%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC003+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 : n012.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 08:56:30 AM UTC 2026
% Result : Theorem 239.40s 42.01s
% Output : CNFRefutation 239.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 51 ( 15 unt; 0 def)
% Number of atoms : 234 ( 63 equ)
% Maximal formula atoms : 29 ( 4 avg)
% Number of connectives : 300 ( 117 ~; 103 |; 59 &)
% ( 1 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 32 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('theBenchmark.p',ax16) ).
fof(ax18,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
file('theBenchmark.p',ax18) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( geq(X5,X2)
& memberP(X,X5)
& X2 != X5
& ssItem(X5) )
| app(X3,X4) != W
| app(app(X3,cons(X2,nil)),X4) != X ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( neq(Z,nil)
& app(Y,X1) = U
& app(app(Y,Z),X1) = V
& ssList(X1) )
& ssList(Z) )
& 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) )
& ( ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( geq(X5,X2)
& memberP(X,X5)
& X2 != X5
& ssItem(X5) )
| app(X3,X4) != W
| app(app(X3,cons(X2,nil)),X4) != X ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( neq(Z,nil)
& app(Y,X1) = U
& app(app(Y,Z),X1) = V
& ssList(X1) )
& ssList(Z) )
& 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) )
| ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ! [X5] :
( ~ geq(X5,X2)
| ~ memberP(X,X5)
| X5 = X2
| ~ ssItem(X5) )
& app(X3,X4) = W
& app(app(X3,cons(X2,nil)),X4) = X
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ~ neq(Z,nil)
| app(Y,X1) != U
| app(app(Y,Z),X1) != V
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ 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(sK3,nil)
& neq(sK5,nil) )
| ( ! [X5] :
( ~ geq(X5,sK4)
| ~ memberP(sK3,X5)
| X5 = sK4
| ~ ssItem(X5) )
& app(sK0,sK1) = sK2
& app(app(sK0,cons(sK4,nil)),sK1) = sK3
& ssList(sK1)
& ssList(sK0)
& ssItem(sK4)
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ~ neq(Z,nil)
| app(Y,X1) != sK6
| app(app(Y,Z),X1) != sK5
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssList(Y) )
& neq(sK5,nil) ) )
& sK2 = sK6
& sK3 = sK5
& ssList(sK3)
& ssList(sK2)
& ssList(sK5)
& ssList(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK5,sK2,sK3,sK4,sK0,sK1]),skolemize(U,sK6),skolemize(V,sK5),skolemize(W,sK2),skolemize(X,sK3),skolemize(X2,sK4),skolemize(X3,sK0),skolemize(X4,sK1)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ! [VAR_0] :
( ~ neq(sK3,nil)
| ~ geq(VAR_0,sK4)
| ~ memberP(sK3,VAR_0)
| VAR_0 = sK4
| ~ ssItem(VAR_0) )
& ( ~ neq(sK3,nil)
| app(sK0,sK1) = sK2 )
& ( ~ neq(sK3,nil)
| app(app(sK0,cons(sK4,nil)),sK1) = sK3 )
& ( ~ neq(sK3,nil)
| ssList(sK1) )
& ( ~ neq(sK3,nil)
| ssList(sK0) )
& ( ~ neq(sK3,nil)
| ssItem(sK4) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ neq(sK3,nil)
| ~ neq(VAR_1,nil)
| app(VAR_0,VAR_2) != sK6
| app(app(VAR_0,VAR_1),VAR_2) != sK5
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0) )
& neq(sK5,nil)
& sK2 = sK6
& sK3 = sK5
& ssList(sK3)
& ssList(sK2)
& ssList(sK5)
& ssList(sK6) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_192,negated_conjecture,
( ~ neq(sK3,nil)
| app(sK0,sK1) = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( ~ neq(sK3,nil)
| app(app(sK0,cons(sK4,nil)),sK1) = sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_194,negated_conjecture,
( ~ neq(sK3,nil)
| ssList(sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
( ~ neq(sK3,nil)
| ssList(sK0) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_196,negated_conjecture,
( ~ neq(sK3,nil)
| ssItem(sK4) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
( ~ neq(sK3,nil)
| ~ neq(B,nil)
| app(A,C) != sK6
| app(app(A,B),C) != sK5
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_198,negated_conjecture,
neq(sK5,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
sK2 = sK6,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_200,negated_conjecture,
sK3 = sK5,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_299,plain,
( cons(B,A) != A
| ~ ssItem(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax18]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_300,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_301,plain,
( ssList(cons(B,A))
| ~ ssItem(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax16]) ).
cnf(c_302,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_16945,negated_conjecture,
( ~ neq(sK3,nil)
| app(sK0,sK1) = sK6 ),
inference(paramod,[status(thm)],[c_199,c_192]) ).
cnf(c_16946,negated_conjecture,
( ~ neq(sK5,nil)
| app(sK0,sK1) = sK6 ),
inference(paramod,[status(thm)],[c_200,c_16945]) ).
cnf(c_553,negated_conjecture,
app(sK0,sK1) = sK6,
inference(resolve,[status(thm)],[c_198,c_16946]) ).
cnf(c_16947,negated_conjecture,
( ~ neq(sK5,nil)
| ~ neq(B,nil)
| app(A,C) != sK6
| app(app(A,B),C) != sK5
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_200,c_197]) ).
cnf(c_554,negated_conjecture,
( ~ neq(B,nil)
| app(A,C) != sK6
| app(app(A,B),C) != sK5
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_198,c_16947]) ).
cnf(c_16948,negated_conjecture,
( ~ neq(sK5,nil)
| ssItem(sK4) ),
inference(paramod,[status(thm)],[c_200,c_196]) ).
cnf(c_555,negated_conjecture,
ssItem(sK4),
inference(resolve,[status(thm)],[c_198,c_16948]) ).
cnf(c_16949,negated_conjecture,
( ~ neq(sK5,nil)
| ssList(sK0) ),
inference(paramod,[status(thm)],[c_200,c_195]) ).
cnf(c_556,negated_conjecture,
ssList(sK0),
inference(resolve,[status(thm)],[c_198,c_16949]) ).
cnf(c_16950,negated_conjecture,
( ~ neq(sK5,nil)
| ssList(sK1) ),
inference(paramod,[status(thm)],[c_200,c_194]) ).
cnf(c_557,negated_conjecture,
ssList(sK1),
inference(resolve,[status(thm)],[c_198,c_16950]) ).
cnf(c_16951,negated_conjecture,
( ~ neq(sK3,nil)
| app(app(sK0,cons(sK4,nil)),sK1) = sK5 ),
inference(paramod,[status(thm)],[c_200,c_193]) ).
cnf(c_16952,negated_conjecture,
( ~ neq(sK5,nil)
| app(app(sK0,cons(sK4,nil)),sK1) = sK5 ),
inference(paramod,[status(thm)],[c_200,c_16951]) ).
cnf(c_558,negated_conjecture,
app(app(sK0,cons(sK4,nil)),sK1) = sK5,
inference(resolve,[status(thm)],[c_198,c_16952]) ).
cnf(c_1877,plain,
( cons(A,nil) != nil
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_300,c_299]) ).
cnf(c_1933,plain,
( ssList(cons(A,nil))
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_301,c_300]) ).
cnf(c_1939,plain,
( nil = A
| neq(A,nil)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_302,c_300]) ).
cnf(c_16953,negated_conjecture,
( ~ neq(cons(sK4,nil),nil)
| app(sK0,sK1) != sK6
| ~ ssList(sK1)
| ~ ssList(cons(sK4,nil))
| ~ ssList(sK0) ),
inference(resolve,[status(thm)],[c_558,c_554]) ).
cnf(c_16954,negated_conjecture,
( ~ neq(cons(sK4,nil),nil)
| sK6 != sK6
| ~ ssList(sK1)
| ~ ssList(cons(sK4,nil))
| ~ ssList(sK0) ),
inference(paramod,[status(thm)],[c_553,c_16953]) ).
cnf(c_16955,negated_conjecture,
( ~ neq(cons(sK4,nil),nil)
| ~ ssList(sK1)
| ~ ssList(cons(sK4,nil))
| ~ ssList(sK0) ),
inference(copy,[status(thm)],[c_16954]) ).
cnf(c_16956,negated_conjecture,
( ~ neq(cons(sK4,nil),nil)
| ~ ssList(sK1)
| ~ ssList(cons(sK4,nil)) ),
inference(resolve,[status(thm)],[c_556,c_16955]) ).
cnf(c_2650,negated_conjecture,
( ~ neq(cons(sK4,nil),nil)
| ~ ssList(cons(sK4,nil)) ),
inference(resolve,[status(thm)],[c_557,c_16956]) ).
cnf(c_4686,plain,
cons(sK4,nil) != nil,
inference(resolve,[status(thm)],[c_1877,c_555]) ).
cnf(c_16896,plain,
ssList(cons(sK4,nil)),
inference(resolve,[status(thm)],[c_1933,c_555]) ).
cnf(c_16900,negated_conjecture,
~ neq(cons(sK4,nil),nil),
inference(resolve,[status(thm)],[c_16896,c_2650]) ).
cnf(c_16957,plain,
( nil = cons(sK4,nil)
| neq(cons(sK4,nil),nil) ),
inference(resolve,[status(thm)],[c_16896,c_1939]) ).
cnf(c_16958,plain,
( cons(sK4,nil) = nil
| neq(cons(sK4,nil),nil) ),
inference(copy,[status(thm)],[c_16957]) ).
cnf(c_16959,plain,
cons(sK4,nil) = nil,
inference(resolve,[status(thm)],[c_16900,c_16958]) ).
cnf(c_16944,plain,
$false,
inference(resolve,[status(thm)],[c_4686,c_16959]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC003+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/10.70 % Computer : n012.cluster.edu
% 0.05/10.70 % Model : x86_64 x86_64
% 0.05/10.70 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/10.70 % Memory : 8046.5625MB
% 0.05/10.70 % OS : Linux 6.8.0-71-generic
% 0.07/10.70 % CPULimit : 300
% 0.07/10.70 % WCLimit : 300
% 0.07/10.70 % DateTime : Sat Sep 26 12:02:31 UTC 2026
% 0.07/10.70 % CPUTime :
% 0.07/10.70 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/10.70 % Process 531437 was started by sandbox on n012,
% 0.07/10.70 % Sat Sep 26 12:02:31 2026
% 0.07/10.70 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/10.71
% 0.07/10.71 % From the command line: assign(max_seconds, 300).
% 239.40/42.01
% 239.40/42.01 % given #500 (I,wt=49): 698 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,E)),cons(C,D)) != A | C != B | ssItem(f33(A)). [factor(362,d,f)].
% 239.40/42.01
% 239.40/42.01 % given #1000 (I,wt=47): 1218 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | app(app(A,cons(B,D)),cons(C,A)) != A | C != B | ssList(f37(A)). [factor(721,a,e)].
% 239.40/42.01
% 239.40/42.01 % given #1500 (T,wt=13): 1937 -ssList(A) | neq(c3,A) | c3 = A. [resolve(302,a,204,a),flip(c)].
% 239.40/42.01
% 239.40/42.01 % given #2000 (F,wt=13): 13209 -ssList(A) | -rearsegP(nil,A) | -rearsegP(A,c4). [resolve(1767,a,300,a),unit_del(d,1957)].
% 239.40/42.01
% 239.40/42.01 % SZS status Theorem for theBenchmark
% 239.40/42.01
% 239.40/42.01 % Proof 1 at 5.17 (+ 1.81) seconds.
% 239.40/42.01 % Length of proof is 31.
% 239.40/42.01 % Level of proof is 5.
% 239.40/42.01 % Maximum clause weight is 41.000.
% 239.40/42.01 % Given clauses 2459.
% 239.40/42.01
% 239.40/42.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------