%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL459+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 07:58:59 AM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 14 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 43 ( 19 ~; 15 |; 4 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 5 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 10 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('theBenchmark.p',modus_ponens) ).
fof(implies_2,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
file('theBenchmark.p',implies_2) ).
fof(and_3,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
file('theBenchmark.p',and_3) ).
fof(kn1,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('theBenchmark.p',kn1) ).
fof(rosser_kn1,conjecture,
kn1,
file('theBenchmark.p',rosser_kn1) ).
fof(rosser_kn1_neg,negated_conjecture,
~ kn1,
inference(assume_negation,[status(cth)],[rosser_kn1]) ).
cnf(c_33,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A)
| ~ modus_ponens ),
inference(clausify,[status(thm)],[modus_ponens]) ).
cnf(c_44,plain,
( is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B)))
| ~ implies_2 ),
inference(clausify,[status(thm)],[implies_2]) ).
cnf(c_52,plain,
( is_a_theorem(implies(A,implies(B,and(A,B))))
| ~ and_3 ),
inference(clausify,[status(thm)],[and_3]) ).
fof(nnf_16,plain,
( ( ? [P] : ~ is_a_theorem(implies(P,and(P,P)))
| kn1 )
& ( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ) ),
inference(fof_nnf,[status(thm)],[kn1]) ).
fof(sk_kn1_sk,plain,
( ( ~ is_a_theorem(implies(sK0,and(sK0,sK0)))
| kn1 )
& ( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(P,sK0)],[nnf_16]) ).
fof(sk_kn1,plain,
( ( ~ is_a_theorem(implies(sK0,and(sK0,sK0)))
| kn1 )
& ! [VAR_0] :
( is_a_theorem(implies(VAR_0,and(VAR_0,VAR_0)))
| ~ kn1 ) ),
inference(cnf_transformation,[status(thm)],[sk_kn1_sk]) ).
cnf(c_67,plain,
( ~ is_a_theorem(implies(sK0,and(sK0,sK0)))
| kn1 ),
inference(split_conjunct,[status(thm)],[sk_kn1]) ).
fof(hilbert_modus_ponens,axiom,
modus_ponens,
file('theBenchmark.p',hilbert_modus_ponens) ).
cnf(c_99,plain,
modus_ponens,
inference(clausify,[status(thm)],[hilbert_modus_ponens]) ).
fof(hilbert_implies_2,axiom,
implies_2,
file('theBenchmark.p',hilbert_implies_2) ).
cnf(c_102,plain,
implies_2,
inference(clausify,[status(thm)],[hilbert_implies_2]) ).
fof(hilbert_and_3,axiom,
and_3,
file('theBenchmark.p',hilbert_and_3) ).
cnf(c_106,plain,
and_3,
inference(clausify,[status(thm)],[hilbert_and_3]) ).
cnf(c_114,negated_conjecture,
~ kn1,
inference(clausify,[status(thm)],[rosser_kn1_neg]) ).
cnf(c_118,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_99,c_33]) ).
cnf(c_121,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_102,c_44]) ).
cnf(c_125,plain,
is_a_theorem(implies(A,implies(B,and(A,B)))),
inference(resolve,[status(thm)],[c_106,c_52]) ).
cnf(c_133,negated_conjecture,
~ is_a_theorem(implies(sK0,and(sK0,sK0))),
inference(resolve,[status(thm)],[c_114,c_67]) ).
cnf(c_168,plain,
( is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_118,c_121]) ).
cnf(c_169,plain,
~ is_a_theorem(implies(sK0,implies(sK0,and(sK0,sK0)))),
inference(resolve,[status(thm)],[c_168,c_133]) ).
cnf(c_167,plain,
$false,
inference(resolve,[status(thm)],[c_125,c_169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL459+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 22:36:33 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 435651 was started by sandbox2 on n005,
% 0.09/0.36 % Fri Sep 25 22:36:33 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.40
% 0.09/0.40 % SZS status Theorem for theBenchmark
% 0.09/0.40
% 0.09/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/0.40 % Length of proof is 18.
% 0.09/0.40 % Level of proof is 3.
% 0.09/0.40 % Maximum clause weight is 31.000.
% 0.09/0.40 % Given clauses 54.
% 0.09/0.40
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------