%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC039+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 : n020.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 08:56:37 AM UTC 2026
% Result : Theorem 13.91s 2.52s
% Output : CNFRefutation 13.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 42 ( 16 unt; 0 def)
% Number of atoms : 202 ( 84 equ)
% Maximal formula atoms : 44 ( 4 avg)
% Number of connectives : 226 ( 66 ~; 78 |; 63 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 25 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax7,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('theBenchmark.p',ax7) ).
fof(ax58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ),
file('theBenchmark.p',ax58) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] :
( lt(Y,X2)
& memberP(Z,X2)
& ssItem(X2) )
| app(app(Z,W),X1) != X
| cons(Y,nil) != W ) ) ) ) )
| nil = U
| U != W
| V != X
| nil != V ) ) ) ) ),
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 )
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] :
( lt(Y,X2)
& memberP(Z,X2)
& ssItem(X2) )
| app(app(Z,W),X1) != X
| cons(Y,nil) != W ) ) ) ) )
| nil = U
| U != W
| V != X
| nil != V ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_213,plain,
( app(app(C,B),D) != A
| ~ ssList(D)
| ~ ssList(C)
| segmentP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax7]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_231,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_285,plain,
( nil = A
| ~ segmentP(nil,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax58]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] :
( ~ lt(Y,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) ) )
& nil != U
& W = U
& X = V
& nil = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg_sk,plain,
( ( ( nil = sK3
& nil = sK2 )
| ( ! [X3] :
( ~ lt(X3,sK8)
| ~ memberP(sK5,X3)
| ~ ssItem(X3) )
& ! [X2] :
( ~ lt(sK8,X2)
| ~ memberP(sK4,X2)
| ~ ssItem(X2) )
& app(app(sK4,sK3),sK5) = sK2
& cons(sK8,nil) = sK3
& ssList(sK5)
& ssList(sK4)
& ssItem(sK8) ) )
& nil != sK0
& sK3 = sK0
& sK2 = sK1
& nil = sK1
& ssList(sK2)
& ssList(sK3)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK3,sK2,sK8,sK4,sK5]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK3),skolemize(X,sK2),skolemize(Y,sK8),skolemize(Z,sK4),skolemize(X1,sK5)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ! [VAR_0] :
( nil = sK3
| ~ lt(VAR_0,sK8)
| ~ memberP(sK5,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( nil = sK2
| ~ lt(VAR_0,sK8)
| ~ memberP(sK5,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( nil = sK3
| ~ lt(sK8,VAR_0)
| ~ memberP(sK4,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( nil = sK2
| ~ lt(sK8,VAR_0)
| ~ memberP(sK4,VAR_0)
| ~ ssItem(VAR_0) )
& ( nil = sK3
| app(app(sK4,sK3),sK5) = sK2 )
& ( nil = sK2
| app(app(sK4,sK3),sK5) = sK2 )
& ( nil = sK3
| cons(sK8,nil) = sK3 )
& ( nil = sK2
| cons(sK8,nil) = sK3 )
& ( nil = sK3
| ssList(sK5) )
& ( nil = sK2
| ssList(sK5) )
& ( nil = sK3
| ssList(sK4) )
& ( nil = sK2
| ssList(sK4) )
& ( nil = sK3
| ssItem(sK8) )
& ( nil = sK2
| ssItem(sK8) )
& nil != sK0
& sK3 = sK0
& sK2 = sK1
& nil = sK1
& ssList(sK2)
& ssList(sK3)
& ssList(sK1)
& ssList(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_327,negated_conjecture,
ssList(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_331,negated_conjecture,
nil = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_332,negated_conjecture,
sK1 = nil,
inference(copy,[status(thm)],[c_331]) ).
cnf(c_333,negated_conjecture,
sK2 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_334,negated_conjecture,
sK2 = nil,
inference(paramod,[status(thm)],[c_332,c_333]) ).
cnf(c_335,negated_conjecture,
sK3 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_336,negated_conjecture,
nil != sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_337,negated_conjecture,
sK0 != nil,
inference(copy,[status(thm)],[c_336]) ).
cnf(c_342,negated_conjecture,
( nil = sK3
| ssList(sK4) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2705,negated_conjecture,
( nil = sK0
| ssList(sK4) ),
inference(paramod,[status(thm)],[c_335,c_342]) ).
cnf(c_2706,negated_conjecture,
( sK0 = nil
| ssList(sK4) ),
inference(copy,[status(thm)],[c_2705]) ).
cnf(c_343,negated_conjecture,
ssList(sK4),
inference(resolve,[status(thm)],[c_337,c_2706]) ).
cnf(c_345,negated_conjecture,
( nil = sK3
| ssList(sK5) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2707,negated_conjecture,
( nil = sK0
| ssList(sK5) ),
inference(paramod,[status(thm)],[c_335,c_345]) ).
cnf(c_2708,negated_conjecture,
( sK0 = nil
| ssList(sK5) ),
inference(copy,[status(thm)],[c_2707]) ).
cnf(c_346,negated_conjecture,
ssList(sK5),
inference(resolve,[status(thm)],[c_337,c_2708]) ).
cnf(c_351,negated_conjecture,
( nil = sK3
| app(app(sK4,sK3),sK5) = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2709,negated_conjecture,
( nil = sK3
| app(app(sK4,sK0),sK5) = sK2 ),
inference(paramod,[status(thm)],[c_335,c_351]) ).
cnf(c_2710,negated_conjecture,
( nil = sK3
| app(app(sK4,sK0),sK5) = nil ),
inference(paramod,[status(thm)],[c_334,c_2709]) ).
cnf(c_2711,negated_conjecture,
( nil = sK0
| app(app(sK4,sK0),sK5) = nil ),
inference(paramod,[status(thm)],[c_335,c_2710]) ).
cnf(c_2712,negated_conjecture,
( sK0 = nil
| app(app(sK4,sK0),sK5) = nil ),
inference(copy,[status(thm)],[c_2711]) ).
cnf(c_352,negated_conjecture,
app(app(sK4,sK0),sK5) = nil,
inference(resolve,[status(thm)],[c_337,c_2712]) ).
cnf(c_2713,negated_conjecture,
( nil = sK0
| ~ segmentP(nil,sK0) ),
inference(resolve,[status(thm)],[c_327,c_285]) ).
cnf(c_2714,negated_conjecture,
( sK0 = nil
| ~ segmentP(nil,sK0) ),
inference(copy,[status(thm)],[c_2713]) ).
cnf(c_2007,negated_conjecture,
~ segmentP(nil,sK0),
inference(resolve,[status(thm)],[c_337,c_2714]) ).
cnf(c_2715,negated_conjecture,
( ~ ssList(sK5)
| ~ ssList(sK4)
| segmentP(nil,sK0)
| ~ ssList(sK0)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_352,c_213]) ).
cnf(c_2716,negated_conjecture,
( ~ ssList(sK5)
| ~ ssList(sK4)
| segmentP(nil,sK0)
| ~ ssList(sK0) ),
inference(resolve,[status(thm)],[c_231,c_2715]) ).
cnf(c_2717,negated_conjecture,
( ~ ssList(sK5)
| ~ ssList(sK4)
| segmentP(nil,sK0) ),
inference(resolve,[status(thm)],[c_327,c_2716]) ).
cnf(c_2718,negated_conjecture,
( ~ ssList(sK5)
| ~ ssList(sK4) ),
inference(resolve,[status(thm)],[c_2007,c_2717]) ).
cnf(c_2719,negated_conjecture,
~ ssList(sK5),
inference(resolve,[status(thm)],[c_343,c_2718]) ).
cnf(c_2704,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_346,c_2719]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC039+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n020.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 12:08:04 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 1498353 was started by sandbox on n020,
% 0.16/0.43 % Sat Sep 26 12:08:04 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.47
% 0.16/0.47 % From the command line: assign(max_seconds, 300).
% 13.91/2.52
% 13.91/2.52 % SZS status Theorem for theBenchmark
% 13.91/2.52
% 13.91/2.52 % Proof 1 at 1.80 (+ 0.15) seconds.
% 13.91/2.52 % Length of proof is 22.
% 13.91/2.52 % Level of proof is 5.
% 13.91/2.52 % Maximum clause weight is 26.000.
% 13.91/2.52 % Given clauses 166.
% 13.91/2.52
% 13.91/2.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------