%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC340-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Thu Sep 24 02:40:51 PM UTC 2026
% Result : Unsatisfiable 14.34s 2.43s
% Output : CNFRefutation 14.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 27
% Syntax : Number of formulae : 86 ( 31 unt; 12 def)
% Number of atoms : 200 ( 12 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 207 ( 93 ~; 102 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 21 ( 19 usr; 13 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27,axiom,
! [U] : ssList(skaf68(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] : ssList(skaf67(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [U] : ssList(skaf66(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [U] : ssItem(skaf65(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [U] : ssItem(skaf64(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f91,axiom,
! [U] :
( totalorderedP(U)
| ~ ssList(U)
| ~ leq(skaf64(U),skaf65(U)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f103,axiom,
! [U,V] :
( leq(U,V)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f164,axiom,
! [U] :
( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U
| totalorderedP(U)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f181,axiom,
! [U,V,W,X,Y,Z] :
( lt(V,X)
| ~ ssList(Z)
| ~ strictorderedP(Z)
| ~ ssItem(V)
| ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(Y)
| app(app(U,cons(V,W)),cons(X,Y)) != Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f186,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f190,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
segmentP(sk4,sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
strictorderedP(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f221,plain,
! [X0] : ssList(skaf68(X0)),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f222,plain,
! [X0] : ssList(skaf67(X0)),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f223,plain,
! [X0] : ssList(skaf66(X0)),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f224,plain,
! [X0] : ssItem(skaf65(X0)),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f225,plain,
! [X0] : ssItem(skaf64(X0)),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f286,plain,
! [X0] :
( totalorderedP(X0)
| ~ ssList(X0)
| ~ leq(skaf64(X0),skaf65(X0)) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f300,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f389,plain,
! [X0] :
( app(app(skaf66(X0),cons(skaf64(X0),skaf67(X0))),cons(skaf65(X0),skaf68(X0))) = X0
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f415,plain,
! [V,X] :
( lt(V,X)
| ! [Z] :
( ~ ssList(Z)
| ~ strictorderedP(Z)
| ~ ssItem(V)
| ~ ssItem(X)
| ! [U] :
( ~ ssList(U)
| ! [W] :
( ~ ssList(W)
| ! [Y] :
( ~ ssList(Y)
| app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) ) ) ),
inference(miniscoping,[status(thm)],[f181]) ).
fof(f416,plain,
! [X0,X1,X2,X3,X4,X5] :
( lt(X1,X3)
| ~ ssList(X5)
| ~ strictorderedP(X5)
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
inference(cnf_transformation,[status(thm)],[f415]) ).
fof(f425,plain,
ssList(sk1),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f429,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f430,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f431,plain,
segmentP(sk4,sk3),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f432,plain,
strictorderedP(sk3),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f433,plain,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f441,definition,
( sQ2_spl
<=> segmentP(sk2,sk1) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( sQ2_spl
| ~ segmentP(sk2,sk1) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,definition,
( sQ3_spl
<=> totalorderedP(sk1) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f446,plain,
( sQ3_spl
| ~ totalorderedP(sk1) ),
inference(component_clause,[status(thm)],[f444]) ).
fof(f447,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f433,f441,f444]) ).
fof(f472,plain,
! [X0,X1,X2,X3,X4] :
( lt(X4,X3)
| ~ ssList(app(app(X2,cons(X4,X1)),cons(X3,X0)))
| ~ strictorderedP(app(app(X2,cons(X4,X1)),cons(X3,X0)))
| ~ ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f416]) ).
fof(f479,plain,
strictorderedP(sk1),
inference(forward_demodulation,[status(thm)],[f430,f432]) ).
fof(f480,plain,
segmentP(sk2,sk3),
inference(forward_demodulation,[status(thm)],[f429,f431]) ).
fof(f481,plain,
segmentP(sk2,sk1),
inference(forward_demodulation,[status(thm)],[f430,f480]) ).
fof(f482,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f443,f481]) ).
fof(f483,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f482]) ).
fof(f502,definition,
( sQ7_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f504,plain,
( sQ7_spl
| ~ ssList(sk1) ),
inference(component_clause,[status(thm)],[f502]) ).
fof(f536,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f504,f425]) ).
fof(f537,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f536]) ).
fof(f10159,plain,
( sQ3_spl
| app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))) = sk1
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f389,f446]) ).
fof(f10161,definition,
( sQ921_spl
<=> app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ921_spl])],[split_symbol_definition]) ).
fof(f10162,plain,
( ~ sQ921_spl
| app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))) = sk1 ),
inference(component_clause,[status(thm)],[f10161]) ).
fof(f10164,plain,
( sQ3_spl
| sQ921_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f10159,f502,f10161,f444]) ).
fof(f10707,plain,
( ~ sQ921_spl
| lt(skaf64(sk1),skaf65(sk1))
| ~ ssList(sk1)
| ~ strictorderedP(app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))))
| ~ ssItem(skaf64(sk1))
| ~ ssItem(skaf65(sk1))
| ~ ssList(skaf66(sk1))
| ~ ssList(skaf67(sk1))
| ~ ssList(skaf68(sk1)) ),
inference(paramodulation,[status(thm)],[f10162,f472]) ).
fof(f10722,definition,
( sQ945_spl
<=> ssList(skaf68(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ945_spl])],[split_symbol_definition]) ).
fof(f10724,plain,
( sQ945_spl
| ~ ssList(skaf68(sk1)) ),
inference(component_clause,[status(thm)],[f10722]) ).
fof(f10725,definition,
( sQ946_spl
<=> ssList(skaf67(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ946_spl])],[split_symbol_definition]) ).
fof(f10727,plain,
( sQ946_spl
| ~ ssList(skaf67(sk1)) ),
inference(component_clause,[status(thm)],[f10725]) ).
fof(f10728,definition,
( sQ947_spl
<=> ssList(skaf66(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ947_spl])],[split_symbol_definition]) ).
fof(f10730,plain,
( sQ947_spl
| ~ ssList(skaf66(sk1)) ),
inference(component_clause,[status(thm)],[f10728]) ).
fof(f10731,definition,
( sQ948_spl
<=> ssItem(skaf65(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ948_spl])],[split_symbol_definition]) ).
fof(f10733,plain,
( sQ948_spl
| ~ ssItem(skaf65(sk1)) ),
inference(component_clause,[status(thm)],[f10731]) ).
fof(f10734,definition,
( sQ949_spl
<=> ssItem(skaf64(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ949_spl])],[split_symbol_definition]) ).
fof(f10736,plain,
( sQ949_spl
| ~ ssItem(skaf64(sk1)) ),
inference(component_clause,[status(thm)],[f10734]) ).
fof(f10737,definition,
( sQ950_spl
<=> leq(skaf64(sk1),skaf65(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ950_spl])],[split_symbol_definition]) ).
fof(f10738,plain,
( ~ sQ950_spl
| leq(skaf64(sk1),skaf65(sk1)) ),
inference(component_clause,[status(thm)],[f10737]) ).
fof(f10745,definition,
( sQ952_spl
<=> strictorderedP(app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1)))) ),
introduced(definition,[new_symbols(definition,[sQ952_spl])],[split_symbol_definition]) ).
fof(f10747,plain,
( sQ952_spl
| ~ strictorderedP(app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1)))) ),
inference(component_clause,[status(thm)],[f10745]) ).
fof(f10748,definition,
( sQ953_spl
<=> lt(skaf64(sk1),skaf65(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ953_spl])],[split_symbol_definition]) ).
fof(f10749,plain,
( ~ sQ953_spl
| lt(skaf64(sk1),skaf65(sk1)) ),
inference(component_clause,[status(thm)],[f10748]) ).
fof(f10751,plain,
( ~ sQ921_spl
| sQ953_spl
| ~ sQ7_spl
| ~ sQ952_spl
| ~ sQ949_spl
| ~ sQ948_spl
| ~ sQ947_spl
| ~ sQ946_spl
| ~ sQ945_spl ),
inference(split_clause,[status(thm)],[f10707,f10722,f10725,f10728,f10731,f10734,f10745,f502,f10748,f10161]) ).
fof(f10796,plain,
( sQ948_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10733,f224]) ).
fof(f10797,plain,
sQ948_spl,
inference(contradiction_clause,[status(thm)],[f10796]) ).
fof(f10798,plain,
( sQ945_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10724,f221]) ).
fof(f10799,plain,
sQ945_spl,
inference(contradiction_clause,[status(thm)],[f10798]) ).
fof(f10800,plain,
( sQ947_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10730,f223]) ).
fof(f10801,plain,
sQ947_spl,
inference(contradiction_clause,[status(thm)],[f10800]) ).
fof(f10802,plain,
( sQ949_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10736,f225]) ).
fof(f10803,plain,
sQ949_spl,
inference(contradiction_clause,[status(thm)],[f10802]) ).
fof(f10804,plain,
( sQ946_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10727,f222]) ).
fof(f10805,plain,
sQ946_spl,
inference(contradiction_clause,[status(thm)],[f10804]) ).
fof(f10806,plain,
( sQ952_spl
| ~ sQ921_spl
| ~ strictorderedP(sk1) ),
inference(forward_demodulation,[status(thm)],[f10162,f10747]) ).
fof(f10807,plain,
( sQ952_spl
| ~ sQ921_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10806,f479]) ).
fof(f10808,plain,
( sQ952_spl
| ~ sQ921_spl ),
inference(contradiction_clause,[status(thm)],[f10807]) ).
fof(f10915,plain,
( ~ sQ950_spl
| totalorderedP(sk1)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f10738,f286]) ).
fof(f10921,plain,
( ~ sQ950_spl
| sQ3_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f10915,f502,f444,f10737]) ).
fof(f10947,plain,
( ~ sQ953_spl
| leq(skaf64(sk1),skaf65(sk1))
| ~ ssItem(skaf64(sk1))
| ~ ssItem(skaf65(sk1)) ),
inference(resolution,[status(thm)],[f10749,f300]) ).
fof(f10961,plain,
( ~ sQ953_spl
| sQ950_spl
| ~ sQ949_spl
| ~ sQ948_spl ),
inference(split_clause,[status(thm)],[f10947,f10731,f10734,f10737,f10748]) ).
fof(f10962,plain,
$false,
inference(sat_refutation,[status(thm)],[f447,f483,f537,f10164,f10751,f10797,f10799,f10801,f10803,f10805,f10808,f10921,f10961]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC340-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 08:17:20 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 14.34/2.43 % Refutation found
% 14.34/2.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 14.34/2.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.65/2.46 % Elapsed time: 2.095545 seconds
% 4.65/2.46 % CPU time: 16.261469 seconds
% 4.65/2.46 % Total memory used: 231.188 MB
% 4.65/2.46 % Net memory used: 218.903 MB
%------------------------------------------------------------------------------