%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC407-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 02:41:07 PM UTC 2026
% Result : Unsatisfiable 0.17s 5.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 19
% Syntax : Number of formulae : 60 ( 18 unt; 8 def)
% Number of atoms : 133 ( 26 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 131 ( 58 ~; 65 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 16 ( 16 !; 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(f196,negated_conjecture,
( nil = sk3
| ssItem(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
( nil = sk3
| cons(sk6,nil) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f200,negated_conjecture,
( nil = sk3
| memberP(sk4,sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f208,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f271,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f391,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(f392,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)],[f391]) ).
fof(f435,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f436,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f437,plain,
ssItem(sk5),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f438,plain,
memberP(sk1,sk5),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f439,plain,
~ memberP(sk2,sk5),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f441,plain,
( nil = sk3
| ssItem(sk6) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f444,plain,
( nil = sk3
| cons(sk6,nil) = sk3 ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f445,plain,
( nil = sk3
| memberP(sk4,sk6) ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f453,definition,
( sQ2_spl
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f460,definition,
( sQ4_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f461,plain,
( ~ sQ4_spl
| nil = sk3 ),
inference(component_clause,[status(thm)],[f460]) ).
fof(f463,plain,
( sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f441,f453,f460]) ).
fof(f464,definition,
( sQ5_spl
<=> cons(sk6,nil) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( ~ sQ5_spl
| cons(sk6,nil) = sk3 ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f468,definition,
( sQ6_spl
<=> memberP(sk4,sk6) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f469,plain,
( ~ sQ6_spl
| memberP(sk4,sk6) ),
inference(component_clause,[status(thm)],[f468]) ).
fof(f472,plain,
( sQ4_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f444,f464,f460]) ).
fof(f473,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f445,f468,f460]) ).
fof(f511,plain,
~ memberP(sk4,sk5),
inference(forward_demodulation,[status(thm)],[f435,f439]) ).
fof(f514,plain,
memberP(sk3,sk5),
inference(forward_demodulation,[status(thm)],[f436,f438]) ).
fof(f516,definition,
( sQ7_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f518,plain,
( sQ7_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f516]) ).
fof(f523,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f518,f208]) ).
fof(f524,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f523]) ).
fof(f535,plain,
! [X0] :
( ~ sQ4_spl
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ),
inference(backward_demodulation,[status(thm)],[f461,f271]) ).
fof(f539,plain,
( ~ sQ4_spl
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f535,f514]) ).
fof(f540,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f539,f437]) ).
fof(f541,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f540]) ).
fof(f560,plain,
! [X0] :
( ~ sQ5_spl
| X0 = sk6
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ~ memberP(sk3,X0) ),
inference(paramodulation,[status(thm)],[f465,f392]) ).
fof(f561,definition,
! [X0] :
( sQ11_spl
<=> ( X0 = sk6
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f562,plain,
! [X0] :
( ~ sQ11_spl
| X0 = sk6
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ),
inference(component_clause,[status(thm)],[f561]) ).
fof(f564,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f560,f561,f516,f453,f464]) ).
fof(f565,plain,
! [X0] :
( ~ sQ11_spl
| X0 = sk6
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f562,f271]) ).
fof(f567,plain,
( ~ sQ11_spl
| sk5 = sk6
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f565,f514]) ).
fof(f572,definition,
( sQ13_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f574,plain,
( sQ13_spl
| ~ ssItem(sk5) ),
inference(component_clause,[status(thm)],[f572]) ).
fof(f575,definition,
( sQ14_spl
<=> sk5 = sk6 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f576,plain,
( ~ sQ14_spl
| sk5 = sk6 ),
inference(component_clause,[status(thm)],[f575]) ).
fof(f578,plain,
( ~ sQ11_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f567,f572,f575,f561]) ).
fof(f579,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f574,f437]) ).
fof(f580,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f579]) ).
fof(f582,plain,
( ~ sQ14_spl
| ~ memberP(sk4,sk6) ),
inference(backward_demodulation,[status(thm)],[f576,f511]) ).
fof(f584,plain,
( ~ sQ14_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f582,f469]) ).
fof(f585,plain,
( ~ sQ14_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f584]) ).
fof(f586,plain,
$false,
inference(sat_refutation,[status(thm)],[f463,f472,f473,f524,f541,f564,f578,f580,f585]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC407-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/5.42 % Computer : n005.cluster.edu
% 0.17/5.42 % Model : x86_64 x86_64
% 0.17/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.42 % Memory : 8046.5625MB
% 0.17/5.42 % OS : Linux 6.8.0-71-generic
% 0.17/5.42 % CPULimit : 300
% 0.17/5.42 % WCLimit : 300
% 0.17/5.42 % DateTime : Mon Sep 21 08:22:08 UTC 2026
% 0.17/5.42 % CPUTime :
% 0.17/5.45 % Drodi V4.1.1
% 0.17/5.47 % Refutation found
% 0.17/5.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/5.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/5.58 % Elapsed time: 0.148294 seconds
% 0.22/5.58 % CPU time: 0.137468 seconds
% 0.22/5.58 % Total memory used: 10.373 MB
% 0.22/5.58 % Net memory used: 10.368 MB
%------------------------------------------------------------------------------