%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC259+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 : n006.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 08:57:18 AM UTC 2026
% Result : Theorem 10.44s 1.79s
% Output : CNFRefutation 10.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 8 unt; 0 def)
% Number of atoms : 155 ( 61 equ)
% Maximal formula atoms : 43 ( 6 avg)
% Number of connectives : 178 ( 48 ~; 61 |; 58 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 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 : 35 ( 0 sgn 23 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax65,axiom,
! [U] :
( ssItem(U)
=> totalorderedP(cons(U,nil)) ),
file('theBenchmark.p',ax65) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(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) ) ) ) )
| totalorderedP(U)
| 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] :
( ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(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) ) ) ) )
| totalorderedP(U)
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_287,plain,
( totalorderedP(cons(A,nil))
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[ax65]) ).
fof(ax66,axiom,
totalorderedP(nil),
file('theBenchmark.p',ax66) ).
cnf(c_288,plain,
totalorderedP(nil),
inference(clausify,[status(thm)],[ax66]) ).
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) ) )
& ~ totalorderedP(U)
& 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 = sK4 )
| ( ! [X3] :
( ~ lt(X3,sK2)
| ~ memberP(sK6,X3)
| ~ ssItem(X3) )
& ! [X2] :
( ~ lt(sK2,X2)
| ~ memberP(sK5,X2)
| ~ ssItem(X2) )
& app(app(sK5,sK0),sK6) = sK4
& cons(sK2,nil) = sK0
& ssList(sK6)
& ssList(sK5)
& ssItem(sK2) ) )
& ~ totalorderedP(sK1)
& sK0 = sK1
& sK4 = sK3
& ssList(sK4)
& ssList(sK0)
& ssList(sK3)
& ssList(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK3,sK0,sK4,sK2,sK5,sK6]),skolemize(U,sK1),skolemize(V,sK3),skolemize(W,sK0),skolemize(X,sK4),skolemize(Y,sK2),skolemize(Z,sK5),skolemize(X1,sK6)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ! [VAR_0] :
( nil = sK0
| ~ lt(VAR_0,sK2)
| ~ memberP(sK6,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( nil = sK4
| ~ lt(VAR_0,sK2)
| ~ memberP(sK6,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( nil = sK0
| ~ lt(sK2,VAR_0)
| ~ memberP(sK5,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( nil = sK4
| ~ lt(sK2,VAR_0)
| ~ memberP(sK5,VAR_0)
| ~ ssItem(VAR_0) )
& ( nil = sK0
| app(app(sK5,sK0),sK6) = sK4 )
& ( nil = sK4
| app(app(sK5,sK0),sK6) = sK4 )
& ( nil = sK0
| cons(sK2,nil) = sK0 )
& ( nil = sK4
| cons(sK2,nil) = sK0 )
& ( nil = sK0
| ssList(sK6) )
& ( nil = sK4
| ssList(sK6) )
& ( nil = sK0
| ssList(sK5) )
& ( nil = sK4
| ssList(sK5) )
& ( nil = sK0
| ssItem(sK2) )
& ( nil = sK4
| ssItem(sK2) )
& ~ totalorderedP(sK1)
& sK0 = sK1
& sK4 = sK3
& ssList(sK4)
& ssList(sK0)
& ssList(sK3)
& ssList(sK1) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_332,negated_conjecture,
sK0 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_333,negated_conjecture,
~ totalorderedP(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_336,negated_conjecture,
( nil = sK0
| ssItem(sK2) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_3577,negated_conjecture,
( nil = sK1
| ssItem(sK2) ),
inference(paramod,[status(thm)],[c_332,c_336]) ).
cnf(c_337,negated_conjecture,
( sK1 = nil
| ssItem(sK2) ),
inference(copy,[status(thm)],[c_3577]) ).
cnf(c_348,negated_conjecture,
( nil = sK0
| cons(sK2,nil) = sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_3578,negated_conjecture,
( nil = sK0
| cons(sK2,nil) = sK1 ),
inference(paramod,[status(thm)],[c_332,c_348]) ).
cnf(c_3579,negated_conjecture,
( nil = sK1
| cons(sK2,nil) = sK1 ),
inference(paramod,[status(thm)],[c_332,c_3578]) ).
cnf(c_349,negated_conjecture,
( sK1 = nil
| cons(sK2,nil) = sK1 ),
inference(copy,[status(thm)],[c_3579]) ).
cnf(c_2519,plain,
( totalorderedP(cons(sK2,nil))
| sK1 = nil ),
inference(resolve,[status(thm)],[c_337,c_287]) ).
cnf(c_3580,plain,
( ~ totalorderedP(nil)
| cons(sK2,nil) = sK1 ),
inference(paramod,[status(thm)],[c_349,c_333]) ).
cnf(c_3548,plain,
cons(sK2,nil) = sK1,
inference(resolve,[status(thm)],[c_288,c_3580]) ).
cnf(c_3581,plain,
( totalorderedP(sK1)
| sK1 = nil ),
inference(paramod,[status(thm)],[c_3548,c_2519]) ).
cnf(c_3555,negated_conjecture,
sK1 = nil,
inference(resolve,[status(thm)],[c_333,c_3581]) ).
cnf(c_3582,negated_conjecture,
~ totalorderedP(nil),
inference(paramod,[status(thm)],[c_3555,c_333]) ).
cnf(c_3576,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_288,c_3582]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC259+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 : n006.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 12:37:40 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 1274107 was started by sandbox2 on n006,
% 0.08/0.35 % Sat Sep 26 12:37:40 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 10.44/1.79
% 10.44/1.79 % SZS status Theorem for theBenchmark
% 10.44/1.79
% 10.44/1.79 % Proof 1 at 1.25 (+ 0.13) seconds.
% 10.44/1.79 % Length of proof is 14.
% 10.44/1.79 % Level of proof is 5.
% 10.44/1.79 % Maximum clause weight is 12.000.
% 10.44/1.79 % Given clauses 169.
% 10.44/1.79
% 10.44/1.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------