%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC024+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 08:56:34 AM UTC 2026
% Result : Theorem 96.20s 12.58s
% Output : CNFRefutation 96.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 20 unt; 0 def)
% Number of atoms : 195 ( 64 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 234 ( 88 ~; 76 |; 53 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 27 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax5,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) ) ) ),
file('theBenchmark.p',ax5) ).
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax42,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,U) ),
file('theBenchmark.p',ax42) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( nil = W
& nil != X )
| ! [Z] :
( ssList(Z)
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( app(X3,cons(X1,nil)) = W
& ssList(X3) )
& app(cons(X1,nil),X2) = Z
& ssList(X2) )
& ssItem(X1) )
| ~ equalelemsP(W)
| app(W,Z) != X ) )
| ? [Y] :
( frontsegP(U,Y)
& frontsegP(V,Y)
& neq(Y,nil)
& 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)
=> ( ( nil = W
& nil != X )
| ! [Z] :
( ssList(Z)
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( app(X3,cons(X1,nil)) = W
& ssList(X3) )
& app(cons(X1,nil),X2) = Z
& ssList(X2) )
& ssItem(X1) )
| ~ equalelemsP(W)
| app(W,Z) != X ) )
| ? [Y] :
( frontsegP(U,Y)
& frontsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != W
| nil = X )
& ? [Z] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( app(X3,cons(X1,nil)) != W
| ~ ssList(X3) )
| app(cons(X1,nil),X2) != Z
| ~ ssList(X2) )
| ~ ssItem(X1) )
& equalelemsP(W)
& app(W,Z) = X
& ssList(Z) )
& ! [Y] :
( ~ frontsegP(U,Y)
| ~ frontsegP(V,Y)
| ~ neq(Y,nil)
| ~ 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,
( ( nil != sK1
| nil = sK0 )
& ! [X1] :
( ! [X2] :
( ! [X3] :
( app(X3,cons(X1,nil)) != sK1
| ~ ssList(X3) )
| app(cons(X1,nil),X2) != sK2
| ~ ssList(X2) )
| ~ ssItem(X1) )
& equalelemsP(sK1)
& app(sK1,sK2) = sK0
& ssList(sK2)
& ! [Y] :
( ~ frontsegP(sK4,Y)
| ~ frontsegP(sK3,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(sK3,nil)
& sK1 = sK4
& sK0 = sK3
& ssList(sK0)
& ssList(sK1)
& ssList(sK3)
& ssList(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK3,sK1,sK0,sK2]),skolemize(U,sK4),skolemize(V,sK3),skolemize(W,sK1),skolemize(X,sK0),skolemize(Z,sK2)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( nil != sK1
| nil = sK0 )
& ! [VAR_0,VAR_1,VAR_2] :
( app(VAR_2,cons(VAR_0,nil)) != sK1
| ~ ssList(VAR_2)
| app(cons(VAR_0,nil),VAR_1) != sK2
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& equalelemsP(sK1)
& app(sK1,sK2) = sK0
& ssList(sK2)
& ! [VAR_0] :
( ~ frontsegP(sK4,VAR_0)
| ~ frontsegP(sK3,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0) )
& neq(sK3,nil)
& sK1 = sK4
& sK0 = sK3
& ssList(sK0)
& ssList(sK1)
& ssList(sK3)
& ssList(sK4) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_192,negated_conjecture,
( nil != sK1
| nil = sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_12932,negated_conjecture,
( nil != sK1
| sK0 = nil ),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_193,negated_conjecture,
( sK1 != nil
| sK0 = nil ),
inference(copy,[status(thm)],[c_12932]) ).
cnf(c_195,negated_conjecture,
app(sK1,sK2) = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_196,negated_conjecture,
ssList(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
( ~ frontsegP(sK4,A)
| ~ frontsegP(sK3,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_198,negated_conjecture,
neq(sK3,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
sK1 = sK4,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_200,negated_conjecture,
sK0 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_201,negated_conjecture,
ssList(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_202,negated_conjecture,
ssList(sK3),
inference(paramod,[status(thm)],[c_200,c_201]) ).
cnf(c_203,negated_conjecture,
ssList(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_204,negated_conjecture,
ssList(sK4),
inference(paramod,[status(thm)],[c_199,c_203]) ).
cnf(c_266,plain,
( frontsegP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax42]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_300,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_302,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_303,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_327,plain,
( app(B,C) != A
| ~ ssList(C)
| frontsegP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax5]) ).
cnf(c_12933,negated_conjecture,
app(sK4,sK2) = sK0,
inference(paramod,[status(thm)],[c_199,c_195]) ).
cnf(c_553,negated_conjecture,
app(sK4,sK2) = sK3,
inference(paramod,[status(thm)],[c_200,c_12933]) ).
cnf(c_12934,negated_conjecture,
( sK1 != nil
| sK3 = nil ),
inference(paramod,[status(thm)],[c_200,c_193]) ).
cnf(c_555,negated_conjecture,
( sK4 != nil
| sK3 = nil ),
inference(paramod,[status(thm)],[c_199,c_12934]) ).
cnf(c_3493,plain,
( ~ frontsegP(sK4,sK4)
| ~ frontsegP(sK3,sK4)
| ~ neq(sK4,nil) ),
inference(resolve,[status(thm)],[c_204,c_197]) ).
cnf(c_4626,plain,
frontsegP(sK4,sK4),
inference(resolve,[status(thm)],[c_266,c_204]) ).
cnf(c_4629,plain,
( ~ frontsegP(sK3,sK4)
| ~ neq(sK4,nil) ),
inference(resolve,[status(thm)],[c_4626,c_3493]) ).
cnf(c_12935,negated_conjecture,
( A = sK4
| neq(sK4,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_302,c_204]) ).
cnf(c_5491,negated_conjecture,
( sK4 = A
| neq(sK4,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_12935]) ).
cnf(c_12936,negated_conjecture,
( nil != sK3
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(resolve,[status(thm)],[c_303,c_198]) ).
cnf(c_12937,negated_conjecture,
( sK3 != nil
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(copy,[status(thm)],[c_12936]) ).
cnf(c_12938,negated_conjecture,
( sK3 != nil
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_202,c_12937]) ).
cnf(c_5506,negated_conjecture,
sK3 != nil,
inference(resolve,[status(thm)],[c_300,c_12938]) ).
cnf(c_5533,negated_conjecture,
sK4 != nil,
inference(resolve,[status(thm)],[c_5506,c_555]) ).
cnf(c_12939,negated_conjecture,
( ~ ssList(sK2)
| frontsegP(sK3,sK4)
| ~ ssList(sK4)
| ~ ssList(sK3) ),
inference(resolve,[status(thm)],[c_553,c_327]) ).
cnf(c_12940,negated_conjecture,
( ~ ssList(sK2)
| frontsegP(sK3,sK4)
| ~ ssList(sK4) ),
inference(resolve,[status(thm)],[c_202,c_12939]) ).
cnf(c_12941,negated_conjecture,
( ~ ssList(sK2)
| frontsegP(sK3,sK4) ),
inference(resolve,[status(thm)],[c_204,c_12940]) ).
cnf(c_10317,negated_conjecture,
frontsegP(sK3,sK4),
inference(resolve,[status(thm)],[c_196,c_12941]) ).
cnf(c_10325,plain,
~ neq(sK4,nil),
inference(resolve,[status(thm)],[c_10317,c_4629]) ).
cnf(c_12942,plain,
( sK4 = nil
| neq(sK4,nil) ),
inference(resolve,[status(thm)],[c_5491,c_300]) ).
cnf(c_12943,plain,
sK4 = nil,
inference(resolve,[status(thm)],[c_10325,c_12942]) ).
cnf(c_12931,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_5533,c_12943]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC024+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 12:04:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2687681 was started by sandbox on n013,
% 0.09/0.36 % Sat Sep 26 12:04:22 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 96.20/12.58
% 96.20/12.58 % given #500 (I,wt=49): 705 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,A)),cons(C,E)) != A | C != B | ssList(f35(A)). [factor(366,a,e)].
% 96.20/12.58
% 96.20/12.58 % given #1000 (I,wt=64): 1236 -ssList(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(C,cons(B,D)),cons(B,D)) != A | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A. [factor(728,d,e)].
% 96.20/12.58
% 96.20/12.58 % SZS status Theorem for theBenchmark
% 96.20/12.58
% 96.20/12.58 % Proof 1 at 3.76 (+ 0.36) seconds.
% 96.20/12.58 % Length of proof is 32.
% 96.20/12.58 % Level of proof is 6.
% 96.20/12.58 % Maximum clause weight is 24.000.
% 96.20/12.58 % Given clauses 1439.
% 96.20/12.58
% 96.20/12.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------