%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL452+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 07:58:58 AM UTC 2026
% Result : Theorem 0.14s 5.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 17 unt; 0 def)
% Number of atoms : 47 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 14 ~; 11 |; 3 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 3 sgn 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(or_1,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ),
file('theBenchmark.p',or_1) ).
fof(cn2,axiom,
( cn2
<=> ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q))) ),
file('theBenchmark.p',cn2) ).
fof(op_or,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('theBenchmark.p',op_or) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
file('theBenchmark.p',op_implies_and) ).
fof(luka_cn2,conjecture,
cn2,
file('theBenchmark.p',luka_cn2) ).
fof(luka_cn2_neg,negated_conjecture,
~ cn2,
inference(assume_negation,[status(cth)],[luka_cn2]) ).
cnf(c_54,plain,
( is_a_theorem(implies(A,or(A,B)))
| ~ or_1 ),
inference(clausify,[status(thm)],[or_1]) ).
fof(nnf_20,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(P,implies(not(P),Q)))
| cn2 )
& ( ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1)))
| ~ cn2 ) ),
inference(fof_nnf,[status(thm)],[cn2]) ).
fof(sk_cn2_sk,plain,
( ( ~ is_a_theorem(implies(sK0,implies(not(sK0),sK1)))
| cn2 )
& ( ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1)))
| ~ cn2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(P,sK0),skolemize(Q,sK1)],[nnf_20]) ).
fof(sk_cn2,plain,
( ( ~ is_a_theorem(implies(sK0,implies(not(sK0),sK1)))
| cn2 )
& ! [VAR_0,VAR_1] :
( is_a_theorem(implies(VAR_0,implies(not(VAR_0),VAR_1)))
| ~ cn2 ) ),
inference(cnf_transformation,[status(thm)],[sk_cn2_sk]) ).
cnf(c_75,plain,
( ~ is_a_theorem(implies(sK0,implies(not(sK0),sK1)))
| cn2 ),
inference(split_conjunct,[status(thm)],[sk_cn2]) ).
cnf(c_88,plain,
( or(A,B) = not(and(not(A),not(B)))
| ~ op_or ),
inference(clausify,[status(thm)],[op_or]) ).
cnf(c_89,plain,
( not(and(not(A),not(B))) = or(A,B)
| ~ op_or ),
inference(copy,[status(thm)],[c_88]) ).
cnf(c_92,plain,
( not(and(A,not(B))) = implies(A,B)
| ~ op_implies_and ),
inference(clausify,[status(thm)],[op_implies_and]) ).
fof(hilbert_op_or,axiom,
op_or,
file('theBenchmark.p',hilbert_op_or) ).
cnf(c_96,plain,
op_or,
inference(clausify,[status(thm)],[hilbert_op_or]) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('theBenchmark.p',hilbert_op_implies_and) ).
cnf(c_97,plain,
op_implies_and,
inference(clausify,[status(thm)],[hilbert_op_implies_and]) ).
fof(hilbert_or_1,axiom,
or_1,
file('theBenchmark.p',hilbert_or_1) ).
cnf(c_107,plain,
or_1,
inference(clausify,[status(thm)],[hilbert_or_1]) ).
cnf(c_115,negated_conjecture,
~ cn2,
inference(clausify,[status(thm)],[luka_cn2_neg]) ).
cnf(c_116,plain,
not(and(not(A),not(B))) = or(A,B),
inference(resolve,[status(thm)],[c_96,c_89]) ).
cnf(c_117,plain,
not(and(A,not(B))) = implies(A,B),
inference(resolve,[status(thm)],[c_97,c_92]) ).
cnf(c_127,plain,
is_a_theorem(implies(A,or(A,B))),
inference(resolve,[status(thm)],[c_107,c_54]) ).
cnf(c_131,negated_conjecture,
~ is_a_theorem(implies(sK0,implies(not(sK0),sK1))),
inference(resolve,[status(thm)],[c_115,c_75]) ).
cnf(c_192,plain,
implies(not(A),B) = or(A,B),
inference(paramod,[status(thm)],[c_117,c_116]) ).
cnf(c_132,plain,
or(A,B) = implies(not(A),B),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_190,plain,
is_a_theorem(implies(A,implies(not(A),B))),
inference(paramod,[status(thm)],[c_132,c_127]) ).
cnf(c_191,plain,
$false,
inference(resolve,[status(thm)],[c_190,c_131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL452+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.38 % Computer : n004.cluster.edu
% 0.08/5.38 % Model : x86_64 x86_64
% 0.08/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.38 % Memory : 8046.5625MB
% 0.08/5.38 % OS : Linux 6.8.0-71-generic
% 0.08/5.38 % CPULimit : 300
% 0.08/5.38 % WCLimit : 300
% 0.08/5.38 % DateTime : Fri Sep 25 22:35:14 UTC 2026
% 0.08/5.38 % CPUTime :
% 0.08/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.38 % Process 167851 was started by sandbox on n004,
% 0.08/5.38 % Fri Sep 25 22:35:14 2026
% 0.08/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/5.39
% 0.08/5.39 % From the command line: assign(max_seconds, 300).
% 0.14/5.42
% 0.14/5.42 % SZS status Theorem for theBenchmark
% 0.14/5.42
% 0.14/5.42 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.14/5.42 % Length of proof is 21.
% 0.14/5.42 % Level of proof is 6.
% 0.14/5.42 % Maximum clause weight is 11.000.
% 0.14/5.42 % Given clauses 52.
% 0.14/5.42
% 0.14/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------