%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC059+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 : n019.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 08:56:42 AM UTC 2026
% Result : Theorem 18.20s 2.80s
% Output : CNFRefutation 18.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 49 ( 15 unt; 0 def)
% Number of atoms : 189 ( 68 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 224 ( 84 ~; 82 |; 46 &)
% ( 1 <=>; 11 =>; 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 : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 26 ( 0 sgn 15 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('theBenchmark.p',ax55) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( ( ~ segmentP(X,W)
| ~ neq(W,nil) )
& neq(X,nil) )
| ( nil = X
& nil != W )
| 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)
=> ( ( ( ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( ( ~ segmentP(X,W)
| ~ neq(W,nil) )
& neq(X,nil) )
| ( nil = X
& nil != W )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& ( ( segmentP(X,W)
& neq(W,nil) )
| ~ neq(X,nil) )
& ( nil != X
| nil = W )
& 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,
( ( ( ! [Y] :
( ~ segmentP(sK0,Y)
| ~ segmentP(sK1,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(sK1,nil) )
| ( nil != sK0
& nil = sK1 ) )
& ( ( segmentP(sK2,sK3)
& neq(sK3,nil) )
| ~ neq(sK2,nil) )
& ( nil != sK2
| nil = sK3 )
& sK3 = sK0
& sK2 = sK1
& ssList(sK2)
& ssList(sK3)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK3,sK2]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK3),skolemize(X,sK2)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ! [VAR_0] :
( ~ segmentP(sK0,VAR_0)
| ~ segmentP(sK1,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0)
| nil != sK0 )
& ( neq(sK1,nil)
| nil != sK0 )
& ! [VAR_0] :
( ~ segmentP(sK0,VAR_0)
| ~ segmentP(sK1,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0)
| nil = sK1 )
& ( neq(sK1,nil)
| nil = sK1 )
& ( segmentP(sK2,sK3)
| ~ neq(sK2,nil) )
& ( neq(sK3,nil)
| ~ neq(sK2,nil) )
& ( nil != sK2
| nil = sK3 )
& sK3 = sK0
& sK2 = sK1
& ssList(sK2)
& ssList(sK3)
& ssList(sK1)
& ssList(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_192,negated_conjecture,
( neq(sK1,nil)
| nil != sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( neq(sK1,nil)
| sK0 != nil ),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_194,negated_conjecture,
( ~ segmentP(sK0,A)
| ~ segmentP(sK1,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
( ~ segmentP(sK0,A)
| ~ segmentP(sK1,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sK1 = nil ),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_196,negated_conjecture,
( neq(sK1,nil)
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
( neq(sK1,nil)
| sK1 = nil ),
inference(copy,[status(thm)],[c_196]) ).
cnf(c_198,negated_conjecture,
( segmentP(sK2,sK3)
| ~ neq(sK2,nil) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
( neq(sK3,nil)
| ~ neq(sK2,nil) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_200,negated_conjecture,
( nil != sK2
| nil = sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_6077,negated_conjecture,
( nil != sK2
| sK3 = nil ),
inference(copy,[status(thm)],[c_200]) ).
cnf(c_201,negated_conjecture,
( sK2 != nil
| sK3 = nil ),
inference(copy,[status(thm)],[c_6077]) ).
cnf(c_202,negated_conjecture,
sK3 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_203,negated_conjecture,
sK2 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_205,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_206,negated_conjecture,
ssList(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_252,plain,
( segmentP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax55]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_303,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_306,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_1649,plain,
( segmentP(sK2,sK3)
| ~ neq(sK1,nil) ),
inference(paramod,[status(thm)],[c_203,c_198]) ).
cnf(c_1650,plain,
( neq(sK3,nil)
| ~ neq(sK1,nil) ),
inference(paramod,[status(thm)],[c_203,c_199]) ).
cnf(c_1651,plain,
( sK1 != nil
| sK3 = nil ),
inference(paramod,[status(thm)],[c_203,c_201]) ).
cnf(c_1778,plain,
segmentP(sK3,sK3),
inference(resolve,[status(thm)],[c_252,c_205]) ).
cnf(c_4865,plain,
( sK1 = nil
| segmentP(sK2,sK3) ),
inference(resolve,[status(thm)],[c_1649,c_197]) ).
cnf(c_4866,plain,
( sK1 = nil
| neq(sK3,nil) ),
inference(resolve,[status(thm)],[c_1650,c_197]) ).
cnf(c_4965,plain,
segmentP(sK0,sK3),
inference(paramod,[status(thm)],[c_202,c_1778]) ).
cnf(c_5574,plain,
( sK1 = nil
| segmentP(sK1,sK3) ),
inference(paramod,[status(thm)],[c_203,c_4865]) ).
cnf(c_6078,negated_conjecture,
( ~ segmentP(sK0,sK3)
| ~ segmentP(sK1,sK3)
| ~ ssList(sK3)
| sK1 = nil
| sK1 = nil ),
inference(resolve,[status(thm)],[c_4866,c_195]) ).
cnf(c_6079,negated_conjecture,
( ~ segmentP(sK0,sK3)
| ~ segmentP(sK1,sK3)
| ~ ssList(sK3)
| sK1 = nil ),
inference(copy,[status(thm)],[c_6078]) ).
cnf(c_6080,negated_conjecture,
( ~ segmentP(sK0,sK3)
| ~ segmentP(sK1,sK3)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_205,c_6079]) ).
cnf(c_5577,negated_conjecture,
( ~ segmentP(sK1,sK3)
| sK1 = nil ),
inference(resolve,[status(thm)],[c_4965,c_6080]) ).
cnf(c_6081,plain,
( sK1 = nil
| sK1 = nil ),
inference(resolve,[status(thm)],[c_5577,c_5574]) ).
cnf(c_5823,plain,
sK1 = nil,
inference(copy,[status(thm)],[c_6081]) ).
cnf(c_5841,plain,
sK3 = nil,
inference(resolve,[status(thm)],[c_5823,c_1651]) ).
cnf(c_6082,plain,
nil = sK0,
inference(paramod,[status(thm)],[c_5841,c_202]) ).
cnf(c_5956,plain,
sK0 = nil,
inference(copy,[status(thm)],[c_6082]) ).
cnf(c_5997,negated_conjecture,
neq(sK1,nil),
inference(resolve,[status(thm)],[c_5956,c_193]) ).
cnf(c_6083,negated_conjecture,
( nil != sK1
| ~ ssList(nil)
| ~ ssList(sK1) ),
inference(resolve,[status(thm)],[c_5997,c_306]) ).
cnf(c_6084,negated_conjecture,
( sK1 != nil
| ~ ssList(nil)
| ~ ssList(sK1) ),
inference(copy,[status(thm)],[c_6083]) ).
cnf(c_6085,negated_conjecture,
( sK1 != nil
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_206,c_6084]) ).
cnf(c_6086,negated_conjecture,
sK1 != nil,
inference(resolve,[status(thm)],[c_303,c_6085]) ).
cnf(c_6076,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_5823,c_6086]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC059+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 12:09:33 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 1256307 was started by sandbox on n019,
% 0.10/0.37 % Sat Sep 26 12:09:33 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.39
% 0.14/0.39 % From the command line: assign(max_seconds, 300).
% 18.20/2.80
% 18.20/2.80 % given #500 (I,wt=47): 701 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,E)),cons(C,A)) != A | C != B | ssList(f35(A)). [factor(369,a,f)].
% 18.20/2.80
% 18.20/2.80 % given #1000 (I,wt=63): 1226 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | app(app(D,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(721,d,e)].
% 18.20/2.80
% 18.20/2.80 % given #1500 (F,wt=31): 5546 app(app(c3,cons(c1,c3)),cons(c1,c5)) != nil. [para(202(a,1),5536(a,1,1,2,2))].
% 18.20/2.80
% 18.20/2.80 % SZS status Theorem for theBenchmark
% 18.20/2.80
% 18.20/2.80 % Proof 1 at 2.18 (+ 0.19) seconds.
% 18.20/2.80 % Length of proof is 34.
% 18.20/2.80 % Level of proof is 9.
% 18.20/2.80 % Maximum clause weight is 19.000.
% 18.20/2.80 % Given clauses 1588.
% 18.20/2.80
% 18.20/2.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------