%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC256-1 : 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 02:40:32 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of formulae : 55 ( 17 unt; 6 def)
% Number of atoms : 119 ( 20 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 126 ( 62 ~; 58 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 19 ( 19 !; 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(f115,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f116,axiom,
! [U,V] :
( singletonP(V)
| ~ ssList(V)
| ~ ssItem(U)
| cons(U,nil) != V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f189,negated_conjecture,
ssList(sk4),
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),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
~ singletonP(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
( nil = sk4
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
( nil = sk4
| cons(sk5,nil) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f207,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f286,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f320,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ neq(U,V)
| U != V ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f321,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f322,plain,
! [V] :
( singletonP(V)
| ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,nil) != V ) ),
inference(miniscoping,[status(thm)],[f116]) ).
fof(f323,plain,
! [X0,X1] :
( singletonP(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,nil) != X1 ),
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(f433,plain,
ssList(sk4),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f434,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f435,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f436,plain,
neq(sk2,nil),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f437,plain,
~ singletonP(sk1),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f438,plain,
( nil = sk4
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f440,plain,
( nil = sk4
| cons(sk5,nil) = sk3 ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f451,definition,
( sQ2_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f454,definition,
( sQ3_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( ~ sQ3_spl
| nil = sk4 ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f457,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f438,f451,f454]) ).
fof(f462,definition,
( sQ5_spl
<=> cons(sk5,nil) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f463,plain,
( ~ sQ5_spl
| cons(sk5,nil) = sk3 ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,plain,
( sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f440,f462,f454]) ).
fof(f479,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f321]) ).
fof(f480,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f479]) ).
fof(f481,plain,
! [X0] :
( singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil))
| ~ ssItem(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f323]) ).
fof(f503,plain,
~ singletonP(sk3),
inference(forward_demodulation,[status(thm)],[f435,f437]) ).
fof(f511,plain,
neq(sk4,nil),
inference(forward_demodulation,[status(thm)],[f434,f436]) ).
fof(f516,plain,
( ~ sQ5_spl
| ssList(sk3)
| ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f463,f286]) ).
fof(f517,definition,
( sQ7_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f519,plain,
( sQ7_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f517]) ).
fof(f520,definition,
( sQ8_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f523,plain,
( ~ sQ5_spl
| sQ8_spl
| ~ sQ7_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f516,f451,f517,f520,f462]) ).
fof(f526,plain,
( ~ sQ3_spl
| neq(sk4,sk4) ),
inference(backward_demodulation,[status(thm)],[f455,f511]) ).
fof(f560,plain,
( ~ sQ3_spl
| ~ ssList(sk4) ),
inference(resolution,[status(thm)],[f526,f480]) ).
fof(f561,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f560,f433]) ).
fof(f562,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f561]) ).
fof(f569,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f207,f519]) ).
fof(f570,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f569]) ).
fof(f579,plain,
( ~ sQ5_spl
| singletonP(cons(sk5,nil))
| ~ ssList(sk3)
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f463,f481]) ).
fof(f584,definition,
( sQ11_spl
<=> singletonP(cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f585,plain,
( ~ sQ11_spl
| singletonP(cons(sk5,nil)) ),
inference(component_clause,[status(thm)],[f584]) ).
fof(f587,plain,
( ~ sQ5_spl
| sQ11_spl
| ~ sQ8_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f579,f451,f520,f584,f462]) ).
fof(f588,plain,
( ~ sQ11_spl
| ~ sQ5_spl
| singletonP(sk3) ),
inference(forward_demodulation,[status(thm)],[f463,f585]) ).
fof(f589,plain,
( ~ sQ11_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f588,f503]) ).
fof(f590,plain,
( ~ sQ11_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f589]) ).
fof(f591,plain,
$false,
inference(sat_refutation,[status(thm)],[f457,f465,f523,f562,f570,f587,f590]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC256-1 : 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 08:09:13 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 0.15/0.39 % Refutation found
% 0.15/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.42 % Elapsed time: 0.046902 seconds
% 0.15/0.42 % CPU time: 0.099452 seconds
% 0.15/0.42 % Total memory used: 24.052 MB
% 0.15/0.42 % Net memory used: 24.026 MB
%------------------------------------------------------------------------------