%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC317-1 : 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 02:40:46 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 17
% Syntax : Number of formulae : 48 ( 9 unt; 8 def)
% Number of atoms : 115 ( 26 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 131 ( 64 ~; 59 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 14 ( 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
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(f199,negated_conjecture,
! [A,B] :
( ~ neq(sk4,nil)
| app(B,cons(A,nil)) != sk2
| app(cons(A,nil),B) != sk1
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f200,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f201,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f202,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f203,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ),
file('/export/starexec/sandbox2/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
| app(cons(A,nil),B) != sk1
| ~ ssList(B)
| ~ ssItem(A) ) ),
inference(miniscoping,[status(thm)],[f199]) ).
fof(f449,plain,
! [X0,X1] :
( ~ neq(sk4,nil)
| app(X1,cons(X0,nil)) != sk2
| app(cons(X0,nil),X1) != 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)
| app(cons(sk5,nil),sk6) = 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
| app(cons(X0,nil),X1) != 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
| app(cons(X0,nil),X1) != 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(f481,definition,
( sQ7_spl
<=> app(cons(sk5,nil),sk6) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f482,plain,
( ~ sQ7_spl
| app(cons(sk5,nil),sk6) = 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(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
| app(cons(X0,nil),X1) != 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
| app(cons(X0,nil),X1) != sk3
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f438,f528]) ).
fof(f539,definition,
( sQ11_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f541,plain,
( sQ11_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f539]) ).
fof(f543,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f541,f211]) ).
fof(f544,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f543]) ).
fof(f550,plain,
( ~ sQ7_spl
| ~ sQ4_spl
| app(sk6,cons(sk5,nil)) != sk4
| ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f529,f482]) ).
fof(f552,plain,
( ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f550,f473,f477,f485,f469,f481]) ).
fof(f557,plain,
$false,
inference(sat_refutation,[status(thm)],[f464,f489,f490,f491,f492,f493,f527,f544,f552]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC317-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n006.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 08:14:43 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.068216 seconds
% 0.13/0.43 % CPU time: 0.176968 seconds
% 0.13/0.43 % Total memory used: 108.976 MB
% 0.13/0.43 % Net memory used: 108.864 MB
%------------------------------------------------------------------------------