%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC239+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 : 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 01:03:05 PM UTC 2026
% Result : Theorem 3.79s 1.31s
% Output : Refutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 12 unt; 0 def)
% Number of atoms : 239 ( 69 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 311 ( 120 ~; 112 |; 64 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 79 ( 59 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| nil = X0
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X0
& ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X5,X7)
| ~ memberP(X6,X7)
| ~ lt(X4,X7)
| leq(X4,X7) ) ) ) ) )
| ( ! [X8] :
( ssItem(X8)
=> ( cons(X8,nil) != X2
| ~ memberP(X3,X8)
| ? [X9] :
( ssItem(X9)
& X8 != X9
& memberP(X3,X9)
& leq(X8,X9) ) ) )
& ( 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
| nil = X0
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X0
& ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X5,X7)
| ~ memberP(X6,X7)
| ~ lt(X4,X7)
| leq(X4,X7) ) ) ) ) )
| ( ! [X8] :
( ssItem(X8)
=> ( cons(X8,nil) != X2
| ~ memberP(X3,X8)
| ? [X9] :
( ssItem(X9)
& X8 != X9
& memberP(X3,X9)
& leq(X8,X9) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& nil != X0
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X0
| ? [X7] :
( memberP(X5,X7)
& memberP(X6,X7)
& lt(X4,X7)
& ~ leq(X4,X7)
& ssItem(X7) ) ) ) )
& ( ? [X8] :
( cons(X8,nil) = X2
& memberP(X3,X8)
& ! [X9] :
( ~ ssItem(X9)
| X8 = X9
| ~ memberP(X3,X9)
| ~ leq(X8,X9) )
& ssItem(X8) )
| ( 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
& nil != X0
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X0
| ? [X7] :
( memberP(X5,X7)
& memberP(X6,X7)
& lt(X4,X7)
& ~ leq(X4,X7)
& ssItem(X7) ) ) ) )
& ( ? [X8] :
( cons(X8,nil) = X2
& memberP(X3,X8)
& ! [X9] :
( ~ ssItem(X9)
| X8 = X9
| ~ memberP(X3,X9)
| ~ leq(X8,X9) )
& ssItem(X8) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f107,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f115,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f118,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f137,plain,
( sK1 = sK3
& sK0 = sK2
& nil != sK0
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK0
| ( memberP(X5,sK4(X4,X5,X6))
& memberP(X6,sK4(X4,X5,X6))
& lt(X4,sK4(X4,X5,X6))
& ~ leq(X4,sK4(X4,X5,X6))
& ssItem(sK4(X4,X5,X6)) ) ) ) )
& ( ( sK2 = cons(sK5,nil)
& memberP(sK3,sK5)
& ! [X9] :
( ~ ssItem(X9)
| sK5 = X9
| ~ memberP(sK3,X9)
| ~ leq(sK5,X9) )
& 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(X7,sK4(X4,X5,X6)),skolemize(X8,sK5)],[f99]) ).
fof(f153,plain,
ssList(sK2),
inference(cnf_transformation,[],[f137]) ).
fof(f155,plain,
( ssItem(sK5)
| nil = sK2 ),
inference(cnf_transformation,[],[f137]) ).
fof(f161,plain,
( sK2 = cons(sK5,nil)
| nil = sK2 ),
inference(cnf_transformation,[],[f137]) ).
fof(f163,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK0
| ssItem(sK4(X4,X5,X6)) ),
inference(cnf_transformation,[],[f137]) ).
fof(f167,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK0
| memberP(X5,sK4(X4,X5,X6)) ),
inference(cnf_transformation,[],[f137]) ).
fof(f168,plain,
nil != sK0,
inference(cnf_transformation,[],[f137]) ).
fof(f169,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f137]) ).
fof(f182,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f190,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f193,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f194,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f216,plain,
nil != sK2,
inference(definition_unfolding,[],[f168,f169]) ).
fof(f217,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK2
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| memberP(X5,sK4(X4,X5,X6)) ),
inference(definition_unfolding,[],[f167,f169]) ).
fof(f221,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK2
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| ssItem(sK4(X4,X5,X6)) ),
inference(definition_unfolding,[],[f163,f169]) ).
fof(f232,plain,
ssItem(sK5),
inference(forward_subsumption_resolution,[],[f155,f216]) ).
fof(f234,plain,
sK2 = cons(sK5,nil),
inference(forward_subsumption_resolution,[],[f161,f216]) ).
fof(f236,plain,
! [X0,X1] :
( sK2 != app(app(X0,sK2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(sK5)
| ssItem(sK4(sK5,X0,X1)) ),
inference(superposition,[],[f221,f234]) ).
fof(f237,plain,
! [X0,X1] :
( sK2 != app(app(X0,sK2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ssItem(sK4(sK5,X0,X1)) ),
inference(forward_subsumption_resolution,[],[f236,f232]) ).
fof(f238,plain,
! [X0,X1] :
( sK2 != app(app(X0,sK2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(sK5)
| memberP(X0,sK4(sK5,X0,X1)) ),
inference(superposition,[],[f217,f234]) ).
fof(f239,plain,
! [X0,X1] :
( sK2 != app(app(X0,sK2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| memberP(X0,sK4(sK5,X0,X1)) ),
inference(forward_subsumption_resolution,[],[f238,f232]) ).
fof(f276,plain,
! [X0] :
( sK2 != app(sK2,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| memberP(nil,sK4(sK5,nil,X0))
| ~ ssList(sK2) ),
inference(superposition,[],[f239,f190]) ).
fof(f277,plain,
! [X0] :
( sK2 != app(sK2,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ssItem(sK4(sK5,nil,X0))
| ~ ssList(sK2) ),
inference(superposition,[],[f237,f190]) ).
fof(f278,plain,
! [X0] :
( sK2 != app(sK2,X0)
| ~ ssList(X0)
| ssItem(sK4(sK5,nil,X0))
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f277,f193]) ).
fof(f279,plain,
! [X0] :
( sK2 != app(sK2,X0)
| ~ ssList(X0)
| memberP(nil,sK4(sK5,nil,X0))
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f276,f193]) ).
fof(f288,plain,
! [X0] :
( sK2 != app(sK2,X0)
| ~ ssList(X0)
| ssItem(sK4(sK5,nil,X0)) ),
inference(forward_subsumption_resolution,[],[f278,f153]) ).
fof(f289,plain,
! [X0] :
( sK2 != app(sK2,X0)
| ~ ssList(X0)
| memberP(nil,sK4(sK5,nil,X0)) ),
inference(forward_subsumption_resolution,[],[f279,f153]) ).
fof(f293,plain,
( sK2 != sK2
| ~ ssList(nil)
| ssItem(sK4(sK5,nil,nil))
| ~ ssList(sK2) ),
inference(superposition,[],[f288,f182]) ).
fof(f294,plain,
( ~ ssList(nil)
| ssItem(sK4(sK5,nil,nil))
| ~ ssList(sK2) ),
inference(trivial_inequality_removal,[],[f293]) ).
fof(f295,plain,
( ssItem(sK4(sK5,nil,nil))
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f294,f193]) ).
fof(f296,plain,
ssItem(sK4(sK5,nil,nil)),
inference(forward_subsumption_resolution,[],[f295,f153]) ).
fof(f297,plain,
( sK2 != sK2
| ~ ssList(nil)
| memberP(nil,sK4(sK5,nil,nil))
| ~ ssList(sK2) ),
inference(superposition,[],[f289,f182]) ).
fof(f298,plain,
( ~ ssList(nil)
| memberP(nil,sK4(sK5,nil,nil))
| ~ ssList(sK2) ),
inference(trivial_inequality_removal,[],[f297]) ).
fof(f299,plain,
( memberP(nil,sK4(sK5,nil,nil))
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f298,f193]) ).
fof(f300,plain,
memberP(nil,sK4(sK5,nil,nil)),
inference(forward_subsumption_resolution,[],[f299,f153]) ).
fof(f301,plain,
~ ssItem(sK4(sK5,nil,nil)),
inference(resolution,[],[f300,f194]) ).
fof(f302,plain,
$false,
inference(forward_subsumption_resolution,[],[f301,f296]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC239+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n019.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 08:38:18 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 3.79/1.31 % (3855529)Detected formulas, will run a generic FOF schedule.
% 3.79/1.31 % (3855540)dis-21_1_sil=8000:lcm=predicate:random_seed=2002411527: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)
% 3.79/1.31 % (3855535)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=672918507:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.79/1.31 % (3855537)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2552048418:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.79/1.31 % (3855538)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1916912772:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.79/1.31 % (3855534)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=379097494:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.79/1.31 % (3855539)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2872367888:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.79/1.31 % (3855536)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=2126479610:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.79/1.31 % (3855538)First to succeed.
% 3.79/1.31 % (3855538)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3855529"
% 3.79/1.31 % (3855540)Instruction limit reached!
% 3.79/1.31 % (3855540)------------------------------
% 3.79/1.31 % (3855540)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.31 % (3855540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.31 % (3855540)CaDiCaL version: 2.1.3
% 3.79/1.31 % (3855540)Termination reason: Instruction limit
% 3.79/1.31 % (3855540)Termination phase: Saturation
% 3.79/1.31 % (3855540)Time elapsed: 0.039 s
% 3.79/1.31 % (3855540)Peak memory usage: 91 MB
% 3.79/1.31 % (3855540)Instructions burned: 130 (million)
% 3.79/1.31 % (3855539)Also succeeded, but the first one will report.
% 3.79/1.31 % (3855537)Instruction limit reached!
% 3.79/1.31 % (3855537)------------------------------
% 3.79/1.31 % (3855537)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.31 % (3855537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.31 % (3855537)CaDiCaL version: 2.1.3
% 3.79/1.31 % (3855537)Termination reason: Instruction limit
% 3.79/1.31 % (3855537)Termination phase: Saturation
% 3.79/1.31 % (3855537)Time elapsed: 0.072 s
% 3.79/1.31 % (3855537)Peak memory usage: 89 MB
% 3.79/1.31 % (3855537)Instructions burned: 110 (million)
% 3.79/1.31 % (3855548)lrs+10_1_sil=8000:sp=occurrence:random_seed=3832759229:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.79/1.31 % (3855548)Also succeeded, but the first one will report.
% 3.79/1.31 % (3855549)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2770592798:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.79/1.31 % (3855538)Refutation found. Thanks to Tanya!
% 3.79/1.31 % SZS status Theorem for theBenchmark
% 3.79/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 3.79/1.31 % (3855538)------------------------------
% 3.79/1.31 % (3855538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.31 % (3855538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.31 % (3855538)CaDiCaL version: 2.1.3
% 3.79/1.31 % (3855538)Termination reason: Refutation
% 3.79/1.31 % (3855538)Time elapsed: 0.005 s
% 3.79/1.31 % (3855538)Peak memory usage: 88 MB
% 3.79/1.31 % (3855538)Instructions burned: 7 (million)
% 3.79/1.31 % (3855538)------------------------------
% 3.79/1.31 % (3855538)------------------------------
% 3.79/1.31 % (3855529)Success in time 0.44 s
% 3.79/1.31 % Vampire exiting
%------------------------------------------------------------------------------