%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC046+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 01:04:25 PM UTC 2026
% Result : Theorem 0.18s 0.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 63 ( 15 unt; 2 def)
% Number of atoms : 224 ( 51 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 248 ( 87 ~; 94 |; 43 &)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 52 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( nil = X0
| ? [X1] :
( ssList(X1)
& ? [X2] :
( ssItem(X2)
& cons(X2,X1) = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax20) ).
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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( nil != X1
| X1 != X3
| X0 != X2
| nil = X0
| ? [X4] :
( ssItem(X4)
& ( ( ~ memberP(X2,X4)
& ! [X5] :
( ssList(X5)
=> ~ segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) )
& memberP(X3,X4) )
| ( memberP(X2,X4)
& ( ~ memberP(X3,X4)
| ? [X5] :
( ssList(X5)
& segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,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)
=> ( nil != X1
| X1 != X3
| X0 != X2
| nil = X0
| ? [X4] :
( ssItem(X4)
& ( ( ~ memberP(X2,X4)
& ! [X5] :
( ssList(X5)
=> ~ segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) )
& memberP(X3,X4) )
| ( memberP(X2,X4)
& ( ~ memberP(X3,X4)
| ? [X5] :
( ssList(X5)
& segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( nil != X1
| X1 != X3
| X0 != X2
| nil = X0
| ? [X4] :
( ssItem(X4)
& ( ( ~ memberP(X2,X4)
& ! [X5] :
( ssList(X5)
=> ~ segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) )
& memberP(X3,X4) )
| ( memberP(X2,X4)
& ( ~ memberP(X3,X4)
| ? [X6] :
( ssList(X6)
& segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil))) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f124,plain,
! [X0] :
( nil = X0
| ? [X1] :
( ssList(X1)
& ? [X2] :
( ssItem(X2)
& cons(X2,X1) = X0 ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f125,plain,
! [X0] :
( nil = X0
| ? [X1] :
( ssList(X1)
& ? [X2] :
( ssItem(X2)
& cons(X2,X1) = X0 ) )
| ~ ssList(X0) ),
inference(flattening,[],[f124]) ).
fof(f148,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(f149,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil = X1
& X1 = X3
& X0 = X2
& nil != X0
& ! [X4] :
( ~ ssItem(X4)
| ( ( memberP(X2,X4)
| ? [X5] :
( segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil)))
& ssList(X5) )
| ~ memberP(X3,X4) )
& ( ~ memberP(X2,X4)
| ( memberP(X3,X4)
& ! [X6] :
( ~ ssList(X6)
| ~ segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil))) ) ) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f223,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil = X1
& X1 = X3
& X0 = X2
& nil != X0
& ! [X4] :
( ~ ssItem(X4)
| ( ( memberP(X2,X4)
| ? [X5] :
( segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil)))
& ssList(X5) )
| ~ memberP(X3,X4) )
& ( ~ memberP(X2,X4)
| ( memberP(X3,X4)
& ! [X6] :
( ~ ssList(X6)
| ~ segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil))) ) ) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f311,plain,
! [X0] :
( ~ ssList(X0)
| cons(sK44(X0),sK43(X0)) = X0
| nil = X0 ),
inference(cnf_transformation,[],[f125]) ).
fof(f312,plain,
! [X0] :
( ~ ssList(X0)
| ssItem(sK44(X0))
| nil = X0 ),
inference(cnf_transformation,[],[f125]) ).
fof(f313,plain,
! [X0] :
( ~ ssList(X0)
| ssList(sK43(X0))
| nil = X0 ),
inference(cnf_transformation,[],[f125]) ).
fof(f336,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| X0 != X1
| memberP(cons(X1,X2),X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f337,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f415,plain,
! [X4] :
( memberP(sK50,X4)
| ~ memberP(sK49,X4)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f223]) ).
fof(f417,plain,
nil != sK47,
inference(cnf_transformation,[],[f223]) ).
fof(f418,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f223]) ).
fof(f419,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f223]) ).
fof(f420,plain,
nil = sK48,
inference(cnf_transformation,[],[f223]) ).
fof(f421,plain,
ssList(sK49),
inference(cnf_transformation,[],[f223]) ).
fof(f424,plain,
nil = sK50,
inference(definition_unfolding,[],[f420,f419]) ).
fof(f428,plain,
! [X0] :
( ssList(sK43(X0))
| ~ ssList(X0)
| sK50 = X0 ),
inference(definition_unfolding,[],[f313,f424]) ).
fof(f429,plain,
! [X0] :
( ~ ssList(X0)
| ssItem(sK44(X0))
| sK50 = X0 ),
inference(definition_unfolding,[],[f312,f424]) ).
fof(f430,plain,
! [X0] :
( ~ ssList(X0)
| cons(sK44(X0),sK43(X0)) = X0
| sK50 = X0 ),
inference(definition_unfolding,[],[f311,f424]) ).
fof(f435,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(sK50,X0) ),
inference(definition_unfolding,[],[f337,f424]) ).
fof(f483,plain,
sK49 != sK50,
inference(definition_unfolding,[],[f417,f424,f418]) ).
fof(f501,plain,
! [X2,X1] :
( ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| memberP(cons(X1,X2),X1) ),
inference(equality_resolution,[],[f336]) ).
fof(f576,plain,
! [X0] :
( ~ ssItem(sK44(X0))
| ~ ssList(X0)
| sK50 = X0 ),
inference(consistent_polarity_flipping,[],[f429]) ).
fof(f594,plain,
! [X2,X1] :
( ssItem(X1)
| ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X1) ),
inference(consistent_polarity_flipping,[],[f501]) ).
fof(f597,plain,
! [X0] :
( memberP(sK50,X0)
| ssItem(X0) ),
inference(consistent_polarity_flipping,[],[f435]) ).
fof(f654,plain,
! [X4] :
( ~ memberP(sK50,X4)
| memberP(sK49,X4)
| ssItem(X4) ),
inference(consistent_polarity_flipping,[],[f415]) ).
fof(f661,plain,
! [X2,X1] :
( ~ memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ssItem(X1) ),
inference(duplicate_literal_removal,[],[f594]) ).
fof(f719,plain,
! [X4] :
( memberP(sK49,X4)
| ssItem(X4) ),
inference(forward_subsumption_resolution,[],[f654,f597]) ).
fof(f739,plain,
( sK49 = cons(sK44(sK49),sK43(sK49))
| sK49 = sK50 ),
inference(resolution,[],[f430,f421]) ).
fof(f741,plain,
sK49 = cons(sK44(sK49),sK43(sK49)),
inference(forward_subsumption_resolution,[],[f739,f483]) ).
fof(f778,definition,
( spl52_13
<=> ssItem(sK44(sK49)) ),
introduced(definition,[new_symbols(definition,[spl52_13])],[avatar_definition]) ).
fof(f779,plain,
( ~ ssItem(sK44(sK49))
| spl52_13 ),
inference(avatar_component_clause,[],[f778]) ).
fof(f780,plain,
( ssItem(sK44(sK49))
| ~ spl52_13 ),
inference(avatar_component_clause,[],[f778]) ).
fof(f790,definition,
( spl52_16
<=> ssList(sK43(sK49)) ),
introduced(definition,[new_symbols(definition,[spl52_16])],[avatar_definition]) ).
fof(f791,plain,
( ssList(sK43(sK49))
| ~ spl52_16 ),
inference(avatar_component_clause,[],[f790]) ).
fof(f792,plain,
( ~ ssList(sK43(sK49))
| spl52_16 ),
inference(avatar_component_clause,[],[f790]) ).
fof(f1290,plain,
( ~ ssList(sK49)
| sK49 = sK50
| spl52_16 ),
inference(resolution,[],[f792,f428]) ).
fof(f1291,plain,
( sK49 = sK50
| spl52_16 ),
inference(forward_subsumption_resolution,[],[f1290,f421]) ).
fof(f1292,plain,
( $false
| spl52_16 ),
inference(forward_subsumption_resolution,[],[f1291,f483]) ).
fof(f1293,plain,
spl52_16,
inference(avatar_contradiction_clause,[],[f1292]) ).
fof(f1306,plain,
( ~ ssList(sK49)
| sK49 = sK50
| ~ spl52_13 ),
inference(resolution,[],[f780,f576]) ).
fof(f1307,plain,
( sK49 = sK50
| ~ spl52_13 ),
inference(forward_subsumption_resolution,[],[f1306,f421]) ).
fof(f1308,plain,
( $false
| ~ spl52_13 ),
inference(forward_subsumption_resolution,[],[f1307,f483]) ).
fof(f1309,plain,
~ spl52_13,
inference(avatar_contradiction_clause,[],[f1308]) ).
fof(f1449,plain,
( ~ memberP(sK49,sK44(sK49))
| ~ ssList(sK43(sK49))
| ssItem(sK44(sK49)) ),
inference(superposition,[],[f661,f741]) ).
fof(f1452,plain,
( ~ ssList(sK43(sK49))
| ssItem(sK44(sK49)) ),
inference(forward_subsumption_resolution,[],[f1449,f719]) ).
fof(f1454,plain,
( ssItem(sK44(sK49))
| ~ spl52_16 ),
inference(forward_subsumption_resolution,[],[f1452,f791]) ).
fof(f1456,plain,
( $false
| spl52_13
| ~ spl52_16 ),
inference(forward_subsumption_resolution,[],[f1454,f779]) ).
fof(f1457,plain,
( spl52_13
| ~ spl52_16 ),
inference(avatar_contradiction_clause,[],[f1456]) ).
cnf(s64,plain,
spl52_16,
inference(sat_conversion,[],[f1293]) ).
cnf(s65,plain,
~ spl52_13,
inference(sat_conversion,[],[f1309]) ).
cnf(s86,plain,
( spl52_13
| ~ spl52_16 ),
inference(sat_conversion,[],[f1457]) ).
cnf(s87,plain,
~ spl52_16,
inference(rat,[],[s86,s65]) ).
cnf(s88,plain,
$false,
inference(rat,[],[s64,s87]) ).
fof(f1458,plain,
$false,
inference(avatar_sat_refutation,[],[s88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC046+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n007.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 07:33:56 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.51 % (2223467)Will run a generic schedule for satisfiability detection.
% 0.18/0.51 % (2223472)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2944701465_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.51 % (2223473)% WARNING: option uhcvi not known.
% 0.18/0.51 % TRYING [1]
% 0.18/0.51 % (2223473)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=691199492:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.51 % (2223474)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3962401882:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.51 % (2223477)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3337106324:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.51 % (2223475)dis+10_1_sil=32000:sp=arity:random_seed=1869178342:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.51 % (2223476)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1028251417:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.51 % TRYING [2]
% 0.18/0.51 % (2223478)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3549723570:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.51 % TRYING [3]
% 0.18/0.51 % TRYING [4]
% 0.18/0.51 % (2223473) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2223467-2223473"...
% 0.18/0.51 % (2223473)...printing done.
% 0.18/0.51 % (2223473)Refutation found. Thanks to Tanya!
% 0.18/0.51 % SZS status Theorem for theBenchmark
% 0.18/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.51 % (2223473)------------------------------
% 0.18/0.51 % (2223473)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.51 % (2223473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.51 % (2223473)CaDiCaL version: 2.1.3
% 0.18/0.51 % (2223473)Termination reason: Refutation
% 0.18/0.51 % (2223473)Time elapsed: 0.021 s
% 0.18/0.51 % (2223473)Peak memory usage: 13 MB
% 0.18/0.51 % (2223473)Instructions burned: 30 (million)
% 0.18/0.51 % (2223467)Success in time 0.073 s
% 0.18/0.51 % Vampire exiting
%------------------------------------------------------------------------------