%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC207+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 : n001.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 01:02:56 PM UTC 2026
% Result : Theorem 3.48s 1.38s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 15 unt; 0 def)
% Number of atoms : 147 ( 55 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 171 ( 59 ~; 51 |; 45 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 39 ( 27 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ neq(X1,nil)
| neq(X0,nil)
| ( ! [X4] :
( ssItem(X4)
=> ( cons(X4,nil) != X2
| ~ memberP(X3,X4)
| ? [X5] :
( ssItem(X5)
& X4 != X5
& memberP(X3,X5)
& leq(X4,X5) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
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)
| neq(X0,nil)
| ( ! [X4] :
( ssItem(X4)
=> ( cons(X4,nil) != X2
| ~ memberP(X3,X4)
| ? [X5] :
( ssItem(X5)
& X4 != X5
& memberP(X3,X5)
& leq(X4,X5) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ~ neq(X0,nil)
& ( ? [X4] :
( cons(X4,nil) = X2
& memberP(X3,X4)
& ! [X5] :
( ~ ssItem(X5)
| X4 = X5
| ~ memberP(X3,X5)
| ~ leq(X4,X5) )
& ssItem(X4) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ~ neq(X0,nil)
& ( ? [X4] :
( cons(X4,nil) = X2
& memberP(X3,X4)
& ! [X5] :
( ~ ssItem(X5)
| X4 = X5
| ~ memberP(X3,X5)
| ~ leq(X4,X5) )
& ssItem(X4) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f107,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f129,plain,
( sK1 = sK3
& sK0 = sK2
& neq(sK1,nil)
& ~ neq(sK0,nil)
& ( ( sK2 = cons(sK4,nil)
& memberP(sK3,sK4)
& ! [X5] :
( ~ ssItem(X5)
| sK4 = X5
| ~ memberP(sK3,X5)
| ~ leq(sK4,X5) )
& ssItem(sK4) )
| ( nil = sK3
& nil = sK2 ) )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f99]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f107]) ).
fof(f145,plain,
ssList(sK2),
inference(cnf_transformation,[],[f129]) ).
fof(f148,plain,
( nil = sK3
| ssItem(sK4) ),
inference(cnf_transformation,[],[f129]) ).
fof(f154,plain,
( sK2 = cons(sK4,nil)
| nil = sK3 ),
inference(cnf_transformation,[],[f129]) ).
fof(f155,plain,
~ neq(sK0,nil),
inference(cnf_transformation,[],[f129]) ).
fof(f156,plain,
neq(sK1,nil),
inference(cnf_transformation,[],[f129]) ).
fof(f157,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f129]) ).
fof(f158,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f129]) ).
fof(f162,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f171,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f174,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f200,plain,
neq(sK3,nil),
inference(definition_unfolding,[],[f156,f158]) ).
fof(f201,plain,
~ neq(sK2,nil),
inference(definition_unfolding,[],[f155,f157]) ).
fof(f257,plain,
( nil != sK2
| ~ ssItem(sK4)
| ~ ssList(nil)
| nil = sK3 ),
inference(superposition,[],[f162,f154]) ).
fof(f259,plain,
( nil != sK2
| ~ ssList(nil)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f257,f148]) ).
fof(f260,plain,
( nil != sK2
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f259,f174]) ).
fof(f271,plain,
( nil = sK2
| ~ ssList(nil)
| ~ ssList(sK2) ),
inference(resolution,[],[f171,f201]) ).
fof(f279,plain,
( nil = sK2
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f271,f174]) ).
fof(f280,plain,
nil = sK2,
inference(forward_subsumption_resolution,[],[f279,f145]) ).
fof(f288,plain,
neq(sK3,sK2),
inference(superposition,[],[f200,f280]) ).
fof(f289,plain,
~ neq(sK2,sK2),
inference(superposition,[],[f201,f280]) ).
fof(f290,plain,
( sK2 != sK2
| sK2 = sK3 ),
inference(superposition,[],[f260,f280]) ).
fof(f291,plain,
sK2 = sK3,
inference(trivial_inequality_removal,[],[f290]) ).
fof(f312,plain,
neq(sK2,sK2),
inference(superposition,[],[f288,f291]) ).
fof(f313,plain,
$false,
inference(forward_subsumption_resolution,[],[f312,f289]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC207+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 08:33:18 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 3.48/1.38 % (215153)Detected formulas, will run a generic FOF schedule.
% 3.48/1.38 % (215264)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=2225342045:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.48/1.38 % (215263)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=3475126358:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.48/1.38 % (215269)dis-21_1_sil=8000:lcm=predicate:random_seed=3309986352: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)
% 3.48/1.38 % (215267)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1196540363:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.48/1.38 % (215266)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2998043112:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.48/1.38 % (215265)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=2075729152:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.48/1.38 % (215268)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1554486173:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.48/1.38 % (215267)First to succeed.
% 3.48/1.38 % (215266)Also succeeded, but the first one will report.
% 3.48/1.38 % (215267)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-215153"
% 3.48/1.38 % (215268)Also succeeded, but the first one will report.
% 3.48/1.38 % (215269)Instruction limit reached!
% 3.48/1.38 % (215269)------------------------------
% 3.48/1.38 % (215269)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.38 % (215269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.38 % (215269)CaDiCaL version: 2.1.3
% 3.48/1.38 % (215269)Termination reason: Instruction limit
% 3.48/1.38 % (215269)Termination phase: Saturation
% 3.48/1.38 % (215269)Time elapsed: 0.073 s
% 3.48/1.38 % (215269)Peak memory usage: 90 MB
% 3.48/1.38 % (215269)Instructions burned: 129 (million)
% 3.48/1.38 % (215324)lrs+10_1_sil=8000:sp=occurrence:random_seed=1485189909:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.48/1.38 % (215324)Also succeeded, but the first one will report.
% 3.48/1.38 % (215267)Refutation found. Thanks to Tanya!
% 3.48/1.38 % SZS status Theorem for theBenchmark
% 3.48/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.38 % (215267)------------------------------
% 3.48/1.38 % (215267)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.38 % (215267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.38 % (215267)CaDiCaL version: 2.1.3
% 3.48/1.38 % (215267)Termination reason: Refutation
% 3.48/1.38 % (215267)Time elapsed: 0.005 s
% 3.48/1.38 % (215267)Peak memory usage: 88 MB
% 3.48/1.38 % (215267)Instructions burned: 5 (million)
% 3.48/1.38 % (215267)------------------------------
% 3.48/1.38 % (215267)------------------------------
% 3.48/1.38 % (215153)Success in time 0.422 s
% 3.48/1.38 % Vampire exiting
%------------------------------------------------------------------------------