%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC316-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 0.14s 0.50s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 17
% Syntax : Number of formulae : 81 ( 21 unt; 0 def)
% Number of atoms : 268 ( 72 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 395 ( 208 ~; 187 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 42 ( 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [U,V] :
( ssList(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,axiom,
! [U,V] :
( tl(cons(U,V)) = V
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,axiom,
! [U,V] :
( hd(cons(U,V)) = U
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f98,axiom,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f100,axiom,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f120,axiom,
! [U,V] :
( app(cons(U,nil),V) = cons(U,V)
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f186,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f187,negated_conjecture,
ssList(sk2),
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,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f200,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f201,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f202,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f203,negated_conjecture,
! [A,B,C,D] :
( ~ neq(sk4,nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1)
| ~ neq(nil,sk1)
| hd(sk1) != D
| cons(D,nil) != C
| ~ ssItem(D)
| app(B,C) != A
| tl(sk1) != B
| ~ ssList(C)
| ~ ssList(B)
| sk2 != A
| ~ ssList(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f211,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f290,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f300,plain,
! [X0,X1] :
( tl(cons(X0,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f301,plain,
! [X0,X1] :
( hd(cons(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f302,plain,
! [V] :
( ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f98]) ).
fof(f303,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f302]) ).
fof(f306,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f334,plain,
! [X0,X1] :
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f434,plain,
ssList(sk1),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f435,plain,
ssList(sk2),
inference(cnf_transformation,[status(thm)],[f187]) ).
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)
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f449,plain,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f450,plain,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk3 ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f451,plain,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f452,plain,
( ~ neq(sk4,nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1)
| ~ neq(nil,sk1)
| ! [D] :
( hd(sk1) != D
| ! [C] :
( cons(D,nil) != C
| ~ ssItem(D)
| ! [A,B] :
( app(B,C) != A
| tl(sk1) != B
| ~ ssList(C)
| ~ ssList(B)
| sk2 != A
| ~ ssList(A) ) ) ) ),
inference(miniscoping,[status(thm)],[f203]) ).
fof(f453,plain,
! [X0,X1,X2,X3] :
( ~ neq(sk4,nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1)
| ~ neq(nil,sk1)
| hd(sk1) != X3
| cons(X3,nil) != X2
| ~ ssItem(X3)
| app(X1,X2) != X0
| tl(sk1) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| sk2 != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f452]) ).
fof(f483,plain,
neq(sk2,nil),
inference(duplicate_literals_removal,[status(thm)],[f440]) ).
fof(f486,plain,
! [X0,X1,X2,X3] :
( ~ neq(sk4,nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1)
| hd(sk1) != X3
| cons(X3,nil) != X2
| ~ ssItem(X3)
| app(X1,X2) != X0
| tl(sk1) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| sk2 != X0
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f453]) ).
fof(f487,plain,
( ~ neq(sk4,nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1)
| ~ ssItem(hd(sk1))
| app(tl(sk1),cons(hd(sk1),nil)) != sk2
| ~ ssList(cons(hd(sk1),nil))
| ~ ssList(tl(sk1))
| ~ ssList(sk2) ),
inference(destructive_equality_resolution,[status(thm)],[f486]) ).
fof(f490,plain,
( ~ neq(sk2,nil)
| ssItem(sk5) ),
inference(forward_demodulation,[status(thm)],[f438,f448]) ).
fof(f491,plain,
ssItem(sk5),
inference(forward_subsumption_resolution,[status(thm)],[f490,f483]) ).
fof(f492,plain,
( ~ neq(sk2,nil)
| ssList(sk6) ),
inference(forward_demodulation,[status(thm)],[f438,f449]) ).
fof(f493,plain,
ssList(sk6),
inference(forward_subsumption_resolution,[status(thm)],[f492,f483]) ).
fof(f496,plain,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk1 ),
inference(forward_demodulation,[status(thm)],[f439,f450]) ).
fof(f497,plain,
( ~ neq(sk2,nil)
| app(cons(sk5,nil),sk6) = sk1 ),
inference(forward_demodulation,[status(thm)],[f438,f496]) ).
fof(f498,plain,
app(cons(sk5,nil),sk6) = sk1,
inference(forward_subsumption_resolution,[status(thm)],[f497,f483]) ).
fof(f509,plain,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk2 ),
inference(forward_demodulation,[status(thm)],[f438,f451]) ).
fof(f510,plain,
( ~ neq(sk2,nil)
| app(sk6,cons(sk5,nil)) = sk2 ),
inference(forward_demodulation,[status(thm)],[f438,f509]) ).
fof(f511,plain,
app(sk6,cons(sk5,nil)) = sk2,
inference(forward_subsumption_resolution,[status(thm)],[f510,f483]) ).
fof(f518,plain,
( ~ neq(sk2,nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1)
| ~ ssItem(hd(sk1))
| app(tl(sk1),cons(hd(sk1),nil)) != sk2
| ~ ssList(cons(hd(sk1),nil))
| ~ ssList(tl(sk1))
| ~ ssList(sk2) ),
inference(forward_demodulation,[status(thm)],[f438,f487]) ).
fof(f519,plain,
( ~ neq(sk2,nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1)
| ~ ssItem(hd(sk1))
| app(tl(sk1),cons(hd(sk1),nil)) != sk2
| ~ ssList(cons(hd(sk1),nil))
| ~ ssList(tl(sk1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f518,f435]) ).
fof(f529,plain,
( sk1 = cons(sk5,sk6)
| ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f498,f334]) ).
fof(f530,plain,
( sk1 = cons(sk5,sk6)
| ~ ssList(sk6) ),
inference(forward_subsumption_resolution,[status(thm)],[f529,f491]) ).
fof(f531,plain,
sk1 = cons(sk5,sk6),
inference(forward_subsumption_resolution,[status(thm)],[f530,f493]) ).
fof(f532,plain,
( hd(sk1) = sk5
| ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f531,f301]) ).
fof(f533,plain,
( tl(sk1) = sk6
| ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f531,f300]) ).
fof(f534,plain,
( ~ ssList(sk6)
| ~ ssItem(sk5)
| sk1 != nil ),
inference(paramodulation,[status(thm)],[f531,f303]) ).
fof(f537,plain,
( hd(sk1) = sk5
| ~ ssList(sk6) ),
inference(forward_subsumption_resolution,[status(thm)],[f532,f491]) ).
fof(f538,plain,
( tl(sk1) = sk6
| ~ ssList(sk6) ),
inference(forward_subsumption_resolution,[status(thm)],[f533,f491]) ).
fof(f539,plain,
( ~ ssList(sk6)
| sk1 != nil ),
inference(forward_subsumption_resolution,[status(thm)],[f534,f491]) ).
fof(f541,plain,
sk1 != nil,
inference(forward_subsumption_resolution,[status(thm)],[f539,f493]) ).
fof(f551,plain,
( ~ neq(sk2,nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1)
| ~ ssItem(sk5)
| app(tl(sk1),cons(hd(sk1),nil)) != sk2
| ~ ssList(cons(hd(sk1),nil))
| ~ ssList(tl(sk1)) ),
inference(backward_demodulation,[status(thm)],[f552,f519]) ).
fof(f552,plain,
hd(sk1) = sk5,
inference(forward_subsumption_resolution,[status(thm)],[f537,f493]) ).
fof(f555,plain,
( ~ neq(sk2,nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1)
| ~ ssItem(sk5)
| app(tl(sk1),cons(hd(sk1),nil)) != sk2
| ~ ssList(cons(sk5,nil))
| ~ ssList(tl(sk1)) ),
inference(forward_demodulation,[status(thm)],[f552,f551]) ).
fof(f556,plain,
( ~ neq(sk2,nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1)
| ~ ssItem(sk5)
| app(tl(sk1),cons(sk5,nil)) != sk2
| ~ ssList(cons(sk5,nil))
| ~ ssList(tl(sk1)) ),
inference(forward_demodulation,[status(thm)],[f552,f555]) ).
fof(f557,plain,
( ~ neq(sk2,nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1)
| app(tl(sk1),cons(sk5,nil)) != sk2
| ~ ssList(cons(sk5,nil))
| ~ ssList(tl(sk1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f556,f491]) ).
fof(f559,plain,
tl(sk1) = sk6,
inference(forward_subsumption_resolution,[status(thm)],[f538,f493]) ).
fof(f563,plain,
( ~ neq(sk2,nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1)
| app(tl(sk1),cons(sk5,nil)) != sk2
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6) ),
inference(forward_demodulation,[status(thm)],[f559,f557]) ).
fof(f564,plain,
( ~ neq(sk2,nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1)
| app(sk6,cons(sk5,nil)) != sk2
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6) ),
inference(forward_demodulation,[status(thm)],[f559,f563]) ).
fof(f565,plain,
( ~ neq(sk2,nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1)
| sk2 != sk2
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6) ),
inference(forward_demodulation,[status(thm)],[f511,f564]) ).
fof(f566,plain,
( ~ neq(sk2,nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6) ),
inference(trivial_equality_resolution,[status(thm)],[f565]) ).
fof(f567,plain,
( ~ neq(sk2,nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1)
| ~ ssList(cons(sk5,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f566,f493]) ).
fof(f568,plain,
( ~ ssList(nil)
| ~ ssItem(sk5)
| ~ neq(sk2,nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1) ),
inference(resolution,[status(thm)],[f567,f290]) ).
fof(f569,plain,
( ~ ssList(nil)
| ~ ssItem(sk5)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1) ),
inference(forward_subsumption_resolution,[status(thm)],[f568,f483]) ).
fof(f630,plain,
( ~ ssList(nil)
| ~ neq(sk1,nil)
| ~ neq(nil,sk1) ),
inference(forward_subsumption_resolution,[status(thm)],[f569,f491]) ).
fof(f632,plain,
( sk1 = nil
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ neq(nil,sk1) ),
inference(resolution,[status(thm)],[f630,f306]) ).
fof(f634,plain,
( sk1 = nil
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ neq(nil,sk1) ),
inference(duplicate_literals_removal,[status(thm)],[f632]) ).
fof(f635,plain,
( sk1 = nil
| ~ ssList(sk1)
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[status(thm)],[f634,f306]) ).
fof(f636,plain,
( sk1 = nil
| ~ ssList(sk1) ),
inference(forward_subsumption_resolution,[status(thm)],[f635,f211]) ).
fof(f637,plain,
sk1 = nil,
inference(resolution,[status(thm)],[f636,f434]) ).
fof(f638,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f637,f541]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC316-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.42 % Computer : n011.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Mon Sep 21 08:14:55 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.45 % Drodi V4.1.1
% 0.14/0.50 % Refutation found
% 0.14/0.50 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.54 % Elapsed time: 0.096448 seconds
% 0.14/0.54 % CPU time: 0.263460 seconds
% 0.14/0.54 % Total memory used: 56.345 MB
% 0.14/0.54 % Net memory used: 56.244 MB
%------------------------------------------------------------------------------