%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC018-1 : 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 : n010.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 01:02:03 PM UTC 2026
% Result : Unsatisfiable 2.53s 1.33s
% Output : Refutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of formulae : 71 ( 14 unt; 4 def)
% Number of atoms : 187 ( 37 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 233 ( 117 ~; 112 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 31 ( 0 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f61,axiom,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause61) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause85) ).
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(f118,axiom,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause115) ).
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(f155,axiom,
! [X2,X0,X1] :
( app(X0,X1) != X2
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| frontsegP(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause144) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
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,
ssList(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
app(sk3,sk5) = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,plain,
sk4 = app(sk3,sk5),
inference(reorient_equations,[],[f207]) ).
fof(f212,negated_conjecture,
( nil = sk4
| nil != sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f214,negated_conjecture,
! [X0] :
( nil = sk2
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ frontsegP(sk2,X0)
| ~ frontsegP(sk1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f215,negated_conjecture,
( nil != sk1
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f216,negated_conjecture,
! [X0] :
( nil != sk1
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ frontsegP(sk2,X0)
| ~ frontsegP(sk1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f220,plain,
! [X0] :
( nil = sk4
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ frontsegP(sk4,X0)
| ~ frontsegP(sk3,X0) ),
inference(definition_unfolding,[],[f214,f204,f204,f205]) ).
fof(f221,plain,
( nil != sk3
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f215,f205,f204]) ).
fof(f222,plain,
! [X0] :
( nil != sk3
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ frontsegP(sk4,X0)
| ~ frontsegP(sk3,X0) ),
inference(definition_unfolding,[],[f216,f205,f204,f205]) ).
fof(f225,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f118]) ).
fof(f226,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1))
| frontsegP(app(X0,X1),X0) ),
inference(equality_resolution,[],[f155]) ).
fof(f228,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f225]) ).
fof(f242,definition,
( spl0_4
<=> ! [X0] :
( ~ ssList(X0)
| ~ frontsegP(sk3,X0)
| ~ frontsegP(sk4,X0)
| ~ neq(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f243,plain,
( ! [X0] :
( ~ neq(X0,nil)
| ~ frontsegP(sk3,X0)
| ~ frontsegP(sk4,X0)
| ~ ssList(X0) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f245,definition,
( spl0_5
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f246,plain,
( nil != sk3
| spl0_5 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f247,plain,
( spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f222,f245,f242]) ).
fof(f249,definition,
( spl0_6
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f250,plain,
( neq(sk4,nil)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f251,plain,
( spl0_6
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f221,f245,f249]) ).
fof(f253,definition,
( spl0_7
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f254,plain,
( nil = sk4
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f255,plain,
( spl0_4
| spl0_7 ),
inference(avatar_split_clause,[],[f220,f253,f242]) ).
fof(f257,plain,
( ~ spl0_5
| spl0_7 ),
inference(avatar_split_clause,[],[f212,f253,f245]) ).
fof(f284,plain,
( ! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ frontsegP(sk3,X0)
| ~ frontsegP(sk4,X0)
| ~ ssList(X0) )
| ~ spl0_4 ),
inference(resolution,[],[f102,f243]) ).
fof(f287,plain,
( ! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ frontsegP(sk3,X0)
| ~ frontsegP(sk4,X0) )
| ~ spl0_4 ),
inference(duplicate_literal_removal,[],[f284]) ).
fof(f288,plain,
( ! [X0] :
( ~ frontsegP(sk4,X0)
| nil = X0
| ~ frontsegP(sk3,X0)
| ~ ssList(X0) )
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f287,f8]) ).
fof(f289,plain,
( nil != sk4
| ~ ssList(sk5)
| ~ ssList(sk3)
| nil = sk3 ),
inference(superposition,[],[f122,f208]) ).
fof(f292,plain,
( nil != sk4
| ~ ssList(sk3)
| nil = sk3 ),
inference(forward_subsumption_resolution,[],[f289,f206]) ).
fof(f293,plain,
( nil != sk4
| nil = sk3 ),
inference(forward_subsumption_resolution,[],[f292,f202]) ).
fof(f294,plain,
( nil != sk4
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f293,f246]) ).
fof(f309,plain,
! [X0,X1] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(forward_subsumption_resolution,[],[f226,f85]) ).
fof(f311,plain,
( frontsegP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(sk5) ),
inference(superposition,[],[f309,f208]) ).
fof(f319,plain,
( frontsegP(sk4,sk3)
| ~ ssList(sk5) ),
inference(forward_subsumption_resolution,[],[f311,f202]) ).
fof(f321,plain,
frontsegP(sk4,sk3),
inference(forward_subsumption_resolution,[],[f319,f206]) ).
fof(f322,plain,
( nil = sk3
| ~ frontsegP(sk3,sk3)
| ~ ssList(sk3)
| ~ spl0_4 ),
inference(resolution,[],[f321,f288]) ).
fof(f328,plain,
( $false
| spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f254,f294]) ).
fof(f329,plain,
( spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f328]) ).
fof(f331,plain,
( nil = sk3
| ~ ssList(sk3)
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f322,f61]) ).
fof(f336,plain,
( nil = sk3
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f331,f202]) ).
fof(f338,plain,
( spl0_5
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f336,f242,f245]) ).
fof(f345,plain,
( neq(nil,nil)
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f250,f254]) ).
fof(f371,plain,
( ~ ssList(nil)
| ~ spl0_6
| ~ spl0_7 ),
inference(resolution,[],[f345,f228]) ).
fof(f372,plain,
( $false
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f371,f8]) ).
fof(f373,plain,
( ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f372]) ).
cnf(s3,plain,
( spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f247]) ).
cnf(s4,plain,
( ~ spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f251]) ).
cnf(s5,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f255]) ).
cnf(s7,plain,
( ~ spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f257]) ).
cnf(s12,plain,
( spl0_5
| ~ spl0_7 ),
inference(sat_conversion,[],[f329]) ).
cnf(s14,plain,
( ~ spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f338]) ).
cnf(s16,plain,
( ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f373]) ).
cnf(s21,plain,
spl0_4,
inference(rat,[],[s12,s3,s5]) ).
cnf(s22,plain,
spl0_5,
inference(rat,[],[s14,s21]) ).
cnf(s23,plain,
spl0_7,
inference(rat,[],[s7,s22]) ).
cnf(s24,plain,
spl0_6,
inference(rat,[],[s4,s22]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s16,s23,s24]) ).
fof(f382,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC018-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n010.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 07:27:18 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.53/1.33 % (1739752)Input is clausal, will run a generic CNF schedule.
% 2.53/1.33 % (1739761)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=367867475:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.53/1.33 % (1739761)First to succeed.
% 2.53/1.33 % (1739761)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1739752"
% 2.53/1.33 % (1739762)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2940080808:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.53/1.33 % (1739760)lrs+10_1_sil=8000:sp=occurrence:random_seed=2494614366:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.53/1.33 % (1739758)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4273587169:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.53/1.33 % (1739759)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2123510022:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.53/1.33 % (1739757)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=3538845801:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.53/1.33 % (1739760)Also succeeded, but the first one will report.
% 2.53/1.33 % (1739763)dis-21_1_sil=8000:lcm=predicate:random_seed=3221227772: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)
% 2.53/1.33 % (1739762)Also succeeded, but the first one will report.
% 2.53/1.33 % (1739763)Instruction limit reached!
% 2.53/1.33 % (1739763)------------------------------
% 2.53/1.33 % (1739763)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.33 % (1739763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.33 % (1739763)CaDiCaL version: 2.1.3
% 2.53/1.33 % (1739763)Termination reason: Instruction limit
% 2.53/1.33 % (1739763)Termination phase: Saturation
% 2.53/1.33 % (1739763)Time elapsed: 0.064 s
% 2.53/1.33 % (1739763)Peak memory usage: 90 MB
% 2.53/1.33 % (1739763)Instructions burned: 118 (million)
% 2.53/1.33 % (1739761)Refutation found. Thanks to Tanya!
% 2.53/1.33 % SZS status Unsatisfiable for theBenchmark
% 2.53/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.53/1.33 % (1739761)------------------------------
% 2.53/1.33 % (1739761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.33 % (1739761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.33 % (1739761)CaDiCaL version: 2.1.3
% 2.53/1.33 % (1739761)Termination reason: Refutation
% 2.53/1.33 % (1739761)Time elapsed: 0.004 s
% 2.53/1.33 % (1739761)Peak memory usage: 89 MB
% 2.53/1.33 % (1739761)Instructions burned: 6 (million)
% 2.53/1.33 % (1739761)------------------------------
% 2.53/1.33 % (1739761)------------------------------
% 2.53/1.33 % (1739752)Success in time 0.273 s
% 2.53/1.33 % Vampire exiting
%------------------------------------------------------------------------------