%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC323+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 : n017.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 3.54s 1.28s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 9 unt; 0 def)
% Number of atoms : 190 ( 76 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 250 ( 105 ~; 82 |; 44 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 3 ( 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 : 58 ( 42 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
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(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
| ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(X4,X5) = X1
& app(X5,X4) = X0 ) )
| ( nil != X2
& nil = X3 )
| ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(cons(X6,nil),X7) != X3
| app(X7,cons(X6,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
| ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(X4,X5) = X1
& app(X5,X4) = X0 ) )
| ( nil != X2
& nil = X3 )
| ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(cons(X6,nil),X7) != X3
| app(X7,cons(X6,nil)) != X2 ) ) )
& neq(X3,nil) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| app(X4,X5) != X1
| app(X5,X4) != X0 ) )
& ( nil = X2
| nil != X3 )
& ( ? [X6] :
( ? [X7] :
( app(cons(X6,nil),X7) = X3
& app(X7,cons(X6,nil)) = X2
& ssList(X7) )
& ssItem(X6) )
| ~ neq(X3,nil) )
& 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)
| ! [X5] :
( ~ ssList(X5)
| app(X4,X5) != X1
| app(X5,X4) != X0 ) )
& ( nil = X2
| nil != X3 )
& ( ? [X6] :
( ? [X7] :
( app(cons(X6,nil),X7) = X3
& app(X7,cons(X6,nil)) = X2
& ssList(X7) )
& ssItem(X6) )
| ~ neq(X3,nil) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f107,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f120,plain,
( sK1 = sK3
& sK0 = sK2
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| app(X4,X5) != sK1
| app(X5,X4) != sK0 ) )
& ( nil = sK2
| nil != sK3 )
& ( ( sK3 = app(cons(sK4,nil),sK5)
& sK2 = app(sK5,cons(sK4,nil))
& ssList(sK5)
& ssItem(sK4) )
| ~ neq(sK3,nil) )
& 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(f125,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f130,plain,
ssList(sK3),
inference(cnf_transformation,[],[f120]) ).
fof(f131,plain,
( ~ neq(sK3,nil)
| ssItem(sK4) ),
inference(cnf_transformation,[],[f120]) ).
fof(f132,plain,
( ~ neq(sK3,nil)
| ssList(sK5) ),
inference(cnf_transformation,[],[f120]) ).
fof(f133,plain,
( sK2 = app(sK5,cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f120]) ).
fof(f134,plain,
( sK3 = app(cons(sK4,nil),sK5)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f120]) ).
fof(f135,plain,
( nil != sK3
| nil = sK2 ),
inference(cnf_transformation,[],[f120]) ).
fof(f136,plain,
! [X4,X5] :
( ~ ssList(X4)
| ~ ssList(X5)
| app(X4,X5) != sK1
| app(X5,X4) != sK0 ),
inference(cnf_transformation,[],[f120]) ).
fof(f137,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f120]) ).
fof(f138,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f120]) ).
fof(f149,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f150,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f162,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f165,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f166,plain,
! [X4,X5] :
( app(X5,X4) != sK2
| ~ ssList(X5)
| app(X4,X5) != sK3
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f136,f138,f137]) ).
fof(f176,plain,
( sK2 != sK2
| ~ ssList(sK5)
| sK3 != app(cons(sK4,nil),sK5)
| ~ ssList(cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(superposition,[],[f166,f133]) ).
fof(f178,plain,
( ~ ssList(sK5)
| sK3 != app(cons(sK4,nil),sK5)
| ~ ssList(cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(trivial_inequality_removal,[],[f176]) ).
fof(f180,plain,
( sK3 != app(cons(sK4,nil),sK5)
| ~ ssList(cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f178,f132]) ).
fof(f181,plain,
( ~ ssList(cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f180,f134]) ).
fof(f182,plain,
! [X0] :
( sK2 != X0
| ~ ssList(X0)
| app(nil,X0) != sK3
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(superposition,[],[f166,f150]) ).
fof(f183,plain,
! [X0] :
( sK2 != X0
| ~ ssList(X0)
| app(nil,X0) != sK3
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f182]) ).
fof(f184,plain,
! [X0] :
( app(nil,X0) != sK3
| ~ ssList(X0)
| sK2 != X0 ),
inference(forward_subsumption_resolution,[],[f183,f165]) ).
fof(f185,plain,
( nil != sK3
| ~ ssList(nil)
| nil != sK2
| ~ ssList(nil) ),
inference(superposition,[],[f184,f150]) ).
fof(f186,plain,
( nil != sK3
| ~ ssList(nil)
| nil != sK2 ),
inference(duplicate_literal_removal,[],[f185]) ).
fof(f187,plain,
( nil != sK3
| nil != sK2 ),
inference(forward_subsumption_resolution,[],[f186,f165]) ).
fof(f188,plain,
nil != sK3,
inference(forward_subsumption_resolution,[],[f187,f135]) ).
fof(f200,plain,
( ~ ssItem(sK4)
| ~ ssList(nil)
| ~ neq(sK3,nil) ),
inference(resolution,[],[f149,f181]) ).
fof(f201,plain,
( ~ ssList(nil)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f200,f131]) ).
fof(f202,plain,
~ neq(sK3,nil),
inference(forward_subsumption_resolution,[],[f201,f165]) ).
fof(f209,plain,
( nil = sK3
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(resolution,[],[f162,f202]) ).
fof(f218,plain,
( ~ ssList(nil)
| ~ ssList(sK3) ),
inference(forward_subsumption_resolution,[],[f209,f188]) ).
fof(f221,plain,
~ ssList(sK3),
inference(forward_subsumption_resolution,[],[f218,f165]) ).
fof(f224,plain,
$false,
inference(forward_subsumption_resolution,[],[f221,f130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC323+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n017.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 09:01:21 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 3.54/1.28 % (3415392)Detected formulas, will run a generic FOF schedule.
% 3.54/1.28 % (3415399)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=2379478018:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.54/1.28 % (3415403)dis-21_1_sil=8000:lcm=predicate:random_seed=468244364: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)
% 3.54/1.28 % (3415400)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=791887053:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.54/1.28 % (3415401)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2097018012:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.54/1.28 % (3415398)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=1609330523:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.54/1.28 % (3415397)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=1580954016:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.54/1.28 % (3415402)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=436477358:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.54/1.28 % (3415401)First to succeed.
% 3.54/1.28 % (3415401)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3415392"
% 3.54/1.28 % (3415400)Also succeeded, but the first one will report.
% 3.54/1.28 % (3415402)Also succeeded, but the first one will report.
% 3.54/1.28 % (3415403)Instruction limit reached!
% 3.54/1.28 % (3415403)------------------------------
% 3.54/1.28 % (3415403)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.28 % (3415403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.28 % (3415403)CaDiCaL version: 2.1.3
% 3.54/1.28 % (3415403)Termination reason: Instruction limit
% 3.54/1.28 % (3415403)Termination phase: Saturation
% 3.54/1.28 % (3415403)Time elapsed: 0.076 s
% 3.54/1.28 % (3415403)Peak memory usage: 90 MB
% 3.54/1.28 % (3415403)Instructions burned: 130 (million)
% 3.54/1.28 % (3415411)lrs+10_1_sil=8000:sp=occurrence:random_seed=1638663838:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.54/1.28 % (3415411)Also succeeded, but the first one will report.
% 3.54/1.28 % (3415401)Refutation found. Thanks to Tanya!
% 3.54/1.28 % SZS status Theorem for theBenchmark
% 3.54/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.54/1.28 % (3415401)------------------------------
% 3.54/1.28 % (3415401)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.28 % (3415401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.28 % (3415401)CaDiCaL version: 2.1.3
% 3.54/1.28 % (3415401)Termination reason: Refutation
% 3.54/1.28 % (3415401)Time elapsed: 0.004 s
% 3.54/1.28 % (3415401)Peak memory usage: 88 MB
% 3.54/1.28 % (3415401)Instructions burned: 5 (million)
% 3.54/1.28 % (3415401)------------------------------
% 3.54/1.28 % (3415401)------------------------------
% 3.54/1.28 % (3415392)Success in time 0.414 s
% 3.54/1.28 % Vampire exiting
%------------------------------------------------------------------------------