%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC023-1 : 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 3.60s 1.45s
% Output : Refutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 49 ( 13 unt; 5 def)
% Number of atoms : 105 ( 9 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 109 ( 53 ~; 51 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 6 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f118,axiom,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause115) ).
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)
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f210,negated_conjecture,
( neq(sk5,nil)
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f211,negated_conjecture,
( frontsegP(sk4,sk5)
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f212,negated_conjecture,
( frontsegP(sk3,sk5)
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f218,plain,
neq(sk4,nil),
inference(definition_unfolding,[],[f206,f204]) ).
fof(f219,plain,
! [X0] :
( ~ neq(X0,nil)
| ~ ssList(X0)
| ~ frontsegP(sk4,X0)
| ~ frontsegP(sk3,X0) ),
inference(definition_unfolding,[],[f207,f204,f205]) ).
fof(f220,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f118]) ).
fof(f226,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f220]) ).
fof(f233,definition,
( spl0_2
<=> frontsegP(sk3,sk5) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f235,plain,
( frontsegP(sk3,sk5)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f238,definition,
( spl0_3
<=> frontsegP(sk4,sk5) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f240,plain,
( frontsegP(sk4,sk5)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f243,definition,
( spl0_4
<=> neq(sk5,nil) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f245,plain,
( neq(sk5,nil)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f248,definition,
( spl0_5
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f250,plain,
( nil = sk4
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f251,plain,
( spl0_5
| spl0_2 ),
inference(avatar_split_clause,[],[f212,f233,f248]) ).
fof(f252,plain,
( spl0_5
| spl0_3 ),
inference(avatar_split_clause,[],[f211,f238,f248]) ).
fof(f253,plain,
( spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f210,f243,f248]) ).
fof(f255,definition,
( spl0_6
<=> ssList(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f257,plain,
( ssList(sk5)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f259,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f208,f255,f248]) ).
fof(f261,plain,
( ~ ssList(sk5)
| ~ frontsegP(sk4,sk5)
| ~ frontsegP(sk3,sk5)
| ~ spl0_4 ),
inference(resolution,[],[f219,f245]) ).
fof(f262,plain,
( ~ frontsegP(sk4,sk5)
| ~ frontsegP(sk3,sk5)
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f261,f257]) ).
fof(f264,plain,
( ~ frontsegP(sk3,sk5)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f262,f240]) ).
fof(f266,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f264,f235]) ).
fof(f267,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f266]) ).
fof(f271,plain,
( neq(nil,nil)
| ~ spl0_5 ),
inference(superposition,[],[f218,f250]) ).
fof(f280,plain,
( ~ ssList(nil)
| ~ spl0_5 ),
inference(resolution,[],[f226,f271]) ).
fof(f281,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f280,f8]) ).
fof(f282,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f281]) ).
cnf(s4,plain,
( spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f251]) ).
cnf(s5,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f252]) ).
cnf(s6,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f253]) ).
cnf(s8,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f259]) ).
cnf(s9,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f267]) ).
cnf(s10,plain,
~ spl0_5,
inference(sat_conversion,[],[f282]) ).
cnf(s11,plain,
spl0_6,
inference(rat,[],[s8,s10]) ).
cnf(s12,plain,
spl0_4,
inference(rat,[],[s6,s10]) ).
cnf(s13,plain,
spl0_3,
inference(rat,[],[s5,s10]) ).
cnf(s14,plain,
~ spl0_2,
inference(rat,[],[s9,s11,s12,s13]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s4,s10,s14]) ).
fof(f283,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC023-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 07:29:32 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.60/1.45 % (621451)Input is clausal, will run a generic CNF schedule.
% 3.60/1.45 % (621456)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=191651676:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.60/1.45 % (621458)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2239499401:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.60/1.45 % (621459)lrs+10_1_sil=8000:sp=occurrence:random_seed=1863145292:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.60/1.45 % (621457)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1973149413:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.60/1.45 % (621459)First to succeed.
% 3.60/1.45 % (621459)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-621451"
% 3.60/1.45 % (621460)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=500264809:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.60/1.45 % (621462)dis-21_1_sil=8000:lcm=predicate:random_seed=226877968: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)
% 3.60/1.45 % (621460)Also succeeded, but the first one will report.
% 3.60/1.45 % (621461)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1896095804:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.60/1.45 % (621461)Also succeeded, but the first one will report.
% 3.60/1.45 % (621462)Instruction limit reached!
% 3.60/1.45 % (621462)------------------------------
% 3.60/1.45 % (621462)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.45 % (621462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.45 % (621462)CaDiCaL version: 2.1.3
% 3.60/1.45 % (621462)Termination reason: Instruction limit
% 3.60/1.45 % (621462)Termination phase: Saturation
% 3.60/1.45 % (621462)Time elapsed: 0.048 s
% 3.60/1.45 % (621462)Peak memory usage: 88 MB
% 3.60/1.45 % (621462)Instructions burned: 119 (million)
% 3.60/1.45 % (621470)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1697257788:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.60/1.45 % (621470)Also succeeded, but the first one will report.
% 3.60/1.45 % (621459)Refutation found. Thanks to Tanya!
% 3.60/1.45 % SZS status Unsatisfiable for theBenchmark
% 3.60/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.60/1.45 % (621459)------------------------------
% 3.60/1.45 % (621459)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.45 % (621459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.45 % (621459)CaDiCaL version: 2.1.3
% 3.60/1.45 % (621459)Termination reason: Refutation
% 3.60/1.45 % (621459)Time elapsed: 0.004 s
% 3.60/1.45 % (621459)Peak memory usage: 89 MB
% 3.60/1.45 % (621459)Instructions burned: 3 (million)
% 3.60/1.45 % (621459)------------------------------
% 3.60/1.45 % (621459)------------------------------
% 3.60/1.45 % (621451)Success in time 0.437 s
% 3.60/1.45 % Vampire exiting
%------------------------------------------------------------------------------