%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC190-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 02:40:20 PM UTC 2026
% Result : Unsatisfiable 0.14s 5.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 15
% Syntax : Number of formulae : 74 ( 21 unt; 0 def)
% Number of atoms : 246 ( 19 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 346 ( 174 ~; 172 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 59 ( 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [U,V] :
( ssList(app(V,U))
| ~ ssList(V)
| ~ ssList(U) ),
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(f138,axiom,
! [U,V,W] :
( memberP(cons(V,W),U)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ ssList(W)
| U != V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f140,axiom,
! [U,V,W] :
( memberP(app(U,W),V)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f141,axiom,
! [U,V,W] :
( memberP(app(W,U),V)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(U)
| ~ memberP(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f175,axiom,
! [U,V,W,X] :
( memberP(X,V)
| ~ ssList(X)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| app(U,cons(V,W)) != X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
ssItem(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
ssList(sk8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
sk5 != sk6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
! [A] :
( ~ memberP(sk3,A)
| sk9 = A
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f207,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f285,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f286,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f352,plain,
! [X0,X1,X2] :
( memberP(cons(X1,X2),X0)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f354,plain,
! [X0,X1,X2] :
( memberP(app(X0,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f355,plain,
! [X0,X1,X2] :
( memberP(app(X2,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f409,plain,
! [V,X] :
( memberP(X,V)
| ~ ssList(X)
| ~ ssItem(V)
| ! [U] :
( ~ ssList(U)
| ! [W] :
( ~ ssList(W)
| app(U,cons(V,W)) != X ) ) ),
inference(miniscoping,[status(thm)],[f175]) ).
fof(f410,plain,
! [X0,X1,X2,X3] :
( memberP(X3,X1)
| ~ ssList(X3)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| app(X0,cons(X1,X2)) != X3 ),
inference(cnf_transformation,[status(thm)],[f409]) ).
fof(f435,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f436,plain,
ssItem(sk5),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f437,plain,
ssItem(sk6),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f438,plain,
ssList(sk7),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f439,plain,
ssList(sk8),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f440,plain,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1,
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f441,plain,
sk5 != sk6,
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f443,plain,
! [X0] :
( ~ memberP(sk3,X0)
| sk9 = X0
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f456,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(destructive_equality_resolution,[status(thm)],[f352]) ).
fof(f457,plain,
! [X0,X1] :
( memberP(cons(X1,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f456]) ).
fof(f463,plain,
! [X0,X1,X2] :
( memberP(app(X1,cons(X2,X0)),X2)
| ~ ssList(app(X1,cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f410]) ).
fof(f475,plain,
! [X0] :
( ~ memberP(sk1,X0)
| sk9 = X0
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f435,f443]) ).
fof(f509,plain,
! [X0] :
( memberP(sk1,X0)
| ~ ssItem(X0)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ~ ssList(sk8)
| ~ memberP(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),X0) ),
inference(paramodulation,[status(thm)],[f440,f354]) ).
fof(f510,plain,
! [X0] :
( memberP(sk1,X0)
| ~ ssItem(X0)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)))
| ~ memberP(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f439]) ).
fof(f557,plain,
! [X0] :
( ~ ssItem(X0)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| ~ memberP(cons(sk6,nil),X0)
| memberP(sk1,X0)
| ~ ssItem(X0)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) ),
inference(resolution,[status(thm)],[f510,f355]) ).
fof(f558,plain,
! [X0] :
( ~ ssItem(X0)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| ~ memberP(app(sk7,cons(sk5,nil)),X0)
| memberP(sk1,X0)
| ~ ssItem(X0)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) ),
inference(resolution,[status(thm)],[f510,f354]) ).
fof(f561,plain,
! [X0] :
( ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| ~ memberP(cons(sk6,nil),X0)
| memberP(sk1,X0)
| ~ ssItem(X0)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) ),
inference(duplicate_literals_removal,[status(thm)],[f557]) ).
fof(f562,plain,
! [X0] :
( ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| ~ memberP(cons(sk6,nil),X0)
| memberP(sk1,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f561,f285]) ).
fof(f563,plain,
! [X0] :
( ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| ~ memberP(app(sk7,cons(sk5,nil)),X0)
| memberP(sk1,X0)
| ~ ssItem(X0)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk6,nil))) ),
inference(duplicate_literals_removal,[status(thm)],[f558]) ).
fof(f564,plain,
! [X0] :
( ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| ~ memberP(app(sk7,cons(sk5,nil)),X0)
| memberP(sk1,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f563,f285]) ).
fof(f565,plain,
! [X0] :
( ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk6,nil))
| ~ memberP(cons(sk6,nil),X0)
| memberP(sk1,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f562,f285]) ).
fof(f566,plain,
! [X0] :
( ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk6,nil))
| ~ memberP(cons(sk6,nil),X0)
| memberP(sk1,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f565,f438]) ).
fof(f568,plain,
( ~ ssItem(sk6)
| ~ ssList(nil)
| ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk6,nil))
| memberP(sk1,sk6)
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f566,f457]) ).
fof(f570,plain,
( ~ ssList(nil)
| ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk6,nil))
| memberP(sk1,sk6)
| ~ ssItem(sk6) ),
inference(duplicate_literals_removal,[status(thm)],[f568]) ).
fof(f571,plain,
( ~ ssList(nil)
| ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk6,nil))
| memberP(sk1,sk6) ),
inference(forward_subsumption_resolution,[status(thm)],[f570,f437]) ).
fof(f572,plain,
( ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk6,nil))
| memberP(sk1,sk6) ),
inference(forward_subsumption_resolution,[status(thm)],[f571,f207]) ).
fof(f573,plain,
( ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssList(cons(sk5,nil))
| memberP(sk1,sk6) ),
inference(resolution,[status(thm)],[f572,f286]) ).
fof(f574,plain,
( ~ ssList(nil)
| ~ ssList(cons(sk5,nil))
| memberP(sk1,sk6) ),
inference(forward_subsumption_resolution,[status(thm)],[f573,f437]) ).
fof(f575,plain,
( ~ ssList(cons(sk5,nil))
| memberP(sk1,sk6) ),
inference(forward_subsumption_resolution,[status(thm)],[f574,f207]) ).
fof(f576,plain,
( ~ ssList(nil)
| ~ ssItem(sk5)
| memberP(sk1,sk6) ),
inference(resolution,[status(thm)],[f575,f286]) ).
fof(f577,plain,
( ~ ssList(nil)
| memberP(sk1,sk6) ),
inference(forward_subsumption_resolution,[status(thm)],[f576,f436]) ).
fof(f578,plain,
memberP(sk1,sk6),
inference(forward_subsumption_resolution,[status(thm)],[f577,f207]) ).
fof(f579,plain,
( sk9 = sk6
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f578,f475]) ).
fof(f580,plain,
sk9 = sk6,
inference(forward_subsumption_resolution,[status(thm)],[f579,f437]) ).
fof(f581,plain,
! [X0] :
( ~ memberP(sk1,X0)
| sk6 = X0
| ~ ssItem(X0) ),
inference(backward_demodulation,[status(thm)],[f580,f475]) ).
fof(f584,plain,
( ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| memberP(sk1,sk5)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f564,f463]) ).
fof(f587,plain,
( ~ ssList(sk7)
| ~ ssList(nil)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| memberP(sk1,sk5)
| ~ ssItem(sk5) ),
inference(duplicate_literals_removal,[status(thm)],[f584]) ).
fof(f588,plain,
( ~ ssList(sk7)
| ~ ssList(nil)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| memberP(sk1,sk5) ),
inference(forward_subsumption_resolution,[status(thm)],[f587,f436]) ).
fof(f624,plain,
( ~ ssList(sk7)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| memberP(sk1,sk5) ),
inference(forward_subsumption_resolution,[status(thm)],[f588,f207]) ).
fof(f625,plain,
( ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ~ ssList(cons(sk6,nil))
| memberP(sk1,sk5) ),
inference(resolution,[status(thm)],[f624,f285]) ).
fof(f626,plain,
( ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ~ ssList(cons(sk6,nil))
| memberP(sk1,sk5) ),
inference(duplicate_literals_removal,[status(thm)],[f625]) ).
fof(f627,plain,
( ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk6,nil))
| memberP(sk1,sk5) ),
inference(forward_subsumption_resolution,[status(thm)],[f626,f438]) ).
fof(f628,plain,
( ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssList(cons(sk5,nil))
| memberP(sk1,sk5) ),
inference(resolution,[status(thm)],[f627,f286]) ).
fof(f629,plain,
( ~ ssList(nil)
| ~ ssList(cons(sk5,nil))
| memberP(sk1,sk5) ),
inference(forward_subsumption_resolution,[status(thm)],[f628,f437]) ).
fof(f630,plain,
( ~ ssList(cons(sk5,nil))
| memberP(sk1,sk5) ),
inference(forward_subsumption_resolution,[status(thm)],[f629,f207]) ).
fof(f631,plain,
( ~ ssList(nil)
| ~ ssItem(sk5)
| memberP(sk1,sk5) ),
inference(resolution,[status(thm)],[f630,f286]) ).
fof(f632,plain,
( ~ ssList(nil)
| memberP(sk1,sk5) ),
inference(forward_subsumption_resolution,[status(thm)],[f631,f436]) ).
fof(f633,plain,
memberP(sk1,sk5),
inference(forward_subsumption_resolution,[status(thm)],[f632,f207]) ).
fof(f634,plain,
( sk6 = sk5
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f633,f581]) ).
fof(f635,plain,
sk6 = sk5,
inference(forward_subsumption_resolution,[status(thm)],[f634,f436]) ).
fof(f636,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f635,f441]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC190-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n004.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 08:03:10 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.39 % Drodi V4.1.1
% 0.14/5.41 % Refutation found
% 0.14/5.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.45 % Elapsed time: 0.057898 seconds
% 0.14/5.45 % CPU time: 0.178906 seconds
% 0.14/5.45 % Total memory used: 99.402 MB
% 0.14/5.45 % Net memory used: 99.218 MB
%------------------------------------------------------------------------------