%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC220+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 01:05:09 PM UTC 2026
% Result : Theorem 0.26s 0.37s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 58 ( 14 unt; 0 def)
% Number of atoms : 292 ( 55 equ)
% Maximal formula atoms : 26 ( 5 avg)
% Number of connectives : 394 ( 160 ~; 152 |; 66 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 84 ( 60 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
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)
| ~ leq(X4,X7)
| leq(X7,X4) ) ) ) ) )
| ( nil != X2
& ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( app(app(X9,cons(X8,nil)),X10) != X2
| ? [X11] :
( ssItem(X11)
& ~ leq(X11,X8)
& memberP(X9,X11)
& memberP(X10,X11)
& leq(X8,X11) ) ) ) ) ) ) ) ) ) ) ),
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)
| ~ leq(X4,X7)
| leq(X7,X4) ) ) ) ) )
| ( nil != X2
& ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( app(app(X9,cons(X8,nil)),X10) != X2
| ? [X11] :
( ssItem(X11)
& ~ leq(X11,X8)
& memberP(X9,X11)
& memberP(X10,X11)
& leq(X8,X11) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f221,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)
& leq(X4,X7)
& ~ leq(X7,X4)
& ssItem(X7) ) ) ) )
& ( nil = X2
| ? [X8] :
( ? [X9] :
( ? [X10] :
( app(app(X9,cons(X8,nil)),X10) = X2
& ! [X11] :
( ~ ssItem(X11)
| leq(X11,X8)
| ~ memberP(X9,X11)
| ~ memberP(X10,X11)
| ~ leq(X8,X11) )
& ssList(X10) )
& ssList(X9) )
& ssItem(X8) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,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)
& leq(X4,X7)
& ~ leq(X7,X4)
& ssItem(X7) ) ) ) )
& ( nil = X2
| ? [X8] :
( ? [X9] :
( ? [X10] :
( app(app(X9,cons(X8,nil)),X10) = X2
& ! [X11] :
( ~ ssItem(X11)
| leq(X11,X8)
| ~ memberP(X9,X11)
| ~ memberP(X10,X11)
| ~ leq(X8,X11) )
& ssList(X10) )
& ssList(X9) )
& ssItem(X8) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& nil != sK53
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK53
| ( memberP(X5,sK57(X4,X5,X6))
& memberP(X6,sK57(X4,X5,X6))
& leq(X4,sK57(X4,X5,X6))
& ~ leq(sK57(X4,X5,X6),X4)
& ssItem(sK57(X4,X5,X6)) ) ) ) )
& ( nil = sK55
| ( sK55 = app(app(sK59,cons(sK58,nil)),sK60)
& ! [X11] :
( ~ ssItem(X11)
| leq(X11,sK58)
| ~ memberP(sK59,X11)
| ~ memberP(sK60,X11)
| ~ leq(sK58,X11) )
& ssList(sK60)
& ssList(sK59)
& ssItem(sK58) ) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59,sK60]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X7,sK57(X4,X5,X6)),skolemize(X8,sK58),skolemize(X9,sK59),skolemize(X10,sK60)],[f222]) ).
fof(f500,plain,
( nil = sK55
| ssItem(sK58) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( nil = sK55
| ssList(sK59) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( nil = sK55
| ssList(sK60) ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
! [X11] :
( nil = sK55
| ~ ssItem(X11)
| leq(X11,sK58)
| ~ memberP(sK59,X11)
| ~ memberP(sK60,X11)
| ~ leq(sK58,X11) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( nil = sK55
| sK55 = app(app(sK59,cons(sK58,nil)),sK60) ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK53
| ssItem(sK57(X4,X5,X6)) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK53
| ~ leq(sK57(X4,X5,X6),X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK53
| leq(X4,sK57(X4,X5,X6)) ),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK53
| memberP(X6,sK57(X4,X5,X6)) ),
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK53
| memberP(X5,sK57(X4,X5,X6)) ),
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
nil != sK53,
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f513,plain,
nil != sK55,
inference(definition_unfolding,[],[f510,f511]) ).
fof(f514,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK55
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| memberP(X5,sK57(X4,X5,X6)) ),
inference(definition_unfolding,[],[f509,f511]) ).
fof(f515,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK55
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| memberP(X6,sK57(X4,X5,X6)) ),
inference(definition_unfolding,[],[f508,f511]) ).
fof(f516,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK55
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| leq(X4,sK57(X4,X5,X6)) ),
inference(definition_unfolding,[],[f507,f511]) ).
fof(f517,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK55
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| ~ leq(sK57(X4,X5,X6),X4) ),
inference(definition_unfolding,[],[f506,f511]) ).
fof(f518,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK55
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| ssItem(sK57(X4,X5,X6)) ),
inference(definition_unfolding,[],[f505,f511]) ).
fof(f572,plain,
ssItem(sK58),
inference(forward_subsumption_resolution,[],[f500,f513]) ).
fof(f605,plain,
ssList(sK59),
inference(forward_subsumption_resolution,[],[f501,f513]) ).
fof(f606,plain,
ssList(sK60),
inference(forward_subsumption_resolution,[],[f502,f513]) ).
fof(f607,plain,
sK55 = app(app(sK59,cons(sK58,nil)),sK60),
inference(forward_subsumption_resolution,[],[f504,f513]) ).
fof(f610,plain,
( sK55 != sK55
| ~ ssList(sK59)
| ~ ssList(sK60)
| ~ ssItem(sK58)
| ~ leq(sK57(sK58,sK59,sK60),sK58) ),
inference(superposition,[],[f517,f607]) ).
fof(f611,plain,
( ~ ssList(sK59)
| ~ ssList(sK60)
| ~ ssItem(sK58)
| ~ leq(sK57(sK58,sK59,sK60),sK58) ),
inference(trivial_inequality_removal,[],[f610]) ).
fof(f615,plain,
( sK55 != sK55
| ~ ssList(sK59)
| ~ ssList(sK60)
| ~ ssItem(sK58)
| ssItem(sK57(sK58,sK59,sK60)) ),
inference(superposition,[],[f518,f607]) ).
fof(f616,plain,
( ~ ssList(sK59)
| ~ ssList(sK60)
| ~ ssItem(sK58)
| ssItem(sK57(sK58,sK59,sK60)) ),
inference(trivial_inequality_removal,[],[f615]) ).
fof(f617,plain,
( ~ ssList(sK60)
| ~ ssItem(sK58)
| ssItem(sK57(sK58,sK59,sK60)) ),
inference(forward_subsumption_resolution,[],[f616,f605]) ).
fof(f618,plain,
( ~ ssItem(sK58)
| ssItem(sK57(sK58,sK59,sK60)) ),
inference(forward_subsumption_resolution,[],[f617,f606]) ).
fof(f619,plain,
ssItem(sK57(sK58,sK59,sK60)),
inference(forward_subsumption_resolution,[],[f618,f572]) ).
fof(f623,plain,
( sK55 != sK55
| ~ ssList(sK59)
| ~ ssList(sK60)
| ~ ssItem(sK58)
| memberP(sK59,sK57(sK58,sK59,sK60)) ),
inference(superposition,[],[f514,f607]) ).
fof(f624,plain,
( ~ ssList(sK59)
| ~ ssList(sK60)
| ~ ssItem(sK58)
| memberP(sK59,sK57(sK58,sK59,sK60)) ),
inference(trivial_inequality_removal,[],[f623]) ).
fof(f625,plain,
( ~ ssList(sK60)
| ~ ssItem(sK58)
| memberP(sK59,sK57(sK58,sK59,sK60)) ),
inference(forward_subsumption_resolution,[],[f624,f605]) ).
fof(f626,plain,
( ~ ssItem(sK58)
| memberP(sK59,sK57(sK58,sK59,sK60)) ),
inference(forward_subsumption_resolution,[],[f625,f606]) ).
fof(f627,plain,
memberP(sK59,sK57(sK58,sK59,sK60)),
inference(forward_subsumption_resolution,[],[f626,f572]) ).
fof(f636,plain,
( sK55 != sK55
| ~ ssList(sK59)
| ~ ssList(sK60)
| ~ ssItem(sK58)
| memberP(sK60,sK57(sK58,sK59,sK60)) ),
inference(superposition,[],[f515,f607]) ).
fof(f637,plain,
( ~ ssList(sK59)
| ~ ssList(sK60)
| ~ ssItem(sK58)
| memberP(sK60,sK57(sK58,sK59,sK60)) ),
inference(trivial_inequality_removal,[],[f636]) ).
fof(f638,plain,
( ~ ssList(sK60)
| ~ ssItem(sK58)
| memberP(sK60,sK57(sK58,sK59,sK60)) ),
inference(forward_subsumption_resolution,[],[f637,f605]) ).
fof(f639,plain,
( ~ ssItem(sK58)
| memberP(sK60,sK57(sK58,sK59,sK60)) ),
inference(forward_subsumption_resolution,[],[f638,f606]) ).
fof(f640,plain,
memberP(sK60,sK57(sK58,sK59,sK60)),
inference(forward_subsumption_resolution,[],[f639,f572]) ).
fof(f653,plain,
! [X11] :
( ~ leq(sK58,X11)
| leq(X11,sK58)
| ~ memberP(sK59,X11)
| ~ memberP(sK60,X11)
| ~ ssItem(X11) ),
inference(forward_subsumption_resolution,[],[f503,f513]) ).
fof(f682,plain,
( sK55 != sK55
| ~ ssList(sK59)
| ~ ssList(sK60)
| ~ ssItem(sK58)
| leq(sK58,sK57(sK58,sK59,sK60)) ),
inference(superposition,[],[f516,f607]) ).
fof(f683,plain,
( ~ ssList(sK59)
| ~ ssList(sK60)
| ~ ssItem(sK58)
| leq(sK58,sK57(sK58,sK59,sK60)) ),
inference(trivial_inequality_removal,[],[f682]) ).
fof(f684,plain,
( ~ ssList(sK60)
| ~ ssItem(sK58)
| leq(sK58,sK57(sK58,sK59,sK60)) ),
inference(forward_subsumption_resolution,[],[f683,f605]) ).
fof(f685,plain,
( ~ ssItem(sK58)
| leq(sK58,sK57(sK58,sK59,sK60)) ),
inference(forward_subsumption_resolution,[],[f684,f606]) ).
fof(f686,plain,
leq(sK58,sK57(sK58,sK59,sK60)),
inference(forward_subsumption_resolution,[],[f685,f572]) ).
fof(f710,plain,
( leq(sK57(sK58,sK59,sK60),sK58)
| ~ memberP(sK59,sK57(sK58,sK59,sK60))
| ~ memberP(sK60,sK57(sK58,sK59,sK60))
| ~ ssItem(sK57(sK58,sK59,sK60)) ),
inference(resolution,[],[f686,f653]) ).
fof(f716,plain,
( ~ ssList(sK60)
| ~ ssItem(sK58)
| ~ leq(sK57(sK58,sK59,sK60),sK58) ),
inference(forward_subsumption_resolution,[],[f611,f605]) ).
fof(f717,plain,
( leq(sK57(sK58,sK59,sK60),sK58)
| ~ memberP(sK60,sK57(sK58,sK59,sK60))
| ~ ssItem(sK57(sK58,sK59,sK60)) ),
inference(forward_subsumption_resolution,[],[f710,f627]) ).
fof(f718,plain,
( ~ ssItem(sK58)
| ~ leq(sK57(sK58,sK59,sK60),sK58) ),
inference(forward_subsumption_resolution,[],[f716,f606]) ).
fof(f719,plain,
( leq(sK57(sK58,sK59,sK60),sK58)
| ~ ssItem(sK57(sK58,sK59,sK60)) ),
inference(forward_subsumption_resolution,[],[f717,f640]) ).
fof(f720,plain,
~ leq(sK57(sK58,sK59,sK60),sK58),
inference(forward_subsumption_resolution,[],[f718,f572]) ).
fof(f721,plain,
leq(sK57(sK58,sK59,sK60),sK58),
inference(forward_subsumption_resolution,[],[f719,f619]) ).
fof(f722,plain,
$false,
inference(global_subsumption,[],[f721,f720]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC220+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.27 % Computer : n009.cluster.edu
% 0.11/0.27 % Model : x86_64 x86_64
% 0.11/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.27 % Memory : 8046.5625MB
% 0.11/0.27 % OS : Linux 6.8.0-71-generic
% 0.11/0.27 % CPULimit : 300
% 0.11/0.27 % WCLimit : 300
% 0.11/0.27 % DateTime : Mon Sep 28 08:32:30 UTC 2026
% 0.26/0.27 % CPUTime :
% 0.26/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.26/0.32 Running first-order model finding
% 0.26/0.32 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.26/0.37 % (2887502)Will run a generic schedule for satisfiability detection.
% 0.26/0.37 % (2887509)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=277323638:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.26/0.37 % (2887508)% WARNING: option uhcvi not known.
% 0.26/0.37 % (2887509) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2887502-2887509"...
% 0.26/0.37 % (2887507)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3304882109_2999 on theBenchmark for (2999ds/0Mi)
% 0.26/0.37 % (2887512)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3735850648:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.26/0.37 % (2887513)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2126215358:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.26/0.37 % (2887509)...printing done.
% 0.26/0.37 % (2887508)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=300871062:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.26/0.37 % (2887510)dis+10_1_sil=32000:sp=arity:random_seed=207934559:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.26/0.37 % (2887511)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1731560993:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.26/0.37 % (2887509)Refutation found. Thanks to Tanya!
% 0.26/0.37 % SZS status Theorem for theBenchmark
% 0.26/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.37 % (2887509)------------------------------
% 0.26/0.37 % (2887509)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.37 % (2887509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.37 % (2887509)CaDiCaL version: 2.1.3
% 0.26/0.37 % (2887509)Termination reason: Refutation
% 0.26/0.37 % (2887509)Time elapsed: 0.011 s
% 0.26/0.37 % (2887509)Peak memory usage: 12 MB
% 0.26/0.37 % (2887509)Instructions burned: 18 (million)
% 0.26/0.37 % (2887502)Success in time 0.038 s
% 0.26/0.37 % Vampire exiting
%------------------------------------------------------------------------------