%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC392-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 02:41:03 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 23
% Syntax : Number of formulae : 73 ( 15 unt; 9 def)
% Number of atoms : 163 ( 39 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 152 ( 62 ~; 81 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f71,axiom,
! [U] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f161,axiom,
! [U,V,W] :
( W = U
| memberP(V,W)
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(V)
| ~ memberP(cons(U,V),W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f190,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
memberP(sk1,sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
~ memberP(sk2,sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
( nil = sk4
| ssItem(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
( nil = sk3
| ssItem(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( nil = sk4
| cons(sk6,nil) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
( nil = sk4
| memberP(sk4,sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f200,negated_conjecture,
( nil = sk3
| cons(sk6,nil) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f201,negated_conjecture,
( nil = sk3
| memberP(sk4,sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f210,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f273,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f393,plain,
! [U,W] :
( W = U
| ! [V] :
( memberP(V,W)
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(V)
| ~ memberP(cons(U,V),W) ) ),
inference(miniscoping,[status(thm)],[f161]) ).
fof(f394,plain,
! [X0,X1,X2] :
( X2 = X0
| memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ memberP(cons(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f393]) ).
fof(f437,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f438,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f439,plain,
ssItem(sk5),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f440,plain,
memberP(sk1,sk5),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f441,plain,
~ memberP(sk2,sk5),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f442,plain,
( nil = sk4
| ssItem(sk6) ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f443,plain,
( nil = sk3
| ssItem(sk6) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f444,plain,
( nil = sk4
| cons(sk6,nil) = sk3 ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f445,plain,
( nil = sk4
| memberP(sk4,sk6) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f448,plain,
( nil = sk3
| cons(sk6,nil) = sk3 ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f449,plain,
( nil = sk3
| memberP(sk4,sk6) ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f459,definition,
( sQ2_spl
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f462,definition,
( sQ3_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f463,plain,
( ~ sQ3_spl
| nil = sk4 ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f442,f459,f462]) ).
fof(f466,definition,
( sQ4_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f467,plain,
( ~ sQ4_spl
| nil = sk3 ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f469,plain,
( sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f443,f459,f466]) ).
fof(f470,definition,
( sQ5_spl
<=> cons(sk6,nil) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( ~ sQ5_spl
| cons(sk6,nil) = sk3 ),
inference(component_clause,[status(thm)],[f470]) ).
fof(f473,plain,
( sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f444,f470,f462]) ).
fof(f474,definition,
( sQ6_spl
<=> memberP(sk4,sk6) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f475,plain,
( ~ sQ6_spl
| memberP(sk4,sk6) ),
inference(component_clause,[status(thm)],[f474]) ).
fof(f477,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f445,f474,f462]) ).
fof(f482,plain,
( sQ4_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f448,f470,f466]) ).
fof(f483,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f449,f474,f466]) ).
fof(f497,plain,
( ~ sQ4_spl
| sk1 = nil ),
inference(backward_demodulation,[status(thm)],[f467,f438]) ).
fof(f498,plain,
( ~ sQ3_spl
| sk2 = nil ),
inference(backward_demodulation,[status(thm)],[f463,f437]) ).
fof(f499,plain,
( ~ sQ4_spl
| memberP(nil,sk5) ),
inference(backward_demodulation,[status(thm)],[f497,f440]) ).
fof(f503,plain,
( ~ sQ3_spl
| ~ memberP(nil,sk5) ),
inference(forward_demodulation,[status(thm)],[f498,f441]) ).
fof(f504,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f499,f503]) ).
fof(f505,plain,
( ~ sQ4_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f504]) ).
fof(f507,plain,
( ~ sQ5_spl
| cons(sk6,nil) = sk1 ),
inference(forward_demodulation,[status(thm)],[f438,f471]) ).
fof(f516,definition,
( sQ9_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f518,plain,
( sQ9_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f516]) ).
fof(f533,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f518,f210]) ).
fof(f534,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f533]) ).
fof(f552,plain,
( ~ sQ6_spl
| memberP(sk2,sk6) ),
inference(forward_demodulation,[status(thm)],[f437,f475]) ).
fof(f555,plain,
! [X0] :
( ~ sQ5_spl
| X0 = sk6
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ~ memberP(sk1,X0) ),
inference(paramodulation,[status(thm)],[f507,f394]) ).
fof(f556,definition,
! [X0] :
( sQ13_spl
<=> ( X0 = sk6
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ memberP(sk1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f557,plain,
! [X0] :
( ~ sQ13_spl
| X0 = sk6
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ memberP(sk1,X0) ),
inference(component_clause,[status(thm)],[f556]) ).
fof(f559,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ9_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f555,f556,f516,f459,f470]) ).
fof(f560,plain,
! [X0] :
( ~ sQ13_spl
| X0 = sk6
| ~ ssItem(X0)
| ~ memberP(sk1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f557,f273]) ).
fof(f577,plain,
( ~ sQ13_spl
| sk5 = sk6
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f560,f440]) ).
fof(f582,definition,
( sQ18_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f584,plain,
( sQ18_spl
| ~ ssItem(sk5) ),
inference(component_clause,[status(thm)],[f582]) ).
fof(f585,definition,
( sQ19_spl
<=> sk5 = sk6 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f586,plain,
( ~ sQ19_spl
| sk5 = sk6 ),
inference(component_clause,[status(thm)],[f585]) ).
fof(f588,plain,
( ~ sQ13_spl
| sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f577,f582,f585,f556]) ).
fof(f589,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f584,f439]) ).
fof(f590,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f589]) ).
fof(f598,plain,
( ~ sQ6_spl
| ~ sQ19_spl
| memberP(sk2,sk5) ),
inference(backward_demodulation,[status(thm)],[f586,f552]) ).
fof(f603,plain,
( ~ sQ6_spl
| ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f598,f441]) ).
fof(f604,plain,
( ~ sQ6_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f603]) ).
fof(f605,plain,
$false,
inference(sat_refutation,[status(thm)],[f465,f469,f473,f477,f482,f483,f505,f534,f559,f588,f590,f604]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC392-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n017.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 08:16:12 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 0.15/0.40 % Refutation found
% 0.15/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.44 % Elapsed time: 0.055428 seconds
% 0.15/0.44 % CPU time: 0.163995 seconds
% 0.15/0.44 % Total memory used: 109.353 MB
% 0.15/0.44 % Net memory used: 109.211 MB
%------------------------------------------------------------------------------