%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC219+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 : n013.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 01:02:59 PM UTC 2026
% Result : Theorem 0.83s 0.94s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 13 unt; 4 def)
% Number of atoms : 257 ( 68 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 330 ( 132 ~; 115 |; 64 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 67 ( 0 sgn 47 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| nil = X0
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X0
& ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X5,X7)
| ~ memberP(X6,X7)
| ~ leq(X4,X7)
| leq(X7,X4) ) ) ) ) )
| ( ! [X8] :
( ssItem(X8)
=> ( cons(X8,nil) != X2
| ~ memberP(X3,X8)
| ? [X9] :
( ssItem(X9)
& X8 != X9
& memberP(X3,X9)
& leq(X9,X8) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
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
| nil = X0
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X0
& ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X5,X7)
| ~ memberP(X6,X7)
| ~ leq(X4,X7)
| leq(X7,X4) ) ) ) ) )
| ( ! [X8] :
( ssItem(X8)
=> ( cons(X8,nil) != X2
| ~ memberP(X3,X8)
| ? [X9] :
( ssItem(X9)
& X8 != X9
& memberP(X3,X9)
& leq(X9,X8) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f134,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f148,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f201,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& nil != X0
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X0
| ? [X7] :
( memberP(X5,X7)
& memberP(X6,X7)
& leq(X4,X7)
& ~ leq(X7,X4)
& ssItem(X7) ) ) ) )
& ( ? [X8] :
( cons(X8,nil) = X2
& memberP(X3,X8)
& ! [X9] :
( ~ ssItem(X9)
| X8 = X9
| ~ memberP(X3,X9)
| ~ leq(X9,X8) )
& ssItem(X8) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& nil != X0
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X0
| ? [X7] :
( memberP(X5,X7)
& memberP(X6,X7)
& leq(X4,X7)
& ~ leq(X7,X4)
& ssItem(X7) ) ) ) )
& ( ? [X8] :
( cons(X8,nil) = X2
& memberP(X3,X8)
& ! [X9] :
( ~ ssItem(X9)
| X8 = X9
| ~ memberP(X3,X9)
| ~ leq(X9,X8) )
& ssItem(X8) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& nil != sK53
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK53
| ( memberP(X5,sK57(X4,X5,X6))
& memberP(X6,sK57(X4,X5,X6))
& leq(X4,sK57(X4,X5,X6))
& ~ leq(sK57(X4,X5,X6),X4)
& ssItem(sK57(X4,X5,X6)) ) ) ) )
& ( ( sK55 = cons(sK58,nil)
& memberP(sK56,sK58)
& ! [X9] :
( ~ ssItem(X9)
| sK58 = X9
| ~ memberP(sK56,X9)
| ~ leq(X9,sK58) )
& ssItem(sK58) )
| ( nil = sK56
& nil = sK55 ) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X7,sK57(X4,X5,X6)),skolemize(X8,sK58)],[f222]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f403,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f419,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f482,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f201]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( ssItem(sK58)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
( sK55 = cons(sK58,nil)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
! [X6,X4,X5] :
( ssItem(sK57(X4,X5,X6))
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK53
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
! [X6,X4,X5] :
( memberP(X6,sK57(X4,X5,X6))
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK53
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f513,plain,
nil != sK53,
inference(cnf_transformation,[],[f296]) ).
fof(f514,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f551,definition,
( spl59_1
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl59_1])],[avatar_definition]) ).
fof(f553,plain,
( nil = sK55
| ~ spl59_1 ),
inference(avatar_component_clause,[],[f551]) ).
fof(f555,definition,
( spl59_2
<=> ssItem(sK58) ),
introduced(definition,[new_symbols(definition,[spl59_2])],[avatar_definition]) ).
fof(f557,plain,
( ssItem(sK58)
| ~ spl59_2 ),
inference(avatar_component_clause,[],[f555]) ).
fof(f558,plain,
( spl59_1
| spl59_2 ),
inference(avatar_split_clause,[],[f500,f555,f551]) ).
fof(f576,definition,
( spl59_6
<=> sK55 = cons(sK58,nil) ),
introduced(definition,[new_symbols(definition,[spl59_6])],[avatar_definition]) ).
fof(f578,plain,
( sK55 = cons(sK58,nil)
| ~ spl59_6 ),
inference(avatar_component_clause,[],[f576]) ).
fof(f579,plain,
( spl59_1
| spl59_6 ),
inference(avatar_split_clause,[],[f506,f576,f551]) ).
fof(f582,definition,
( spl59_7
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl59_7])],[avatar_definition]) ).
fof(f583,plain,
( ssList(nil)
| ~ spl59_7 ),
inference(avatar_component_clause,[],[f582]) ).
fof(f615,plain,
spl59_7,
inference(avatar_split_clause,[],[f389,f582]) ).
fof(f618,plain,
( sK53 = cons(sK58,nil)
| ~ spl59_6 ),
inference(forward_demodulation,[],[f578,f514]) ).
fof(f621,plain,
! [X0,X1] :
( ~ ssItem(sK57(X0,X1,nil))
| ~ ssList(X1)
| ~ ssList(nil)
| sK53 != app(app(X1,cons(X0,nil)),nil)
| ~ ssItem(X0) ),
inference(resolution,[],[f419,f511]) ).
fof(f624,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(nil)
| sK53 != app(app(X1,cons(X0,nil)),nil)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[],[f621,f508]) ).
fof(f626,plain,
( ! [X0,X1] :
( sK53 != app(app(X1,cons(X0,nil)),nil)
| ~ ssList(X1)
| ~ ssItem(X0) )
| ~ spl59_7 ),
inference(forward_subsumption_resolution,[],[f624,f583]) ).
fof(f629,plain,
( ! [X0] :
( sK53 != app(app(X0,sK53),nil)
| ~ ssList(X0)
| ~ ssItem(sK58) )
| ~ spl59_6
| ~ spl59_7 ),
inference(superposition,[],[f626,f618]) ).
fof(f630,plain,
( ! [X0] :
( sK53 != app(app(X0,sK53),nil)
| ~ ssList(X0) )
| ~ spl59_2
| ~ spl59_6
| ~ spl59_7 ),
inference(forward_subsumption_resolution,[],[f629,f557]) ).
fof(f648,plain,
( sK53 != app(sK53,nil)
| ~ ssList(nil)
| ~ ssList(sK53)
| ~ spl59_2
| ~ spl59_6
| ~ spl59_7 ),
inference(superposition,[],[f630,f403]) ).
fof(f649,plain,
( sK53 != app(sK53,nil)
| ~ ssList(sK53)
| ~ spl59_2
| ~ spl59_6
| ~ spl59_7 ),
inference(forward_subsumption_resolution,[],[f648,f583]) ).
fof(f652,plain,
( sK53 != app(sK53,nil)
| ~ spl59_2
| ~ spl59_6
| ~ spl59_7 ),
inference(forward_subsumption_resolution,[],[f649,f496]) ).
fof(f657,plain,
( sK53 != sK53
| ~ ssList(sK53)
| ~ spl59_2
| ~ spl59_6
| ~ spl59_7 ),
inference(superposition,[],[f652,f482]) ).
fof(f658,plain,
( ~ ssList(sK53)
| ~ spl59_2
| ~ spl59_6
| ~ spl59_7 ),
inference(trivial_inequality_removal,[],[f657]) ).
fof(f659,plain,
( $false
| ~ spl59_2
| ~ spl59_6
| ~ spl59_7 ),
inference(forward_subsumption_resolution,[],[f658,f496]) ).
fof(f660,plain,
( ~ spl59_2
| ~ spl59_6
| ~ spl59_7 ),
inference(avatar_contradiction_clause,[],[f659]) ).
fof(f715,plain,
( nil = sK53
| ~ spl59_1 ),
inference(superposition,[],[f553,f514]) ).
fof(f720,plain,
( $false
| ~ spl59_1 ),
inference(forward_subsumption_resolution,[],[f715,f513]) ).
fof(f721,plain,
~ spl59_1,
inference(avatar_contradiction_clause,[],[f720]) ).
cnf(s1,plain,
( spl59_1
| spl59_2 ),
inference(sat_conversion,[],[f558]) ).
cnf(s7,plain,
( spl59_1
| spl59_6 ),
inference(sat_conversion,[],[f579]) ).
cnf(s17,plain,
spl59_7,
inference(sat_conversion,[],[f615]) ).
cnf(s18,plain,
( ~ spl59_2
| ~ spl59_6
| ~ spl59_7 ),
inference(sat_conversion,[],[f660]) ).
cnf(s30,plain,
~ spl59_1,
inference(sat_conversion,[],[f721]) ).
cnf(s35,plain,
spl59_6,
inference(rat,[],[s7,s30]) ).
cnf(s36,plain,
~ spl59_2,
inference(rat,[],[s18,s17,s35]) ).
cnf(s40,plain,
$false,
inference(rat,[],[s1,s36,s30]) ).
fof(f722,plain,
$false,
inference(avatar_sat_refutation,[],[s40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC219+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n013.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 08:31:36 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running first-order theorem proving
% 0.08/0.20 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
% 0.83/0.94 % (1024075)Detected formulas, will run a generic FOF schedule.
% 0.83/0.94 % (1024085)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2997016172:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.83/0.94 % (1024085)First to succeed.
% 0.83/0.94 % (1024085)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1024075"
% 0.83/0.94 % (1024082)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=3283858481:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.83/0.94 % (1024083)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=780651228:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.83/0.94 % (1024081)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=2784588597:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.83/0.94 % (1024084)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4169227097:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.83/0.94 % (1024080)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=2037891573:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.83/0.94 % (1024084)Also succeeded, but the first one will report.
% 0.83/0.94 % (1024086)dis-21_1_sil=8000:lcm=predicate:random_seed=2131784168: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)
% 0.83/0.94 % (1024083)Instruction limit reached!
% 0.83/0.94 % (1024083)------------------------------
% 0.83/0.94 % (1024083)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.83/0.94 % (1024083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.94 % (1024083)CaDiCaL version: 2.1.3
% 0.83/0.94 % (1024083)Termination reason: Instruction limit
% 0.83/0.94 % (1024083)Termination phase: Saturation
% 0.83/0.94 % (1024083)Time elapsed: 0.072 s
% 0.83/0.94 % (1024083)Peak memory usage: 90 MB
% 0.83/0.94 % (1024083)Instructions burned: 109 (million)
% 0.83/0.94 % (1024086)Instruction limit reached!
% 0.83/0.94 % (1024086)------------------------------
% 0.83/0.94 % (1024086)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.83/0.94 % (1024086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.94 % (1024086)CaDiCaL version: 2.1.3
% 0.83/0.94 % (1024086)Termination reason: Instruction limit
% 0.83/0.94 % (1024086)Termination phase: Saturation
% 0.83/0.94 % (1024086)Time elapsed: 0.071 s
% 0.83/0.94 % (1024086)Peak memory usage: 91 MB
% 0.83/0.94 % (1024086)Instructions burned: 129 (million)
% 0.83/0.94 % (1024085)Refutation found. Thanks to Tanya!
% 0.83/0.94 % SZS status Theorem for theBenchmark
% 0.83/0.94 % SZS output start Proof for theBenchmark
% See solution above
% 2.64/1.12 % (1024085)------------------------------
% 2.64/1.12 % (1024085)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.12 % (1024085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.12 % (1024085)CaDiCaL version: 2.1.3
% 2.64/1.12 % (1024085)Termination reason: Refutation
% 2.64/1.12 % (1024085)Time elapsed: 0.007 s
% 2.64/1.12 % (1024085)Peak memory usage: 90 MB
% 2.64/1.12 % (1024085)Instructions burned: 17 (million)
% 2.64/1.12 % (1024085)------------------------------
% 2.64/1.12 % (1024085)------------------------------
% 2.64/1.12 % (1024075)Success in time 0.295 s
% 2.64/1.12 % Vampire exiting
%------------------------------------------------------------------------------