%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC380+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 : n002.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 01:03:43 PM UTC 2026
% Result : Theorem 1.04s 0.95s
% Output : Refutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 6 unt; 1 def)
% Number of atoms : 225 ( 54 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 283 ( 103 ~; 93 |; 68 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 151 ( 127 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( X0 = X1
| memberP(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax37) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax81) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssItem(X4)
& cons(X4,nil) = X0
& memberP(X1,X4) )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( cons(X5,nil) != X2
| app(cons(X5,nil),X6) != X3 ) ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
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
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssItem(X4)
& cons(X4,nil) = X0
& memberP(X1,X4) )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( cons(X5,nil) != X2
| app(cons(X5,nil),X6) != X3 ) ) ) )
& ( ~ 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] :
( ~ ssItem(X4)
| cons(X4,nil) != X0
| ~ memberP(X1,X4) )
& ? [X5] :
( ? [X6] :
( cons(X5,nil) = X2
& app(cons(X5,nil),X6) = X3
& ssList(X6) )
& ssItem(X5) ) )
| ( 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] :
( ~ ssItem(X4)
| cons(X4,nil) != X0
| ~ memberP(X1,X4) )
& ? [X5] :
( ? [X6] :
( cons(X5,nil) = X2
& app(cons(X5,nil),X6) = X3
& ssList(X6) )
& ssItem(X5) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f110,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(cons(X1,X2),X0)
<=> ( X0 = X1
| memberP(X2,X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f124,definition,
! [X1,X0,X2,X3] :
( ( neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != X0
| ~ memberP(X1,X4) )
& ? [X5] :
( ? [X6] :
( cons(X5,nil) = X2
& app(cons(X5,nil),X6) = X3
& ssList(X6) )
& ssItem(X5) ) )
| ~ sP0(X1,X0,X2,X3) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f125,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( sP0(X1,X0,X2,X3)
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f99,f124]) ).
fof(f126,plain,
! [X1,X0,X2,X3] :
( ( neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != X0
| ~ memberP(X1,X4) )
& ? [X5] :
( ? [X6] :
( cons(X5,nil) = X2
& app(cons(X5,nil),X6) = X3
& ssList(X6) )
& ssItem(X5) ) )
| ~ sP0(X1,X0,X2,X3) ),
inference(nnf_transformation,[],[f124]) ).
fof(f127,plain,
! [X0,X1,X2,X3] :
( ( neq(X0,nil)
& ! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != X1
| ~ memberP(X0,X4) )
& ? [X5] :
( ? [X6] :
( cons(X5,nil) = X2
& app(cons(X5,nil),X6) = X3
& ssList(X6) )
& ssItem(X5) ) )
| ~ sP0(X0,X1,X2,X3) ),
inference(rectify,[],[f126]) ).
fof(f128,plain,
! [X0,X1,X2,X3] :
( ( neq(X0,nil)
& ! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != X1
| ~ memberP(X0,X4) )
& cons(sK1(X2,X3),nil) = X2
& app(cons(sK1(X2,X3),nil),sK2(X2,X3)) = X3
& ssList(sK2(X2,X3))
& ssItem(sK1(X2,X3)) )
| ~ sP0(X0,X1,X2,X3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X5,sK1(X2,X3)),skolemize(X6,sK2(X2,X3))],[f127]) ).
fof(f129,plain,
( sK4 = sK6
& sK3 = sK5
& ( sP0(sK4,sK3,sK5,sK6)
| ( neq(sK4,nil)
& ~ neq(sK6,nil) ) )
& ssList(sK6)
& ssList(sK5)
& ssList(sK4)
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f125]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( X0 != X1
& ~ memberP(X2,X0) ) )
& ( X0 = X1
| memberP(X2,X0)
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f121]) ).
fof(f137,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( X0 != X1
& ~ memberP(X2,X0) ) )
& ( X0 = X1
| memberP(X2,X0)
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f136]) ).
fof(f143,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssItem(sK1(X2,X3)) ),
inference(cnf_transformation,[],[f128]) ).
fof(f144,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssList(sK2(X2,X3)) ),
inference(cnf_transformation,[],[f128]) ).
fof(f145,plain,
! [X2,X3,X0,X1] :
( app(cons(sK1(X2,X3),nil),sK2(X2,X3)) = X3
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f128]) ).
fof(f146,plain,
! [X2,X3,X0,X1] :
( cons(sK1(X2,X3),nil) = X2
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f128]) ).
fof(f147,plain,
! [X2,X3,X0,X1,X4] :
( ~ ssItem(X4)
| cons(X4,nil) != X1
| ~ memberP(X0,X4)
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f128]) ).
fof(f153,plain,
( sP0(sK4,sK3,sK5,sK6)
| ~ neq(sK6,nil) ),
inference(cnf_transformation,[],[f129]) ).
fof(f154,plain,
( sP0(sK4,sK3,sK5,sK6)
| neq(sK4,nil) ),
inference(cnf_transformation,[],[f129]) ).
fof(f155,plain,
sK3 = sK5,
inference(cnf_transformation,[],[f129]) ).
fof(f156,plain,
sK4 = sK6,
inference(cnf_transformation,[],[f129]) ).
fof(f173,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f187,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f195,plain,
( sP0(sK6,sK5,sK5,sK6)
| neq(sK6,nil) ),
inference(definition_unfolding,[],[f154,f156,f155,f156]) ).
fof(f196,plain,
( sP0(sK6,sK5,sK5,sK6)
| ~ neq(sK6,nil) ),
inference(definition_unfolding,[],[f153,f156,f155]) ).
fof(f199,plain,
! [X2,X3,X0,X4] :
( ~ sP0(X0,cons(X4,nil),X2,X3)
| ~ memberP(X0,X4)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f147]) ).
fof(f204,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f187]) ).
fof(f206,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f204]) ).
fof(f210,plain,
sP0(sK6,sK5,sK5,sK6),
inference(forward_subsumption_resolution,[],[f196,f195]) ).
fof(f257,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sP0(X1,X0,X3,X4)
| ~ memberP(X1,sK1(X0,X2))
| ~ ssItem(sK1(X0,X2))
| ~ sP0(X5,X6,X0,X2) ),
inference(superposition,[],[f199,f146]) ).
fof(f258,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sP0(X5,X6,X0,X2)
| ~ memberP(X1,sK1(X0,X2))
| ~ sP0(X1,X0,X3,X4) ),
inference(forward_subsumption_resolution,[],[f257,f143]) ).
fof(f288,plain,
! [X2,X3,X0,X1] :
( cons(sK1(X1,X0),sK2(X1,X0)) = X0
| ~ ssItem(sK1(X1,X0))
| ~ ssList(sK2(X1,X0))
| ~ sP0(X2,X3,X1,X0) ),
inference(superposition,[],[f173,f145]) ).
fof(f299,plain,
! [X2,X3,X0,X1] :
( cons(sK1(X1,X0),sK2(X1,X0)) = X0
| ~ ssList(sK2(X1,X0))
| ~ sP0(X2,X3,X1,X0) ),
inference(forward_subsumption_resolution,[],[f288,f143]) ).
fof(f301,plain,
! [X2,X3,X0,X1] :
( cons(sK1(X1,X0),sK2(X1,X0)) = X0
| ~ sP0(X2,X3,X1,X0) ),
inference(forward_subsumption_resolution,[],[f299,f144]) ).
fof(f1076,plain,
! [X2,X3,X0,X1] :
( memberP(X0,sK1(X1,X0))
| ~ ssList(sK2(X1,X0))
| ~ ssItem(sK1(X1,X0))
| ~ sP0(X2,X3,X1,X0) ),
inference(superposition,[],[f206,f301]) ).
fof(f1077,plain,
! [X2,X3,X0,X1] :
( memberP(X0,sK1(X1,X0))
| ~ ssItem(sK1(X1,X0))
| ~ sP0(X2,X3,X1,X0) ),
inference(forward_subsumption_resolution,[],[f1076,f144]) ).
fof(f1088,plain,
! [X2,X3,X0,X1] :
( memberP(X0,sK1(X1,X0))
| ~ sP0(X2,X3,X1,X0) ),
inference(forward_subsumption_resolution,[],[f1077,f143]) ).
fof(f1108,plain,
! [X2,X0,X1] :
( ~ sP0(X0,sK5,X1,X2)
| ~ memberP(X0,sK1(sK5,sK6)) ),
inference(resolution,[],[f258,f210]) ).
fof(f1111,plain,
~ memberP(sK6,sK1(sK5,sK6)),
inference(resolution,[],[f1108,f210]) ).
fof(f1115,plain,
! [X0,X1] : ~ sP0(X0,X1,sK5,sK6),
inference(resolution,[],[f1111,f1088]) ).
fof(f1116,plain,
$false,
inference(resolution,[],[f1115,f210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC380+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n002.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 09:24:52 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 1.04/0.95 % (231776)Detected formulas, will run a generic FOF schedule.
% 1.04/0.95 % (231785)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2117705888:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.04/0.95 % (231785)First to succeed.
% 1.04/0.95 % (231785)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-231776"
% 1.04/0.95 % (231781)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=1446584145:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.04/0.95 % (231784)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1480589139:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.04/0.95 % (231783)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=2794414514:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.04/0.95 % (231782)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=2880009230:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.04/0.95 % (231786)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3071041479:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.04/0.95 % (231787)dis-21_1_sil=8000:lcm=predicate:random_seed=1773583986: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)
% 1.04/0.95 % (231784)Instruction limit reached!
% 1.04/0.95 % (231784)------------------------------
% 1.04/0.95 % (231784)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.04/0.95 % (231784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.95 % (231784)CaDiCaL version: 2.1.3
% 1.04/0.95 % (231784)Termination reason: Instruction limit
% 1.04/0.95 % (231784)Termination phase: Saturation
% 1.04/0.95 % (231784)Time elapsed: 0.071 s
% 1.04/0.95 % (231784)Peak memory usage: 89 MB
% 1.04/0.95 % (231784)Instructions burned: 110 (million)
% 1.04/0.95 % (231787)Instruction limit reached!
% 1.04/0.95 % (231787)------------------------------
% 1.04/0.95 % (231787)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.04/0.95 % (231787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.95 % (231787)CaDiCaL version: 2.1.3
% 1.04/0.95 % (231787)Termination reason: Instruction limit
% 1.04/0.95 % (231787)Termination phase: Saturation
% 1.04/0.95 % (231787)Time elapsed: 0.072 s
% 1.04/0.95 % (231787)Peak memory usage: 90 MB
% 1.04/0.95 % (231787)Instructions burned: 129 (million)
% 1.04/0.95 % (231786)Instruction limit reached!
% 1.04/0.95 % (231786)------------------------------
% 1.04/0.95 % (231786)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.04/0.95 % (231786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.95 % (231786)CaDiCaL version: 2.1.3
% 1.04/0.95 % (231786)Termination reason: Instruction limit
% 1.04/0.95 % (231786)Termination phase: Saturation
% 1.04/0.95 % (231786)Time elapsed: 0.091 s
% 1.04/0.95 % (231786)Peak memory usage: 90 MB
% 1.04/0.95 % (231786)Instructions burned: 139 (million)
% 1.04/0.95 % (231785)Refutation found. Thanks to Tanya!
% 1.04/0.95 % SZS status Theorem for theBenchmark
% 1.04/0.95 % SZS output start Proof for theBenchmark
% See solution above
% 2.71/1.15 % (231785)------------------------------
% 2.71/1.15 % (231785)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.15 % (231785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.15 % (231785)CaDiCaL version: 2.1.3
% 2.71/1.15 % (231785)Termination reason: Refutation
% 2.71/1.15 % (231785)Time elapsed: 0.011 s
% 2.71/1.15 % (231785)Peak memory usage: 88 MB
% 2.71/1.15 % (231785)Instructions burned: 30 (million)
% 2.71/1.15 % (231785)------------------------------
% 2.71/1.15 % (231785)------------------------------
% 2.71/1.15 % (231776)Success in time 0.29 s
% 2.71/1.15 % Vampire exiting
%------------------------------------------------------------------------------