%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC004-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 02:39:33 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.41s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 25
% Syntax : Number of formulae : 71 ( 9 unt; 12 def)
% Number of atoms : 196 ( 34 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 244 ( 119 ~; 113 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 13 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
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(f100,axiom,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f190,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f200,negated_conjecture,
! [A,B,C] :
( ~ neq(sk4,nil)
| ~ neq(B,nil)
| app(A,C) != sk1
| app(app(A,B),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f201,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f202,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f203,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f204,negated_conjecture,
( ~ neq(sk4,nil)
| app(app(sk6,cons(sk5,nil)),sk7) = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f205,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,sk7) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f213,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f292,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f306,plain,
! [V] :
( ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,V) != V ) ),
inference(miniscoping,[status(thm)],[f99]) ).
fof(f307,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != X1 ),
inference(cnf_transformation,[status(thm)],[f306]) ).
fof(f308,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f440,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f441,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f442,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f451,plain,
( ~ neq(sk4,nil)
| ! [B] :
( ~ neq(B,nil)
| ! [A,C] :
( app(A,C) != sk1
| app(app(A,B),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ) ) ),
inference(miniscoping,[status(thm)],[f200]) ).
fof(f452,plain,
! [X0,X1,X2] :
( ~ neq(sk4,nil)
| ~ neq(X1,nil)
| app(X0,X2) != sk1
| app(app(X0,X1),X2) != sk2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f451]) ).
fof(f453,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f454,plain,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f455,plain,
( ~ neq(sk4,nil)
| ssList(sk7) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f456,plain,
( ~ neq(sk4,nil)
| app(app(sk6,cons(sk5,nil)),sk7) = sk4 ),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f457,plain,
( ~ neq(sk4,nil)
| app(sk6,sk7) = sk3 ),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f465,definition,
( sQ2_spl
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( ~ sQ2_spl
| neq(sk2,nil) ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f468,plain,
sQ2_spl,
inference(split_clause,[status(thm)],[f442,f465]) ).
fof(f469,definition,
( sQ3_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( sQ3_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f469]) ).
fof(f473,definition,
! [X0,X1,X2] :
( sQ4_spl
<=> ( ~ neq(X1,nil)
| app(X0,X2) != sk1
| app(app(X0,X1),X2) != sk2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f474,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| ~ neq(X1,nil)
| app(X0,X2) != sk1
| app(app(X0,X1),X2) != sk2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f473]) ).
fof(f477,definition,
( sQ5_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f481,definition,
( sQ6_spl
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f485,definition,
( sQ7_spl
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f489,definition,
( sQ8_spl
<=> app(app(sk6,cons(sk5,nil)),sk7) = sk4 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f490,plain,
( ~ sQ8_spl
| app(app(sk6,cons(sk5,nil)),sk7) = sk4 ),
inference(component_clause,[status(thm)],[f489]) ).
fof(f493,definition,
( sQ9_spl
<=> app(sk6,sk7) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f497,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f452,f473,f469]) ).
fof(f498,plain,
( ~ sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f453,f477,f469]) ).
fof(f499,plain,
( ~ sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f454,f481,f469]) ).
fof(f500,plain,
( ~ sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f455,f485,f469]) ).
fof(f501,plain,
( ~ sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f456,f489,f469]) ).
fof(f502,plain,
( ~ sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f457,f493,f469]) ).
fof(f534,plain,
( ~ sQ2_spl
| neq(sk4,nil) ),
inference(forward_demodulation,[status(thm)],[f440,f466]) ).
fof(f535,plain,
( sQ3_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f471,f534]) ).
fof(f536,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f535]) ).
fof(f537,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| ~ neq(X1,nil)
| app(X0,X2) != sk1
| app(app(X0,X1),X2) != sk4
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f440,f474]) ).
fof(f538,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| ~ neq(X1,nil)
| app(X0,X2) != sk3
| app(app(X0,X1),X2) != sk4
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f441,f537]) ).
fof(f553,definition,
( sQ13_spl
<=> ssList(cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f555,plain,
( sQ13_spl
| ~ ssList(cons(sk5,nil)) ),
inference(component_clause,[status(thm)],[f553]) ).
fof(f557,plain,
( ~ sQ8_spl
| ~ sQ4_spl
| ~ neq(cons(sk5,nil),nil)
| app(sk6,sk7) != sk3
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6) ),
inference(resolution,[status(thm)],[f538,f490]) ).
fof(f561,definition,
( sQ14_spl
<=> neq(cons(sk5,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f563,plain,
( sQ14_spl
| ~ neq(cons(sk5,nil),nil) ),
inference(component_clause,[status(thm)],[f561]) ).
fof(f564,plain,
( ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ14_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f557,f481,f553,f485,f493,f561,f473,f489]) ).
fof(f582,plain,
( sQ13_spl
| ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f292,f555]) ).
fof(f583,definition,
( sQ19_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f585,plain,
( sQ19_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f583]) ).
fof(f586,plain,
( sQ13_spl
| ~ sQ19_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f582,f477,f583,f553]) ).
fof(f587,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f585,f213]) ).
fof(f588,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f587]) ).
fof(f589,plain,
( sQ14_spl
| cons(sk5,nil) = nil
| ~ ssList(cons(sk5,nil))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f308,f563]) ).
fof(f593,definition,
( sQ20_spl
<=> cons(sk5,nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f594,plain,
( ~ sQ20_spl
| cons(sk5,nil) = nil ),
inference(component_clause,[status(thm)],[f593]) ).
fof(f596,plain,
( sQ14_spl
| sQ20_spl
| ~ sQ13_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f589,f583,f553,f593,f561]) ).
fof(f633,plain,
( ~ sQ20_spl
| ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f594,f307]) ).
fof(f636,plain,
( ~ sQ20_spl
| ~ sQ19_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f633,f477,f583,f593]) ).
fof(f642,plain,
$false,
inference(sat_refutation,[status(thm)],[f468,f497,f498,f499,f500,f501,f502,f536,f564,f586,f588,f596,f636]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC004-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n006.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
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 07:48:12 UTC 2026
% 0.16/0.36 % CPUTime :
% 0.16/0.38 % Drodi V4.1.1
% 0.16/0.41 % Refutation found
% 0.16/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.45 % Elapsed time: 0.067918 seconds
% 0.16/0.45 % CPU time: 0.188945 seconds
% 0.16/0.45 % Total memory used: 109.212 MB
% 0.16/0.45 % Net memory used: 109.060 MB
%------------------------------------------------------------------------------