%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC185+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 : n011.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 01:02:50 PM UTC 2026
% Result : Theorem 1.86s 1.40s
% Output : Refutation 1.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 26 ( 10 unt; 0 def)
% Number of atoms : 140 ( 27 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 183 ( 69 ~; 54 |; 46 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 49 ( 29 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X2
& ( memberP(X5,X4)
| memberP(X6,X4) ) ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(app(X8,cons(X7,nil)),X9) != X0
| ( ~ memberP(X8,X7)
& ~ memberP(X9,X7) ) ) ) ) ) ) ) ) ) ),
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
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X2
& ( memberP(X5,X4)
| memberP(X6,X4) ) ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(app(X8,cons(X7,nil)),X9) != X0
| ( ~ memberP(X8,X7)
& ~ memberP(X9,X7) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X2
| ( ~ memberP(X5,X4)
& ~ memberP(X6,X4) ) ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(X8,cons(X7,nil)),X9) = X0
& ( memberP(X8,X7)
| memberP(X9,X7) )
& ssList(X9) )
& ssList(X8) )
& ssItem(X7) )
& 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] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X2
| ( ~ memberP(X5,X4)
& ~ memberP(X6,X4) ) ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(X8,cons(X7,nil)),X9) = X0
& ( memberP(X8,X7)
| memberP(X9,X7) )
& ssList(X9) )
& ssList(X8) )
& ssItem(X7) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f122,plain,
( sK1 = sK3
& sK0 = sK2
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK2
| ( ~ memberP(X5,X4)
& ~ memberP(X6,X4) ) ) ) )
& sK0 = app(app(sK5,cons(sK4,nil)),sK6)
& ( memberP(sK5,sK4)
| memberP(sK6,sK4) )
& ssList(sK6)
& ssList(sK5)
& ssItem(sK4)
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X7,sK4),skolemize(X8,sK5),skolemize(X9,sK6)],[f99]) ).
fof(f138,plain,
ssItem(sK4),
inference(cnf_transformation,[],[f122]) ).
fof(f139,plain,
ssList(sK5),
inference(cnf_transformation,[],[f122]) ).
fof(f140,plain,
ssList(sK6),
inference(cnf_transformation,[],[f122]) ).
fof(f141,plain,
( memberP(sK6,sK4)
| memberP(sK5,sK4) ),
inference(cnf_transformation,[],[f122]) ).
fof(f142,plain,
sK0 = app(app(sK5,cons(sK4,nil)),sK6),
inference(cnf_transformation,[],[f122]) ).
fof(f143,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK2
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| ~ memberP(X6,X4) ),
inference(cnf_transformation,[],[f122]) ).
fof(f144,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK2
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| ~ memberP(X5,X4) ),
inference(cnf_transformation,[],[f122]) ).
fof(f145,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f122]) ).
fof(f181,plain,
sK2 = app(app(sK5,cons(sK4,nil)),sK6),
inference(definition_unfolding,[],[f142,f145]) ).
fof(f190,plain,
( sK2 != sK2
| ~ ssList(sK5)
| ~ ssList(sK6)
| ~ ssItem(sK4)
| ~ memberP(sK6,sK4) ),
inference(superposition,[],[f143,f181]) ).
fof(f191,plain,
( ~ ssList(sK5)
| ~ ssList(sK6)
| ~ ssItem(sK4)
| ~ memberP(sK6,sK4) ),
inference(trivial_inequality_removal,[],[f190]) ).
fof(f192,plain,
( ~ ssList(sK6)
| ~ ssItem(sK4)
| ~ memberP(sK6,sK4) ),
inference(forward_subsumption_resolution,[],[f191,f139]) ).
fof(f193,plain,
( ~ ssItem(sK4)
| ~ memberP(sK6,sK4) ),
inference(forward_subsumption_resolution,[],[f192,f140]) ).
fof(f194,plain,
~ memberP(sK6,sK4),
inference(forward_subsumption_resolution,[],[f193,f138]) ).
fof(f195,plain,
memberP(sK5,sK4),
inference(resolution,[],[f194,f141]) ).
fof(f196,plain,
( sK2 != sK2
| ~ ssList(sK5)
| ~ ssList(sK6)
| ~ ssItem(sK4)
| ~ memberP(sK5,sK4) ),
inference(superposition,[],[f144,f181]) ).
fof(f197,plain,
( ~ ssList(sK5)
| ~ ssList(sK6)
| ~ ssItem(sK4)
| ~ memberP(sK5,sK4) ),
inference(trivial_inequality_removal,[],[f196]) ).
fof(f198,plain,
( ~ ssList(sK6)
| ~ ssItem(sK4)
| ~ memberP(sK5,sK4) ),
inference(forward_subsumption_resolution,[],[f197,f139]) ).
fof(f199,plain,
( ~ ssItem(sK4)
| ~ memberP(sK5,sK4) ),
inference(forward_subsumption_resolution,[],[f198,f140]) ).
fof(f200,plain,
~ memberP(sK5,sK4),
inference(forward_subsumption_resolution,[],[f199,f138]) ).
fof(f201,plain,
$false,
inference(forward_subsumption_resolution,[],[f195,f200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC185+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.38 % Computer : n011.cluster.edu
% 0.08/0.38 % Model : x86_64 x86_64
% 0.08/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.38 % Memory : 8046.5625MB
% 0.08/0.38 % OS : Linux 6.8.0-71-generic
% 0.08/0.38 % CPULimit : 300
% 0.08/0.38 % WCLimit : 300
% 0.08/0.38 % DateTime : Mon Sep 28 08:21:31 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.08/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.42 Running first-order theorem proving
% 0.08/0.42 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
% 1.86/1.40 % (3244835)Detected formulas, will run a generic FOF schedule.
% 1.86/1.40 % (3244840)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=2663995731:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.86/1.40 % (3244845)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3896840583:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.86/1.40 % (3244842)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=2070369552:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.86/1.40 % (3244846)dis-21_1_sil=8000:lcm=predicate:random_seed=3131503787: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)
% 1.86/1.40 % (3244844)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1987058014:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.86/1.40 % (3244841)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=194611334:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.86/1.40 % (3244843)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1764850981:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.86/1.40 % (3244844)First to succeed.
% 1.86/1.40 % (3244844)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3244835"
% 1.86/1.40 % (3244843)Also succeeded, but the first one will report.
% 1.86/1.40 % (3244846)Also succeeded, but the first one will report.
% 1.86/1.40 % (3244845)Also succeeded, but the first one will report.
% 1.86/1.40 % (3244844)Refutation found. Thanks to Tanya!
% 1.86/1.40 % SZS status Theorem for theBenchmark
% 1.86/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 1.86/1.40 % (3244844)------------------------------
% 1.86/1.40 % (3244844)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.86/1.40 % (3244844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.86/1.40 % (3244844)CaDiCaL version: 2.1.3
% 1.86/1.40 % (3244844)Termination reason: Refutation
% 1.86/1.40 % (3244844)Time elapsed: 0.003 s
% 1.86/1.40 % (3244844)Peak memory usage: 88 MB
% 1.86/1.40 % (3244844)Instructions burned: 3 (million)
% 1.86/1.40 % (3244844)------------------------------
% 1.86/1.40 % (3244844)------------------------------
% 1.86/1.40 % (3244835)Success in time 0.442 s
% 1.86/1.40 % Vampire exiting
%------------------------------------------------------------------------------