%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC040+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 01:02:09 PM UTC 2026
% Result : Theorem 2.76s 1.36s
% Output : Refutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 12 unt; 2 def)
% Number of atoms : 93 ( 52 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 102 ( 29 ~; 21 |; 40 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 24 ( 12 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( nil != X1
| X1 != X3
| X0 != X2
| nil = X0
| ( 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) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( nil != X1
| X1 != X3
| X0 != X2
| nil = X0
| ( 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) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil = X1
& X1 = X3
& X0 = X2
& nil != X0
& ( nil = X2
| nil != X3 )
& ( ? [X4] :
( ? [X5] :
( app(cons(X4,nil),X5) = X2
& app(X5,cons(X4,nil)) = X3
& ssList(X5) )
& ssItem(X4) )
| ~ neq(X3,nil) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil = X1
& X1 = X3
& X0 = X2
& nil != X0
& ( nil = X2
| nil != X3 )
& ( ? [X4] :
( ? [X5] :
( app(cons(X4,nil),X5) = X2
& app(X5,cons(X4,nil)) = X3
& ssList(X5) )
& ssItem(X4) )
| ~ neq(X3,nil) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f120,plain,
( nil = sK1
& sK1 = sK3
& sK0 = sK2
& nil != sK0
& ( nil = sK2
| nil != sK3 )
& ( ( sK2 = app(cons(sK4,nil),sK5)
& sK3 = 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(X4,sK4),skolemize(X5,sK5)],[f99]) ).
fof(f135,plain,
( nil = sK2
| nil != sK3 ),
inference(cnf_transformation,[],[f120]) ).
fof(f136,plain,
nil != sK0,
inference(cnf_transformation,[],[f120]) ).
fof(f137,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f120]) ).
fof(f138,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f120]) ).
fof(f139,plain,
nil = sK1,
inference(cnf_transformation,[],[f120]) ).
fof(f167,plain,
nil = sK3,
inference(definition_unfolding,[],[f139,f138]) ).
fof(f168,plain,
sK2 != sK3,
inference(definition_unfolding,[],[f136,f167,f137]) ).
fof(f169,plain,
( sK2 = sK3
| sK3 != sK3 ),
inference(definition_unfolding,[],[f135,f167,f167]) ).
fof(f187,definition,
~ sP10(sK2),
introduced(definition,[new_symbols(definition,[sP10])],[inequality_splitting_name_introduction]) ).
fof(f188,plain,
sP10(sK3),
inference(inequality_splitting,[],[f168,f187]) ).
fof(f189,definition,
~ sP11(sK3),
introduced(definition,[new_symbols(definition,[sP11])],[inequality_splitting_name_introduction]) ).
fof(f190,plain,
( sK2 = sK3
| sP11(sK3) ),
inference(inequality_splitting,[],[f169,f189]) ).
fof(f204,plain,
sK2 = sK3,
inference(forward_subsumption_resolution,[],[f190,f189]) ).
fof(f205,plain,
~ sP10(sK3),
inference(superposition,[],[f187,f204]) ).
fof(f207,plain,
$false,
inference(forward_subsumption_resolution,[],[f205,f188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC040+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 07:33:06 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.76/1.36 % (1003371)Detected formulas, will run a generic FOF schedule.
% 2.76/1.36 % (1003379)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1196059435:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.76/1.36 % (1003379)First to succeed.
% 2.76/1.36 % (1003379)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1003371"
% 2.76/1.36 % (1003377)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=1396043379:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.76/1.36 % (1003376)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=3727575379:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.76/1.36 % (1003378)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=2453039716:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.76/1.36 % (1003382)dis-21_1_sil=8000:lcm=predicate:random_seed=2559473686: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)
% 2.76/1.36 % (1003380)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3645359582:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.76/1.36 % (1003381)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1899612027:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.76/1.36 % (1003380)Also succeeded, but the first one will report.
% 2.76/1.36 % (1003382)Also succeeded, but the first one will report.
% 2.76/1.36 % (1003381)Also succeeded, but the first one will report.
% 2.76/1.36 % (1003379)Refutation found. Thanks to Tanya!
% 2.76/1.36 % SZS status Theorem for theBenchmark
% 2.76/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.76/1.36 % (1003379)------------------------------
% 2.76/1.36 % (1003379)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.36 % (1003379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.36 % (1003379)CaDiCaL version: 2.1.3
% 2.76/1.36 % (1003379)Termination reason: Refutation
% 2.76/1.36 % (1003379)Time elapsed: 0.002 s
% 2.76/1.36 % (1003379)Peak memory usage: 89 MB
% 2.76/1.36 % (1003379)Instructions burned: 3 (million)
% 2.76/1.36 % (1003379)------------------------------
% 2.76/1.36 % (1003379)------------------------------
% 2.76/1.36 % (1003371)Success in time 0.31 s
% 2.76/1.36 % Vampire exiting
%------------------------------------------------------------------------------