%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWX200+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 09:16:18 AM UTC 2026
% Result : Theorem 0.16s 0.45s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 9 unt; 0 def)
% Number of atoms : 27 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 10 ~; 5 |; 1 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 5 sgn 5 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_007,axiom,
! [Z] : ~ leqNat(s(Z),z),
file('theBenchmark.p',axiom_007) ).
fof(axiom_009,axiom,
! [Y] : merge(nil,Y) = Y,
file('theBenchmark.p',axiom_009) ).
fof(axiom_015,axiom,
! [Y,Y2,Xs] :
( ord(cons(Y,cons(Y2,Xs)))
<=> ( ord(cons(Y2,Xs))
& leqNat(Y,Y2) ) ),
file('theBenchmark.p',axiom_015) ).
fof(goal_016,conjecture,
? [Xs,Ys] :
~ ( ord(Xs)
=> ( ~ ord(Ys)
=> ord(merge(Xs,Ys)) ) ),
file('theBenchmark.p',goal_016) ).
fof(goal_016_neg,negated_conjecture,
~ ? [Xs,Ys] :
~ ( ord(Xs)
=> ( ~ ord(Ys)
=> ord(merge(Xs,Ys)) ) ),
inference(assume_negation,[status(cth)],[goal_016]) ).
cnf(c_22,plain,
~ leqNat(s(A),z),
inference(clausify,[status(thm)],[axiom_007]) ).
cnf(c_25,plain,
merge(nil,A) = A,
inference(clausify,[status(thm)],[axiom_009]) ).
fof(axiom_013,axiom,
ord(nil),
file('theBenchmark.p',axiom_013) ).
cnf(c_29,plain,
ord(nil),
inference(clausify,[status(thm)],[axiom_013]) ).
cnf(c_31,plain,
( leqNat(A,B)
| ~ ord(cons(A,cons(B,C))) ),
inference(clausify,[status(thm)],[axiom_015]) ).
cnf(c_34,negated_conjecture,
( ord(merge(A,B))
| ord(B)
| ~ ord(A) ),
inference(clausify,[status(thm)],[goal_016_neg]) ).
cnf(c_42,plain,
~ ord(cons(s(A),cons(z,B))),
inference(resolve,[status(thm)],[c_31,c_22]) ).
cnf(c_48,negated_conjecture,
( ord(merge(nil,A))
| ord(A) ),
inference(resolve,[status(thm)],[c_34,c_29]) ).
cnf(c_49,negated_conjecture,
( ord(A)
| ord(A) ),
inference(paramod,[status(thm)],[c_25,c_48]) ).
cnf(c_46,negated_conjecture,
ord(A),
inference(copy,[status(thm)],[c_49]) ).
cnf(c_47,plain,
$false,
inference(resolve,[status(thm)],[c_46,c_42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWX200+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n002.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 16:57:35 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 2248513 was started by sandbox on n002,
% 0.16/0.43 % Sat Sep 26 16:57:35 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 0.16/0.45
% 0.16/0.45 % SZS status Theorem for theBenchmark
% 0.16/0.45
% 0.16/0.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/0.45 % Length of proof is 12.
% 0.16/0.45 % Level of proof is 3.
% 0.16/0.45 % Maximum clause weight is 9.000.
% 0.16/0.45 % Given clauses 19.
% 0.16/0.45
% 0.16/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------