%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC419+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 : n016.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 01:03:54 PM UTC 2026
% Result : Theorem 3.68s 1.29s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 14 unt; 0 def)
% Number of atoms : 157 ( 59 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 198 ( 83 ~; 67 |; 36 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 51 ( 39 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ~ neq(X1,nil)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X1
& app(app(X6,cons(X4,nil)),X5) = X0 ) ) )
| ( nil != X2
& nil = X3 )
| ( ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ~ ssList(X8)
| app(cons(X7,nil),X8) != X3
| app(X8,cons(X7,nil)) != X2 ) )
& neq(X3,nil) ) ) ) ) ),
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
| ~ neq(X1,nil)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X1
& app(app(X6,cons(X4,nil)),X5) = X0 ) ) )
| ( nil != X2
& nil = X3 )
| ( ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ~ ssList(X8)
| app(cons(X7,nil),X8) != X3
| app(X8,cons(X7,nil)) != X2 ) )
& neq(X3,nil) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X1
| app(app(X6,cons(X4,nil)),X5) != X0 ) ) )
& ( nil = X2
| nil != X3 )
& ( ? [X7] :
( ? [X8] :
( ssList(X8)
& app(cons(X7,nil),X8) = X3
& app(X8,cons(X7,nil)) = X2 )
& ssItem(X7) )
| ~ neq(X3,nil) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f106,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f114,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f119,plain,
( ssList(sK3)
& sK1 = sK3
& sK0 = sK2
& neq(sK1,nil)
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK1
| app(app(X6,cons(X4,nil)),X5) != sK0 ) ) )
& ( nil = sK2
| nil != sK3 )
& ( ( ssList(sK5)
& sK3 = app(cons(sK4,nil),sK5)
& sK2 = app(sK5,cons(sK4,nil))
& ssItem(sK4) )
| ~ neq(sK3,nil) )
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X7,sK4),skolemize(X8,sK5)],[f98]) ).
fof(f128,plain,
ssList(sK2),
inference(cnf_transformation,[],[f119]) ).
fof(f129,plain,
( ssItem(sK4)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f119]) ).
fof(f130,plain,
( sK2 = app(sK5,cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f119]) ).
fof(f131,plain,
( sK3 = app(cons(sK4,nil),sK5)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f119]) ).
fof(f132,plain,
( ssList(sK5)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f119]) ).
fof(f134,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK1
| app(app(X6,cons(X4,nil)),X5) != sK0 ),
inference(cnf_transformation,[],[f119]) ).
fof(f135,plain,
neq(sK1,nil),
inference(cnf_transformation,[],[f119]) ).
fof(f136,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f119]) ).
fof(f137,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f119]) ).
fof(f149,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f150,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f158,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f165,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f166,plain,
neq(sK3,nil),
inference(definition_unfolding,[],[f135,f137]) ).
fof(f167,plain,
! [X6,X4,X5] :
( app(app(X6,cons(X4,nil)),X5) != sK2
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK3
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f134,f137,f136]) ).
fof(f177,plain,
ssItem(sK4),
inference(forward_subsumption_resolution,[],[f129,f166]) ).
fof(f178,plain,
ssList(sK5),
inference(forward_subsumption_resolution,[],[f132,f166]) ).
fof(f179,plain,
sK2 = app(sK5,cons(sK4,nil)),
inference(forward_subsumption_resolution,[],[f130,f166]) ).
fof(f180,plain,
sK3 = app(cons(sK4,nil),sK5),
inference(forward_subsumption_resolution,[],[f131,f166]) ).
fof(f181,plain,
! [X0] :
( sK2 != app(sK2,X0)
| ~ ssList(X0)
| ~ ssList(sK5)
| sK3 != app(app(X0,cons(sK4,nil)),sK5)
| ~ ssItem(sK4) ),
inference(superposition,[],[f167,f179]) ).
fof(f182,plain,
! [X0] :
( sK2 != app(sK2,X0)
| ~ ssList(X0)
| sK3 != app(app(X0,cons(sK4,nil)),sK5)
| ~ ssItem(sK4) ),
inference(forward_subsumption_resolution,[],[f181,f178]) ).
fof(f183,plain,
! [X0] :
( sK3 != app(app(X0,cons(sK4,nil)),sK5)
| ~ ssList(X0)
| sK2 != app(sK2,X0) ),
inference(forward_subsumption_resolution,[],[f182,f177]) ).
fof(f194,plain,
( sK3 != app(cons(sK4,nil),sK5)
| ~ ssList(nil)
| sK2 != app(sK2,nil)
| ~ ssList(cons(sK4,nil)) ),
inference(superposition,[],[f183,f158]) ).
fof(f196,plain,
( ~ ssList(nil)
| sK2 != app(sK2,nil)
| ~ ssList(cons(sK4,nil)) ),
inference(forward_subsumption_resolution,[],[f194,f180]) ).
fof(f198,plain,
( sK2 != app(sK2,nil)
| ~ ssList(cons(sK4,nil)) ),
inference(forward_subsumption_resolution,[],[f196,f165]) ).
fof(f199,plain,
( sK2 != sK2
| ~ ssList(cons(sK4,nil))
| ~ ssList(sK2) ),
inference(superposition,[],[f198,f150]) ).
fof(f200,plain,
( ~ ssList(cons(sK4,nil))
| ~ ssList(sK2) ),
inference(trivial_inequality_removal,[],[f199]) ).
fof(f201,plain,
~ ssList(cons(sK4,nil)),
inference(forward_subsumption_resolution,[],[f200,f128]) ).
fof(f214,plain,
( ~ ssItem(sK4)
| ~ ssList(nil) ),
inference(resolution,[],[f149,f201]) ).
fof(f215,plain,
~ ssList(nil),
inference(forward_subsumption_resolution,[],[f214,f177]) ).
fof(f216,plain,
$false,
inference(forward_subsumption_resolution,[],[f215,f165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC419+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n016.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 09:39:38 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running first-order theorem proving
% 0.08/0.20 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
% 3.68/1.29 % (3511332)Detected formulas, will run a generic FOF schedule.
% 3.68/1.29 % (3511338)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=1239409372:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.68/1.29 % (3511342)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3133220019:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.68/1.29 % (3511343)dis-21_1_sil=8000:lcm=predicate:random_seed=1057798443: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)
% 3.68/1.29 % (3511341)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1784052817:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.68/1.29 % (3511339)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=3475217324:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.68/1.29 % (3511337)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=1075658496:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.68/1.29 % (3511340)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3992999321:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.68/1.29 % (3511341)First to succeed.
% 3.68/1.29 % (3511341)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3511332"
% 3.68/1.29 % (3511342)Also succeeded, but the first one will report.
% 3.68/1.29 % (3511340)Also succeeded, but the first one will report.
% 3.68/1.29 % (3511343)Instruction limit reached!
% 3.68/1.29 % (3511343)------------------------------
% 3.68/1.29 % (3511343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.29 % (3511343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.29 % (3511343)CaDiCaL version: 2.1.3
% 3.68/1.29 % (3511343)Termination reason: Instruction limit
% 3.68/1.29 % (3511343)Termination phase: Saturation
% 3.68/1.29 % (3511343)Time elapsed: 0.075 s
% 3.68/1.29 % (3511343)Peak memory usage: 90 MB
% 3.68/1.29 % (3511343)Instructions burned: 130 (million)
% 3.68/1.29 % (3511351)lrs+10_1_sil=8000:sp=occurrence:random_seed=37640464:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.68/1.29 % (3511341)Refutation found. Thanks to Tanya!
% 3.68/1.29 % SZS status Theorem for theBenchmark
% 3.68/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.68/1.29 % (3511341)------------------------------
% 3.68/1.29 % (3511341)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.29 % (3511341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.29 % (3511341)CaDiCaL version: 2.1.3
% 3.68/1.29 % (3511341)Termination reason: Refutation
% 3.68/1.29 % (3511341)Time elapsed: 0.005 s
% 3.68/1.29 % (3511341)Peak memory usage: 88 MB
% 3.68/1.29 % (3511341)Instructions burned: 5 (million)
% 3.68/1.29 % (3511341)------------------------------
% 3.68/1.29 % (3511341)------------------------------
% 3.68/1.29 % (3511332)Success in time 0.445 s
% 3.68/1.29 % Vampire exiting
%------------------------------------------------------------------------------