%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC312-1 : 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 02:40:45 PM UTC 2026
% Result : Unsatisfiable 0.03s 0.39s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 48 ( 11 unt; 0 def)
% Number of atoms : 105 ( 47 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 118 ( 61 ~; 57 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
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(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,
( nil != sk4
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( neq(sk2,nil)
| nil = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
! [A,B] :
( app(B,cons(A,nil)) != sk1
| app(cons(A,nil),B) != sk2
| ~ ssList(B)
| ~ ssItem(A)
| nil = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f208,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f321,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ neq(U,V)
| U != V ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f322,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f321]) ).
fof(f435,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f436,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f437,plain,
( nil != sk4
| nil = sk3 ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f438,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f439,plain,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f440,plain,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk4 ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f441,plain,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk3 ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f442,plain,
( neq(sk2,nil)
| nil = sk2 ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f443,plain,
! [X0,X1] :
( app(X1,cons(X0,nil)) != sk1
| app(cons(X0,nil),X1) != sk2
| ~ ssList(X1)
| ~ ssItem(X0)
| nil = sk2 ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f444,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f453,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f322]) ).
fof(f454,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f453]) ).
fof(f477,plain,
( nil != sk4
| nil = sk1 ),
inference(forward_demodulation,[status(thm)],[f436,f437]) ).
fof(f478,plain,
( nil != sk2
| nil = sk1 ),
inference(forward_demodulation,[status(thm)],[f435,f477]) ).
fof(f479,plain,
( ~ neq(sk2,nil)
| ssItem(sk5) ),
inference(forward_demodulation,[status(thm)],[f435,f438]) ).
fof(f480,plain,
( ~ neq(sk2,nil)
| ssList(sk6) ),
inference(forward_demodulation,[status(thm)],[f435,f439]) ).
fof(f483,plain,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk2 ),
inference(forward_demodulation,[status(thm)],[f435,f440]) ).
fof(f484,plain,
( ~ neq(sk2,nil)
| app(cons(sk5,nil),sk6) = sk2 ),
inference(forward_demodulation,[status(thm)],[f435,f483]) ).
fof(f487,plain,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk1 ),
inference(forward_demodulation,[status(thm)],[f436,f441]) ).
fof(f488,plain,
( ~ neq(sk2,nil)
| app(sk6,cons(sk5,nil)) = sk1 ),
inference(forward_demodulation,[status(thm)],[f435,f487]) ).
fof(f489,plain,
( ~ neq(sk2,nil)
| app(cons(sk5,nil),sk6) != sk2
| ~ ssList(sk6)
| ~ ssItem(sk5)
| nil = sk2 ),
inference(resolution,[status(thm)],[f443,f488]) ).
fof(f490,plain,
( ~ neq(sk2,nil)
| app(cons(sk5,nil),sk6) != sk2
| ~ ssList(sk6)
| nil = sk2 ),
inference(forward_subsumption_resolution,[status(thm)],[f489,f479]) ).
fof(f491,plain,
( ~ neq(sk2,nil)
| app(cons(sk5,nil),sk6) != sk2
| nil = sk2 ),
inference(forward_subsumption_resolution,[status(thm)],[f490,f480]) ).
fof(f492,plain,
( ~ neq(sk2,nil)
| ~ neq(sk2,nil)
| nil = sk2 ),
inference(resolution,[status(thm)],[f491,f484]) ).
fof(f493,plain,
( ~ neq(sk2,nil)
| nil = sk2 ),
inference(duplicate_literals_removal,[status(thm)],[f492]) ).
fof(f494,plain,
nil = sk2,
inference(forward_subsumption_resolution,[status(thm)],[f493,f442]) ).
fof(f501,plain,
( neq(nil,nil)
| nil != sk1 ),
inference(backward_demodulation,[status(thm)],[f494,f444]) ).
fof(f508,plain,
( nil != nil
| nil = sk1 ),
inference(backward_demodulation,[status(thm)],[f494,f478]) ).
fof(f512,plain,
nil = sk1,
inference(trivial_equality_resolution,[status(thm)],[f508]) ).
fof(f521,plain,
( neq(nil,nil)
| nil != nil ),
inference(forward_demodulation,[status(thm)],[f512,f501]) ).
fof(f522,plain,
neq(nil,nil),
inference(trivial_equality_resolution,[status(thm)],[f521]) ).
fof(f524,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[f522,f454]) ).
fof(f525,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f524,f208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC312-1 : 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
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 08:14:28 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.37 % Drodi V4.1.1
% 0.03/0.39 % Refutation found
% 0.03/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.03/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.03/0.43 % Elapsed time: 0.063313 seconds
% 0.03/0.43 % CPU time: 0.168337 seconds
% 0.03/0.43 % Total memory used: 108.688 MB
% 0.03/0.43 % Net memory used: 108.545 MB
%------------------------------------------------------------------------------