%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC217+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 08:57:11 AM UTC 2026
% Result : Theorem 30.30s 9.24s
% Output : CNFRefutation 30.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 17 unt; 0 def)
% Number of atoms : 156 ( 52 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 170 ( 60 ~; 51 |; 38 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 18 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax18,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
file('theBenchmark.p',ax18) ).
fof(ax41,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( frontsegP(V,U)
& frontsegP(U,V) )
=> U = V ) ) ),
file('theBenchmark.p',ax41) ).
fof(ax45,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,nil) ),
file('theBenchmark.p',ax45) ).
fof(ax46,axiom,
! [U] :
( ssList(U)
=> ( frontsegP(nil,U)
<=> nil = U ) ),
file('theBenchmark.p',ax46) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ! [Y] :
( ssItem(Y)
=> ( ~ memberP(X,Y)
| cons(Y,nil) != W ) ) )
| ( nil = X
& nil != W )
| neq(U,nil)
| ~ 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)
& ! [Y] :
( ssItem(Y)
=> ( ~ memberP(X,Y)
| cons(Y,nil) != W ) ) )
| ( nil = X
& nil != W )
| neq(U,nil)
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ neq(X,nil)
| ? [Y] :
( memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) ) )
& ( nil != X
| nil = W )
& ~ neq(U,nil)
& 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)
| ( memberP(sK2,sK0)
& cons(sK0,nil) = sK1
& ssItem(sK0) ) )
& ( nil != sK2
| nil = sK1 )
& ~ neq(sK3,nil)
& neq(sK4,nil)
& sK1 = sK3
& sK2 = sK4
& ssList(sK2)
& ssList(sK1)
& ssList(sK4)
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK1,sK2,sK0]),skolemize(U,sK3),skolemize(V,sK4),skolemize(W,sK1),skolemize(X,sK2),skolemize(Y,sK0)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ neq(sK2,nil)
| memberP(sK2,sK0) )
& ( ~ neq(sK2,nil)
| cons(sK0,nil) = sK1 )
& ( ~ neq(sK2,nil)
| ssItem(sK0) )
& ( nil != sK2
| nil = sK1 )
& ~ neq(sK3,nil)
& neq(sK4,nil)
& sK1 = sK3
& sK2 = sK4
& ssList(sK2)
& ssList(sK1)
& ssList(sK4)
& ssList(sK3) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_191,negated_conjecture,
( ~ neq(sK2,nil)
| cons(sK0,nil) = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
( ~ neq(sK2,nil)
| ssItem(sK0) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
~ neq(sK3,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_196,negated_conjecture,
neq(sK4,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
sK1 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_198,negated_conjecture,
sK2 = sK4,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_200,negated_conjecture,
ssList(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_202,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_257,plain,
( nil != A
| frontsegP(nil,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax46]) ).
cnf(c_259,plain,
( frontsegP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax45]) ).
cnf(c_265,plain,
( B = A
| ~ frontsegP(B,A)
| ~ frontsegP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax41]) ).
cnf(c_297,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_298,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_300,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_7138,plain,
( ~ neq(sK4,nil)
| cons(sK0,nil) = sK1 ),
inference(paramod,[status(thm)],[c_198,c_191]) ).
cnf(c_1644,negated_conjecture,
cons(sK0,nil) = sK1,
inference(resolve,[status(thm)],[c_196,c_7138]) ).
cnf(c_7139,plain,
( ~ neq(sK4,nil)
| ssItem(sK0) ),
inference(paramod,[status(thm)],[c_198,c_192]) ).
cnf(c_1645,negated_conjecture,
ssItem(sK0),
inference(resolve,[status(thm)],[c_196,c_7139]) ).
cnf(c_7140,negated_conjecture,
( nil != sK3
| frontsegP(nil,sK3) ),
inference(resolve,[status(thm)],[c_257,c_202]) ).
cnf(c_1787,negated_conjecture,
( sK3 != nil
| frontsegP(nil,sK3) ),
inference(copy,[status(thm)],[c_7140]) ).
cnf(c_1793,plain,
frontsegP(sK1,nil),
inference(resolve,[status(thm)],[c_259,c_200]) ).
cnf(c_7141,negated_conjecture,
( A = sK3
| neq(sK3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_300,c_202]) ).
cnf(c_1856,negated_conjecture,
( sK3 = A
| neq(sK3,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_7141]) ).
cnf(c_6122,plain,
( cons(sK0,A) != A
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_1645,c_297]) ).
cnf(c_7142,plain,
( sK1 = nil
| ~ frontsegP(nil,sK1)
| ~ ssList(sK1)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_1793,c_265]) ).
cnf(c_7143,plain,
( sK1 = nil
| ~ frontsegP(nil,sK1)
| ~ ssList(sK1) ),
inference(resolve,[status(thm)],[c_298,c_7142]) ).
cnf(c_6373,negated_conjecture,
( sK1 = nil
| ~ frontsegP(nil,sK1) ),
inference(resolve,[status(thm)],[c_200,c_7143]) ).
cnf(c_6998,plain,
( sK1 = nil
| ~ frontsegP(nil,sK3) ),
inference(paramod,[status(thm)],[c_197,c_6373]) ).
cnf(c_7005,plain,
cons(sK0,nil) != nil,
inference(resolve,[status(thm)],[c_6122,c_298]) ).
cnf(c_7010,plain,
sK1 != nil,
inference(paramod,[status(thm)],[c_1644,c_7005]) ).
cnf(c_7013,plain,
~ frontsegP(nil,sK3),
inference(resolve,[status(thm)],[c_7010,c_6998]) ).
cnf(c_7049,negated_conjecture,
sK3 != nil,
inference(resolve,[status(thm)],[c_7013,c_1787]) ).
cnf(c_7144,plain,
( sK3 = nil
| neq(sK3,nil) ),
inference(resolve,[status(thm)],[c_1856,c_298]) ).
cnf(c_7145,negated_conjecture,
sK3 = nil,
inference(resolve,[status(thm)],[c_195,c_7144]) ).
cnf(c_7137,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_7049,c_7145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC217+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n013.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Sat Sep 26 12:31:42 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.37 % Process 2734972 was started by sandbox on n013,
% 0.10/5.37 % Sat Sep 26 12:31:42 2026
% 0.10/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.39
% 0.10/5.39 % From the command line: assign(max_seconds, 300).
% 30.30/9.24
% 30.30/9.24 % given #500 (I,wt=46): 697 -ssList(A) | -ssItem(B) | -ssList(C) | -ssList(D) | -ssList(E) | app(app(C,cons(B,D)),cons(B,E)) != A | ssList(f35(A)). [factor(364,b,c),xx(g)].
% 30.30/9.24
% 30.30/9.24 % given #1000 (I,wt=64): 1222 -ssList(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(C,cons(B,D)),cons(B,A)) != A | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A. [factor(717,b,c),xx(f)].
% 30.30/9.24
% 30.30/9.24 % given #1500 (T,wt=11): 6186 -segmentP(nil,c3) | c3 = nil. [resolve(1767,a,248,d),unit_del(a,298),unit_del(b,202)].
% 30.30/9.24
% 30.30/9.24 % SZS status Theorem for theBenchmark
% 30.30/9.24
% 30.30/9.24 % Proof 1 at 3.52 (+ 0.29) seconds.
% 30.30/9.24 % Length of proof is 33.
% 30.30/9.24 % Level of proof is 8.
% 30.30/9.24 % Maximum clause weight is 19.000.
% 30.30/9.24 % Given clauses 1539.
% 30.30/9.24
% 30.30/9.24 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------