%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC013+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 : n008.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 01:02:02 PM UTC 2026
% Result : Theorem 3.32s 1.14s
% Output : Refutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 11 unt; 0 def)
% Number of atoms : 243 ( 73 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 338 ( 144 ~; 128 |; 50 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 66 ( 50 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& X2 != X4
& ? [X5] :
( ssItem(X5)
& cons(X5,nil) = X4
& hd(X3) = X5
& neq(nil,X3) ) )
| ? [X6] :
( ssList(X6)
& X0 = X6
& ? [X7] :
( ssItem(X7)
& cons(X7,nil) = X6
& hd(X1) = X7
& neq(nil,X1) ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
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
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& X2 != X4
& ? [X5] :
( ssItem(X5)
& cons(X5,nil) = X4
& hd(X3) = X5
& neq(nil,X3) ) )
| ? [X6] :
( ssList(X6)
& X0 = X6
& ? [X7] :
( ssItem(X7)
& cons(X7,nil) = X6
& hd(X1) = X7
& neq(nil,X1) ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| X2 = X4
| ! [X5] :
( ~ ssItem(X5)
| cons(X5,nil) != X4
| hd(X3) != X5
| ~ neq(nil,X3) ) )
& ! [X6] :
( ~ ssList(X6)
| X0 != X6
| ! [X7] :
( ~ ssItem(X7)
| cons(X7,nil) != X6
| hd(X1) != X7
| ~ neq(nil,X1) ) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| X2 = X4
| ! [X5] :
( ~ ssItem(X5)
| cons(X5,nil) != X4
| hd(X3) != X5
| ~ neq(nil,X3) ) )
& ! [X6] :
( ~ ssList(X6)
| X0 != X6
| ! [X7] :
( ~ ssItem(X7)
| cons(X7,nil) != X6
| hd(X1) != X7
| ~ neq(nil,X1) ) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f107,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f114,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f115,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f114]) ).
fof(f127,plain,
( sK1 = sK3
& sK0 = sK2
& ( ( neq(sK1,nil)
& ! [X4] :
( ~ ssList(X4)
| sK2 = X4
| ! [X5] :
( ~ ssItem(X5)
| cons(X5,nil) != X4
| hd(sK3) != X5
| ~ neq(nil,sK3) ) )
& ! [X6] :
( ~ ssList(X6)
| sK0 != X6
| ! [X7] :
( ~ ssItem(X7)
| cons(X7,nil) != X6
| hd(sK1) != X7
| ~ neq(nil,sK1) ) ) )
| ( neq(sK1,nil)
& ~ neq(sK3,nil) ) )
& 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(f130,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f107]) ).
fof(f137,plain,
ssList(sK2),
inference(cnf_transformation,[],[f127]) ).
fof(f138,plain,
ssList(sK3),
inference(cnf_transformation,[],[f127]) ).
fof(f139,plain,
! [X6,X7] :
( ~ ssList(X6)
| sK0 != X6
| ~ ssItem(X7)
| cons(X7,nil) != X6
| hd(sK1) != X7
| ~ neq(nil,sK1)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f127]) ).
fof(f141,plain,
! [X4,X5] :
( ~ ssList(X4)
| sK2 = X4
| ~ ssItem(X5)
| cons(X5,nil) != X4
| hd(sK3) != X5
| ~ neq(nil,sK3)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f127]) ).
fof(f144,plain,
( neq(sK1,nil)
| neq(sK1,nil) ),
inference(cnf_transformation,[],[f127]) ).
fof(f145,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f127]) ).
fof(f146,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f127]) ).
fof(f157,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f158,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f159,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f162,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f167,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f179,plain,
( neq(sK3,nil)
| neq(sK3,nil) ),
inference(definition_unfolding,[],[f144,f146,f146]) ).
fof(f183,plain,
! [X6,X7] :
( ~ ssList(X6)
| sK2 != X6
| ~ ssItem(X7)
| cons(X7,nil) != X6
| hd(sK3) != X7
| ~ neq(nil,sK3)
| ~ neq(sK3,nil) ),
inference(definition_unfolding,[],[f139,f145,f146,f146]) ).
fof(f188,plain,
! [X5] :
( ~ ssList(cons(X5,nil))
| cons(X5,nil) = sK2
| ~ ssItem(X5)
| hd(sK3) != X5
| ~ neq(nil,sK3)
| ~ neq(sK3,nil) ),
inference(equality_resolution,[],[f141]) ).
fof(f189,plain,
( ~ ssList(cons(hd(sK3),nil))
| sK2 = cons(hd(sK3),nil)
| ~ ssItem(hd(sK3))
| ~ neq(nil,sK3)
| ~ neq(sK3,nil) ),
inference(equality_resolution,[],[f188]) ).
fof(f192,plain,
! [X7] :
( ~ ssList(sK2)
| ~ ssItem(X7)
| cons(X7,nil) != sK2
| hd(sK3) != X7
| ~ neq(nil,sK3)
| ~ neq(sK3,nil) ),
inference(equality_resolution,[],[f183]) ).
fof(f193,plain,
( ~ ssList(sK2)
| ~ ssItem(hd(sK3))
| sK2 != cons(hd(sK3),nil)
| ~ neq(nil,sK3)
| ~ neq(sK3,nil) ),
inference(equality_resolution,[],[f192]) ).
fof(f194,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f158]) ).
fof(f200,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f194]) ).
fof(f201,plain,
neq(sK3,nil),
inference(duplicate_literal_removal,[],[f179]) ).
fof(f202,plain,
( ~ ssItem(hd(sK3))
| sK2 != cons(hd(sK3),nil)
| ~ neq(nil,sK3)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f193,f137]) ).
fof(f203,plain,
( sK2 != cons(hd(sK3),nil)
| ~ ssItem(hd(sK3))
| ~ neq(nil,sK3) ),
inference(forward_subsumption_resolution,[],[f202,f201]) ).
fof(f204,plain,
( ~ ssList(cons(hd(sK3),nil))
| ~ ssItem(hd(sK3))
| ~ neq(nil,sK3)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f189,f203]) ).
fof(f205,plain,
( ~ ssList(cons(hd(sK3),nil))
| ~ ssItem(hd(sK3))
| ~ neq(nil,sK3) ),
inference(forward_subsumption_resolution,[],[f204,f201]) ).
fof(f206,plain,
( ~ ssItem(hd(sK3))
| ~ ssList(nil)
| ~ ssItem(hd(sK3))
| ~ neq(nil,sK3) ),
inference(resolution,[],[f157,f205]) ).
fof(f207,plain,
( ~ ssItem(hd(sK3))
| ~ ssList(nil)
| ~ neq(nil,sK3) ),
inference(duplicate_literal_removal,[],[f206]) ).
fof(f208,plain,
( ~ neq(nil,sK3)
| ~ ssItem(hd(sK3)) ),
inference(forward_subsumption_resolution,[],[f207,f162]) ).
fof(f215,plain,
( nil = sK3
| ~ ssList(sK3)
| ~ ssList(nil)
| ~ ssItem(hd(sK3)) ),
inference(resolution,[],[f159,f208]) ).
fof(f218,plain,
( nil = sK3
| ~ ssList(sK3)
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f215,f167]) ).
fof(f219,plain,
( nil = sK3
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f218,f138]) ).
fof(f220,plain,
nil = sK3,
inference(forward_subsumption_resolution,[],[f219,f162]) ).
fof(f224,plain,
neq(sK3,sK3),
inference(superposition,[],[f201,f220]) ).
fof(f233,plain,
~ ssList(sK3),
inference(resolution,[],[f224,f200]) ).
fof(f235,plain,
$false,
inference(forward_subsumption_resolution,[],[f233,f138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC013+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n008.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 07:26:25 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 3.32/1.14 % (2076638)Detected formulas, will run a generic FOF schedule.
% 3.32/1.14 % (2076646)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=665697684:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.32/1.14 % (2076643)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=1330980738:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.32/1.14 % (2076649)dis-21_1_sil=8000:lcm=predicate:random_seed=4182940631: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)
% 3.32/1.14 % (2076647)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1656755229:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.32/1.14 % (2076648)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3067632412:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.32/1.14 % (2076645)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=2970576268:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.32/1.14 % (2076644)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=1618461650:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.32/1.14 % (2076647)First to succeed.
% 3.32/1.14 % (2076647)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2076638"
% 3.32/1.14 % (2076646)Also succeeded, but the first one will report.
% 3.32/1.14 % (2076648)Also succeeded, but the first one will report.
% 3.32/1.14 % (2076649)Instruction limit reached!
% 3.32/1.14 % (2076649)------------------------------
% 3.32/1.14 % (2076649)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.14 % (2076649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.14 % (2076649)CaDiCaL version: 2.1.3
% 3.32/1.14 % (2076649)Termination reason: Instruction limit
% 3.32/1.14 % (2076649)Termination phase: Saturation
% 3.32/1.14 % (2076649)Time elapsed: 0.071 s
% 3.32/1.14 % (2076649)Peak memory usage: 90 MB
% 3.32/1.14 % (2076649)Instructions burned: 129 (million)
% 3.32/1.14 % (2076657)lrs+10_1_sil=8000:sp=occurrence:random_seed=1714236225:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.32/1.14 % (2076657)Also succeeded, but the first one will report.
% 3.32/1.14 % (2076647)Refutation found. Thanks to Tanya!
% 3.32/1.14 % SZS status Theorem for theBenchmark
% 3.32/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 3.32/1.14 % (2076647)------------------------------
% 3.32/1.14 % (2076647)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.14 % (2076647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.14 % (2076647)CaDiCaL version: 2.1.3
% 3.32/1.14 % (2076647)Termination reason: Refutation
% 3.32/1.14 % (2076647)Time elapsed: 0.004 s
% 3.32/1.14 % (2076647)Peak memory usage: 88 MB
% 3.32/1.14 % (2076647)Instructions burned: 5 (million)
% 3.32/1.14 % (2076647)------------------------------
% 3.32/1.14 % (2076647)------------------------------
% 3.32/1.14 % (2076638)Success in time 0.422 s
% 3.32/1.14 % Vampire exiting
%------------------------------------------------------------------------------