%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC399+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 : n006.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 01:03:49 PM UTC 2026
% Result : Theorem 2.78s 1.16s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 47 ( 18 unt; 1 def)
% Number of atoms : 222 ( 39 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 286 ( 111 ~; 107 |; 52 &)
% ( 3 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 57 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X1,X0)
| memberP(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ~ ssList(X5)
| app(app(X4,X2),X5) != X3
| ~ equalelemsP(X2)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X4
& ? [X8] :
( ssList(X8)
& app(cons(X6,nil),X8) = X2 ) ) )
| ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X5
& ? [X11] :
( ssList(X11)
& app(X11,cons(X9,nil)) = X2 ) ) ) ) )
| ! [X12] :
( ~ ssItem(X12)
| ~ memberP(X0,X12)
| memberP(X1,X12) )
| ( nil != X3
& nil = X2 ) ) ) ) ),
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
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ~ ssList(X5)
| app(app(X4,X2),X5) != X3
| ~ equalelemsP(X2)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X4
& ? [X8] :
( ssList(X8)
& app(cons(X6,nil),X8) = X2 ) ) )
| ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X5
& ? [X11] :
( ssList(X11)
& app(X11,cons(X9,nil)) = X2 ) ) ) ) )
| ! [X12] :
( ~ ssItem(X12)
| ~ memberP(X0,X12)
| memberP(X1,X12) )
| ( nil != X3
& nil = X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ? [X4] :
( ? [X5] :
( ssList(X5)
& app(app(X4,X2),X5) = X3
& equalelemsP(X2)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != X4
| ! [X8] :
( ~ ssList(X8)
| app(cons(X6,nil),X8) != X2 ) ) )
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| app(cons(X9,nil),X10) != X5
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != X2 ) ) ) )
& ssList(X4) )
& ? [X12] :
( ssItem(X12)
& memberP(X0,X12)
& ~ memberP(X1,X12) )
& ( nil = X3
| nil != X2 ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(app(X1,X2),X0)
<=> ( memberP(X1,X0)
| memberP(X2,X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f124,plain,
( ssList(sK3)
& sK1 = sK3
& sK0 = sK2
& ssList(sK5)
& sK3 = app(app(sK4,sK2),sK5)
& equalelemsP(sK2)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != sK4
| ! [X8] :
( ~ ssList(X8)
| app(cons(X6,nil),X8) != sK2 ) ) )
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| app(cons(X9,nil),X10) != sK5
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != sK2 ) ) )
& ssList(sK4)
& ssItem(sK6)
& memberP(sK0,sK6)
& ~ memberP(sK1,sK6)
& ( nil = sK3
| nil != sK2 )
& 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(X4,sK4),skolemize(X5,sK5),skolemize(X12,sK6)],[f98]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X1,X0)
& ~ memberP(X2,X0) ) )
& ( memberP(X1,X0)
| memberP(X2,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f119]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X1,X0)
& ~ memberP(X2,X0) ) )
& ( memberP(X1,X0)
| memberP(X2,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f131]) ).
fof(f139,plain,
ssList(sK0),
inference(cnf_transformation,[],[f124]) ).
fof(f143,plain,
~ memberP(sK1,sK6),
inference(cnf_transformation,[],[f124]) ).
fof(f144,plain,
memberP(sK0,sK6),
inference(cnf_transformation,[],[f124]) ).
fof(f145,plain,
ssItem(sK6),
inference(cnf_transformation,[],[f124]) ).
fof(f146,plain,
ssList(sK4),
inference(cnf_transformation,[],[f124]) ).
fof(f150,plain,
sK3 = app(app(sK4,sK2),sK5),
inference(cnf_transformation,[],[f124]) ).
fof(f151,plain,
ssList(sK5),
inference(cnf_transformation,[],[f124]) ).
fof(f152,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f124]) ).
fof(f153,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f124]) ).
fof(f176,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f183,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f184,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f198,plain,
memberP(sK2,sK6),
inference(definition_unfolding,[],[f144,f152]) ).
fof(f199,plain,
~ memberP(sK3,sK6),
inference(definition_unfolding,[],[f143,f153]) ).
fof(f201,plain,
ssList(sK2),
inference(definition_unfolding,[],[f139,f152]) ).
fof(f254,plain,
! [X0] :
( memberP(sK3,X0)
| ~ memberP(app(sK4,sK2),X0)
| ~ ssList(sK5)
| ~ ssList(app(sK4,sK2))
| ~ ssItem(X0) ),
inference(superposition,[],[f184,f150]) ).
fof(f260,plain,
! [X0] :
( memberP(sK3,X0)
| ~ memberP(app(sK4,sK2),X0)
| ~ ssList(app(sK4,sK2))
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[],[f254,f151]) ).
fof(f289,definition,
( spl30_3
<=> ssList(app(sK4,sK2)) ),
introduced(definition,[new_symbols(definition,[spl30_3])],[avatar_definition]) ).
fof(f290,plain,
( ssList(app(sK4,sK2))
| ~ spl30_3 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f291,plain,
( ~ ssList(app(sK4,sK2))
| spl30_3 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f363,plain,
( ~ ssList(sK2)
| ~ ssList(sK4)
| spl30_3 ),
inference(resolution,[],[f291,f176]) ).
fof(f365,plain,
( ~ ssList(sK4)
| spl30_3 ),
inference(forward_subsumption_resolution,[],[f363,f201]) ).
fof(f366,plain,
( $false
| spl30_3 ),
inference(forward_subsumption_resolution,[],[f365,f146]) ).
fof(f367,plain,
spl30_3,
inference(avatar_contradiction_clause,[],[f366]) ).
fof(f881,plain,
( ! [X0] :
( ~ memberP(app(sK4,sK2),X0)
| memberP(sK3,X0)
| ~ ssItem(X0) )
| ~ spl30_3 ),
inference(forward_subsumption_resolution,[],[f260,f290]) ).
fof(f996,plain,
( ! [X0] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ memberP(sK2,X0)
| ~ ssList(sK2)
| ~ ssList(sK4)
| ~ ssItem(X0) )
| ~ spl30_3 ),
inference(resolution,[],[f881,f183]) ).
fof(f1000,plain,
( ! [X0] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ memberP(sK2,X0)
| ~ ssList(sK2)
| ~ ssList(sK4) )
| ~ spl30_3 ),
inference(duplicate_literal_removal,[],[f996]) ).
fof(f1001,plain,
( ! [X0] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ memberP(sK2,X0)
| ~ ssList(sK4) )
| ~ spl30_3 ),
inference(forward_subsumption_resolution,[],[f1000,f201]) ).
fof(f1002,plain,
( ! [X0] :
( ~ memberP(sK2,X0)
| ~ ssItem(X0)
| memberP(sK3,X0) )
| ~ spl30_3 ),
inference(forward_subsumption_resolution,[],[f1001,f146]) ).
fof(f1861,plain,
( ~ ssItem(sK6)
| memberP(sK3,sK6)
| ~ spl30_3 ),
inference(resolution,[],[f1002,f198]) ).
fof(f1862,plain,
( memberP(sK3,sK6)
| ~ spl30_3 ),
inference(forward_subsumption_resolution,[],[f1861,f145]) ).
fof(f1863,plain,
( $false
| ~ spl30_3 ),
inference(forward_subsumption_resolution,[],[f1862,f199]) ).
fof(f1864,plain,
~ spl30_3,
inference(avatar_contradiction_clause,[],[f1863]) ).
cnf(s13,plain,
spl30_3,
inference(sat_conversion,[],[f367]) ).
cnf(s66,plain,
~ spl30_3,
inference(sat_conversion,[],[f1864]) ).
cnf(s78,plain,
$false,
inference(rat,[],[s13,s66]) ).
fof(f1865,plain,
$false,
inference(avatar_sat_refutation,[],[s78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC399+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n006.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 09:30:25 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 2.78/1.16 % (3837815)Detected formulas, will run a generic FOF schedule.
% 2.78/1.16 % (3837944)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1058926390:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.78/1.16 % (3837944)First to succeed.
% 2.78/1.16 % (3837944)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3837815"
% 2.78/1.16 % (3837942)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=501595588:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.78/1.16 % (3837941)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=377715439:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.78/1.16 % (3837943)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=263891570:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.78/1.16 % (3837948)dis-21_1_sil=8000:lcm=predicate:random_seed=2726721508: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)
% 2.78/1.16 % (3837946)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2489155507:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.78/1.16 % (3837945)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4220591978:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.78/1.16 % (3837948)Instruction limit reached!
% 2.78/1.16 % (3837948)------------------------------
% 2.78/1.16 % (3837948)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.16 % (3837948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.16 % (3837948)CaDiCaL version: 2.1.3
% 2.78/1.16 % (3837948)Termination reason: Instruction limit
% 2.78/1.16 % (3837948)Termination phase: Saturation
% 2.78/1.16 % (3837948)Time elapsed: 0.070 s
% 2.78/1.16 % (3837948)Peak memory usage: 91 MB
% 2.78/1.16 % (3837948)Instructions burned: 131 (million)
% 2.78/1.16 % (3837945)Also succeeded, but the first one will report.
% 2.78/1.16 % (3837946)Also succeeded, but the first one will report.
% 2.78/1.16 % (3837944)Refutation found. Thanks to Tanya!
% 2.78/1.16 % SZS status Theorem for theBenchmark
% 2.78/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.78/1.16 % (3837944)------------------------------
% 2.78/1.16 % (3837944)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.16 % (3837944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.16 % (3837944)CaDiCaL version: 2.1.3
% 2.78/1.16 % (3837944)Termination reason: Refutation
% 2.78/1.16 % (3837944)Time elapsed: 0.020 s
% 2.78/1.16 % (3837944)Peak memory usage: 90 MB
% 2.78/1.16 % (3837944)Instructions burned: 54 (million)
% 2.78/1.16 % (3837944)------------------------------
% 2.78/1.16 % (3837944)------------------------------
% 2.78/1.16 % (3837815)Success in time 0.31 s
% 2.78/1.16 % Vampire exiting
%------------------------------------------------------------------------------