%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC096-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 02:39:56 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 18
% Syntax : Number of formulae : 56 ( 9 unt; 9 def)
% Number of atoms : 141 ( 31 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 169 ( 84 ~; 76 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 17 ( 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f199,negated_conjecture,
! [A,B] :
( ~ neq(sk4,nil)
| app(B,cons(A,nil)) != sk2
| cons(A,nil) != sk1
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f200,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f201,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f202,negated_conjecture,
( ~ neq(sk4,nil)
| cons(sk5,nil) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f203,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f211,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f438,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f439,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f440,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f448,plain,
( ~ neq(sk4,nil)
| ! [A,B] :
( app(B,cons(A,nil)) != sk2
| cons(A,nil) != sk1
| ~ ssList(B)
| ~ ssItem(A) ) ),
inference(miniscoping,[status(thm)],[f199]) ).
fof(f449,plain,
! [X0,X1] :
( ~ neq(sk4,nil)
| app(X1,cons(X0,nil)) != sk2
| cons(X0,nil) != sk1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f448]) ).
fof(f450,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f451,plain,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f452,plain,
( ~ neq(sk4,nil)
| cons(sk5,nil) = sk3 ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f453,plain,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f461,definition,
( sQ2_spl
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f462,plain,
( ~ sQ2_spl
| neq(sk2,nil) ),
inference(component_clause,[status(thm)],[f461]) ).
fof(f464,plain,
sQ2_spl,
inference(split_clause,[status(thm)],[f440,f461]) ).
fof(f465,definition,
( sQ3_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f467,plain,
( sQ3_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f469,definition,
! [X0,X1] :
( sQ4_spl
<=> ( app(X1,cons(X0,nil)) != sk2
| cons(X0,nil) != sk1
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f470,plain,
! [X0,X1] :
( ~ sQ4_spl
| app(X1,cons(X0,nil)) != sk2
| cons(X0,nil) != sk1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f469]) ).
fof(f473,definition,
( sQ5_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f477,definition,
( sQ6_spl
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f478,plain,
( ~ sQ6_spl
| ssList(sk6) ),
inference(component_clause,[status(thm)],[f477]) ).
fof(f481,definition,
( sQ7_spl
<=> cons(sk5,nil) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f482,plain,
( ~ sQ7_spl
| cons(sk5,nil) = sk3 ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f485,definition,
( sQ8_spl
<=> app(sk6,cons(sk5,nil)) = sk4 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f486,plain,
( ~ sQ8_spl
| app(sk6,cons(sk5,nil)) = sk4 ),
inference(component_clause,[status(thm)],[f485]) ).
fof(f489,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f449,f469,f465]) ).
fof(f490,plain,
( ~ sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f450,f473,f465]) ).
fof(f491,plain,
( ~ sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f451,f477,f465]) ).
fof(f492,plain,
( ~ sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f452,f481,f465]) ).
fof(f493,plain,
( ~ sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f453,f485,f465]) ).
fof(f525,plain,
( ~ sQ2_spl
| neq(sk4,nil) ),
inference(forward_demodulation,[status(thm)],[f438,f462]) ).
fof(f526,plain,
( sQ3_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f467,f525]) ).
fof(f527,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f526]) ).
fof(f528,plain,
! [X0,X1] :
( ~ sQ4_spl
| app(X1,cons(X0,nil)) != sk2
| cons(X0,nil) != sk3
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f439,f470]) ).
fof(f529,plain,
! [X0,X1] :
( ~ sQ4_spl
| app(X1,cons(X0,nil)) != sk4
| cons(X0,nil) != sk3
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f438,f528]) ).
fof(f531,definition,
( sQ9_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f533,plain,
( sQ9_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f531]) ).
fof(f538,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f533,f211]) ).
fof(f539,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f538]) ).
fof(f540,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| app(sk6,sk3) = sk4 ),
inference(forward_demodulation,[status(thm)],[f482,f486]) ).
fof(f546,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ4_spl
| app(X0,sk3) != sk4
| cons(sk5,nil) != sk3
| ~ ssList(X0)
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f482,f529]) ).
fof(f547,definition,
! [X0] :
( sQ12_spl
<=> ( app(X0,sk3) != sk4
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f548,plain,
! [X0] :
( ~ sQ12_spl
| app(X0,sk3) != sk4
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f547]) ).
fof(f550,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| sQ12_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f546,f473,f547,f481,f469]) ).
fof(f551,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ12_spl
| ~ ssList(sk6) ),
inference(resolution,[status(thm)],[f548,f540]) ).
fof(f553,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f551,f478]) ).
fof(f554,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f553]) ).
fof(f555,plain,
$false,
inference(sat_refutation,[status(thm)],[f464,f489,f490,f491,f492,f493,f527,f539,f550,f554]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC096-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n015.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % 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 07:58:52 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.047945 seconds
% 0.13/0.41 % CPU time: 0.155370 seconds
% 0.13/0.41 % Total memory used: 109.027 MB
% 0.13/0.41 % Net memory used: 108.910 MB
%------------------------------------------------------------------------------