%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC010-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 02:39:34 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 18
% Syntax : Number of formulae : 52 ( 6 unt; 9 def)
% Number of atoms : 129 ( 28 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 148 ( 71 ~; 68 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f201,negated_conjecture,
! [A,B,C] :
( ~ neq(sk4,nil)
| app(B,C) != sk1
| app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f202,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f203,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f204,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f205,negated_conjecture,
( ~ neq(sk4,nil)
| app(app(sk6,cons(sk5,nil)),sk7) = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f206,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,sk7) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f442,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f443,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f444,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f455,plain,
( ~ neq(sk4,nil)
| ! [B,C] :
( app(B,C) != sk1
| ! [A] :
( app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ) ) ),
inference(miniscoping,[status(thm)],[f201]) ).
fof(f456,plain,
! [X0,X1,X2] :
( ~ neq(sk4,nil)
| app(X1,X2) != sk1
| app(app(X1,cons(X0,nil)),X2) != sk2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f455]) ).
fof(f457,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f458,plain,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f459,plain,
( ~ neq(sk4,nil)
| ssList(sk7) ),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f460,plain,
( ~ neq(sk4,nil)
| app(app(sk6,cons(sk5,nil)),sk7) = sk4 ),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f461,plain,
( ~ neq(sk4,nil)
| app(sk6,sk7) = sk3 ),
inference(cnf_transformation,[status(thm)],[f206]) ).
fof(f471,definition,
( sQ2_spl
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f472,plain,
( ~ sQ2_spl
| neq(sk2,nil) ),
inference(component_clause,[status(thm)],[f471]) ).
fof(f474,plain,
sQ2_spl,
inference(split_clause,[status(thm)],[f444,f471]) ).
fof(f475,definition,
( sQ3_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f477,plain,
( sQ3_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f475]) ).
fof(f479,definition,
! [X0,X1,X2] :
( sQ4_spl
<=> ( app(X1,X2) != sk1
| app(app(X1,cons(X0,nil)),X2) != sk2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f480,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| app(X1,X2) != sk1
| app(app(X1,cons(X0,nil)),X2) != sk2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f479]) ).
fof(f483,definition,
( sQ5_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f487,definition,
( sQ6_spl
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f491,definition,
( sQ7_spl
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f495,definition,
( sQ8_spl
<=> app(app(sk6,cons(sk5,nil)),sk7) = sk4 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f496,plain,
( ~ sQ8_spl
| app(app(sk6,cons(sk5,nil)),sk7) = sk4 ),
inference(component_clause,[status(thm)],[f495]) ).
fof(f499,definition,
( sQ9_spl
<=> app(sk6,sk7) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f500,plain,
( ~ sQ9_spl
| app(sk6,sk7) = sk3 ),
inference(component_clause,[status(thm)],[f499]) ).
fof(f507,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f456,f479,f475]) ).
fof(f508,plain,
( ~ sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f457,f483,f475]) ).
fof(f509,plain,
( ~ sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f458,f487,f475]) ).
fof(f510,plain,
( ~ sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f459,f491,f475]) ).
fof(f511,plain,
( ~ sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f460,f495,f475]) ).
fof(f512,plain,
( ~ sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f461,f499,f475]) ).
fof(f526,plain,
( sQ3_spl
| ~ neq(sk2,nil) ),
inference(forward_demodulation,[status(thm)],[f442,f477]) ).
fof(f527,plain,
( sQ3_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f526,f472]) ).
fof(f528,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f527]) ).
fof(f529,plain,
( ~ sQ8_spl
| app(app(sk6,cons(sk5,nil)),sk7) = sk2 ),
inference(forward_demodulation,[status(thm)],[f442,f496]) ).
fof(f530,plain,
( ~ sQ9_spl
| app(sk6,sk7) = sk1 ),
inference(forward_demodulation,[status(thm)],[f443,f500]) ).
fof(f538,plain,
( ~ sQ4_spl
| ~ sQ8_spl
| app(sk6,sk7) != sk1
| ~ ssList(sk7)
| ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f529,f480]) ).
fof(f541,definition,
( sQ12_spl
<=> app(sk6,sk7) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f543,plain,
( sQ12_spl
| app(sk6,sk7) != sk1 ),
inference(component_clause,[status(thm)],[f541]) ).
fof(f544,plain,
( ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f538,f483,f487,f491,f541,f495,f479]) ).
fof(f556,plain,
( sQ12_spl
| ~ sQ9_spl
| sk1 != sk1 ),
inference(forward_demodulation,[status(thm)],[f530,f543]) ).
fof(f557,plain,
( sQ12_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f556]) ).
fof(f558,plain,
( sQ12_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f557]) ).
fof(f559,plain,
$false,
inference(sat_refutation,[status(thm)],[f474,f507,f508,f509,f510,f511,f512,f528,f544,f558]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC010-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 07:49:23 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.37 % Refutation found
% 0.12/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.048160 seconds
% 0.12/0.40 % CPU time: 0.147389 seconds
% 0.12/0.40 % Total memory used: 108.911 MB
% 0.12/0.40 % Net memory used: 108.757 MB
%------------------------------------------------------------------------------