%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC060+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 : 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 08:56:42 AM UTC 2026
% Result : Theorem 22.32s 3.64s
% Output : CNFRefutation 22.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 6
% Syntax : Number of formulae : 63 ( 16 unt; 0 def)
% Number of atoms : 229 ( 93 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 256 ( 90 ~; 106 |; 46 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 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 : 32 ( 0 sgn 18 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax54,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( segmentP(V,U)
& segmentP(U,V) )
=> U = V ) ) ),
file('theBenchmark.p',ax54) ).
fof(ax55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('theBenchmark.p',ax55) ).
fof(ax57,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('theBenchmark.p',ax57) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( ~ segmentP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ( ( ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( ~ segmentP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ( ( ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( segmentP(X,W)
& neq(W,nil) )
| ( nil = W
& nil = X ) )
& ( ( ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& 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,
( ( ( segmentP(sK1,sK0)
& neq(sK0,nil) )
| ( nil = sK0
& nil = sK1 ) )
& ( ( ! [Y] :
( ~ segmentP(sK2,Y)
| ~ segmentP(sK3,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(sK3,nil) )
| ( nil != sK2
& nil = sK3 ) )
& sK0 = sK2
& sK1 = sK3
& ssList(sK1)
& ssList(sK0)
& ssList(sK3)
& ssList(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK0,sK1]),skolemize(U,sK2),skolemize(V,sK3),skolemize(W,sK0),skolemize(X,sK1)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( segmentP(sK1,sK0)
| nil = sK0 )
& ( neq(sK0,nil)
| nil = sK0 )
& ( segmentP(sK1,sK0)
| nil = sK1 )
& ( neq(sK0,nil)
| nil = sK1 )
& ! [VAR_0] :
( ~ segmentP(sK2,VAR_0)
| ~ segmentP(sK3,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0)
| nil != sK2 )
& ( neq(sK3,nil)
| nil != sK2 )
& ! [VAR_0] :
( ~ segmentP(sK2,VAR_0)
| ~ segmentP(sK3,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0)
| nil = sK3 )
& ( neq(sK3,nil)
| nil = sK3 )
& sK0 = sK2
& sK1 = sK3
& ssList(sK1)
& ssList(sK0)
& ssList(sK3)
& ssList(sK2) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_190,negated_conjecture,
( segmentP(sK1,sK0)
| nil = sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
( segmentP(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_200,negated_conjecture,
( neq(sK3,nil)
| nil != sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_201,negated_conjecture,
( neq(sK3,nil)
| sK2 != nil ),
inference(copy,[status(thm)],[c_200]) ).
cnf(c_202,negated_conjecture,
( ~ segmentP(sK2,A)
| ~ segmentP(sK3,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil = sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_203,negated_conjecture,
( ~ segmentP(sK2,A)
| ~ segmentP(sK3,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sK3 = nil ),
inference(copy,[status(thm)],[c_202]) ).
cnf(c_206,negated_conjecture,
sK0 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_207,negated_conjecture,
sK1 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_209,negated_conjecture,
ssList(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_210,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_211,negated_conjecture,
ssList(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_254,plain,
( segmentP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax57]) ).
cnf(c_256,plain,
( segmentP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax55]) ).
cnf(c_257,plain,
( B = A
| ~ segmentP(B,A)
| ~ segmentP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax54]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_307,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_310,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_1657,plain,
( segmentP(sK1,sK2)
| sK0 = nil ),
inference(paramod,[status(thm)],[c_206,c_191]) ).
cnf(c_1658,plain,
( neq(sK2,nil)
| sK0 = nil ),
inference(paramod,[status(thm)],[c_206,c_193]) ).
cnf(c_1661,plain,
( segmentP(sK3,sK0)
| sK0 = nil ),
inference(paramod,[status(thm)],[c_207,c_191]) ).
cnf(c_1785,plain,
segmentP(sK0,nil),
inference(resolve,[status(thm)],[c_254,c_209]) ).
cnf(c_1791,plain,
segmentP(sK2,sK2),
inference(resolve,[status(thm)],[c_256,c_211]) ).
cnf(c_11322,negated_conjecture,
( sK1 = nil
| nil != sK0
| ~ ssList(nil)
| ~ ssList(sK0) ),
inference(resolve,[status(thm)],[c_310,c_197]) ).
cnf(c_11323,negated_conjecture,
( sK1 = nil
| sK0 != nil
| ~ ssList(nil)
| ~ ssList(sK0) ),
inference(copy,[status(thm)],[c_11322]) ).
cnf(c_11324,negated_conjecture,
( sK1 = nil
| sK0 != nil
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_209,c_11323]) ).
cnf(c_1892,negated_conjecture,
( sK1 = nil
| sK0 != nil ),
inference(resolve,[status(thm)],[c_307,c_11324]) ).
cnf(c_11325,plain,
( sK0 = nil
| ~ segmentP(nil,sK0)
| ~ ssList(sK0)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_1785,c_257]) ).
cnf(c_11326,plain,
( sK0 = nil
| ~ segmentP(nil,sK0)
| ~ ssList(sK0) ),
inference(resolve,[status(thm)],[c_307,c_11325]) ).
cnf(c_4960,negated_conjecture,
( sK0 = nil
| ~ segmentP(nil,sK0) ),
inference(resolve,[status(thm)],[c_209,c_11326]) ).
cnf(c_5010,plain,
( segmentP(sK3,sK2)
| sK0 = nil ),
inference(paramod,[status(thm)],[c_207,c_1657]) ).
cnf(c_11327,negated_conjecture,
( ~ segmentP(sK2,sK2)
| ~ segmentP(sK3,sK2)
| ~ ssList(sK2)
| sK3 = nil
| sK0 = nil ),
inference(resolve,[status(thm)],[c_1658,c_203]) ).
cnf(c_11328,negated_conjecture,
( ~ segmentP(sK2,sK2)
| ~ segmentP(sK3,sK2)
| sK3 = nil
| sK0 = nil ),
inference(resolve,[status(thm)],[c_211,c_11327]) ).
cnf(c_5013,negated_conjecture,
( ~ segmentP(sK3,sK2)
| sK3 = nil
| sK0 = nil ),
inference(resolve,[status(thm)],[c_1791,c_11328]) ).
cnf(c_11329,plain,
( sK0 = nil
| sK3 = nil
| sK0 = nil ),
inference(resolve,[status(thm)],[c_5013,c_5010]) ).
cnf(c_10139,plain,
( sK3 = nil
| sK0 = nil ),
inference(copy,[status(thm)],[c_11329]) ).
cnf(c_10140,plain,
( sK1 = nil
| sK3 = nil ),
inference(resolve,[status(thm)],[c_10139,c_1892]) ).
cnf(c_11330,plain,
( nil = sK3
| sK3 = nil ),
inference(paramod,[status(thm)],[c_10140,c_207]) ).
cnf(c_11331,plain,
( sK3 = nil
| sK3 = nil ),
inference(copy,[status(thm)],[c_11330]) ).
cnf(c_10180,plain,
sK3 = nil,
inference(copy,[status(thm)],[c_11331]) ).
cnf(c_10303,plain,
( segmentP(nil,sK0)
| sK0 = nil ),
inference(paramod,[status(thm)],[c_10180,c_1661]) ).
cnf(c_11332,plain,
( sK0 = nil
| sK0 = nil ),
inference(resolve,[status(thm)],[c_10303,c_4960]) ).
cnf(c_10684,plain,
sK0 = nil,
inference(copy,[status(thm)],[c_11332]) ).
cnf(c_11333,plain,
nil = sK2,
inference(paramod,[status(thm)],[c_10684,c_206]) ).
cnf(c_10970,plain,
sK2 = nil,
inference(copy,[status(thm)],[c_11333]) ).
cnf(c_11053,negated_conjecture,
neq(sK3,nil),
inference(resolve,[status(thm)],[c_10970,c_201]) ).
cnf(c_11334,negated_conjecture,
( nil != sK3
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(resolve,[status(thm)],[c_11053,c_310]) ).
cnf(c_11335,negated_conjecture,
( sK3 != nil
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(copy,[status(thm)],[c_11334]) ).
cnf(c_11336,negated_conjecture,
( sK3 != nil
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_210,c_11335]) ).
cnf(c_11337,negated_conjecture,
sK3 != nil,
inference(resolve,[status(thm)],[c_307,c_11336]) ).
cnf(c_11321,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_10180,c_11337]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC060+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 12:08:51 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 2694615 was started by sandbox2 on n013,
% 0.08/0.35 % Sat Sep 26 12:08:51 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 22.32/3.64
% 22.32/3.64 % given #500 (I,wt=49): 704 -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(373,a,e)].
% 22.32/3.64
% 22.32/3.64 % given #1000 (I,wt=64): 1229 -ssList(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(C,cons(B,A)),cons(B,D)) != A | app(app(f35(A),cons(f33(A),f36(A))),cons(f34(A),f37(A))) = A. [factor(725,b,c),xx(f)].
% 22.32/3.64
% 22.32/3.64 % given #1500 (F,wt=33): 5659 app(app(c4,cons(c1,c6)),cons(c1,c6)) != nil. [para(207(a,1),5644(a,1,1,1))].
% 22.32/3.64
% 22.32/3.64 % SZS status Theorem for theBenchmark
% 22.32/3.64
% 22.32/3.64 % Proof 1 at 2.88 (+ 0.32) seconds.
% 22.32/3.64 % Length of proof is 42.
% 22.32/3.64 % Level of proof is 12.
% 22.32/3.64 % Maximum clause weight is 19.000.
% 22.32/3.64 % Given clauses 1896.
% 22.32/3.64
% 22.32/3.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------