%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC046+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 : n019.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 01:02:11 PM UTC 2026
% Result : Theorem 3.31s 1.35s
% Output : Refutation 3.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 43 ( 9 unt; 0 def)
% Number of atoms : 221 ( 58 equ)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 272 ( 94 ~; 96 |; 60 &)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 81 ( 59 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( nil = X0
| ? [X1] :
( ssList(X1)
& ? [X2] :
( ssItem(X2)
& cons(X2,X1) = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( X0 = X1
| memberP(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( nil != X1
| X1 != X3
| X0 != X2
| nil = X0
| ? [X4] :
( ssItem(X4)
& ( ( ~ memberP(X2,X4)
& ! [X5] :
( ssList(X5)
=> ~ segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) )
& memberP(X3,X4) )
| ( memberP(X2,X4)
& ( ~ memberP(X3,X4)
| ? [X5] :
( ssList(X5)
& segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,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)
=> ( nil != X1
| X1 != X3
| X0 != X2
| nil = X0
| ? [X4] :
( ssItem(X4)
& ( ( ~ memberP(X2,X4)
& ! [X5] :
( ssList(X5)
=> ~ segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) )
& memberP(X3,X4) )
| ( memberP(X2,X4)
& ( ~ memberP(X3,X4)
| ? [X5] :
( ssList(X5)
& segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( nil != X1
| X1 != X3
| X0 != X2
| nil = X0
| ? [X4] :
( ssItem(X4)
& ( ( ~ memberP(X2,X4)
& ! [X5] :
( ssList(X5)
=> ~ segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) )
& memberP(X3,X4) )
| ( memberP(X2,X4)
& ( ~ memberP(X3,X4)
| ? [X6] :
( ssList(X6)
& segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil))) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil = X1
& X1 = X3
& X0 = X2
& nil != X0
& ! [X4] :
( ~ ssItem(X4)
| ( ( memberP(X2,X4)
| ? [X5] :
( segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil)))
& ssList(X5) )
| ~ memberP(X3,X4) )
& ( ~ memberP(X2,X4)
| ( memberP(X3,X4)
& ! [X6] :
( ~ ssList(X6)
| ~ segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil))) ) ) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil = X1
& X1 = X3
& X0 = X2
& nil != X0
& ! [X4] :
( ~ ssItem(X4)
| ( ( memberP(X2,X4)
| ? [X5] :
( segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil)))
& ssList(X5) )
| ~ memberP(X3,X4) )
& ( ~ memberP(X2,X4)
| ( memberP(X3,X4)
& ! [X6] :
( ~ ssList(X6)
| ~ segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil))) ) ) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f99]) ).
fof(f102,plain,
! [X0] :
( nil = X0
| ? [X1] :
( ssList(X1)
& ? [X2] :
( ssItem(X2)
& cons(X2,X1) = X0 ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f103,plain,
! [X0] :
( nil = X0
| ? [X1] :
( ssList(X1)
& ? [X2] :
( ssItem(X2)
& cons(X2,X1) = X0 ) )
| ~ ssList(X0) ),
inference(flattening,[],[f102]) ).
fof(f119,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(cons(X1,X2),X0)
<=> ( X0 = X1
| memberP(X2,X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f133,plain,
( nil = sK1
& sK1 = sK3
& sK0 = sK2
& nil != sK0
& ! [X4] :
( ~ ssItem(X4)
| ( ( memberP(sK2,X4)
| ( segmentP(sK3,app(app(cons(X4,nil),sK4(X4)),cons(X4,nil)))
& ssList(sK4(X4)) )
| ~ memberP(sK3,X4) )
& ( ~ memberP(sK2,X4)
| ( memberP(sK3,X4)
& ! [X6] :
( ~ ssList(X6)
| ~ segmentP(sK3,app(app(cons(X4,nil),X6),cons(X4,nil))) ) ) ) ) )
& 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(X5,sK4(X4))],[f100]) ).
fof(f135,plain,
! [X0] :
( nil = X0
| ( ssList(sK7(X0))
& ssItem(sK8(X0))
& cons(sK8(X0),sK7(X0)) = X0 )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X1,sK7(X0)),skolemize(X2,sK8(X0))],[f103]) ).
fof(f138,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( X0 != X1
& ~ memberP(X2,X0) ) )
& ( X0 = X1
| memberP(X2,X0)
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f120]) ).
fof(f139,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( X0 != X1
& ~ memberP(X2,X0) ) )
& ( X0 = X1
| memberP(X2,X0)
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f138]) ).
fof(f151,plain,
ssList(sK2),
inference(cnf_transformation,[],[f133]) ).
fof(f154,plain,
! [X4] :
( ~ ssItem(X4)
| ~ memberP(sK2,X4)
| memberP(sK3,X4) ),
inference(cnf_transformation,[],[f133]) ).
fof(f157,plain,
nil != sK0,
inference(cnf_transformation,[],[f133]) ).
fof(f158,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f133]) ).
fof(f159,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f133]) ).
fof(f160,plain,
nil = sK1,
inference(cnf_transformation,[],[f133]) ).
fof(f165,plain,
! [X0] :
( nil = X0
| cons(sK8(X0),sK7(X0)) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f166,plain,
! [X0] :
( nil = X0
| ssItem(sK8(X0))
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f167,plain,
! [X0] :
( nil = X0
| ssList(sK7(X0))
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f184,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f187,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f206,plain,
nil = sK3,
inference(definition_unfolding,[],[f160,f159]) ).
fof(f207,plain,
sK2 != sK3,
inference(definition_unfolding,[],[f157,f206,f158]) ).
fof(f213,plain,
! [X0] :
( ssList(sK7(X0))
| sK3 = X0
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f167,f206]) ).
fof(f214,plain,
! [X0] :
( ssItem(sK8(X0))
| sK3 = X0
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f166,f206]) ).
fof(f215,plain,
! [X0] :
( cons(sK8(X0),sK7(X0)) = X0
| sK3 = X0
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f165,f206]) ).
fof(f223,plain,
! [X0] :
( ~ memberP(sK3,X0)
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f184,f206]) ).
fof(f229,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f187]) ).
fof(f233,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f229]) ).
fof(f235,plain,
! [X4] :
( ~ memberP(sK2,X4)
| ~ ssItem(X4) ),
inference(forward_subsumption_resolution,[],[f154,f223]) ).
fof(f259,plain,
! [X0] :
( memberP(X0,sK8(X0))
| ~ ssList(sK7(X0))
| ~ ssItem(sK8(X0))
| sK3 = X0
| ~ ssList(X0) ),
inference(superposition,[],[f233,f215]) ).
fof(f260,plain,
! [X0] :
( memberP(X0,sK8(X0))
| ~ ssItem(sK8(X0))
| sK3 = X0
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f259,f213]) ).
fof(f261,plain,
! [X0] :
( memberP(X0,sK8(X0))
| sK3 = X0
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f260,f214]) ).
fof(f263,plain,
( sK2 = sK3
| ~ ssList(sK2)
| ~ ssItem(sK8(sK2)) ),
inference(resolution,[],[f261,f235]) ).
fof(f264,plain,
( sK2 = sK3
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f263,f214]) ).
fof(f265,plain,
~ ssList(sK2),
inference(forward_subsumption_resolution,[],[f264,f207]) ).
fof(f266,plain,
$false,
inference(forward_subsumption_resolution,[],[f265,f151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC046+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n019.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 07:36:04 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 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
% 3.31/1.35 % (3831660)Detected formulas, will run a generic FOF schedule.
% 3.31/1.35 % (3831665)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=2705223478:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.31/1.35 % (3831666)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=984003256:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.31/1.35 % (3831670)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3929617821:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.31/1.35 % (3831669)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1870208642:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.31/1.35 % (3831668)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1328311636:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.31/1.35 % (3831667)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=59501520:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.31/1.35 % (3831669)First to succeed.
% 3.31/1.35 % (3831669)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3831660"
% 3.31/1.35 % (3831670)Also succeeded, but the first one will report.
% 3.31/1.35 % (3831671)dis-21_1_sil=8000:lcm=predicate:random_seed=1531834459: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)
% 3.31/1.35 % (3831668)Also succeeded, but the first one will report.
% 3.31/1.35 % (3831671)Instruction limit reached!
% 3.31/1.35 % (3831671)------------------------------
% 3.31/1.35 % (3831671)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/1.35 % (3831671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.35 % (3831671)CaDiCaL version: 2.1.3
% 3.31/1.35 % (3831671)Termination reason: Instruction limit
% 3.31/1.35 % (3831671)Termination phase: Saturation
% 3.31/1.35 % (3831671)Time elapsed: 0.073 s
% 3.31/1.35 % (3831671)Peak memory usage: 89 MB
% 3.31/1.35 % (3831671)Instructions burned: 130 (million)
% 3.31/1.35 % (3831679)lrs+10_1_sil=8000:sp=occurrence:random_seed=2010450362:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.31/1.35 % (3831679)Also succeeded, but the first one will report.
% 3.31/1.35 % (3831669)Refutation found. Thanks to Tanya!
% 3.31/1.35 % SZS status Theorem for theBenchmark
% 3.31/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.31/1.35 % (3831669)------------------------------
% 3.31/1.35 % (3831669)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/1.35 % (3831669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.35 % (3831669)CaDiCaL version: 2.1.3
% 3.31/1.35 % (3831669)Termination reason: Refutation
% 3.31/1.35 % (3831669)Time elapsed: 0.005 s
% 3.31/1.35 % (3831669)Peak memory usage: 88 MB
% 3.31/1.35 % (3831669)Instructions burned: 5 (million)
% 3.31/1.35 % (3831669)------------------------------
% 3.31/1.35 % (3831669)------------------------------
% 3.31/1.35 % (3831660)Success in time 0.402 s
% 3.31/1.35 % Vampire exiting
%------------------------------------------------------------------------------