%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC020+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 : n006.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 01:02:04 PM UTC 2026
% Result : Theorem 0.15s 1.21s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 33 ( 8 unt; 0 def)
% Number of atoms : 138 ( 54 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 167 ( 62 ~; 56 |; 40 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 26 ( 16 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& frontsegP(X1,X4)
& frontsegP(X0,X4) )
| ( nil = X1
& nil = X0 )
| ( ( nil != X3
| nil != X2 )
& ( ~ neq(X2,nil)
| ~ frontsegP(X3,X2) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& frontsegP(X1,X4)
& frontsegP(X0,X4) )
| ( nil = X1
& nil = X0 )
| ( ( nil != X3
| nil != X2 )
& ( ~ neq(X2,nil)
| ~ frontsegP(X3,X2) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ frontsegP(X1,X4)
| ~ frontsegP(X0,X4) )
& ( nil != X1
| nil != X0 )
& ( ( nil = X3
& nil = X2 )
| ( neq(X2,nil)
& frontsegP(X3,X2) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ frontsegP(X1,X4)
| ~ frontsegP(X0,X4) )
& ( nil != X1
| nil != X0 )
& ( ( nil = X3
& nil = X2 )
| ( neq(X2,nil)
& frontsegP(X3,X2) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f107,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f131,plain,
( sK1 = sK3
& sK0 = sK2
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ frontsegP(sK1,X4)
| ~ frontsegP(sK0,X4) )
& ( nil != sK1
| nil != sK0 )
& ( ( nil = sK3
& nil = sK2 )
| ( neq(sK2,nil)
& frontsegP(sK3,sK2) ) )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f99]) ).
fof(f146,plain,
ssList(sK2),
inference(cnf_transformation,[],[f131]) ).
fof(f148,plain,
( frontsegP(sK3,sK2)
| nil = sK2 ),
inference(cnf_transformation,[],[f131]) ).
fof(f149,plain,
( neq(sK2,nil)
| nil = sK2 ),
inference(cnf_transformation,[],[f131]) ).
fof(f150,plain,
( frontsegP(sK3,sK2)
| nil = sK3 ),
inference(cnf_transformation,[],[f131]) ).
fof(f151,plain,
( neq(sK2,nil)
| nil = sK3 ),
inference(cnf_transformation,[],[f131]) ).
fof(f152,plain,
( nil != sK1
| nil != sK0 ),
inference(cnf_transformation,[],[f131]) ).
fof(f153,plain,
! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ frontsegP(sK1,X4)
| ~ frontsegP(sK0,X4) ),
inference(cnf_transformation,[],[f131]) ).
fof(f154,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f131]) ).
fof(f155,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f131]) ).
fof(f168,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f196,plain,
! [X4] :
( ~ frontsegP(sK3,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| ~ frontsegP(sK2,X4) ),
inference(definition_unfolding,[],[f153,f155,f154]) ).
fof(f197,plain,
( nil != sK3
| nil != sK2 ),
inference(definition_unfolding,[],[f152,f155,f154]) ).
fof(f211,plain,
( ~ neq(sK2,nil)
| ~ ssList(sK2)
| ~ frontsegP(sK2,sK2)
| nil = sK3 ),
inference(resolution,[],[f196,f150]) ).
fof(f212,plain,
( ~ neq(sK2,nil)
| ~ ssList(sK2)
| ~ frontsegP(sK2,sK2)
| nil = sK2 ),
inference(resolution,[],[f196,f148]) ).
fof(f213,plain,
( ~ ssList(sK2)
| ~ frontsegP(sK2,sK2)
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f212,f149]) ).
fof(f214,plain,
( ~ ssList(sK2)
| ~ frontsegP(sK2,sK2)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f211,f151]) ).
fof(f215,plain,
( ~ frontsegP(sK2,sK2)
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f213,f146]) ).
fof(f216,plain,
( ~ frontsegP(sK2,sK2)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f214,f146]) ).
fof(f223,plain,
( ~ ssList(sK2)
| nil = sK3 ),
inference(resolution,[],[f168,f216]) ).
fof(f224,plain,
( ~ ssList(sK2)
| nil = sK2 ),
inference(resolution,[],[f168,f215]) ).
fof(f226,plain,
nil = sK2,
inference(forward_subsumption_resolution,[],[f224,f146]) ).
fof(f227,plain,
nil = sK3,
inference(forward_subsumption_resolution,[],[f223,f146]) ).
fof(f232,plain,
( sK2 != sK3
| sK2 != sK2 ),
inference(superposition,[],[f197,f226]) ).
fof(f235,plain,
sK2 != sK3,
inference(trivial_inequality_removal,[],[f232]) ).
fof(f236,plain,
sK2 = sK3,
inference(superposition,[],[f227,f226]) ).
fof(f245,plain,
$false,
inference(forward_subsumption_resolution,[],[f236,f235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC020+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 07:27:56 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.15/1.21 % (3796388)Detected formulas, will run a generic FOF schedule.
% 0.15/1.21 % (3796398)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1943364985:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.15/1.21 % (3796397)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2147425002:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.15/1.21 % (3796399)dis-21_1_sil=8000:lcm=predicate:random_seed=3541009020:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.15/1.21 % (3796396)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1356023394:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.15/1.21 % (3796395)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1970635727:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.15/1.21 % (3796393)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=3712513291:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.15/1.21 % (3796394)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3963126391:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.15/1.21 % (3796397)First to succeed.
% 0.15/1.21 % (3796396)Also succeeded, but the first one will report.
% 0.15/1.21 % (3796397)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3796388"
% 0.15/1.21 % (3796399)Also succeeded, but the first one will report.
% 0.15/1.21 % (3796398)Also succeeded, but the first one will report.
% 0.15/1.21 % (3796397)Refutation found. Thanks to Tanya!
% 0.15/1.21 % SZS status Theorem for theBenchmark
% 0.15/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.21 % (3796397)------------------------------
% 0.15/1.21 % (3796397)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.21 % (3796397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.21 % (3796397)CaDiCaL version: 2.1.3
% 0.15/1.21 % (3796397)Termination reason: Refutation
% 0.15/1.21 % (3796397)Time elapsed: 0.004 s
% 0.15/1.21 % (3796397)Peak memory usage: 88 MB
% 0.15/1.21 % (3796397)Instructions burned: 4 (million)
% 0.15/1.21 % (3796397)------------------------------
% 0.15/1.21 % (3796397)------------------------------
% 0.15/1.21 % (3796388)Success in time 0.406 s
% 0.15/1.21 % Vampire exiting
%------------------------------------------------------------------------------