%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC264-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 02:40:34 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.91s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 26
% Syntax : Number of formulae : 85 ( 28 unt; 11 def)
% Number of atoms : 230 ( 10 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 273 ( 128 ~; 134 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 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 : 74 ( 74 !; 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(f85,axiom,
! [U,V] :
( ssList(app(V,U))
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [U,V] :
( ssList(cons(U,V))
| ~ ssList(V)
| ~ ssItem(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(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
strictorderedP(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
~ totalorderedP(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f220,plain,
! [X0] : ssList(skaf68(X0)),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f221,plain,
! [X0] : ssList(skaf67(X0)),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f222,plain,
! [X0] : ssList(skaf66(X0)),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f223,plain,
! [X0] : ssItem(skaf65(X0)),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f224,plain,
! [X0] : ssItem(skaf64(X0)),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f279,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f280,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f285,plain,
! [X0] :
( totalorderedP(X0)
| ~ ssList(X0)
| ~ leq(skaf64(X0),skaf65(X0)) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f299,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f388,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(f414,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(f415,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)],[f414]) ).
fof(f424,plain,
ssList(sk1),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f429,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f430,plain,
strictorderedP(sk3),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f431,plain,
~ totalorderedP(sk1),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f463,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)],[f415]) ).
fof(f470,plain,
strictorderedP(sk1),
inference(forward_demodulation,[status(thm)],[f429,f430]) ).
fof(f573,plain,
! [X0,X1,X2,X3,X4] :
( lt(X3,X0)
| ~ strictorderedP(app(app(X2,cons(X3,X4)),cons(X0,X1)))
| ~ ssItem(X3)
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ ssList(X1)
| ~ ssList(app(X2,cons(X3,X4)))
| ~ ssList(cons(X0,X1)) ),
inference(resolution,[status(thm)],[f279,f463]) ).
fof(f597,definition,
( sQ10_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f599,plain,
( sQ10_spl
| ~ ssList(sk1) ),
inference(component_clause,[status(thm)],[f597]) ).
fof(f615,plain,
! [X0,X1,X2,X3,X4] :
( lt(X1,X4)
| ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(X4,X3)))
| ~ ssItem(X1)
| ~ ssItem(X4)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[f573,f280]) ).
fof(f616,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssList(X2)
| ~ ssList(cons(X4,X1))
| lt(X4,X3)
| ~ strictorderedP(app(app(X2,cons(X4,X1)),cons(X3,X0)))
| ~ ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f615,f279]) ).
fof(f617,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssList(cons(X4,X1))
| lt(X4,X3)
| ~ strictorderedP(app(app(X2,cons(X4,X1)),cons(X3,X0)))
| ~ ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f616]) ).
fof(f618,plain,
! [X0,X1,X2,X3,X4] :
( lt(X4,X3)
| ~ strictorderedP(app(app(X2,cons(X4,X1)),cons(X3,X0)))
| ~ ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f617,f280]) ).
fof(f1056,definition,
( sQ48_spl
<=> strictorderedP(sk1) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f1058,plain,
( sQ48_spl
| ~ strictorderedP(sk1) ),
inference(component_clause,[status(thm)],[f1056]) ).
fof(f1069,definition,
( sQ52_spl
<=> totalorderedP(sk1) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f1070,plain,
( ~ sQ52_spl
| totalorderedP(sk1) ),
inference(component_clause,[status(thm)],[f1069]) ).
fof(f1105,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f599,f424]) ).
fof(f1106,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f1105]) ).
fof(f1793,plain,
( ~ sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1070,f431]) ).
fof(f1794,plain,
~ sQ52_spl,
inference(contradiction_clause,[status(thm)],[f1793]) ).
fof(f2944,plain,
( sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1058,f470]) ).
fof(f2945,plain,
sQ48_spl,
inference(contradiction_clause,[status(thm)],[f2944]) ).
fof(f4359,plain,
( app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))) = sk1
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f388,f431]) ).
fof(f4369,definition,
( sQ408_spl
<=> app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ408_spl])],[split_symbol_definition]) ).
fof(f4370,plain,
( ~ sQ408_spl
| app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))) = sk1 ),
inference(component_clause,[status(thm)],[f4369]) ).
fof(f4372,plain,
( sQ408_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f4359,f597,f4369]) ).
fof(f4383,plain,
( ~ sQ408_spl
| lt(skaf64(sk1),skaf65(sk1))
| ~ strictorderedP(sk1)
| ~ ssItem(skaf64(sk1))
| ~ ssItem(skaf65(sk1))
| ~ ssList(skaf66(sk1))
| ~ ssList(skaf67(sk1))
| ~ ssList(skaf68(sk1)) ),
inference(paramodulation,[status(thm)],[f4370,f618]) ).
fof(f4399,definition,
( sQ409_spl
<=> ssList(skaf68(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ409_spl])],[split_symbol_definition]) ).
fof(f4401,plain,
( sQ409_spl
| ~ ssList(skaf68(sk1)) ),
inference(component_clause,[status(thm)],[f4399]) ).
fof(f4402,definition,
( sQ410_spl
<=> ssList(skaf67(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ410_spl])],[split_symbol_definition]) ).
fof(f4404,plain,
( sQ410_spl
| ~ ssList(skaf67(sk1)) ),
inference(component_clause,[status(thm)],[f4402]) ).
fof(f4405,definition,
( sQ411_spl
<=> ssList(skaf66(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ411_spl])],[split_symbol_definition]) ).
fof(f4407,plain,
( sQ411_spl
| ~ ssList(skaf66(sk1)) ),
inference(component_clause,[status(thm)],[f4405]) ).
fof(f4408,definition,
( sQ412_spl
<=> ssItem(skaf65(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ412_spl])],[split_symbol_definition]) ).
fof(f4410,plain,
( sQ412_spl
| ~ ssItem(skaf65(sk1)) ),
inference(component_clause,[status(thm)],[f4408]) ).
fof(f4411,definition,
( sQ413_spl
<=> ssItem(skaf64(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ413_spl])],[split_symbol_definition]) ).
fof(f4413,plain,
( sQ413_spl
| ~ ssItem(skaf64(sk1)) ),
inference(component_clause,[status(thm)],[f4411]) ).
fof(f4414,definition,
( sQ414_spl
<=> lt(skaf64(sk1),skaf65(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ414_spl])],[split_symbol_definition]) ).
fof(f4415,plain,
( ~ sQ414_spl
| lt(skaf64(sk1),skaf65(sk1)) ),
inference(component_clause,[status(thm)],[f4414]) ).
fof(f4437,plain,
( ~ sQ408_spl
| sQ414_spl
| ~ sQ48_spl
| ~ sQ413_spl
| ~ sQ412_spl
| ~ sQ411_spl
| ~ sQ410_spl
| ~ sQ409_spl ),
inference(split_clause,[status(thm)],[f4383,f4399,f4402,f4405,f4408,f4411,f1056,f4414,f4369]) ).
fof(f4441,definition,
( sQ421_spl
<=> leq(skaf64(sk1),skaf65(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ421_spl])],[split_symbol_definition]) ).
fof(f4442,plain,
( ~ sQ421_spl
| leq(skaf64(sk1),skaf65(sk1)) ),
inference(component_clause,[status(thm)],[f4441]) ).
fof(f4513,plain,
( sQ412_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4410,f223]) ).
fof(f4514,plain,
sQ412_spl,
inference(contradiction_clause,[status(thm)],[f4513]) ).
fof(f4515,plain,
( sQ409_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4401,f220]) ).
fof(f4516,plain,
sQ409_spl,
inference(contradiction_clause,[status(thm)],[f4515]) ).
fof(f4517,plain,
( sQ413_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4413,f224]) ).
fof(f4518,plain,
sQ413_spl,
inference(contradiction_clause,[status(thm)],[f4517]) ).
fof(f4519,plain,
( sQ411_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4407,f222]) ).
fof(f4520,plain,
sQ411_spl,
inference(contradiction_clause,[status(thm)],[f4519]) ).
fof(f4521,plain,
( sQ410_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4404,f221]) ).
fof(f4522,plain,
sQ410_spl,
inference(contradiction_clause,[status(thm)],[f4521]) ).
fof(f4527,plain,
( ~ sQ414_spl
| leq(skaf64(sk1),skaf65(sk1))
| ~ ssItem(skaf64(sk1))
| ~ ssItem(skaf65(sk1)) ),
inference(resolution,[status(thm)],[f4415,f299]) ).
fof(f4544,plain,
( ~ sQ414_spl
| sQ421_spl
| ~ sQ413_spl
| ~ sQ412_spl ),
inference(split_clause,[status(thm)],[f4527,f4408,f4411,f4441,f4414]) ).
fof(f4629,plain,
( ~ sQ421_spl
| totalorderedP(sk1)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f4442,f285]) ).
fof(f4632,plain,
( ~ sQ421_spl
| sQ52_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f4629,f597,f1069,f4441]) ).
fof(f4641,plain,
$false,
inference(sat_refutation,[status(thm)],[f1106,f1794,f2945,f4372,f4437,f4514,f4516,f4518,f4520,f4522,f4544,f4632]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC264-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.52 % Computer : n002.cluster.edu
% 0.09/0.52 % Model : x86_64 x86_64
% 0.09/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.52 % Memory : 8046.5625MB
% 0.09/0.52 % OS : Linux 6.8.0-71-generic
% 0.09/0.52 % CPULimit : 300
% 0.09/0.52 % WCLimit : 300
% 0.09/0.52 % DateTime : Mon Sep 21 08:13:03 UTC 2026
% 0.09/0.53 % CPUTime :
% 0.09/0.54 % Drodi V4.1.1
% 0.13/0.91 % Refutation found
% 0.13/0.91 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.93 % Elapsed time: 0.401504 seconds
% 0.13/0.93 % CPU time: 2.883514 seconds
% 0.13/0.93 % Total memory used: 157.171 MB
% 0.13/0.93 % Net memory used: 154.845 MB
%------------------------------------------------------------------------------