
( spl0_3
<=> frontsegP(sk3,sk4) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f246,plain,
( ~ frontsegP(sk3,sk4)
| spl0_3 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f248,definition,
( spl0_4
<=> frontsegP(sk4,sk4) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f250,plain,
( ~ frontsegP(sk4,sk4)
| spl0_4 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f251,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f242,f248,f244]) ).
fof(f287,plain,
( frontsegP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(sk5) ),
inference(superposition,[],[f231,f210]) ).
fof(f292,plain,
( frontsegP(sk4,sk3)
| ~ ssList(sk5) ),
inference(forward_subsumption_resolution,[],[f287,f202]) ).
fof(f293,plain,
frontsegP(sk4,sk3),
inference(forward_subsumption_resolution,[],[f292,f208]) ).
fof(f294,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0)
| ~ frontsegP(sk4,X0)
| ~ frontsegP(sk3,X0) ),
inference(resolution,[],[f102,f218]) ).
fof(f299,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ frontsegP(sk4,X0)
| ~ frontsegP(sk3,X0) ),
inference(duplicate_literal_removal,[],[f294]) ).
fof(f300,plain,
! [X0] :
( ~ frontsegP(sk4,X0)
| nil = X0
| ~ ssList(X0)
| ~ frontsegP(sk3,X0) ),
inference(forward_subsumption_resolution,[],[f299,f8]) ).
fof(f301,plain,
( nil = sk3
| ~ ssList(sk3)
| ~ frontsegP(sk3,sk3) ),
inference(resolution,[],[f300,f293]) ).
fof(f305,plain,
( ~ ssList(sk3)
| ~ frontsegP(sk3,sk3)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f301,f235]) ).
fof(f306,plain,
( ~ frontsegP(sk3,sk3)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f305,f202]) ).
fof(f312,plain,
( ~ ssList(sk3)
| spl0_1 ),
inference(resolution,[],[f306,f61]) ).
fof(f313,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f312,f202]) ).
fof(f314,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f313]) ).
fof(f318,plain,
( ~ frontsegP(nil,sk4)
| ~ spl0_1
| spl0_3 ),
inference(superposition,[],[f246,f234]) ).
fof(f321,plain,
( frontsegP(sk4,nil)
| ~ spl0_1 ),
inference(superposition,[],[f293,f234]) ).
fof(f322,plain,
( frontsegP(nil,nil)
| ~ spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f321,f239]) ).
fof(f323,plain,
( ~ frontsegP(nil,nil)
| ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(forward_demodulation,[],[f318,f239]) ).
fof(f325,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f323,f322]) ).
fof(f326,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(avatar_contradiction_clause,[],[f325]) ).
fof(f328,plain,
( ~ frontsegP(nil,nil)
| ~ spl0_2
| spl0_4 ),
inference(forward_demodulation,[],[f250,f239]) ).
fof(f330,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f328,f322]) ).
fof(f331,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(avatar_contradiction_clause,[],[f330]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f240]) ).
cnf(s2,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f251]) ).
cnf(s3,plain,
spl0_1,
inference(sat_conversion,[],[f314]) ).
cnf(s4,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f326]) ).
cnf(s5,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f331]) ).
cnf(s6,plain,
spl0_2,
inference(rat,[],[s1,s3]) ).
cnf(s7,plain,
spl0_4,
inference(rat,[],[s5,s3,s6]) ).
cnf(s8,plain,
spl0_3,
inference(rat,[],[s4,s3,s6]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s2,s7,s8]) ).
fof(f332,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC024-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 07:29:46 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 2.77/1.34 % (621857)Input is clausal, will run a generic CNF schedule.
% 2.77/1.34 % (621865)lrs+10_1_sil=8000:sp=occurrence:random_seed=3087783393:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.77/1.34 % (621865)First to succeed.
% 2.77/1.34 % (621865)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-621857"
% 2.77/1.34 % (621863)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2235943787:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.77/1.34 % (621864)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2039340301:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.77/1.34 % (621866)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3075405169:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.77/1.34 % (621862)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=4124864642:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.77/1.34 % (621868)dis-21_1_sil=8000:lcm=predicate:random_seed=350110075: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)
% 2.77/1.34 % (621867)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=594351548:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.77/1.34 % (621866)Also succeeded, but the first one will report.
% 2.77/1.34 % (621867)Also succeeded, but the first one will report.
% 2.77/1.34 % (621868)Instruction limit reached!
% 2.77/1.34 % (621868)------------------------------
% 2.77/1.34 % (621868)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.34 % (621868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.34 % (621868)CaDiCaL version: 2.1.3
% 2.77/1.34 % (621868)Termination reason: Instruction limit
% 2.77/1.34 % (621868)Termination phase: Saturation
% 2.77/1.34 % (621868)Time elapsed: 0.063 s
% 2.77/1.34 % (621868)Peak memory usage: 89 MB
% 2.77/1.34 % (621868)Instructions burned: 118 (million)
% 2.77/1.34 % (621865)Refutation found. Thanks to Tanya!
% 2.77/1.34 % SZS status Unsatisfiable for theBenchmark
% 2.77/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.77/1.34 % (621865)------------------------------
% 2.77/1.34 % (621865)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.34 % (621865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.34 % (621865)CaDiCaL version: 2.1.3
% 2.77/1.34 % (621865)Termination reason: Refutation
% 2.77/1.34 % (621865)Time elapsed: 0.003 s
% 2.77/1.34 % (621865)Peak memory usage: 89 MB
% 2.77/1.34 % (621865)Instructions burned: 6 (million)
% 2.77/1.34 % (621865)------------------------------
% 2.77/1.34 % (621865)------------------------------
% 2.77/1.34 % (621857)Success in time 0.313 s
% 2.77/1.34 % Vampire exiting
%------------------------------------------------------------------------------