%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC198+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 : 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 01:02:54 PM UTC 2026
% Result : Theorem 2.59s 1.26s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 62 ( 11 unt; 4 def)
% Number of atoms : 254 ( 60 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 315 ( 123 ~; 113 |; 57 &)
% ( 6 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 53 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [X0] :
( ssItem(X0)
& ? [X1] :
( ssItem(X1)
& X0 != X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
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/sandbox/benchmark/theBenchmark.p',ax37) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssItem(X4)
& ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X0,X5)
| X4 = X5 ) ) )
| ( ! [X6] :
( ssItem(X6)
=> ( cons(X6,nil) != X2
| ~ memberP(X3,X6)
| ? [X7] :
( ssItem(X7)
& X6 != X7
& memberP(X3,X7)
& leq(X6,X7) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/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] :
( ssItem(X4)
& ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X0,X5)
| X4 = X5 ) ) )
| ( ! [X6] :
( ssItem(X6)
=> ( cons(X6,nil) != X2
| ~ memberP(X3,X6)
| ? [X7] :
( ssItem(X7)
& X6 != X7
& memberP(X3,X7)
& leq(X6,X7) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssItem(X4)
| ? [X5] :
( memberP(X0,X5)
& X4 != X5
& ssItem(X5) ) )
& ( ? [X6] :
( cons(X6,nil) = X2
& memberP(X3,X6)
& ! [X7] :
( ~ ssItem(X7)
| X6 = X7
| ~ memberP(X3,X7)
| ~ leq(X6,X7) )
& ssItem(X6) )
| ( 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
& ! [X4] :
( ~ ssItem(X4)
| ? [X5] :
( memberP(X0,X5)
& X4 != X5
& ssItem(X5) ) )
& ( ? [X6] :
( cons(X6,nil) = X2
& memberP(X3,X6)
& ! [X7] :
( ~ ssItem(X7)
| X6 = X7
| ~ memberP(X3,X7)
| ~ leq(X6,X7) )
& ssItem(X6) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f107,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f108,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(f116,plain,
( sK1 = sK3
& sK0 = sK2
& ! [X4] :
( ~ ssItem(X4)
| ( memberP(sK0,sK4(X4))
& sK4(X4) != X4
& ssItem(sK4(X4)) ) )
& ( ( sK2 = cons(sK5,nil)
& memberP(sK3,sK5)
& ! [X7] :
( ~ ssItem(X7)
| sK5 = X7
| ~ memberP(sK3,X7)
| ~ leq(sK5,X7) )
& ssItem(sK5) )
| ( nil = sK3
& nil = sK2 ) )
& 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(X5,sK4(X4)),skolemize(X6,sK5)],[f99]) ).
fof(f117,plain,
( ssItem(sK6)
& ssItem(sK7)
& sK6 != sK7 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f2]) ).
fof(f119,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,[],[f108]) ).
fof(f120,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,[],[f119]) ).
fof(f130,plain,
( ssItem(sK5)
| nil = sK2 ),
inference(cnf_transformation,[],[f116]) ).
fof(f136,plain,
( sK2 = cons(sK5,nil)
| nil = sK2 ),
inference(cnf_transformation,[],[f116]) ).
fof(f138,plain,
! [X4] :
( ssItem(sK4(X4))
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f116]) ).
fof(f139,plain,
! [X4] :
( sK4(X4) != X4
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f116]) ).
fof(f140,plain,
! [X4] :
( ~ ssItem(X4)
| memberP(sK0,sK4(X4)) ),
inference(cnf_transformation,[],[f116]) ).
fof(f141,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f116]) ).
fof(f145,plain,
ssItem(sK6),
inference(cnf_transformation,[],[f117]) ).
fof(f154,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f155,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f169,plain,
! [X4] :
( memberP(sK2,sK4(X4))
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f140,f141]) ).
fof(f180,definition,
( spl14_1
<=> nil = sK2 ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f182,plain,
( nil = sK2
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f184,definition,
( spl14_2
<=> ssItem(sK5) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f186,plain,
( ssItem(sK5)
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f187,plain,
( spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f130,f184,f180]) ).
fof(f205,definition,
( spl14_6
<=> sK2 = cons(sK5,nil) ),
introduced(definition,[new_symbols(definition,[spl14_6])],[avatar_definition]) ).
fof(f207,plain,
( sK2 = cons(sK5,nil)
| ~ spl14_6 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f208,plain,
( spl14_1
| spl14_6 ),
inference(avatar_split_clause,[],[f136,f205,f180]) ).
fof(f211,plain,
( ! [X0] :
( memberP(cons(sK5,nil),sK4(X0))
| ~ ssItem(X0) )
| ~ spl14_6 ),
inference(superposition,[],[f169,f207]) ).
fof(f214,plain,
( ! [X0] :
( ~ ssItem(X0)
| memberP(nil,sK4(X0))
| sK5 = sK4(X0)
| ~ ssList(nil)
| ~ ssItem(sK5)
| ~ ssItem(sK4(X0)) )
| ~ spl14_6 ),
inference(resolution,[],[f211,f156]) ).
fof(f215,plain,
( ! [X0] :
( ~ ssItem(X0)
| memberP(nil,sK4(X0))
| sK5 = sK4(X0)
| ~ ssItem(sK5)
| ~ ssItem(sK4(X0)) )
| ~ spl14_6 ),
inference(forward_subsumption_resolution,[],[f214,f154]) ).
fof(f216,plain,
( ! [X0] :
( ~ ssItem(X0)
| memberP(nil,sK4(X0))
| sK5 = sK4(X0)
| ~ ssItem(sK4(X0)) )
| ~ spl14_2
| ~ spl14_6 ),
inference(forward_subsumption_resolution,[],[f215,f186]) ).
fof(f217,plain,
( ! [X0] :
( ~ ssItem(X0)
| sK5 = sK4(X0)
| ~ ssItem(sK4(X0)) )
| ~ spl14_2
| ~ spl14_6 ),
inference(forward_subsumption_resolution,[],[f216,f155]) ).
fof(f218,plain,
( ! [X0] :
( sK5 = sK4(X0)
| ~ ssItem(X0) )
| ~ spl14_2
| ~ spl14_6 ),
inference(forward_subsumption_resolution,[],[f217,f138]) ).
fof(f221,plain,
( ! [X0] :
( sK5 != X0
| ~ ssItem(X0)
| ~ ssItem(X0) )
| ~ spl14_2
| ~ spl14_6 ),
inference(superposition,[],[f139,f218]) ).
fof(f224,plain,
( ! [X0] :
( sK5 != X0
| ~ ssItem(X0) )
| ~ spl14_2
| ~ spl14_6 ),
inference(duplicate_literal_removal,[],[f221]) ).
fof(f229,definition,
( spl14_7
<=> ! [X0] : ~ ssItem(X0) ),
introduced(definition,[new_symbols(definition,[spl14_7])],[avatar_definition]) ).
fof(f230,plain,
( ! [X0] : ~ ssItem(X0)
| ~ spl14_7 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f239,plain,
( $false
| ~ spl14_7 ),
inference(resolution,[],[f230,f145]) ).
fof(f243,plain,
~ spl14_7,
inference(avatar_contradiction_clause,[],[f239]) ).
fof(f245,plain,
( ~ ssItem(sK5)
| ~ spl14_2
| ~ spl14_6 ),
inference(equality_resolution,[],[f224]) ).
fof(f246,plain,
( $false
| ~ spl14_2
| ~ spl14_6 ),
inference(forward_subsumption_resolution,[],[f245,f186]) ).
fof(f247,plain,
( ~ spl14_2
| ~ spl14_6 ),
inference(avatar_contradiction_clause,[],[f246]) ).
fof(f249,plain,
( ! [X0] :
( memberP(nil,sK4(X0))
| ~ ssItem(X0) )
| ~ spl14_1 ),
inference(superposition,[],[f169,f182]) ).
fof(f269,plain,
( ! [X0] :
( ~ ssItem(X0)
| ~ ssItem(sK4(X0)) )
| ~ spl14_1 ),
inference(resolution,[],[f249,f155]) ).
fof(f270,plain,
( ! [X0] : ~ ssItem(X0)
| ~ spl14_1 ),
inference(forward_subsumption_resolution,[],[f269,f138]) ).
fof(f271,plain,
( spl14_7
| ~ spl14_1 ),
inference(avatar_split_clause,[],[f270,f180,f229]) ).
cnf(s1,plain,
( spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f187]) ).
cnf(s7,plain,
( spl14_1
| spl14_6 ),
inference(sat_conversion,[],[f208]) ).
cnf(s12,plain,
~ spl14_7,
inference(sat_conversion,[],[f243]) ).
cnf(s14,plain,
( ~ spl14_2
| ~ spl14_6 ),
inference(sat_conversion,[],[f247]) ).
cnf(s15,plain,
( ~ spl14_1
| spl14_7 ),
inference(sat_conversion,[],[f271]) ).
cnf(s16,plain,
~ spl14_1,
inference(rat,[],[s15,s12]) ).
cnf(s19,plain,
spl14_6,
inference(rat,[],[s7,s16]) ).
cnf(s20,plain,
~ spl14_2,
inference(rat,[],[s14,s19]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s1,s20,s16]) ).
fof(f272,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC198+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 08:31:33 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 2.59/1.26 % (212196)Detected formulas, will run a generic FOF schedule.
% 2.59/1.26 % (212207)dis-21_1_sil=8000:lcm=predicate:random_seed=4002453954: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)
% 2.59/1.26 % (212206)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4001685555:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.59/1.26 % (212202)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=228654173:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.59/1.26 % (212203)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=2568526939:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.59/1.26 % (212201)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=923391579:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.59/1.26 % (212205)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2520682380:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.59/1.26 % (212204)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3571413664:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.59/1.26 % (212204)First to succeed.
% 2.59/1.26 % (212204)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-212196"
% 2.59/1.26 % (212205)Also succeeded, but the first one will report.
% 2.59/1.26 % (212207)Instruction limit reached!
% 2.59/1.26 % (212207)------------------------------
% 2.59/1.26 % (212207)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.26 % (212207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.26 % (212207)CaDiCaL version: 2.1.3
% 2.59/1.26 % (212207)Termination reason: Instruction limit
% 2.59/1.26 % (212207)Termination phase: Saturation
% 2.59/1.26 % (212207)Time elapsed: 0.040 s
% 2.59/1.26 % (212207)Peak memory usage: 89 MB
% 2.59/1.26 % (212207)Instructions burned: 133 (million)
% 2.59/1.26 % (212206)Instruction limit reached!
% 2.59/1.26 % (212206)------------------------------
% 2.59/1.26 % (212206)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.26 % (212206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.26 % (212206)CaDiCaL version: 2.1.3
% 2.59/1.26 % (212206)Termination reason: Instruction limit
% 2.59/1.26 % (212206)Termination phase: Saturation
% 2.59/1.26 % (212206)Time elapsed: 0.100 s
% 2.59/1.26 % (212206)Peak memory usage: 90 MB
% 2.59/1.26 % (212206)Instructions burned: 140 (million)
% 2.59/1.26 % (212215)lrs+10_1_sil=8000:sp=occurrence:random_seed=1205039809:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.59/1.26 % (212215)Also succeeded, but the first one will report.
% 2.59/1.26 % (212216)lrs+10_1_sil=32000:urr=on:br=off:random_seed=645980245:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.59/1.26 % (212204)Refutation found. Thanks to Tanya!
% 2.59/1.26 % SZS status Theorem for theBenchmark
% 2.59/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.45 % (212204)------------------------------
% 3.47/1.45 % (212204)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.45 % (212204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.45 % (212204)CaDiCaL version: 2.1.3
% 3.47/1.45 % (212204)Termination reason: Refutation
% 3.47/1.45 % (212204)Time elapsed: 0.006 s
% 3.47/1.45 % (212204)Peak memory usage: 89 MB
% 3.47/1.45 % (212204)Instructions burned: 6 (million)
% 3.47/1.45 % (212204)------------------------------
% 3.47/1.45 % (212204)------------------------------
% 3.47/1.45 % (212196)Success in time 0.408 s
% 3.47/1.45 % Vampire exiting
%------------------------------------------------------------------------------