%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC023+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 27.54s 4.41s
% Output : CNFRefutation 27.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 41 ( 14 unt; 0 def)
% Number of atoms : 162 ( 48 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 174 ( 53 ~; 61 |; 47 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 25 ( 0 sgn 15 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [Z] :
( ssList(Z)
=> ( ~ frontsegP(W,Z)
| ~ frontsegP(X,Z)
| ~ neq(Z,nil) ) ) )
| ? [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)
=> ( ~ frontsegP(W,Z)
| ~ frontsegP(X,Z)
| ~ neq(Z,nil) ) ) )
| ? [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] :
( frontsegP(W,Z)
& frontsegP(X,Z)
& neq(Z,nil)
& 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 = sK0
& nil = sK2 )
| ( frontsegP(sK0,sK1)
& frontsegP(sK2,sK1)
& neq(sK1,nil)
& ssList(sK1) ) )
& ! [Y] :
( ~ frontsegP(sK4,Y)
| ~ frontsegP(sK3,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(sK3,nil)
& sK0 = sK4
& sK2 = sK3
& ssList(sK2)
& ssList(sK0)
& ssList(sK3)
& ssList(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK3,sK0,sK2,sK1]),skolemize(U,sK4),skolemize(V,sK3),skolemize(W,sK0),skolemize(X,sK2),skolemize(Z,sK1)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( nil = sK0
| frontsegP(sK0,sK1) )
& ( nil = sK2
| frontsegP(sK0,sK1) )
& ( nil = sK0
| frontsegP(sK2,sK1) )
& ( nil = sK2
| frontsegP(sK2,sK1) )
& ( nil = sK0
| neq(sK1,nil) )
& ( nil = sK2
| neq(sK1,nil) )
& ( nil = sK0
| ssList(sK1) )
& ( nil = sK2
| ssList(sK1) )
& ! [VAR_0] :
( ~ frontsegP(sK4,VAR_0)
| ~ frontsegP(sK3,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0) )
& neq(sK3,nil)
& sK0 = sK4
& sK2 = sK3
& ssList(sK2)
& ssList(sK0)
& ssList(sK3)
& ssList(sK4) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_192,negated_conjecture,
( nil = sK2
| frontsegP(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( sK2 = nil
| frontsegP(sK0,sK1) ),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_196,negated_conjecture,
( nil = sK2
| frontsegP(sK2,sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
( sK2 = nil
| frontsegP(sK2,sK1) ),
inference(copy,[status(thm)],[c_196]) ).
cnf(c_200,negated_conjecture,
( nil = sK2
| neq(sK1,nil) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_201,negated_conjecture,
( sK2 = nil
| neq(sK1,nil) ),
inference(copy,[status(thm)],[c_200]) ).
cnf(c_204,negated_conjecture,
( nil = sK2
| ssList(sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_205,negated_conjecture,
( sK2 = nil
| ssList(sK1) ),
inference(copy,[status(thm)],[c_204]) ).
cnf(c_206,negated_conjecture,
( ~ frontsegP(sK4,A)
| ~ frontsegP(sK3,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_207,negated_conjecture,
neq(sK3,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_208,negated_conjecture,
sK0 = sK4,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_209,negated_conjecture,
sK2 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_210,negated_conjecture,
ssList(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_211,negated_conjecture,
ssList(sK3),
inference(paramod,[status(thm)],[c_209,c_210]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_309,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_312,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_4420,negated_conjecture,
( sK2 = nil
| frontsegP(sK4,sK1) ),
inference(paramod,[status(thm)],[c_208,c_193]) ).
cnf(c_561,negated_conjecture,
( sK3 = nil
| frontsegP(sK4,sK1) ),
inference(paramod,[status(thm)],[c_209,c_4420]) ).
cnf(c_563,negated_conjecture,
( sK3 = nil
| ssList(sK1) ),
inference(paramod,[status(thm)],[c_209,c_205]) ).
cnf(c_564,negated_conjecture,
( sK3 = nil
| neq(sK1,nil) ),
inference(paramod,[status(thm)],[c_209,c_201]) ).
cnf(c_4421,negated_conjecture,
( sK2 = nil
| frontsegP(sK3,sK1) ),
inference(paramod,[status(thm)],[c_209,c_197]) ).
cnf(c_565,negated_conjecture,
( sK3 = nil
| frontsegP(sK3,sK1) ),
inference(paramod,[status(thm)],[c_209,c_4421]) ).
cnf(c_4422,negated_conjecture,
( nil != sK3
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(resolve,[status(thm)],[c_312,c_207]) ).
cnf(c_4423,negated_conjecture,
( sK3 != nil
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(copy,[status(thm)],[c_4422]) ).
cnf(c_4424,negated_conjecture,
( sK3 != nil
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_211,c_4423]) ).
cnf(c_2037,negated_conjecture,
sK3 != nil,
inference(resolve,[status(thm)],[c_309,c_4424]) ).
cnf(c_2064,negated_conjecture,
frontsegP(sK3,sK1),
inference(resolve,[status(thm)],[c_2037,c_565]) ).
cnf(c_2065,negated_conjecture,
neq(sK1,nil),
inference(resolve,[status(thm)],[c_2037,c_564]) ).
cnf(c_2066,negated_conjecture,
ssList(sK1),
inference(resolve,[status(thm)],[c_2037,c_563]) ).
cnf(c_2067,negated_conjecture,
frontsegP(sK4,sK1),
inference(resolve,[status(thm)],[c_2037,c_561]) ).
cnf(c_4425,negated_conjecture,
( ~ frontsegP(sK4,sK1)
| ~ frontsegP(sK3,sK1)
| ~ neq(sK1,nil) ),
inference(resolve,[status(thm)],[c_2066,c_206]) ).
cnf(c_4426,negated_conjecture,
( ~ frontsegP(sK4,sK1)
| ~ frontsegP(sK3,sK1) ),
inference(resolve,[status(thm)],[c_2065,c_4425]) ).
cnf(c_4427,negated_conjecture,
~ frontsegP(sK4,sK1),
inference(resolve,[status(thm)],[c_2064,c_4426]) ).
cnf(c_4419,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2067,c_4427]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC023+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n010.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 12:05:16 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.36 % Process 3243821 was started by sandbox2 on n010,
% 0.07/0.36 % Sat Sep 26 12:05:16 2026
% 0.07/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.40
% 0.07/0.40 % From the command line: assign(max_seconds, 300).
% 27.54/4.41
% 27.54/4.41 % given #500 (I,wt=37): 714 -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(375,a,e)].
% 27.54/4.41
% 27.54/4.41 % given #1000 (I,wt=52): 1234 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | app(app(A,cons(B,A)),cons(C,D)) != A | C != B | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A. [factor(734,a,d)].
% 27.54/4.41
% 27.54/4.41 % SZS status Theorem for theBenchmark
% 27.54/4.41
% 27.54/4.41 % Proof 1 at 3.37 (+ 0.49) seconds.
% 27.54/4.41 % Length of proof is 28.
% 27.54/4.41 % Level of proof is 5.
% 27.54/4.41 % Maximum clause weight is 13.000.
% 27.54/4.41 % Given clauses 1388.
% 27.54/4.41
% 27.54/4.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------