%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC020+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 : n014.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 08:56:33 AM UTC 2026
% Result : Theorem 15.07s 4.51s
% Output : CNFRefutation 15.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 11 unt; 0 def)
% Number of atoms : 164 ( 63 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 183 ( 64 ~; 66 |; 41 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 26 ( 0 sgn 14 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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)
=> ( ( ( ~ frontsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ( nil = U
& nil = V )
| ? [Y] :
( frontsegP(U,Y)
& frontsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| 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)
=> ( ( ( ~ frontsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ( nil = U
& nil = V )
| ? [Y] :
( frontsegP(U,Y)
& frontsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( frontsegP(X,W)
& neq(W,nil) )
| ( nil = W
& nil = X ) )
& ( nil != U
| nil != V )
& ! [Y] :
( ~ frontsegP(U,Y)
| ~ frontsegP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& 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,
( ( ( frontsegP(sK1,sK0)
& neq(sK0,nil) )
| ( nil = sK0
& nil = sK1 ) )
& ( nil != sK3
| nil != sK2 )
& ! [Y] :
( ~ frontsegP(sK3,Y)
| ~ frontsegP(sK2,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& sK0 = sK3
& sK1 = sK2
& ssList(sK1)
& ssList(sK0)
& ssList(sK2)
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK2,sK0,sK1]),skolemize(U,sK3),skolemize(V,sK2),skolemize(W,sK0),skolemize(X,sK1)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( frontsegP(sK1,sK0)
| nil = sK0 )
& ( neq(sK0,nil)
| nil = sK0 )
& ( frontsegP(sK1,sK0)
| nil = sK1 )
& ( neq(sK0,nil)
| nil = sK1 )
& ( nil != sK3
| nil != sK2 )
& ! [VAR_0] :
( ~ frontsegP(sK3,VAR_0)
| ~ frontsegP(sK2,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0) )
& sK0 = sK3
& sK1 = sK2
& ssList(sK1)
& ssList(sK0)
& ssList(sK2)
& ssList(sK3) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_190,negated_conjecture,
( frontsegP(sK1,sK0)
| nil = sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
( frontsegP(sK1,sK0)
| sK0 = nil ),
inference(copy,[status(thm)],[c_190]) ).
cnf(c_192,negated_conjecture,
( neq(sK0,nil)
| nil = sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( neq(sK0,nil)
| sK0 = nil ),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_196,negated_conjecture,
( neq(sK0,nil)
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
( neq(sK0,nil)
| sK1 = nil ),
inference(copy,[status(thm)],[c_196]) ).
cnf(c_198,negated_conjecture,
( nil != sK3
| nil != sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_4062,negated_conjecture,
( nil != sK3
| sK2 != nil ),
inference(copy,[status(thm)],[c_198]) ).
cnf(c_199,negated_conjecture,
( sK3 != nil
| sK2 != nil ),
inference(copy,[status(thm)],[c_4062]) ).
cnf(c_200,negated_conjecture,
( ~ frontsegP(sK3,A)
| ~ frontsegP(sK2,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_201,negated_conjecture,
sK0 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_202,negated_conjecture,
sK1 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_205,negated_conjecture,
ssList(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_206,negated_conjecture,
ssList(sK3),
inference(paramod,[status(thm)],[c_201,c_205]) ).
cnf(c_268,plain,
( frontsegP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax42]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_302,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_305,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_4063,negated_conjecture,
( neq(sK0,nil)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_202,c_197]) ).
cnf(c_551,negated_conjecture,
( neq(sK3,nil)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_201,c_4063]) ).
cnf(c_4064,negated_conjecture,
( neq(sK0,nil)
| sK3 = nil ),
inference(paramod,[status(thm)],[c_201,c_193]) ).
cnf(c_553,negated_conjecture,
( neq(sK3,nil)
| sK3 = nil ),
inference(paramod,[status(thm)],[c_201,c_4064]) ).
cnf(c_4065,negated_conjecture,
( frontsegP(sK1,sK0)
| sK3 = nil ),
inference(paramod,[status(thm)],[c_201,c_191]) ).
cnf(c_4066,negated_conjecture,
( frontsegP(sK2,sK0)
| sK3 = nil ),
inference(paramod,[status(thm)],[c_202,c_4065]) ).
cnf(c_554,negated_conjecture,
( frontsegP(sK2,sK3)
| sK3 = nil ),
inference(paramod,[status(thm)],[c_201,c_4066]) ).
cnf(c_1856,plain,
frontsegP(sK3,sK3),
inference(resolve,[status(thm)],[c_268,c_206]) ).
cnf(c_4067,negated_conjecture,
( A != sK3
| ~ neq(sK3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_305,c_206]) ).
cnf(c_2021,negated_conjecture,
( sK3 != A
| ~ neq(sK3,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_4067]) ).
cnf(c_2423,plain,
( sK3 != nil
| neq(sK3,nil) ),
inference(resolve,[status(thm)],[c_551,c_199]) ).
cnf(c_4068,negated_conjecture,
( ~ frontsegP(sK3,sK3)
| ~ neq(sK3,nil)
| ~ ssList(sK3)
| sK3 = nil ),
inference(resolve,[status(thm)],[c_554,c_200]) ).
cnf(c_4069,negated_conjecture,
( ~ frontsegP(sK3,sK3)
| ~ neq(sK3,nil)
| sK3 = nil ),
inference(resolve,[status(thm)],[c_206,c_4068]) ).
cnf(c_2517,negated_conjecture,
( ~ neq(sK3,nil)
| sK3 = nil ),
inference(resolve,[status(thm)],[c_1856,c_4069]) ).
cnf(c_4036,plain,
( sK3 != nil
| ~ neq(sK3,nil) ),
inference(resolve,[status(thm)],[c_2021,c_302]) ).
cnf(c_4070,negated_conjecture,
( neq(sK3,nil)
| neq(sK3,nil) ),
inference(resolve,[status(thm)],[c_2423,c_553]) ).
cnf(c_4059,negated_conjecture,
neq(sK3,nil),
inference(copy,[status(thm)],[c_4070]) ).
cnf(c_4060,plain,
sK3 != nil,
inference(resolve,[status(thm)],[c_4059,c_4036]) ).
cnf(c_4071,negated_conjecture,
~ neq(sK3,nil),
inference(resolve,[status(thm)],[c_4060,c_2517]) ).
cnf(c_4061,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_4059,c_4071]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC020+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 12:04:17 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3095701 was started by sandbox on n014,
% 0.10/0.37 % Sat Sep 26 12:04:17 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.40
% 0.10/0.40 % From the command line: assign(max_seconds, 300).
% 15.07/4.51
% 15.07/4.51 % given #500 (I,wt=37): 699 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,D)),cons(C,E)) != A | C != B | ssItem(f34(A)). [factor(366,d,e)].
% 15.07/4.51
% 15.07/4.51 % given #1000 (I,wt=32): 1219 -ssList(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(C,cons(B,C)),cons(B,D)) != A | ssList(f37(A)). [factor(719,c,d)].
% 15.07/4.51
% 15.07/4.51 % SZS status Theorem for theBenchmark
% 15.07/4.51
% 15.07/4.51 % Proof 1 at 1.80 (+ 0.31) seconds.
% 15.07/4.51 % Length of proof is 30.
% 15.07/4.51 % Level of proof is 7.
% 15.07/4.51 % Maximum clause weight is 13.000.
% 15.07/4.51 % Given clauses 1470.
% 15.07/4.51
% 15.07/4.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------