%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC039-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 02:39:42 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.63s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 26
% Syntax : Number of formulae : 75 ( 14 unt; 11 def)
% Number of atoms : 173 ( 54 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 177 ( 79 ~; 87 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 12 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
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(f99,axiom,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f118,axiom,
! [U,V] :
( nil = U
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f119,axiom,
! [U,V] :
( nil = V
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f190,negated_conjecture,
nil = sk2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
nil != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
( nil = sk3
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f202,negated_conjecture,
( nil = sk3
| ssList(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f203,negated_conjecture,
( nil = sk3
| ssList(sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f204,negated_conjecture,
( nil = sk3
| cons(sk5,nil) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f205,negated_conjecture,
( nil = sk3
| app(app(sk6,sk3),sk7) = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f215,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f293,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f294,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f308,plain,
! [V] :
( ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,V) != V ) ),
inference(miniscoping,[status(thm)],[f99]) ).
fof(f309,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != X1 ),
inference(cnf_transformation,[status(thm)],[f308]) ).
fof(f334,plain,
! [U] :
( nil = U
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f335,plain,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f334]) ).
fof(f336,plain,
! [V] :
( nil = V
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f337,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f336]) ).
fof(f442,plain,
nil = sk2,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f443,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f444,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f445,plain,
nil != sk1,
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f447,plain,
( nil = sk3
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f456,plain,
( nil = sk3
| ssList(sk6) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f457,plain,
( nil = sk3
| ssList(sk7) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f458,plain,
( nil = sk3
| cons(sk5,nil) = sk3 ),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f459,plain,
( nil = sk3
| app(app(sk6,sk3),sk7) = sk4 ),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f471,definition,
( sQ2_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f478,definition,
( sQ4_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f479,plain,
( ~ sQ4_spl
| nil = sk3 ),
inference(component_clause,[status(thm)],[f478]) ).
fof(f481,plain,
( sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f447,f471,f478]) ).
fof(f482,definition,
( sQ5_spl
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f486,definition,
( sQ6_spl
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f490,definition,
( sQ7_spl
<=> cons(sk5,nil) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f491,plain,
( ~ sQ7_spl
| cons(sk5,nil) = sk3 ),
inference(component_clause,[status(thm)],[f490]) ).
fof(f494,definition,
( sQ8_spl
<=> app(app(sk6,sk3),sk7) = sk4 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f495,plain,
( ~ sQ8_spl
| app(app(sk6,sk3),sk7) = sk4 ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f506,plain,
( sQ4_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f456,f482,f478]) ).
fof(f507,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f457,f486,f478]) ).
fof(f508,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f458,f490,f478]) ).
fof(f509,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f459,f494,f478]) ).
fof(f524,plain,
nil = sk4,
inference(forward_demodulation,[status(thm)],[f442,f443]) ).
fof(f526,plain,
( ~ sQ4_spl
| sk1 = nil ),
inference(backward_demodulation,[status(thm)],[f479,f444]) ).
fof(f527,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f526,f445]) ).
fof(f528,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f527]) ).
fof(f529,plain,
( ~ sQ8_spl
| app(app(sk6,sk3),sk7) = nil ),
inference(forward_demodulation,[status(thm)],[f524,f495]) ).
fof(f531,plain,
( ~ sQ7_spl
| cons(sk5,nil) = sk1 ),
inference(forward_demodulation,[status(thm)],[f444,f491]) ).
fof(f532,plain,
( ~ sQ7_spl
| ssList(sk1)
| ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f531,f294]) ).
fof(f533,definition,
( sQ11_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f535,plain,
( sQ11_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f533]) ).
fof(f536,definition,
( sQ12_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f539,plain,
( ~ sQ7_spl
| sQ12_spl
| ~ sQ11_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f532,f471,f533,f536,f490]) ).
fof(f540,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f535,f215]) ).
fof(f541,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f540]) ).
fof(f542,plain,
( ~ sQ7_spl
| ~ ssList(nil)
| ~ ssItem(sk5)
| sk1 != nil ),
inference(paramodulation,[status(thm)],[f531,f309]) ).
fof(f543,definition,
( sQ13_spl
<=> sk1 = nil ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f546,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ2_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f542,f543,f471,f533,f490]) ).
fof(f549,plain,
( ~ sQ8_spl
| app(app(sk6,sk1),sk7) = nil ),
inference(forward_demodulation,[status(thm)],[f444,f529]) ).
fof(f551,definition,
( sQ14_spl
<=> ssList(app(sk6,sk1)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f553,plain,
( sQ14_spl
| ~ ssList(app(sk6,sk1)) ),
inference(component_clause,[status(thm)],[f551]) ).
fof(f560,plain,
( ~ sQ8_spl
| nil = app(sk6,sk1)
| ~ ssList(app(sk6,sk1))
| ~ ssList(sk7) ),
inference(resolution,[status(thm)],[f335,f549]) ).
fof(f564,definition,
( sQ16_spl
<=> nil = app(sk6,sk1) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f565,plain,
( ~ sQ16_spl
| nil = app(sk6,sk1) ),
inference(component_clause,[status(thm)],[f564]) ).
fof(f567,plain,
( ~ sQ8_spl
| sQ16_spl
| ~ sQ14_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f560,f486,f551,f564,f494]) ).
fof(f585,plain,
( sQ14_spl
| ~ ssList(sk6)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f553,f293]) ).
fof(f586,plain,
( sQ14_spl
| ~ sQ5_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f585,f536,f482,f551]) ).
fof(f590,plain,
( ~ sQ16_spl
| nil = sk1
| ~ ssList(sk6)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f565,f337]) ).
fof(f595,plain,
( ~ sQ16_spl
| sQ13_spl
| ~ sQ5_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f590,f536,f482,f543,f564]) ).
fof(f603,plain,
$false,
inference(sat_refutation,[status(thm)],[f481,f506,f507,f508,f509,f528,f539,f541,f546,f567,f586,f595]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC039-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.58 % Computer : n001.cluster.edu
% 0.09/0.58 % Model : x86_64 x86_64
% 0.09/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.58 % Memory : 8046.5625MB
% 0.09/0.58 % OS : Linux 6.8.0-71-generic
% 0.09/0.58 % CPULimit : 300
% 0.09/0.58 % WCLimit : 300
% 0.09/0.58 % DateTime : Mon Sep 21 07:56:16 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.60 % Drodi V4.1.1
% 0.14/0.63 % Refutation found
% 0.14/0.63 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.66 % Elapsed time: 0.064308 seconds
% 0.14/0.66 % CPU time: 0.178741 seconds
% 0.14/0.66 % Total memory used: 109.477 MB
% 0.14/0.66 % Net memory used: 109.335 MB
%------------------------------------------------------------------------------