%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC273-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 02:40:36 PM UTC 2026
% Result : Unsatisfiable 22.03s 3.42s
% Output : CNFRefutation 23.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 24
% Syntax : Number of formulae : 77 ( 27 unt; 11 def)
% Number of atoms : 184 ( 10 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 197 ( 90 ~; 96 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 19 ( 17 usr; 12 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27,axiom,
! [U] : ssList(skaf68(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] : ssList(skaf67(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [U] : ssList(skaf66(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [U] : ssItem(skaf65(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [U] : ssItem(skaf64(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f91,axiom,
! [U] :
( totalorderedP(U)
| ~ ssList(U)
| ~ leq(skaf64(U),skaf65(U)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f103,axiom,
! [U,V] :
( leq(U,V)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f186,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
strictorderedP(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
~ totalorderedP(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f222,plain,
! [X0] : ssList(skaf68(X0)),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f223,plain,
! [X0] : ssList(skaf67(X0)),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f224,plain,
! [X0] : ssList(skaf66(X0)),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f225,plain,
! [X0] : ssItem(skaf65(X0)),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f226,plain,
! [X0] : ssItem(skaf64(X0)),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f287,plain,
! [X0] :
( totalorderedP(X0)
| ~ ssList(X0)
| ~ leq(skaf64(X0),skaf65(X0)) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f301,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f390,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(f416,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(f417,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)],[f416]) ).
fof(f426,plain,
ssList(sk1),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f431,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f433,plain,
strictorderedP(sk3),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f435,plain,
~ totalorderedP(sk1),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f467,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)],[f417]) ).
fof(f474,plain,
strictorderedP(sk1),
inference(forward_demodulation,[status(thm)],[f431,f433]) ).
fof(f498,definition,
( sQ5_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f500,plain,
( sQ5_spl
| ~ ssList(sk1) ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f535,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f500,f426]) ).
fof(f536,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f535]) ).
fof(f4432,definition,
( sQ568_spl
<=> totalorderedP(sk1) ),
introduced(definition,[new_symbols(definition,[sQ568_spl])],[split_symbol_definition]) ).
fof(f4433,plain,
( ~ sQ568_spl
| totalorderedP(sk1) ),
inference(component_clause,[status(thm)],[f4432]) ).
fof(f4543,plain,
( ~ sQ568_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4433,f435]) ).
fof(f4544,plain,
~ sQ568_spl,
inference(contradiction_clause,[status(thm)],[f4543]) ).
fof(f7339,plain,
( app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))) = sk1
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f390,f435]) ).
fof(f7343,definition,
( sQ768_spl
<=> app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ768_spl])],[split_symbol_definition]) ).
fof(f7344,plain,
( ~ sQ768_spl
| app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))) = sk1 ),
inference(component_clause,[status(thm)],[f7343]) ).
fof(f7346,plain,
( sQ768_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f7339,f498,f7343]) ).
fof(f7411,plain,
( ~ sQ768_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)],[f7344,f467]) ).
fof(f7424,definition,
( sQ773_spl
<=> ssList(skaf68(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ773_spl])],[split_symbol_definition]) ).
fof(f7426,plain,
( sQ773_spl
| ~ ssList(skaf68(sk1)) ),
inference(component_clause,[status(thm)],[f7424]) ).
fof(f7427,definition,
( sQ774_spl
<=> ssList(skaf67(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ774_spl])],[split_symbol_definition]) ).
fof(f7429,plain,
( sQ774_spl
| ~ ssList(skaf67(sk1)) ),
inference(component_clause,[status(thm)],[f7427]) ).
fof(f7430,definition,
( sQ775_spl
<=> ssList(skaf66(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ775_spl])],[split_symbol_definition]) ).
fof(f7432,plain,
( sQ775_spl
| ~ ssList(skaf66(sk1)) ),
inference(component_clause,[status(thm)],[f7430]) ).
fof(f7433,definition,
( sQ776_spl
<=> ssItem(skaf65(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ776_spl])],[split_symbol_definition]) ).
fof(f7435,plain,
( sQ776_spl
| ~ ssItem(skaf65(sk1)) ),
inference(component_clause,[status(thm)],[f7433]) ).
fof(f7436,definition,
( sQ777_spl
<=> ssItem(skaf64(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ777_spl])],[split_symbol_definition]) ).
fof(f7438,plain,
( sQ777_spl
| ~ ssItem(skaf64(sk1)) ),
inference(component_clause,[status(thm)],[f7436]) ).
fof(f7439,definition,
( sQ778_spl
<=> lt(skaf64(sk1),skaf65(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ778_spl])],[split_symbol_definition]) ).
fof(f7440,plain,
( ~ sQ778_spl
| lt(skaf64(sk1),skaf65(sk1)) ),
inference(component_clause,[status(thm)],[f7439]) ).
fof(f7443,definition,
( sQ779_spl
<=> leq(skaf64(sk1),skaf65(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ779_spl])],[split_symbol_definition]) ).
fof(f7444,plain,
( ~ sQ779_spl
| leq(skaf64(sk1),skaf65(sk1)) ),
inference(component_clause,[status(thm)],[f7443]) ).
fof(f7451,definition,
( sQ781_spl
<=> strictorderedP(app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1)))) ),
introduced(definition,[new_symbols(definition,[sQ781_spl])],[split_symbol_definition]) ).
fof(f7453,plain,
( sQ781_spl
| ~ strictorderedP(app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1)))) ),
inference(component_clause,[status(thm)],[f7451]) ).
fof(f7454,plain,
( ~ sQ768_spl
| sQ778_spl
| ~ sQ5_spl
| ~ sQ781_spl
| ~ sQ777_spl
| ~ sQ776_spl
| ~ sQ775_spl
| ~ sQ774_spl
| ~ sQ773_spl ),
inference(split_clause,[status(thm)],[f7411,f7424,f7427,f7430,f7433,f7436,f7451,f498,f7439,f7343]) ).
fof(f7497,plain,
( sQ776_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7435,f225]) ).
fof(f7498,plain,
sQ776_spl,
inference(contradiction_clause,[status(thm)],[f7497]) ).
fof(f7499,plain,
( sQ773_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7426,f222]) ).
fof(f7500,plain,
sQ773_spl,
inference(contradiction_clause,[status(thm)],[f7499]) ).
fof(f7501,plain,
( sQ775_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7432,f224]) ).
fof(f7502,plain,
sQ775_spl,
inference(contradiction_clause,[status(thm)],[f7501]) ).
fof(f7503,plain,
( sQ777_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7438,f226]) ).
fof(f7504,plain,
sQ777_spl,
inference(contradiction_clause,[status(thm)],[f7503]) ).
fof(f7505,plain,
( sQ774_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7429,f223]) ).
fof(f7506,plain,
sQ774_spl,
inference(contradiction_clause,[status(thm)],[f7505]) ).
fof(f7507,plain,
( ~ sQ779_spl
| totalorderedP(sk1)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f7444,f287]) ).
fof(f7511,plain,
( ~ sQ779_spl
| sQ568_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f7507,f498,f4432,f7443]) ).
fof(f7529,plain,
( ~ sQ778_spl
| leq(skaf64(sk1),skaf65(sk1))
| ~ ssItem(skaf64(sk1))
| ~ ssItem(skaf65(sk1)) ),
inference(resolution,[status(thm)],[f7440,f301]) ).
fof(f7546,plain,
( ~ sQ778_spl
| sQ779_spl
| ~ sQ777_spl
| ~ sQ776_spl ),
inference(split_clause,[status(thm)],[f7529,f7433,f7436,f7443,f7439]) ).
fof(f7547,plain,
( sQ781_spl
| ~ sQ768_spl
| ~ strictorderedP(sk1) ),
inference(forward_demodulation,[status(thm)],[f7344,f7453]) ).
fof(f7548,plain,
( sQ781_spl
| ~ sQ768_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7547,f474]) ).
fof(f7549,plain,
( sQ781_spl
| ~ sQ768_spl ),
inference(contradiction_clause,[status(thm)],[f7548]) ).
fof(f7550,plain,
$false,
inference(sat_refutation,[status(thm)],[f536,f4544,f7346,f7454,f7498,f7500,f7502,f7504,f7506,f7511,f7546,f7549]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC273-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 08:08:52 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 22.03/3.42 % Refutation found
% 22.03/3.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 22.03/3.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 23.45/3.48 % Elapsed time: 3.092670 seconds
% 23.45/3.48 % CPU time: 23.953597 seconds
% 23.45/3.48 % Total memory used: 242.364 MB
% 23.45/3.48 % Net memory used: 231.771 MB
%------------------------------------------------------------------------------