%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC012+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 : n019.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 2.73s 1.35s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 18 unt; 6 def)
% Number of atoms : 225 ( 37 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 282 ( 115 ~; 112 |; 40 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 40 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).
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)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X1
& app(X5,X6) = X0 ) ) )
| ! [X7] :
( ssItem(X7)
=> app(X2,cons(X7,nil)) != 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)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X1
& app(X5,X6) = X0 ) ) )
| ! [X7] :
( ssItem(X7)
=> app(X2,cons(X7,nil)) != 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)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X1
| app(X5,X6) != X0 ) ) )
& ? [X7] :
( app(X2,cons(X7,nil)) = X3
& ssItem(X7) ) )
| ( 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)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X1
| app(X5,X6) != X0 ) ) )
& ? [X7] :
( app(X2,cons(X7,nil)) = X3
& ssItem(X7) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f107,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f120,plain,
( sK1 = sK3
& sK0 = sK2
& ( ( neq(sK1,nil)
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK1
| app(X5,X6) != sK0 ) ) )
& sK3 = app(sK2,cons(sK4,nil))
& ssItem(sK4) )
| ( 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,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X7,sK4)],[f99]) ).
fof(f127,plain,
ssList(sK0),
inference(cnf_transformation,[],[f120]) ).
fof(f128,plain,
ssList(sK1),
inference(cnf_transformation,[],[f120]) ).
fof(f131,plain,
( ssItem(sK4)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f120]) ).
fof(f133,plain,
( sK3 = app(sK2,cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f120]) ).
fof(f135,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK1
| app(X5,X6) != sK0
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f120]) ).
fof(f138,plain,
( neq(sK1,nil)
| neq(sK1,nil) ),
inference(cnf_transformation,[],[f120]) ).
fof(f139,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f120]) ).
fof(f140,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f120]) ).
fof(f152,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f167,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f168,plain,
( neq(sK3,nil)
| neq(sK3,nil) ),
inference(definition_unfolding,[],[f138,f140,f140]) ).
fof(f171,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK3
| app(X5,X6) != sK2
| ~ neq(sK3,nil) ),
inference(definition_unfolding,[],[f135,f140,f139]) ).
fof(f174,plain,
ssList(sK3),
inference(definition_unfolding,[],[f128,f140]) ).
fof(f175,plain,
ssList(sK2),
inference(definition_unfolding,[],[f127,f139]) ).
fof(f179,definition,
~ sP11(sK3),
introduced(definition,[new_symbols(definition,[sP11])],[inequality_splitting_name_introduction]) ).
fof(f180,definition,
~ sP12(sK2),
introduced(definition,[new_symbols(definition,[sP12])],[inequality_splitting_name_introduction]) ).
fof(f181,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| sP11(app(app(X5,cons(X4,nil)),X6))
| sP12(app(X5,X6))
| ~ neq(sK3,nil) ),
inference(inequality_splitting,[],[f171,f180,f179]) ).
fof(f197,plain,
neq(sK3,nil),
inference(duplicate_literal_removal,[],[f168]) ).
fof(f199,definition,
( spl19_1
<=> neq(sK3,nil) ),
introduced(definition,[new_symbols(definition,[spl19_1])],[avatar_definition]) ).
fof(f203,definition,
( spl19_2
<=> ssItem(sK4) ),
introduced(definition,[new_symbols(definition,[spl19_2])],[avatar_definition]) ).
fof(f205,plain,
( ssItem(sK4)
| ~ spl19_2 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f206,plain,
( ~ spl19_1
| spl19_2 ),
inference(avatar_split_clause,[],[f131,f203,f199]) ).
fof(f209,definition,
( spl19_3
<=> sK3 = app(sK2,cons(sK4,nil)) ),
introduced(definition,[new_symbols(definition,[spl19_3])],[avatar_definition]) ).
fof(f211,plain,
( sK3 = app(sK2,cons(sK4,nil))
| ~ spl19_3 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f212,plain,
( ~ spl19_1
| spl19_3 ),
inference(avatar_split_clause,[],[f133,f209,f199]) ).
fof(f215,definition,
( spl19_4
<=> ! [X6,X4,X5] :
( ~ ssItem(X4)
| sP12(app(X5,X6))
| sP11(app(app(X5,cons(X4,nil)),X6))
| ~ ssList(X6)
| ~ ssList(X5) ) ),
introduced(definition,[new_symbols(definition,[spl19_4])],[avatar_definition]) ).
fof(f216,plain,
( ! [X6,X4,X5] :
( sP11(app(app(X5,cons(X4,nil)),X6))
| sP12(app(X5,X6))
| ~ ssItem(X4)
| ~ ssList(X6)
| ~ ssList(X5) )
| ~ spl19_4 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f217,plain,
( ~ spl19_1
| spl19_4 ),
inference(avatar_split_clause,[],[f181,f215,f199]) ).
fof(f222,plain,
spl19_1,
inference(avatar_split_clause,[],[f197,f199]) ).
fof(f304,plain,
( ! [X0] :
( sP11(app(sK3,X0))
| sP12(app(sK2,X0))
| ~ ssItem(sK4)
| ~ ssList(X0)
| ~ ssList(sK2) )
| ~ spl19_3
| ~ spl19_4 ),
inference(superposition,[],[f216,f211]) ).
fof(f320,plain,
( ! [X0] :
( sP11(app(sK3,X0))
| sP12(app(sK2,X0))
| ~ ssList(X0)
| ~ ssList(sK2) )
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f304,f205]) ).
fof(f330,plain,
( ! [X0] :
( sP12(app(sK2,X0))
| sP11(app(sK3,X0))
| ~ ssList(X0) )
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f320,f175]) ).
fof(f376,plain,
( sP12(sK2)
| sP11(app(sK3,nil))
| ~ ssList(nil)
| ~ ssList(sK2)
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4 ),
inference(superposition,[],[f330,f152]) ).
fof(f380,plain,
( sP11(app(sK3,nil))
| ~ ssList(nil)
| ~ ssList(sK2)
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f376,f180]) ).
fof(f384,plain,
( sP11(app(sK3,nil))
| ~ ssList(sK2)
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f380,f167]) ).
fof(f387,plain,
( sP11(app(sK3,nil))
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f384,f175]) ).
fof(f427,plain,
( sP11(sK3)
| ~ ssList(sK3)
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4 ),
inference(superposition,[],[f387,f152]) ).
fof(f430,plain,
( ~ ssList(sK3)
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f427,f179]) ).
fof(f432,plain,
( $false
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f430,f174]) ).
fof(f433,plain,
( ~ spl19_2
| ~ spl19_3
| ~ spl19_4 ),
inference(avatar_contradiction_clause,[],[f432]) ).
cnf(s1,plain,
( ~ spl19_1
| spl19_2 ),
inference(sat_conversion,[],[f206]) ).
cnf(s3,plain,
( ~ spl19_1
| spl19_3 ),
inference(sat_conversion,[],[f212]) ).
cnf(s5,plain,
( ~ spl19_1
| spl19_4 ),
inference(sat_conversion,[],[f217]) ).
cnf(s7,plain,
spl19_1,
inference(sat_conversion,[],[f222]) ).
cnf(s26,plain,
( ~ spl19_2
| ~ spl19_3
| ~ spl19_4 ),
inference(sat_conversion,[],[f433]) ).
cnf(s28,plain,
spl19_4,
inference(rat,[],[s5,s7]) ).
cnf(s29,plain,
spl19_3,
inference(rat,[],[s3,s7]) ).
cnf(s30,plain,
~ spl19_2,
inference(rat,[],[s26,s28,s29]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s1,s30,s7]) ).
fof(f440,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC012+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 07:25:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 2.73/1.35 % (3826661)Detected formulas, will run a generic FOF schedule.
% 2.73/1.35 % (3826669)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1255688913:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.73/1.35 % (3826669)First to succeed.
% 2.73/1.35 % (3826669)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3826661"
% 2.73/1.35 % (3826666)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=2337228543:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.73/1.35 % (3826670)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1801442131:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.73/1.35 % (3826672)dis-21_1_sil=8000:lcm=predicate:random_seed=1047282364: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)
% 2.73/1.35 % (3826668)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=1642469221:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.73/1.35 % (3826667)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=668986678:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.73/1.35 % (3826670)Also succeeded, but the first one will report.
% 2.73/1.35 % (3826671)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2559446399:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.73/1.35 % (3826671)Also succeeded, but the first one will report.
% 2.73/1.35 % (3826672)Instruction limit reached!
% 2.73/1.35 % (3826672)------------------------------
% 2.73/1.35 % (3826672)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.35 % (3826672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.35 % (3826672)CaDiCaL version: 2.1.3
% 2.73/1.35 % (3826672)Termination reason: Instruction limit
% 2.73/1.35 % (3826672)Termination phase: Saturation
% 2.73/1.35 % (3826672)Time elapsed: 0.075 s
% 2.73/1.35 % (3826672)Peak memory usage: 90 MB
% 2.73/1.35 % (3826672)Instructions burned: 129 (million)
% 2.73/1.35 % (3826669)Refutation found. Thanks to Tanya!
% 2.73/1.35 % SZS status Theorem for theBenchmark
% 2.73/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/1.35 % (3826669)------------------------------
% 2.73/1.35 % (3826669)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.35 % (3826669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.35 % (3826669)CaDiCaL version: 2.1.3
% 2.73/1.35 % (3826669)Termination reason: Refutation
% 2.73/1.35 % (3826669)Time elapsed: 0.005 s
% 2.73/1.35 % (3826669)Peak memory usage: 89 MB
% 2.73/1.35 % (3826669)Instructions burned: 10 (million)
% 2.73/1.35 % (3826669)------------------------------
% 2.73/1.35 % (3826669)------------------------------
% 2.73/1.35 % (3826661)Success in time 0.308 s
% 2.73/1.35 % Vampire exiting
%------------------------------------------------------------------------------