%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC313+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 01:03:25 PM UTC 2026
% Result : Theorem 3.53s 1.25s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 47 ( 10 unt; 0 def)
% Number of atoms : 224 ( 107 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 283 ( 106 ~; 107 |; 55 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 80 ( 58 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
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(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).
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)
& app(X5,cons(X4,nil)) != X2
& app(cons(X4,nil),X5) = X3 ) )
| ( nil != X2
& nil = X3 )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X1
& app(X7,cons(X6,nil)) = X0 ) ) ) ) ) ) ) ) ),
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)
& app(X5,cons(X4,nil)) != X2
& app(cons(X4,nil),X5) = X3 ) )
| ( nil != X2
& nil = X3 )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X1
& app(X7,cons(X6,nil)) = X0 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| app(X5,cons(X4,nil)) = X2
| app(cons(X4,nil),X5) != X3 ) )
& ( nil = X2
| nil != X3 )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(cons(X6,nil),X7) != X1
| app(X7,cons(X6,nil)) != X0 ) ) ) )
& 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)
| app(X5,cons(X4,nil)) = X2
| app(cons(X4,nil),X5) != X3 ) )
& ( nil = X2
| nil != X3 )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(cons(X6,nil),X7) != X1
| app(X7,cons(X6,nil)) != X0 ) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f101,plain,
! [X0] :
( nil = X0
| ? [X1] :
( ssList(X1)
& ? [X2] :
( ssItem(X2)
& cons(X2,X1) = X0 ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f102,plain,
! [X0] :
( nil = X0
| ? [X1] :
( ssList(X1)
& ? [X2] :
( ssItem(X2)
& cons(X2,X1) = X0 ) )
| ~ ssList(X0) ),
inference(flattening,[],[f101]) ).
fof(f110,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f120,plain,
( sK1 = sK3
& sK0 = sK2
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| app(X5,cons(X4,nil)) = sK2
| app(cons(X4,nil),X5) != sK3 ) )
& ( nil = sK2
| nil != sK3 )
& ( ( nil = sK1
& nil != sK0 )
| ( neq(sK1,nil)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(cons(X6,nil),X7) != sK1
| app(X7,cons(X6,nil)) != sK0 ) ) ) )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f99]) ).
fof(f122,plain,
! [X0] :
( nil = X0
| ( ssList(sK6(X0))
& ssItem(sK7(X0))
& cons(sK7(X0),sK6(X0)) = X0 )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X1,sK6(X0)),skolemize(X2,sK7(X0))],[f102]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f129,plain,
ssList(sK2),
inference(cnf_transformation,[],[f120]) ).
fof(f130,plain,
ssList(sK3),
inference(cnf_transformation,[],[f120]) ).
fof(f132,plain,
( nil != sK0
| neq(sK1,nil) ),
inference(cnf_transformation,[],[f120]) ).
fof(f133,plain,
! [X6,X7] :
( nil = sK1
| ~ ssItem(X6)
| ~ ssList(X7)
| app(cons(X6,nil),X7) != sK1
| app(X7,cons(X6,nil)) != sK0 ),
inference(cnf_transformation,[],[f120]) ).
fof(f135,plain,
( nil != sK3
| nil = sK2 ),
inference(cnf_transformation,[],[f120]) ).
fof(f136,plain,
! [X4,X5] :
( app(cons(X4,nil),X5) != sK3
| ~ ssList(X5)
| app(X5,cons(X4,nil)) = sK2
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f120]) ).
fof(f137,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f120]) ).
fof(f138,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f120]) ).
fof(f143,plain,
! [X0] :
( cons(sK7(X0),sK6(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f144,plain,
! [X0] :
( ssItem(sK7(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f145,plain,
! [X0] :
( ssList(sK6(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f155,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f161,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f167,plain,
! [X6,X7] :
( nil = sK3
| ~ ssItem(X6)
| ~ ssList(X7)
| app(cons(X6,nil),X7) != sK3
| app(X7,cons(X6,nil)) != sK2 ),
inference(definition_unfolding,[],[f133,f138,f138,f137]) ).
fof(f168,plain,
( nil != sK2
| neq(sK3,nil) ),
inference(definition_unfolding,[],[f132,f137,f138]) ).
fof(f174,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f161]) ).
fof(f177,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f174]) ).
fof(f179,plain,
! [X6,X7] :
( app(cons(X6,nil),X7) != sK3
| ~ ssItem(X6)
| ~ ssList(X7)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f167,f136]) ).
fof(f209,plain,
! [X0,X1] :
( cons(X0,X1) != sK3
| ~ ssItem(X0)
| ~ ssList(X1)
| nil = sK3
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(superposition,[],[f179,f155]) ).
fof(f218,plain,
! [X0,X1] :
( cons(X0,X1) != sK3
| ~ ssItem(X0)
| ~ ssList(X1)
| nil = sK3 ),
inference(duplicate_literal_removal,[],[f209]) ).
fof(f220,plain,
! [X0] :
( sK3 != X0
| ~ ssItem(sK7(X0))
| ~ ssList(sK6(X0))
| nil = sK3
| nil = X0
| ~ ssList(X0) ),
inference(superposition,[],[f218,f143]) ).
fof(f221,plain,
! [X0] :
( sK3 != X0
| ~ ssList(sK6(X0))
| nil = sK3
| nil = X0
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f220,f144]) ).
fof(f222,plain,
! [X0] :
( sK3 != X0
| nil = sK3
| nil = X0
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f221,f145]) ).
fof(f241,plain,
( nil = sK3
| nil = sK3
| ~ ssList(sK3) ),
inference(equality_resolution,[],[f222]) ).
fof(f242,plain,
( nil = sK3
| ~ ssList(sK3) ),
inference(duplicate_literal_removal,[],[f241]) ).
fof(f243,plain,
nil = sK3,
inference(forward_subsumption_resolution,[],[f242,f130]) ).
fof(f244,plain,
( sK3 != sK3
| sK2 = sK3 ),
inference(superposition,[],[f135,f243]) ).
fof(f250,plain,
( sK2 != sK3
| neq(sK3,sK3) ),
inference(superposition,[],[f168,f243]) ).
fof(f254,plain,
sK2 = sK3,
inference(trivial_inequality_removal,[],[f244]) ).
fof(f346,plain,
neq(sK3,sK3),
inference(forward_subsumption_resolution,[],[f250,f254]) ).
fof(f347,plain,
neq(sK2,sK2),
inference(forward_demodulation,[],[f346,f254]) ).
fof(f348,plain,
~ ssList(sK2),
inference(resolution,[],[f347,f177]) ).
fof(f350,plain,
$false,
inference(forward_subsumption_resolution,[],[f348,f129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC313+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n011.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Mon Sep 28 09:01:00 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running first-order theorem proving
% 0.09/0.20 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
% 3.53/1.25 % (3259623)Detected formulas, will run a generic FOF schedule.
% 3.53/1.25 % (3259630)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=2912677375:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.53/1.25 % (3259633)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2945550718:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.53/1.25 % (3259631)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3602935782:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.53/1.25 % (3259632)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=275298027:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.53/1.25 % (3259629)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=245142217:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.53/1.25 % (3259628)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=2993303859:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.53/1.25 % (3259632)First to succeed.
% 3.53/1.25 % (3259632)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3259623"
% 3.53/1.25 % (3259633)Also succeeded, but the first one will report.
% 3.53/1.25 % (3259634)dis-21_1_sil=8000:lcm=predicate:random_seed=1765359844: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)
% 3.53/1.25 % (3259631)Also succeeded, but the first one will report.
% 3.53/1.25 % (3259634)Instruction limit reached!
% 3.53/1.25 % (3259634)------------------------------
% 3.53/1.25 % (3259634)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.25 % (3259634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.25 % (3259634)CaDiCaL version: 2.1.3
% 3.53/1.25 % (3259634)Termination reason: Instruction limit
% 3.53/1.25 % (3259634)Termination phase: Saturation
% 3.53/1.25 % (3259634)Time elapsed: 0.076 s
% 3.53/1.25 % (3259634)Peak memory usage: 90 MB
% 3.53/1.25 % (3259634)Instructions burned: 130 (million)
% 3.53/1.25 % (3259642)lrs+10_1_sil=8000:sp=occurrence:random_seed=1242326847:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.53/1.25 % (3259632)Refutation found. Thanks to Tanya!
% 3.53/1.25 % SZS status Theorem for theBenchmark
% 3.53/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.25 % (3259632)------------------------------
% 3.53/1.25 % (3259632)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.25 % (3259632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.25 % (3259632)CaDiCaL version: 2.1.3
% 3.53/1.25 % (3259632)Termination reason: Refutation
% 3.53/1.25 % (3259632)Time elapsed: 0.006 s
% 3.53/1.25 % (3259632)Peak memory usage: 88 MB
% 3.53/1.25 % (3259632)Instructions burned: 9 (million)
% 3.53/1.25 % (3259632)------------------------------
% 3.53/1.25 % (3259632)------------------------------
% 3.53/1.25 % (3259623)Success in time 0.418 s
% 3.53/1.25 % Vampire exiting
%------------------------------------------------------------------------------