%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC322+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 : n003.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 01:03:27 PM UTC 2026
% Result : Theorem 0.20s 1.31s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 1
% Syntax : Number of formulae : 56 ( 12 unt; 0 def)
% Number of atoms : 201 ( 118 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 229 ( 84 ~; 87 |; 46 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 42 ( 26 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& app(cons(X4,nil),X5) != X2
& app(X5,cons(X4,nil)) = X3 ) )
| ( nil != X2
& nil = X3 )
| ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(X7,cons(X6,nil)) != X1
| app(cons(X6,nil),X7) = X0 ) ) )
& ( 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
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& app(cons(X4,nil),X5) != X2
& app(X5,cons(X4,nil)) = X3 ) )
| ( nil != X2
& nil = X3 )
| ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(X7,cons(X6,nil)) != X1
| app(cons(X6,nil),X7) = X0 ) ) )
& ( nil != X1
| nil = X0 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| app(cons(X4,nil),X5) = X2
| app(X5,cons(X4,nil)) != X3 ) )
& ( nil = X2
| nil != X3 )
& ( ? [X6] :
( ? [X7] :
( app(X7,cons(X6,nil)) = X1
& app(cons(X6,nil),X7) != X0
& ssList(X7) )
& ssItem(X6) )
| ( nil = X1
& nil != X0 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| app(cons(X4,nil),X5) = X2
| app(X5,cons(X4,nil)) != X3 ) )
& ( nil = X2
| nil != X3 )
& ( ? [X6] :
( ? [X7] :
( app(X7,cons(X6,nil)) = X1
& app(cons(X6,nil),X7) != X0
& ssList(X7) )
& ssItem(X6) )
| ( nil = X1
& nil != X0 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f118,plain,
( sK1 = sK3
& sK0 = sK2
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| app(cons(X4,nil),X5) = sK2
| app(X5,cons(X4,nil)) != sK3 ) )
& ( nil = sK2
| nil != sK3 )
& ( ( sK1 = app(sK5,cons(sK4,nil))
& sK0 != app(cons(sK4,nil),sK5)
& ssList(sK5)
& ssItem(sK4) )
| ( nil = sK1
& nil != sK0 ) )
& ssList(sK3)
& 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(X6,sK4),skolemize(X7,sK5)],[f99]) ).
fof(f127,plain,
( ssItem(sK4)
| nil != sK0 ),
inference(cnf_transformation,[],[f118]) ).
fof(f128,plain,
( ssItem(sK4)
| nil = sK1 ),
inference(cnf_transformation,[],[f118]) ).
fof(f129,plain,
( ssList(sK5)
| nil != sK0 ),
inference(cnf_transformation,[],[f118]) ).
fof(f130,plain,
( ssList(sK5)
| nil = sK1 ),
inference(cnf_transformation,[],[f118]) ).
fof(f131,plain,
( sK0 != app(cons(sK4,nil),sK5)
| nil != sK0 ),
inference(cnf_transformation,[],[f118]) ).
fof(f132,plain,
( sK0 != app(cons(sK4,nil),sK5)
| nil = sK1 ),
inference(cnf_transformation,[],[f118]) ).
fof(f133,plain,
( sK1 = app(sK5,cons(sK4,nil))
| nil != sK0 ),
inference(cnf_transformation,[],[f118]) ).
fof(f134,plain,
( sK1 = app(sK5,cons(sK4,nil))
| nil = sK1 ),
inference(cnf_transformation,[],[f118]) ).
fof(f135,plain,
( nil != sK3
| nil = sK2 ),
inference(cnf_transformation,[],[f118]) ).
fof(f136,plain,
! [X4,X5] :
( app(X5,cons(X4,nil)) != sK3
| ~ ssList(X5)
| app(cons(X4,nil),X5) = sK2
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f118]) ).
fof(f137,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f118]) ).
fof(f138,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f118]) ).
fof(f162,plain,
( sK3 = app(sK5,cons(sK4,nil))
| nil = sK3 ),
inference(definition_unfolding,[],[f134,f138,f138]) ).
fof(f163,plain,
( nil != sK2
| sK3 = app(sK5,cons(sK4,nil)) ),
inference(definition_unfolding,[],[f133,f138,f137]) ).
fof(f164,plain,
( sK2 != app(cons(sK4,nil),sK5)
| nil = sK3 ),
inference(definition_unfolding,[],[f132,f137,f138]) ).
fof(f165,plain,
( sK2 != app(cons(sK4,nil),sK5)
| nil != sK2 ),
inference(definition_unfolding,[],[f131,f137,f137]) ).
fof(f166,plain,
( nil = sK3
| ssList(sK5) ),
inference(definition_unfolding,[],[f130,f138]) ).
fof(f167,plain,
( nil != sK2
| ssList(sK5) ),
inference(definition_unfolding,[],[f129,f137]) ).
fof(f168,plain,
( nil = sK3
| ssItem(sK4) ),
inference(definition_unfolding,[],[f128,f138]) ).
fof(f169,plain,
( nil != sK2
| ssItem(sK4) ),
inference(definition_unfolding,[],[f127,f137]) ).
fof(f175,plain,
( sK2 != sK3
| ssList(sK5)
| ssList(sK5) ),
inference(superposition,[],[f167,f166]) ).
fof(f176,plain,
( sK2 != sK3
| ssList(sK5) ),
inference(duplicate_literal_removal,[],[f175]) ).
fof(f178,plain,
( sK2 != sK3
| ssItem(sK4)
| ssItem(sK4) ),
inference(superposition,[],[f169,f168]) ).
fof(f180,plain,
( sK2 != sK3
| ssItem(sK4) ),
inference(duplicate_literal_removal,[],[f178]) ).
fof(f181,plain,
( sK3 != sK3
| sK2 = sK3
| ssItem(sK4) ),
inference(superposition,[],[f135,f168]) ).
fof(f182,plain,
( sK3 != sK3
| sK2 = sK3
| ssList(sK5) ),
inference(superposition,[],[f135,f166]) ).
fof(f183,plain,
( sK2 = sK3
| ssList(sK5) ),
inference(trivial_inequality_removal,[],[f182]) ).
fof(f184,plain,
( sK2 = sK3
| ssItem(sK4) ),
inference(trivial_inequality_removal,[],[f181]) ).
fof(f185,plain,
ssList(sK5),
inference(forward_subsumption_resolution,[],[f183,f176]) ).
fof(f188,plain,
ssItem(sK4),
inference(forward_subsumption_resolution,[],[f184,f180]) ).
fof(f193,plain,
( sK3 != sK3
| ~ ssList(sK5)
| sK2 = app(cons(sK4,nil),sK5)
| ~ ssItem(sK4)
| nil = sK3 ),
inference(superposition,[],[f136,f162]) ).
fof(f194,plain,
( ~ ssList(sK5)
| sK2 = app(cons(sK4,nil),sK5)
| ~ ssItem(sK4)
| nil = sK3 ),
inference(trivial_inequality_removal,[],[f193]) ).
fof(f195,plain,
( ~ ssList(sK5)
| ~ ssItem(sK4)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f194,f164]) ).
fof(f196,plain,
( ~ ssList(sK5)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f195,f168]) ).
fof(f197,plain,
nil = sK3,
inference(forward_subsumption_resolution,[],[f196,f185]) ).
fof(f198,plain,
( sK3 != sK3
| sK2 = sK3 ),
inference(superposition,[],[f135,f197]) ).
fof(f199,plain,
! [X0,X1] :
( sK3 != app(X0,cons(X1,sK3))
| ~ ssList(X0)
| sK2 = app(cons(X1,sK3),X0)
| ~ ssItem(X1) ),
inference(superposition,[],[f136,f197]) ).
fof(f200,plain,
( sK2 != sK3
| sK3 = app(sK5,cons(sK4,sK3)) ),
inference(superposition,[],[f163,f197]) ).
fof(f201,plain,
( sK2 != app(cons(sK4,sK3),sK5)
| sK2 != sK3 ),
inference(superposition,[],[f165,f197]) ).
fof(f204,plain,
sK2 = sK3,
inference(trivial_inequality_removal,[],[f198]) ).
fof(f210,plain,
sK3 = app(sK5,cons(sK4,sK3)),
inference(forward_subsumption_resolution,[],[f200,f204]) ).
fof(f211,plain,
sK2 = app(sK5,cons(sK4,sK2)),
inference(forward_demodulation,[],[f210,f204]) ).
fof(f213,plain,
sK2 != app(cons(sK4,sK3),sK5),
inference(forward_subsumption_resolution,[],[f201,f204]) ).
fof(f214,plain,
sK2 != app(cons(sK4,sK2),sK5),
inference(forward_demodulation,[],[f213,f204]) ).
fof(f215,plain,
! [X0,X1] :
( sK2 != app(X0,cons(X1,sK2))
| ~ ssList(X0)
| sK2 = app(cons(X1,sK3),X0)
| ~ ssItem(X1) ),
inference(forward_demodulation,[],[f199,f204]) ).
fof(f216,plain,
! [X0,X1] :
( sK2 != app(X0,cons(X1,sK2))
| sK2 = app(cons(X1,sK2),X0)
| ~ ssList(X0)
| ~ ssItem(X1) ),
inference(forward_demodulation,[],[f215,f204]) ).
fof(f219,plain,
( sK2 != sK2
| sK2 = app(cons(sK4,sK2),sK5)
| ~ ssList(sK5)
| ~ ssItem(sK4) ),
inference(superposition,[],[f216,f211]) ).
fof(f220,plain,
( sK2 = app(cons(sK4,sK2),sK5)
| ~ ssList(sK5)
| ~ ssItem(sK4) ),
inference(trivial_inequality_removal,[],[f219]) ).
fof(f221,plain,
( ~ ssList(sK5)
| ~ ssItem(sK4) ),
inference(forward_subsumption_resolution,[],[f220,f214]) ).
fof(f222,plain,
~ ssItem(sK4),
inference(forward_subsumption_resolution,[],[f221,f185]) ).
fof(f223,plain,
$false,
inference(forward_subsumption_resolution,[],[f222,f188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC322+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n003.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Mon Sep 28 09:07:09 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 Running first-order theorem proving
% 0.11/0.22 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
% 0.20/1.31 % (1451069)Detected formulas, will run a generic FOF schedule.
% 0.20/1.31 % (1451074)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=3380448377:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.20/1.31 % (1451079)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3193609068:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.20/1.31 % (1451077)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2685788974:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.20/1.31 % (1451076)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=873189076:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.20/1.31 % (1451078)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1436470736:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.20/1.31 % (1451075)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=2896787163:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.20/1.31 % (1451080)dis-21_1_sil=8000:lcm=predicate:random_seed=1776925634: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)
% 0.20/1.31 % (1451078)First to succeed.
% 0.20/1.31 % (1451078)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1451069"
% 0.20/1.31 % (1451080)Also succeeded, but the first one will report.
% 0.20/1.31 % (1451077)Also succeeded, but the first one will report.
% 0.20/1.31 % (1451079)Also succeeded, but the first one will report.
% 0.20/1.31 % (1451078)Refutation found. Thanks to Tanya!
% 0.20/1.31 % SZS status Theorem for theBenchmark
% 0.20/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.31 % (1451078)------------------------------
% 0.20/1.31 % (1451078)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.31 % (1451078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.31 % (1451078)CaDiCaL version: 2.1.3
% 0.20/1.31 % (1451078)Termination reason: Refutation
% 0.20/1.31 % (1451078)Time elapsed: 0.004 s
% 0.20/1.31 % (1451078)Peak memory usage: 88 MB
% 0.20/1.31 % (1451078)Instructions burned: 5 (million)
% 0.20/1.31 % (1451078)------------------------------
% 0.20/1.31 % (1451078)------------------------------
% 0.20/1.31 % (1451069)Success in time 0.446 s
% 0.20/1.31 % Vampire exiting
%------------------------------------------------------------------------------