%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC272-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 02:40:35 PM UTC 2026
% Result : Unsatisfiable 67.05s 12.07s
% Output : CNFRefutation 67.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 28
% Syntax : Number of formulae : 91 ( 31 unt; 12 def)
% Number of atoms : 212 ( 13 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 224 ( 103 ~; 109 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 13 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 51 ( 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f73,axiom,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [U,V] :
( ssList(app(V,U))
| ~ ssList(V)
| ~ ssList(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(f188,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
strictorderedP(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
~ totalorderedP(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f205,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f224,plain,
! [X0] : ssList(skaf68(X0)),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f225,plain,
! [X0] : ssList(skaf67(X0)),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f226,plain,
! [X0] : ssList(skaf66(X0)),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f227,plain,
! [X0] : ssItem(skaf65(X0)),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f228,plain,
! [X0] : ssItem(skaf64(X0)),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f271,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f283,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f289,plain,
! [X0] :
( totalorderedP(X0)
| ~ ssList(X0)
| ~ leq(skaf64(X0),skaf65(X0)) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f303,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f392,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(f418,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(f419,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)],[f418]) ).
fof(f430,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f433,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f436,plain,
strictorderedP(sk3),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f439,plain,
~ totalorderedP(sk1),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f479,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)],[f419]) ).
fof(f486,plain,
~ totalorderedP(sk3),
inference(forward_demodulation,[status(thm)],[f433,f439]) ).
fof(f522,plain,
! [X0] :
( ssList(app(sk3,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f283,f430]) ).
fof(f828,plain,
app(sk3,nil) = sk3,
inference(resolution,[status(thm)],[f271,f430]) ).
fof(f832,definition,
( sQ8_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f834,plain,
( sQ8_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f832]) ).
fof(f844,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f834,f205]) ).
fof(f845,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f844]) ).
fof(f1011,plain,
( ssList(sk3)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f828,f522]) ).
fof(f1020,definition,
( sQ21_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f1023,plain,
( sQ21_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1011,f832,f1020]) ).
fof(f1742,plain,
! [X0] :
( ~ ssItem(skaf64(X0))
| ~ ssItem(skaf65(X0))
| ~ lt(skaf64(X0),skaf65(X0))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f289,f303]) ).
fof(f1743,plain,
! [X0] :
( ~ ssItem(skaf64(X0))
| ~ lt(skaf64(X0),skaf65(X0))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1742,f227]) ).
fof(f3864,plain,
( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3
| ~ ssList(sk3) ),
inference(resolution,[status(thm)],[f392,f486]) ).
fof(f3865,definition,
( sQ96_spl
<=> app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f3866,plain,
( ~ sQ96_spl
| app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3 ),
inference(component_clause,[status(thm)],[f3865]) ).
fof(f3868,plain,
( sQ96_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3864,f1020,f3865]) ).
fof(f5485,definition,
( sQ199_spl
<=> strictorderedP(sk3) ),
introduced(definition,[new_symbols(definition,[sQ199_spl])],[split_symbol_definition]) ).
fof(f5487,plain,
( sQ199_spl
| ~ strictorderedP(sk3) ),
inference(component_clause,[status(thm)],[f5485]) ).
fof(f8374,definition,
( sQ367_spl
<=> totalorderedP(sk3) ),
introduced(definition,[new_symbols(definition,[sQ367_spl])],[split_symbol_definition]) ).
fof(f8375,plain,
( ~ sQ367_spl
| totalorderedP(sk3) ),
inference(component_clause,[status(thm)],[f8374]) ).
fof(f8467,plain,
( sQ199_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5487,f436]) ).
fof(f8468,plain,
sQ199_spl,
inference(contradiction_clause,[status(thm)],[f8467]) ).
fof(f10156,plain,
( ~ sQ367_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8375,f486]) ).
fof(f10157,plain,
~ sQ367_spl,
inference(contradiction_clause,[status(thm)],[f10156]) ).
fof(f27159,plain,
( ~ sQ96_spl
| lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))))
| ~ strictorderedP(sk3)
| ~ ssItem(skaf64(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf66(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssList(skaf68(sk3)) ),
inference(paramodulation,[status(thm)],[f3866,f479]) ).
fof(f27169,definition,
( sQ1033_spl
<=> ssList(skaf68(sk3)) ),
introduced(definition,[new_symbols(definition,[sQ1033_spl])],[split_symbol_definition]) ).
fof(f27171,plain,
( sQ1033_spl
| ~ ssList(skaf68(sk3)) ),
inference(component_clause,[status(thm)],[f27169]) ).
fof(f27172,definition,
( sQ1034_spl
<=> ssList(skaf67(sk3)) ),
introduced(definition,[new_symbols(definition,[sQ1034_spl])],[split_symbol_definition]) ).
fof(f27174,plain,
( sQ1034_spl
| ~ ssList(skaf67(sk3)) ),
inference(component_clause,[status(thm)],[f27172]) ).
fof(f27175,definition,
( sQ1035_spl
<=> ssList(skaf66(sk3)) ),
introduced(definition,[new_symbols(definition,[sQ1035_spl])],[split_symbol_definition]) ).
fof(f27177,plain,
( sQ1035_spl
| ~ ssList(skaf66(sk3)) ),
inference(component_clause,[status(thm)],[f27175]) ).
fof(f27178,definition,
( sQ1036_spl
<=> ssItem(skaf65(sk3)) ),
introduced(definition,[new_symbols(definition,[sQ1036_spl])],[split_symbol_definition]) ).
fof(f27180,plain,
( sQ1036_spl
| ~ ssItem(skaf65(sk3)) ),
inference(component_clause,[status(thm)],[f27178]) ).
fof(f27181,definition,
( sQ1037_spl
<=> ssItem(skaf64(sk3)) ),
introduced(definition,[new_symbols(definition,[sQ1037_spl])],[split_symbol_definition]) ).
fof(f27183,plain,
( sQ1037_spl
| ~ ssItem(skaf64(sk3)) ),
inference(component_clause,[status(thm)],[f27181]) ).
fof(f27184,definition,
( sQ1038_spl
<=> ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ),
introduced(definition,[new_symbols(definition,[sQ1038_spl])],[split_symbol_definition]) ).
fof(f27186,plain,
( sQ1038_spl
| ~ ssList(app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))) ),
inference(component_clause,[status(thm)],[f27184]) ).
fof(f27187,definition,
( sQ1039_spl
<=> lt(skaf64(sk3),skaf65(sk3)) ),
introduced(definition,[new_symbols(definition,[sQ1039_spl])],[split_symbol_definition]) ).
fof(f27188,plain,
( ~ sQ1039_spl
| lt(skaf64(sk3),skaf65(sk3)) ),
inference(component_clause,[status(thm)],[f27187]) ).
fof(f27194,plain,
( ~ sQ96_spl
| sQ1039_spl
| ~ sQ1038_spl
| ~ sQ199_spl
| ~ sQ1037_spl
| ~ sQ1036_spl
| ~ sQ1035_spl
| ~ sQ1034_spl
| ~ sQ1033_spl ),
inference(split_clause,[status(thm)],[f27159,f27169,f27172,f27175,f27178,f27181,f5485,f27184,f27187,f3865]) ).
fof(f27243,plain,
( sQ1036_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f27180,f227]) ).
fof(f27244,plain,
sQ1036_spl,
inference(contradiction_clause,[status(thm)],[f27243]) ).
fof(f27245,plain,
( sQ1033_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f27171,f224]) ).
fof(f27246,plain,
sQ1033_spl,
inference(contradiction_clause,[status(thm)],[f27245]) ).
fof(f27247,plain,
( sQ1038_spl
| ~ sQ96_spl
| ~ ssList(sk3) ),
inference(forward_demodulation,[status(thm)],[f3866,f27186]) ).
fof(f27248,plain,
( sQ1038_spl
| ~ sQ96_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f27247,f430]) ).
fof(f27249,plain,
( sQ1038_spl
| ~ sQ96_spl ),
inference(contradiction_clause,[status(thm)],[f27248]) ).
fof(f27250,plain,
( sQ1035_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f27177,f226]) ).
fof(f27251,plain,
sQ1035_spl,
inference(contradiction_clause,[status(thm)],[f27250]) ).
fof(f28172,plain,
( sQ1037_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f27183,f228]) ).
fof(f28173,plain,
sQ1037_spl,
inference(contradiction_clause,[status(thm)],[f28172]) ).
fof(f28174,plain,
( sQ1034_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f27174,f225]) ).
fof(f28175,plain,
sQ1034_spl,
inference(contradiction_clause,[status(thm)],[f28174]) ).
fof(f34979,plain,
! [X0] :
( ~ lt(skaf64(X0),skaf65(X0))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1743,f228]) ).
fof(f34980,plain,
( ~ sQ1039_spl
| totalorderedP(sk3)
| ~ ssList(sk3) ),
inference(resolution,[status(thm)],[f34979,f27188]) ).
fof(f34981,plain,
( ~ sQ1039_spl
| sQ367_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f34980,f1020,f8374,f27187]) ).
fof(f34982,plain,
$false,
inference(sat_refutation,[status(thm)],[f845,f1023,f3868,f8468,f10157,f27194,f27244,f27246,f27249,f27251,f28173,f28175,f34981]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC272-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/3.43 % Computer : n002.cluster.edu
% 0.10/3.43 % Model : x86_64 x86_64
% 0.10/3.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/3.43 % Memory : 8046.5625MB
% 0.10/3.43 % OS : Linux 6.8.0-71-generic
% 0.10/3.44 % CPULimit : 300
% 0.10/3.44 % WCLimit : 300
% 0.10/3.44 % DateTime : Mon Sep 21 08:13:21 UTC 2026
% 0.10/3.44 % CPUTime :
% 0.10/3.45 % Drodi V4.1.1
% 67.05/12.07 % Refutation found
% 67.05/12.07 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 67.05/12.07 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 67.05/12.16 % Elapsed time: 8.691768 seconds
% 67.05/12.16 % CPU time: 68.463477 seconds
% 67.05/12.16 % Total memory used: 432.067 MB
% 67.05/12.16 % Net memory used: 401.286 MB
%------------------------------------------------------------------------------