%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC153-1 : 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 : n004.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 01:02:41 PM UTC 2026
% Result : Unsatisfiable 2.80s 1.71s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of formulae : 79 ( 20 unt; 5 def)
% Number of atoms : 290 ( 14 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 417 ( 206 ~; 206 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f206,negated_conjecture,
sk3 = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f207,plain,
sk1 = sk3,
inference(reorient_equations,[],[f206]) ).
fof(f208,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4) != sk3
| ~ leq(X1,X0)
| leq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f209,plain,
! [X2,X3,X0,X1,X4] :
( sk3 != app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssItem(X0)
| ~ leq(X1,X0)
| leq(X0,X1) ),
inference(reorient_equations,[],[f208]) ).
fof(f210,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4) != sk3
| ~ leq(X1,X0)
| ~ ssItem(X5)
| ~ memberP(X3,X5)
| leq(X0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f211,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk3 != app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssItem(X0)
| ~ leq(X1,X0)
| ~ ssItem(X5)
| ~ memberP(X3,X5)
| leq(X0,X5) ),
inference(reorient_equations,[],[f210]) ).
fof(f212,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4) != sk3
| ~ leq(X1,X0)
| ~ ssItem(X5)
| ~ memberP(X3,X5)
| leq(X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f213,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk3 != app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssItem(X0)
| ~ leq(X1,X0)
| ~ ssItem(X5)
| ~ memberP(X3,X5)
| leq(X5,X1) ),
inference(reorient_equations,[],[f212]) ).
fof(f214,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f215,negated_conjecture,
ssItem(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f216,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f217,negated_conjecture,
ssList(sk8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f218,negated_conjecture,
ssList(sk9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f219,negated_conjecture,
app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f220,plain,
sk1 = app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9),
inference(reorient_equations,[],[f219]) ).
fof(f221,negated_conjecture,
leq(sk6,sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f222,negated_conjecture,
( ssItem(sk10)
| ~ leq(sk5,sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
fof(f223,negated_conjecture,
( memberP(sk8,sk10)
| ~ leq(sk5,sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
fof(f224,negated_conjecture,
( ~ leq(sk10,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk5,sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_19) ).
fof(f227,plain,
sk3 = app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9),
inference(definition_unfolding,[],[f220,f207]) ).
fof(f242,definition,
( spl0_3
<=> leq(sk5,sk6) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f243,plain,
( ~ leq(sk5,sk6)
| spl0_3 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f245,definition,
( spl0_4
<=> leq(sk5,sk10) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f246,plain,
( ~ leq(sk5,sk10)
| spl0_4 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f248,definition,
( spl0_5
<=> leq(sk10,sk6) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f249,plain,
( ~ leq(sk10,sk6)
| spl0_5 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f250,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f224,f248,f245,f242]) ).
fof(f252,definition,
( spl0_6
<=> memberP(sk8,sk10) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f253,plain,
( memberP(sk8,sk10)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f254,plain,
( ~ spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f223,f252,f242]) ).
fof(f256,definition,
( spl0_7
<=> ssItem(sk10) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f257,plain,
( ssItem(sk10)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f258,plain,
( ~ spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f222,f256,f242]) ).
fof(f262,plain,
( sk3 != sk3
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ leq(sk6,sk5)
| leq(sk5,sk6) ),
inference(superposition,[],[f209,f227]) ).
fof(f263,plain,
( ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ leq(sk6,sk5)
| leq(sk5,sk6) ),
inference(trivial_inequality_removal,[],[f262]) ).
fof(f264,plain,
( ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ leq(sk6,sk5)
| leq(sk5,sk6) ),
inference(forward_subsumption_resolution,[],[f263,f215]) ).
fof(f266,plain,
( ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ leq(sk6,sk5)
| leq(sk5,sk6) ),
inference(forward_subsumption_resolution,[],[f264,f216]) ).
fof(f268,plain,
( ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ leq(sk6,sk5)
| leq(sk5,sk6) ),
inference(forward_subsumption_resolution,[],[f266,f217]) ).
fof(f276,plain,
( ~ ssItem(sk5)
| ~ leq(sk6,sk5)
| leq(sk5,sk6) ),
inference(forward_subsumption_resolution,[],[f268,f218]) ).
fof(f277,plain,
( ~ leq(sk6,sk5)
| leq(sk5,sk6) ),
inference(forward_subsumption_resolution,[],[f276,f214]) ).
fof(f278,plain,
leq(sk5,sk6),
inference(forward_subsumption_resolution,[],[f277,f221]) ).
fof(f279,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f278,f243]) ).
fof(f280,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f279]) ).
fof(f282,plain,
! [X0] :
( sk3 != sk3
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ leq(sk6,sk5)
| ~ ssItem(X0)
| ~ memberP(sk8,X0)
| leq(sk5,X0) ),
inference(superposition,[],[f211,f227]) ).
fof(f283,plain,
! [X0] :
( ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ leq(sk6,sk5)
| ~ ssItem(X0)
| ~ memberP(sk8,X0)
| leq(sk5,X0) ),
inference(trivial_inequality_removal,[],[f282]) ).
fof(f284,plain,
! [X0] :
( ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ leq(sk6,sk5)
| ~ ssItem(X0)
| ~ memberP(sk8,X0)
| leq(sk5,X0) ),
inference(forward_subsumption_resolution,[],[f283,f215]) ).
fof(f286,plain,
! [X0] :
( ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ leq(sk6,sk5)
| ~ ssItem(X0)
| ~ memberP(sk8,X0)
| leq(sk5,X0) ),
inference(forward_subsumption_resolution,[],[f284,f216]) ).
fof(f288,plain,
! [X0] :
( ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ leq(sk6,sk5)
| ~ ssItem(X0)
| ~ memberP(sk8,X0)
| leq(sk5,X0) ),
inference(forward_subsumption_resolution,[],[f286,f217]) ).
fof(f296,plain,
! [X0] :
( ~ ssItem(sk5)
| ~ leq(sk6,sk5)
| ~ ssItem(X0)
| ~ memberP(sk8,X0)
| leq(sk5,X0) ),
inference(forward_subsumption_resolution,[],[f288,f218]) ).
fof(f297,plain,
! [X0] :
( ~ leq(sk6,sk5)
| ~ ssItem(X0)
| ~ memberP(sk8,X0)
| leq(sk5,X0) ),
inference(forward_subsumption_resolution,[],[f296,f214]) ).
fof(f298,plain,
! [X0] :
( ~ memberP(sk8,X0)
| ~ ssItem(X0)
| leq(sk5,X0) ),
inference(forward_subsumption_resolution,[],[f297,f221]) ).
fof(f300,plain,
! [X0] :
( sk3 != sk3
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ leq(sk6,sk5)
| ~ ssItem(X0)
| ~ memberP(sk8,X0)
| leq(X0,sk6) ),
inference(superposition,[],[f213,f227]) ).
fof(f301,plain,
! [X0] :
( ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ leq(sk6,sk5)
| ~ ssItem(X0)
| ~ memberP(sk8,X0)
| leq(X0,sk6) ),
inference(trivial_inequality_removal,[],[f300]) ).
fof(f302,plain,
! [X0] :
( ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ leq(sk6,sk5)
| ~ ssItem(X0)
| ~ memberP(sk8,X0)
| leq(X0,sk6) ),
inference(forward_subsumption_resolution,[],[f301,f215]) ).
fof(f303,plain,
! [X0] :
( ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ leq(sk6,sk5)
| ~ ssItem(X0)
| ~ memberP(sk8,X0)
| leq(X0,sk6) ),
inference(forward_subsumption_resolution,[],[f302,f216]) ).
fof(f304,plain,
! [X0] :
( ~ ssList(sk9)
| ~ ssItem(sk5)
| ~ leq(sk6,sk5)
| ~ ssItem(X0)
| ~ memberP(sk8,X0)
| leq(X0,sk6) ),
inference(forward_subsumption_resolution,[],[f303,f217]) ).
fof(f305,plain,
! [X0] :
( ~ ssItem(sk5)
| ~ leq(sk6,sk5)
| ~ ssItem(X0)
| ~ memberP(sk8,X0)
| leq(X0,sk6) ),
inference(forward_subsumption_resolution,[],[f304,f218]) ).
fof(f306,plain,
! [X0] :
( ~ leq(sk6,sk5)
| ~ ssItem(X0)
| ~ memberP(sk8,X0)
| leq(X0,sk6) ),
inference(forward_subsumption_resolution,[],[f305,f214]) ).
fof(f307,plain,
! [X0] :
( ~ memberP(sk8,X0)
| ~ ssItem(X0)
| leq(X0,sk6) ),
inference(forward_subsumption_resolution,[],[f306,f221]) ).
fof(f308,plain,
( ~ ssItem(sk10)
| leq(sk5,sk10)
| ~ spl0_6 ),
inference(resolution,[],[f298,f253]) ).
fof(f309,plain,
( leq(sk5,sk10)
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f308,f257]) ).
fof(f310,plain,
( $false
| spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f309,f246]) ).
fof(f311,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f310]) ).
fof(f312,plain,
( ~ ssItem(sk10)
| leq(sk10,sk6)
| ~ spl0_6 ),
inference(resolution,[],[f307,f253]) ).
fof(f313,plain,
( leq(sk10,sk6)
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f312,f257]) ).
fof(f314,plain,
( $false
| spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f313,f249]) ).
fof(f315,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f314]) ).
cnf(s2,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f250]) ).
cnf(s3,plain,
( ~ spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f254]) ).
cnf(s4,plain,
( ~ spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f258]) ).
cnf(s7,plain,
spl0_3,
inference(sat_conversion,[],[f280]) ).
cnf(s9,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f311]) ).
cnf(s10,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f315]) ).
cnf(s11,plain,
spl0_7,
inference(rat,[],[s4,s7]) ).
cnf(s12,plain,
spl0_6,
inference(rat,[],[s3,s7]) ).
cnf(s13,plain,
spl0_5,
inference(rat,[],[s10,s11,s12]) ).
cnf(s14,plain,
spl0_4,
inference(rat,[],[s9,s11,s12]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s2,s13,s14,s7]) ).
fof(f316,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC153-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.41 % Computer : n004.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Mon Sep 28 08:10:37 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.47 Running first-order theorem proving
% 0.16/0.47 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
% 2.80/1.71 % (198279)Input is clausal, will run a generic CNF schedule.
% 2.80/1.71 % (198284)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=2258120391:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.80/1.71 % (198288)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3574144506:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.80/1.71 % (198287)lrs+10_1_sil=8000:sp=occurrence:random_seed=2696089772:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.80/1.71 % (198285)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2045818311:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.80/1.71 % (198289)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=408374256:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.80/1.71 % (198286)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3022063776:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.80/1.71 % (198287)Also succeeded, but the first one will report.
% 2.80/1.71 % (198288)First to succeed.
% 2.80/1.71 % (198288)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-198279"
% 2.80/1.71 % (198289)Also succeeded, but the first one will report.
% 2.80/1.71 % (198290)dis-21_1_sil=8000:lcm=predicate:random_seed=665389280:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.80/1.71 % (198290)Also succeeded, but the first one will report.
% 2.80/1.71 % (198288)Refutation found. Thanks to Tanya!
% 2.80/1.71 % SZS status Unsatisfiable for theBenchmark
% 2.80/1.71 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/1.90 % (198288)------------------------------
% 0.24/1.90 % (198288)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.24/1.90 % (198288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/1.90 % (198288)CaDiCaL version: 2.1.3
% 0.24/1.90 % (198288)Termination reason: Refutation
% 0.24/1.90 % (198288)Time elapsed: 0.009 s
% 0.24/1.90 % (198288)Peak memory usage: 89 MB
% 0.24/1.90 % (198288)Instructions burned: 6 (million)
% 0.24/1.90 % (198288)------------------------------
% 0.24/1.90 % (198288)------------------------------
% 0.24/1.90 % (198279)Success in time 0.701 s
% 0.24/1.90 % Vampire exiting
%------------------------------------------------------------------------------