%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC415+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 : Sun Sep 27 08:57:45 AM UTC 2026
% Result : Theorem 102.87s 24.20s
% Output : CNFRefutation 102.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 50 ( 15 unt; 0 def)
% Number of atoms : 206 ( 76 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 270 ( 114 ~; 103 |; 40 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 43 ( 0 sgn 17 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax24,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ssList(tl(U)) ) ),
file('theBenchmark.p',ax24) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ? [Z] :
( neq(nil,V)
& U = Z
& tl(V) = Z
& ssList(Z) )
| ? [Y] :
( neq(nil,X)
& tl(X) = Y
& W != Y
& ssList(Y) )
| ~ neq(V,nil) ) )
| U != W
| V != X ) ) ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ? [Z] :
( neq(nil,V)
& U = Z
& tl(V) = Z
& ssList(Z) )
| ? [Y] :
( neq(nil,X)
& tl(X) = Y
& W != Y
& ssList(Y) )
| ~ neq(V,nil) ) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| ( ! [Z] :
( ~ neq(nil,V)
| Z != U
| tl(V) != Z
| ~ ssList(Z) )
& ! [Y] :
( ~ neq(nil,X)
| tl(X) != Y
| Y = W
| ~ ssList(Y) )
& neq(V,nil) ) )
& W = U
& X = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg_sk,plain,
( ( ( ~ neq(sK2,nil)
& neq(sK0,nil) )
| ( ! [Z] :
( ~ neq(nil,sK0)
| Z != sK1
| tl(sK0) != Z
| ~ ssList(Z) )
& ! [Y] :
( ~ neq(nil,sK2)
| tl(sK2) != Y
| Y = sK3
| ~ ssList(Y) )
& neq(sK0,nil) ) )
& sK3 = sK1
& sK2 = sK0
& ssList(sK2)
& ssList(sK3)
& ssList(sK0)
& ssList(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK3,sK2]),skolemize(U,sK1),skolemize(V,sK0),skolemize(W,sK3),skolemize(X,sK2)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ! [VAR_0] :
( ~ neq(sK2,nil)
| ~ neq(nil,sK0)
| VAR_0 != sK1
| tl(sK0) != VAR_0
| ~ ssList(VAR_0) )
& ! [VAR_0] :
( ~ neq(sK2,nil)
| ~ neq(nil,sK2)
| tl(sK2) != VAR_0
| VAR_0 = sK3
| ~ ssList(VAR_0) )
& neq(sK0,nil)
& sK3 = sK1
& sK2 = sK0
& ssList(sK2)
& ssList(sK3)
& ssList(sK0)
& ssList(sK1) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_190,negated_conjecture,
( ~ neq(sK2,nil)
| ~ neq(nil,sK0)
| A != sK1
| tl(sK0) != A
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
( ~ neq(sK2,nil)
| ~ neq(nil,sK0)
| sK1 != A
| tl(sK0) != A
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_190]) ).
cnf(c_192,negated_conjecture,
( ~ neq(sK2,nil)
| ~ neq(nil,sK2)
| tl(sK2) != A
| A = sK3
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( ~ neq(sK2,nil)
| ~ neq(nil,sK2)
| tl(sK2) != A
| sK3 = A
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_194,negated_conjecture,
neq(sK0,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
sK3 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_196,negated_conjecture,
sK2 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
ssList(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_198,negated_conjecture,
ssList(sK0),
inference(paramod,[status(thm)],[c_196,c_197]) ).
cnf(c_199,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_200,negated_conjecture,
ssList(sK1),
inference(paramod,[status(thm)],[c_195,c_199]) ).
cnf(c_286,plain,
( ssList(tl(A))
| nil = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax24]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_296,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_298,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_299,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_11580,negated_conjecture,
( ~ neq(sK2,nil)
| ~ neq(nil,sK2)
| tl(sK2) != A
| sK1 = A
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_195,c_193]) ).
cnf(c_11581,negated_conjecture,
( ~ neq(sK2,nil)
| ~ neq(nil,sK2)
| tl(sK0) != A
| sK1 = A
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_196,c_11580]) ).
cnf(c_11582,negated_conjecture,
( ~ neq(sK2,nil)
| ~ neq(nil,sK0)
| tl(sK0) != A
| sK1 = A
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_196,c_11581]) ).
cnf(c_11583,negated_conjecture,
( ~ neq(sK0,nil)
| ~ neq(nil,sK0)
| tl(sK0) != A
| sK1 = A
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_196,c_11582]) ).
cnf(c_545,negated_conjecture,
( ~ neq(nil,sK0)
| tl(sK0) != A
| sK1 = A
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_194,c_11583]) ).
cnf(c_11584,negated_conjecture,
( ~ neq(sK0,nil)
| ~ neq(nil,sK0)
| sK1 != A
| tl(sK0) != A
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_196,c_191]) ).
cnf(c_546,negated_conjecture,
( ~ neq(nil,sK0)
| sK1 != A
| tl(sK0) != A
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_194,c_11584]) ).
cnf(c_11585,negated_conjecture,
( ssList(tl(sK0))
| nil = sK0 ),
inference(resolve,[status(thm)],[c_286,c_198]) ).
cnf(c_3731,negated_conjecture,
( ssList(tl(sK0))
| sK0 = nil ),
inference(copy,[status(thm)],[c_11585]) ).
cnf(c_11586,plain,
( A = nil
| neq(nil,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_298,c_296]) ).
cnf(c_4509,plain,
( nil = A
| neq(nil,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_11586]) ).
cnf(c_11587,negated_conjecture,
( nil != sK0
| ~ ssList(nil)
| ~ ssList(sK0) ),
inference(resolve,[status(thm)],[c_299,c_194]) ).
cnf(c_11588,negated_conjecture,
( sK0 != nil
| ~ ssList(nil)
| ~ ssList(sK0) ),
inference(copy,[status(thm)],[c_11587]) ).
cnf(c_11589,negated_conjecture,
( sK0 != nil
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_198,c_11588]) ).
cnf(c_4521,negated_conjecture,
sK0 != nil,
inference(resolve,[status(thm)],[c_296,c_11589]) ).
cnf(c_4528,negated_conjecture,
ssList(tl(sK0)),
inference(resolve,[status(thm)],[c_4521,c_3731]) ).
cnf(c_11590,plain,
( ~ neq(nil,sK0)
| sK1 = tl(sK0)
| ~ ssList(tl(sK0)) ),
inference(xxres,[status(thm)],[c_545]) ).
cnf(c_11591,plain,
( ~ neq(nil,sK0)
| tl(sK0) = sK1
| ~ ssList(tl(sK0)) ),
inference(copy,[status(thm)],[c_11590]) ).
cnf(c_9417,plain,
( ~ neq(nil,sK0)
| tl(sK0) = sK1 ),
inference(resolve,[status(thm)],[c_4528,c_11591]) ).
cnf(c_11592,negated_conjecture,
( ~ neq(nil,sK0)
| sK1 != sK1
| tl(sK0) != sK1 ),
inference(resolve,[status(thm)],[c_546,c_200]) ).
cnf(c_9419,negated_conjecture,
( ~ neq(nil,sK0)
| tl(sK0) != sK1 ),
inference(copy,[status(thm)],[c_11592]) ).
cnf(c_11593,negated_conjecture,
( nil = sK0
| neq(nil,sK0) ),
inference(resolve,[status(thm)],[c_4509,c_198]) ).
cnf(c_11594,negated_conjecture,
( sK0 = nil
| neq(nil,sK0) ),
inference(copy,[status(thm)],[c_11593]) ).
cnf(c_11575,negated_conjecture,
neq(nil,sK0),
inference(resolve,[status(thm)],[c_4521,c_11594]) ).
cnf(c_11577,negated_conjecture,
tl(sK0) != sK1,
inference(resolve,[status(thm)],[c_11575,c_9419]) ).
cnf(c_11595,plain,
~ neq(nil,sK0),
inference(resolve,[status(thm)],[c_11577,c_9417]) ).
cnf(c_11579,plain,
$false,
inference(resolve,[status(thm)],[c_11575,c_11595]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC415+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.38 % Computer : n013.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Sat Sep 26 13:00:15 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.38 % Process 2800711 was started by sandbox on n013,
% 0.09/10.38 % Sat Sep 26 13:00:15 2026
% 0.09/10.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/10.42
% 0.15/10.42 % From the command line: assign(max_seconds, 300).
% 102.87/24.20
% 102.87/24.20 % given #500 (I,wt=49): 702 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,A)),cons(C,E)) != A | C != B | ssList(f36(A)). [factor(364,a,e)].
% 102.87/24.20
% 102.87/24.20 % given #1000 (I,wt=46): 1233 -ssList(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(C,cons(B,A)),cons(B,D)) != A | f34(A) = f33(A). [factor(723,b,c),xx(f)].
% 102.87/24.20
% 102.87/24.20 % SZS status Theorem for theBenchmark
% 102.87/24.20
% 102.87/24.20 % Proof 1 at 5.16 (+ 0.49) seconds.
% 102.87/24.20 % Length of proof is 29.
% 102.87/24.20 % Level of proof is 6.
% 102.87/24.20 % Maximum clause weight is 25.000.
% 102.87/24.20 % Given clauses 1403.
% 102.87/24.20
% 102.87/24.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------