%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC019+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 : 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 01:02:04 PM UTC 2026
% Result : Theorem 3.49s 1.44s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 15 unt; 3 def)
% Number of atoms : 154 ( 44 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 178 ( 72 ~; 57 |; 33 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 35 ( 0 sgn 25 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f42,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| X3 != X2
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& frontsegP(X1,X4)
& frontsegP(X0,X4) )
| ( nil = X1
& nil = X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| X3 != X2
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& frontsegP(X1,X4)
& frontsegP(X0,X4) )
| ( nil = X1
& nil = X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f153,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& X2 = X3
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ frontsegP(X1,X4)
| ~ frontsegP(X0,X4) )
& ( nil != X1
| nil != X0 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& X2 = X3
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ frontsegP(X1,X4)
| ~ frontsegP(X0,X4) )
& ( nil != X1
| nil != X0 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f273,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& sK55 = sK56
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ frontsegP(sK54,X4)
| ~ frontsegP(sK53,X4) )
& ( nil != sK54
| nil != sK53 )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56)],[f222]) ).
fof(f387,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f423,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( nil != sK54
| nil != sK53 ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ frontsegP(sK54,X4)
| ~ frontsegP(sK53,X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
sK55 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f540,definition,
( spl57_1
<=> nil = sK53 ),
introduced(definition,[new_symbols(definition,[spl57_1])],[avatar_definition]) ).
fof(f544,definition,
( spl57_2
<=> nil = sK54 ),
introduced(definition,[new_symbols(definition,[spl57_2])],[avatar_definition]) ).
fof(f546,plain,
( nil != sK54
| spl57_2 ),
inference(avatar_component_clause,[],[f544]) ).
fof(f547,plain,
( ~ spl57_1
| ~ spl57_2 ),
inference(avatar_split_clause,[],[f500,f544,f540]) ).
fof(f549,definition,
( spl57_3
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl57_3])],[avatar_definition]) ).
fof(f550,plain,
( ssList(nil)
| ~ spl57_3 ),
inference(avatar_component_clause,[],[f549]) ).
fof(f582,plain,
spl57_3,
inference(avatar_split_clause,[],[f389,f549]) ).
fof(f586,plain,
sK54 = sK55,
inference(superposition,[],[f502,f504]) ).
fof(f588,plain,
sK53 = sK54,
inference(forward_demodulation,[],[f586,f503]) ).
fof(f591,plain,
! [X4] :
( ~ frontsegP(sK53,X4)
| ~ ssList(X4)
| ~ neq(X4,nil)
| ~ frontsegP(sK53,X4) ),
inference(forward_demodulation,[],[f501,f588]) ).
fof(f592,plain,
! [X4] :
( ~ frontsegP(sK53,X4)
| ~ ssList(X4)
| ~ neq(X4,nil) ),
inference(duplicate_literal_removal,[],[f591]) ).
fof(f593,plain,
( ~ ssList(sK53)
| ~ ssList(sK53)
| ~ neq(sK53,nil) ),
inference(resolution,[],[f423,f592]) ).
fof(f594,plain,
( ~ ssList(sK53)
| ~ neq(sK53,nil) ),
inference(duplicate_literal_removal,[],[f593]) ).
fof(f595,plain,
~ neq(sK53,nil),
inference(forward_subsumption_resolution,[],[f594,f496]) ).
fof(f637,plain,
( nil = sK53
| ~ ssList(nil)
| ~ ssList(sK53) ),
inference(resolution,[],[f387,f595]) ).
fof(f648,plain,
( nil != sK53
| spl57_2 ),
inference(forward_demodulation,[],[f546,f588]) ).
fof(f649,plain,
( nil = sK53
| ~ ssList(sK53)
| ~ spl57_3 ),
inference(forward_subsumption_resolution,[],[f637,f550]) ).
fof(f650,plain,
( ~ spl57_1
| spl57_2 ),
inference(avatar_split_clause,[],[f648,f544,f540]) ).
fof(f651,plain,
( nil = sK53
| ~ spl57_3 ),
inference(forward_subsumption_resolution,[],[f649,f496]) ).
fof(f652,plain,
( spl57_1
| ~ spl57_3 ),
inference(avatar_split_clause,[],[f651,f549,f540]) ).
cnf(s1,plain,
( ~ spl57_1
| ~ spl57_2 ),
inference(sat_conversion,[],[f547]) ).
cnf(s10,plain,
spl57_3,
inference(sat_conversion,[],[f582]) ).
cnf(s13,plain,
( ~ spl57_1
| spl57_2 ),
inference(sat_conversion,[],[f650]) ).
cnf(s14,plain,
( spl57_1
| ~ spl57_3 ),
inference(sat_conversion,[],[f652]) ).
cnf(s15,plain,
spl57_1,
inference(rat,[],[s14,s10]) ).
cnf(s16,plain,
spl57_2,
inference(rat,[],[s13,s15]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s1,s16,s15]) ).
fof(f653,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC019+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 07:26:47 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 3.49/1.44 % (619808)Detected formulas, will run a generic FOF schedule.
% 3.49/1.44 % (619814)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=3119371546:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.49/1.44 % (619818)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2248935287:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.49/1.44 % (619815)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=2036320331:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.49/1.44 % (619813)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=4130137468:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.49/1.44 % (619817)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=453523824:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.49/1.44 % (619816)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2615972787:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.49/1.44 % (619819)dis-21_1_sil=8000:lcm=predicate:random_seed=2246514854: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)
% 3.49/1.44 % (619818)First to succeed.
% 3.49/1.44 % (619818)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-619808"
% 3.49/1.44 % (619816)Also succeeded, but the first one will report.
% 3.49/1.44 % (619817)Also succeeded, but the first one will report.
% 3.49/1.44 % (619819)Also succeeded, but the first one will report.
% 3.49/1.44 % (619818)Refutation found. Thanks to Tanya!
% 3.49/1.44 % SZS status Theorem for theBenchmark
% 3.49/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.44 % (619818)------------------------------
% 3.49/1.44 % (619818)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.44 % (619818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.44 % (619818)CaDiCaL version: 2.1.3
% 3.49/1.44 % (619818)Termination reason: Refutation
% 3.49/1.44 % (619818)Time elapsed: 0.011 s
% 3.49/1.44 % (619818)Peak memory usage: 90 MB
% 3.49/1.44 % (619818)Instructions burned: 15 (million)
% 3.49/1.44 % (619818)------------------------------
% 3.49/1.44 % (619818)------------------------------
% 3.49/1.44 % (619808)Success in time 0.413 s
% 3.49/1.44 % Vampire exiting
%------------------------------------------------------------------------------