%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL512+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 : n009.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 07:59:05 AM UTC 2026
% Result : Theorem 0.20s 0.49s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 12 unt; 0 def)
% Number of atoms : 38 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 14 ~; 10 |; 3 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 2 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(equivalence_1,axiom,
( equivalence_1
<=> ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(X,Y))) ),
file('theBenchmark.p',equivalence_1) ).
fof(kn2,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
file('theBenchmark.p',kn2) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
file('theBenchmark.p',op_equiv) ).
fof(hilbert_equivalence_1,conjecture,
equivalence_1,
file('theBenchmark.p',hilbert_equivalence_1) ).
fof(hilbert_equivalence_1_neg,negated_conjecture,
~ equivalence_1,
inference(assume_negation,[status(cth)],[hilbert_equivalence_1]) ).
fof(nnf_13,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(equiv(X,Y),implies(X,Y)))
| equivalence_1 )
& ( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ equivalence_1 ) ),
inference(fof_nnf,[status(thm)],[equivalence_1]) ).
fof(sk_equivalence_1_sk,plain,
( ( ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK0,sK1)))
| equivalence_1 )
& ( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ equivalence_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_13]) ).
fof(sk_equivalence_1,plain,
( ( ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK0,sK1)))
| equivalence_1 )
& ! [VAR_0,VAR_1] :
( is_a_theorem(implies(equiv(VAR_0,VAR_1),implies(VAR_0,VAR_1)))
| ~ equivalence_1 ) ),
inference(cnf_transformation,[status(thm)],[sk_equivalence_1_sk]) ).
cnf(c_61,plain,
( ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK0,sK1)))
| equivalence_1 ),
inference(split_conjunct,[status(thm)],[sk_equivalence_1]) ).
cnf(c_68,plain,
( is_a_theorem(implies(and(A,B),A))
| ~ kn2 ),
inference(clausify,[status(thm)],[kn2]) ).
cnf(c_94,plain,
( and(implies(A,B),implies(B,A)) = equiv(A,B)
| ~ op_equiv ),
inference(clausify,[status(thm)],[op_equiv]) ).
cnf(c_95,plain,
( equiv(A,B) = and(implies(A,B),implies(B,A))
| ~ op_equiv ),
inference(copy,[status(thm)],[c_94]) ).
fof(rosser_op_equiv,axiom,
op_equiv,
file('theBenchmark.p',rosser_op_equiv) ).
cnf(c_98,plain,
op_equiv,
inference(clausify,[status(thm)],[rosser_op_equiv]) ).
fof(rosser_kn2,axiom,
kn2,
file('theBenchmark.p',rosser_kn2) ).
cnf(c_101,plain,
kn2,
inference(clausify,[status(thm)],[rosser_kn2]) ).
cnf(c_104,negated_conjecture,
~ equivalence_1,
inference(clausify,[status(thm)],[hilbert_equivalence_1_neg]) ).
cnf(c_107,plain,
equiv(A,B) = and(implies(A,B),implies(B,A)),
inference(resolve,[status(thm)],[c_98,c_95]) ).
cnf(c_110,plain,
is_a_theorem(implies(and(A,B),A)),
inference(resolve,[status(thm)],[c_101,c_68]) ).
cnf(c_113,negated_conjecture,
~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK0,sK1))),
inference(resolve,[status(thm)],[c_104,c_61]) ).
cnf(c_137,plain,
~ is_a_theorem(implies(and(implies(sK0,sK1),implies(sK1,sK0)),implies(sK0,sK1))),
inference(paramod,[status(thm)],[c_107,c_113]) ).
cnf(c_136,plain,
$false,
inference(resolve,[status(thm)],[c_110,c_137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL512+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.44 % Computer : n009.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.44 % CPULimit : 300
% 0.20/0.44 % WCLimit : 300
% 0.20/0.45 % DateTime : Fri Sep 25 22:40:44 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.45 % Process 2750353 was started by sandbox on n009,
% 0.20/0.45 % Fri Sep 25 22:40:44 2026
% 0.20/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.20/0.47
% 0.20/0.47 % From the command line: assign(max_seconds, 300).
% 0.20/0.49
% 0.20/0.49 % SZS status Theorem for theBenchmark
% 0.20/0.49
% 0.20/0.49 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.20/0.49 % Length of proof is 15.
% 0.20/0.49 % Level of proof is 4.
% 0.20/0.49 % Maximum clause weight is 27.000.
% 0.20/0.49 % Given clauses 58.
% 0.20/0.49
% 0.20/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------