%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC322-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 02:40:47 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.50s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of formulae : 66 ( 5 unt; 9 def)
% Number of atoms : 145 ( 59 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 140 ( 61 ~; 70 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 10 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 4 ( 4 !; 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,
! [A,B] :
( app(B,cons(A,nil)) != sk4
| app(cons(A,nil),B) = sk3
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
( nil != sk4
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
( nil = sk2
| ssItem(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
( nil != sk1
| ssItem(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
( nil = sk2
| ssList(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( nil = sk2
| app(sk6,cons(sk5,nil)) = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
( nil = sk2
| app(cons(sk5,nil),sk6) != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
( nil != sk1
| ssList(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f200,negated_conjecture,
( nil != sk1
| app(sk6,cons(sk5,nil)) = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f201,negated_conjecture,
( nil != sk1
| app(cons(sk5,nil),sk6) != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f436,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f437,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f438,plain,
! [X0,X1] :
( app(X1,cons(X0,nil)) != sk4
| app(cons(X0,nil),X1) = sk3
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f439,plain,
( nil != sk4
| nil = sk3 ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f440,plain,
( nil = sk2
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f441,plain,
( nil != sk1
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f442,plain,
( nil = sk2
| ssList(sk6) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f443,plain,
( nil = sk2
| app(sk6,cons(sk5,nil)) = sk2 ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f444,plain,
( nil = sk2
| app(cons(sk5,nil),sk6) != sk1 ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f445,plain,
( nil != sk1
| ssList(sk6) ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f446,plain,
( nil != sk1
| app(sk6,cons(sk5,nil)) = sk2 ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f447,plain,
( nil != sk1
| app(cons(sk5,nil),sk6) != sk1 ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f455,definition,
( sQ2_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f456,plain,
( ~ sQ2_spl
| nil = sk3 ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f458,definition,
( sQ3_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f460,plain,
( sQ3_spl
| nil != sk4 ),
inference(component_clause,[status(thm)],[f458]) ).
fof(f461,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f439,f455,f458]) ).
fof(f462,definition,
( sQ4_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f465,definition,
( sQ5_spl
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( ~ sQ5_spl
| nil = sk2 ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f468,plain,
( sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f440,f462,f465]) ).
fof(f469,definition,
( sQ6_spl
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( sQ6_spl
| nil != sk1 ),
inference(component_clause,[status(thm)],[f469]) ).
fof(f472,plain,
( ~ sQ6_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f441,f462,f469]) ).
fof(f473,definition,
( sQ7_spl
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f476,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f442,f473,f465]) ).
fof(f477,definition,
( sQ8_spl
<=> app(sk6,cons(sk5,nil)) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f478,plain,
( ~ sQ8_spl
| app(sk6,cons(sk5,nil)) = sk2 ),
inference(component_clause,[status(thm)],[f477]) ).
fof(f480,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f443,f477,f465]) ).
fof(f481,definition,
( sQ9_spl
<=> app(cons(sk5,nil),sk6) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f483,plain,
( sQ9_spl
| app(cons(sk5,nil),sk6) != sk1 ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f484,plain,
( sQ5_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f444,f481,f465]) ).
fof(f485,plain,
( ~ sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f445,f473,f469]) ).
fof(f486,plain,
( ~ sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f446,f477,f469]) ).
fof(f487,plain,
( ~ sQ6_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f447,f481,f469]) ).
fof(f519,plain,
( sQ6_spl
| nil != sk3 ),
inference(forward_demodulation,[status(thm)],[f437,f471]) ).
fof(f520,plain,
( sQ6_spl
| ~ sQ5_spl
| sk4 != sk3 ),
inference(backward_demodulation,[status(thm)],[f522,f519]) ).
fof(f522,plain,
( ~ sQ5_spl
| nil = sk4 ),
inference(forward_demodulation,[status(thm)],[f436,f466]) ).
fof(f525,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| sk4 = sk3 ),
inference(forward_demodulation,[status(thm)],[f522,f456]) ).
fof(f526,plain,
( sQ6_spl
| ~ sQ5_spl
| ~ sQ2_spl
| sk4 != sk4 ),
inference(forward_demodulation,[status(thm)],[f525,f520]) ).
fof(f527,plain,
( sQ6_spl
| ~ sQ5_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f526]) ).
fof(f528,plain,
( sQ6_spl
| ~ sQ5_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f527]) ).
fof(f529,plain,
( ~ sQ8_spl
| app(sk6,cons(sk5,nil)) = sk4 ),
inference(forward_demodulation,[status(thm)],[f436,f478]) ).
fof(f531,plain,
( sQ9_spl
| app(cons(sk5,nil),sk6) != sk3 ),
inference(forward_demodulation,[status(thm)],[f437,f483]) ).
fof(f532,plain,
( sQ9_spl
| app(sk6,cons(sk5,nil)) != sk4
| ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f438,f531]) ).
fof(f533,definition,
( sQ10_spl
<=> app(sk6,cons(sk5,nil)) = sk4 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f535,plain,
( sQ10_spl
| app(sk6,cons(sk5,nil)) != sk4 ),
inference(component_clause,[status(thm)],[f533]) ).
fof(f536,plain,
( sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f532,f462,f473,f533,f481]) ).
fof(f537,plain,
( sQ10_spl
| ~ sQ8_spl
| sk4 != sk4 ),
inference(forward_demodulation,[status(thm)],[f529,f535]) ).
fof(f538,plain,
( sQ10_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f537]) ).
fof(f539,plain,
( sQ10_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f538]) ).
fof(f540,plain,
( ~ sQ5_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f522,f460]) ).
fof(f541,plain,
( ~ sQ5_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f540]) ).
fof(f542,plain,
$false,
inference(sat_refutation,[status(thm)],[f461,f468,f472,f476,f480,f484,f485,f486,f487,f528,f536,f539,f541]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC322-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n009.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Mon Sep 21 08:15:13 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.49 % Drodi V4.1.1
% 0.16/0.50 % Refutation found
% 0.16/0.50 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.57 % Elapsed time: 0.113858 seconds
% 0.16/0.57 % CPU time: 0.120115 seconds
% 0.16/0.57 % Total memory used: 10.226 MB
% 0.16/0.57 % Net memory used: 10.216 MB
%------------------------------------------------------------------------------