%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC320+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 2.75s 1.14s
% Output : Refutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 39 ( 7 unt; 0 def)
% Number of atoms : 176 ( 94 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 236 ( 99 ~; 91 |; 38 &)
% ( 0 <=>; 8 =>; 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 : 34 ( 24 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ( nil != X2
& nil = X3 )
| ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ~ ssList(X5)
| app(cons(X4,nil),X5) != X2
| app(X5,cons(X4,nil)) != X3 ) )
& neq(X3,nil) )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X0
& app(X7,cons(X6,nil)) = X1 ) ) ) ) ) ) ) ),
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
| ( nil != X2
& nil = X3 )
| ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ~ ssList(X5)
| app(cons(X4,nil),X5) != X2
| app(X5,cons(X4,nil)) != X3 ) )
& neq(X3,nil) )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X0
& app(X7,cons(X6,nil)) = X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ( nil = X2
| nil != X3 )
& ( ? [X4] :
( ? [X5] :
( ssList(X5)
& app(cons(X4,nil),X5) = X2
& app(X5,cons(X4,nil)) = X3 )
& ssItem(X4) )
| ~ neq(X3,nil) )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(cons(X6,nil),X7) != X0
| app(X7,cons(X6,nil)) != X1 ) ) ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f119,plain,
( ssList(sK3)
& sK1 = sK3
& sK0 = sK2
& ( nil = sK2
| nil != sK3 )
& ( ( ssList(sK5)
& sK2 = app(cons(sK4,nil),sK5)
& sK3 = app(sK5,cons(sK4,nil))
& ssItem(sK4) )
| ~ neq(sK3,nil) )
& ( ( nil = sK1
& nil != sK0 )
| ( neq(sK1,nil)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(cons(X6,nil),X7) != sK0
| app(X7,cons(X6,nil)) != sK1 ) ) ) )
& 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(X4,sK4),skolemize(X5,sK5)],[f98]) ).
fof(f129,plain,
! [X6,X7] :
( nil != sK0
| ~ ssItem(X6)
| ~ ssList(X7)
| app(cons(X6,nil),X7) != sK0
| app(X7,cons(X6,nil)) != sK1 ),
inference(cnf_transformation,[],[f119]) ).
fof(f130,plain,
( nil != sK0
| neq(sK1,nil) ),
inference(cnf_transformation,[],[f119]) ).
fof(f131,plain,
! [X6,X7] :
( nil = sK1
| ~ ssItem(X6)
| ~ ssList(X7)
| app(cons(X6,nil),X7) != sK0
| app(X7,cons(X6,nil)) != sK1 ),
inference(cnf_transformation,[],[f119]) ).
fof(f132,plain,
( nil = sK1
| neq(sK1,nil) ),
inference(cnf_transformation,[],[f119]) ).
fof(f133,plain,
( ~ neq(sK3,nil)
| ssItem(sK4) ),
inference(cnf_transformation,[],[f119]) ).
fof(f134,plain,
( sK3 = app(sK5,cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f119]) ).
fof(f135,plain,
( sK2 = app(cons(sK4,nil),sK5)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f119]) ).
fof(f136,plain,
( ~ neq(sK3,nil)
| ssList(sK5) ),
inference(cnf_transformation,[],[f119]) ).
fof(f137,plain,
( nil != sK3
| nil = sK2 ),
inference(cnf_transformation,[],[f119]) ).
fof(f138,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f119]) ).
fof(f139,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f119]) ).
fof(f168,plain,
( neq(sK3,nil)
| nil = sK3 ),
inference(definition_unfolding,[],[f132,f139,f139]) ).
fof(f169,plain,
! [X6,X7] :
( app(cons(X6,nil),X7) != sK2
| ~ ssItem(X6)
| ~ ssList(X7)
| nil = sK3
| app(X7,cons(X6,nil)) != sK3 ),
inference(definition_unfolding,[],[f131,f139,f138,f139]) ).
fof(f170,plain,
( nil != sK2
| neq(sK3,nil) ),
inference(definition_unfolding,[],[f130,f138,f139]) ).
fof(f171,plain,
! [X6,X7] :
( app(cons(X6,nil),X7) != sK2
| ~ ssItem(X6)
| ~ ssList(X7)
| nil != sK2
| app(X7,cons(X6,nil)) != sK3 ),
inference(definition_unfolding,[],[f129,f138,f138,f139]) ).
fof(f181,plain,
( nil = sK3
| ssList(sK5) ),
inference(resolution,[],[f168,f136]) ).
fof(f182,plain,
( nil = sK3
| ssItem(sK4) ),
inference(resolution,[],[f168,f133]) ).
fof(f223,plain,
( sK2 != sK2
| ~ ssItem(sK4)
| ~ ssList(sK5)
| nil = sK3
| sK3 != app(sK5,cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(superposition,[],[f169,f135]) ).
fof(f224,plain,
( ~ ssItem(sK4)
| ~ ssList(sK5)
| nil = sK3
| sK3 != app(sK5,cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(trivial_inequality_removal,[],[f223]) ).
fof(f225,plain,
( ~ ssList(sK5)
| nil = sK3
| sK3 != app(sK5,cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f224,f182]) ).
fof(f226,plain,
( nil = sK3
| sK3 != app(sK5,cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f225,f181]) ).
fof(f227,plain,
( sK3 != app(sK5,cons(sK4,nil))
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f226,f168]) ).
fof(f233,plain,
( sK2 != sK2
| ~ ssItem(sK4)
| ~ ssList(sK5)
| nil != sK2
| sK3 != app(sK5,cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(superposition,[],[f171,f135]) ).
fof(f234,plain,
( ~ ssItem(sK4)
| ~ ssList(sK5)
| nil != sK2
| sK3 != app(sK5,cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(trivial_inequality_removal,[],[f233]) ).
fof(f235,plain,
( ~ ssList(sK5)
| nil != sK2
| sK3 != app(sK5,cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f234,f133]) ).
fof(f238,plain,
( nil != sK2
| sK3 != app(sK5,cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f235,f136]) ).
fof(f239,plain,
( nil != sK2
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f238,f134]) ).
fof(f240,plain,
nil != sK2,
inference(forward_subsumption_resolution,[],[f239,f170]) ).
fof(f258,plain,
( sK3 != sK3
| nil = sK3
| ~ neq(sK3,nil) ),
inference(superposition,[],[f227,f134]) ).
fof(f259,plain,
( nil = sK3
| ~ neq(sK3,nil) ),
inference(trivial_inequality_removal,[],[f258]) ).
fof(f260,plain,
nil = sK3,
inference(forward_subsumption_resolution,[],[f259,f168]) ).
fof(f265,plain,
( sK3 != sK3
| sK2 = sK3 ),
inference(superposition,[],[f137,f260]) ).
fof(f273,plain,
sK2 != sK3,
inference(superposition,[],[f240,f260]) ).
fof(f274,plain,
sK2 = sK3,
inference(trivial_inequality_removal,[],[f265]) ).
fof(f296,plain,
$false,
inference(forward_subsumption_resolution,[],[f274,f273]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC320+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 09:00:48 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 2.75/1.14 % (3414335)Detected formulas, will run a generic FOF schedule.
% 2.75/1.14 % (3414344)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3990485768:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.75/1.14 % (3414344)First to succeed.
% 2.75/1.14 % (3414344)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3414335"
% 2.75/1.14 % (3414340)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=1099996639:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.75/1.14 % (3414341)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=854258254:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.75/1.14 % (3414342)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=796963497:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.75/1.14 % (3414343)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2459697728:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.75/1.14 % (3414345)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3519608467:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.75/1.14 % (3414346)dis-21_1_sil=8000:lcm=predicate:random_seed=129972414: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)
% 2.75/1.14 % (3414343)Also succeeded, but the first one will report.
% 2.75/1.14 % (3414346)Also succeeded, but the first one will report.
% 2.75/1.14 % (3414345)Also succeeded, but the first one will report.
% 2.75/1.14 % (3414344)Refutation found. Thanks to Tanya!
% 2.75/1.14 % SZS status Theorem for theBenchmark
% 2.75/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 2.75/1.14 % (3414344)------------------------------
% 2.75/1.14 % (3414344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.14 % (3414344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.14 % (3414344)CaDiCaL version: 2.1.3
% 2.75/1.14 % (3414344)Termination reason: Refutation
% 2.75/1.14 % (3414344)Time elapsed: 0.003 s
% 2.75/1.14 % (3414344)Peak memory usage: 88 MB
% 2.75/1.14 % (3414344)Instructions burned: 6 (million)
% 2.75/1.14 % (3414344)------------------------------
% 2.75/1.14 % (3414344)------------------------------
% 2.75/1.14 % (3414335)Success in time 0.296 s
% 2.75/1.14 % Vampire exiting
%------------------------------------------------------------------------------