%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL506+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 07:59:04 AM UTC 2026
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 8 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 11 ~; 8 |; 3 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 2 sgn 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(and_1,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ),
file('theBenchmark.p',and_1) ).
fof(kn2,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
file('theBenchmark.p',kn2) ).
fof(hilbert_and_1,conjecture,
and_1,
file('theBenchmark.p',hilbert_and_1) ).
fof(hilbert_and_1_neg,negated_conjecture,
~ and_1,
inference(assume_negation,[status(cth)],[hilbert_and_1]) ).
fof(nnf_7,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),X))
| and_1 )
& ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ) ),
inference(fof_nnf,[status(thm)],[and_1]) ).
fof(sk_and_1_sk,plain,
( ( ~ is_a_theorem(implies(and(sK0,sK1),sK0))
| and_1 )
& ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_7]) ).
fof(sk_and_1,plain,
( ( ~ is_a_theorem(implies(and(sK0,sK1),sK0))
| and_1 )
& ! [VAR_0,VAR_1] :
( is_a_theorem(implies(and(VAR_0,VAR_1),VAR_0))
| ~ and_1 ) ),
inference(cnf_transformation,[status(thm)],[sk_and_1_sk]) ).
cnf(c_49,plain,
( ~ is_a_theorem(implies(and(sK0,sK1),sK0))
| and_1 ),
inference(split_conjunct,[status(thm)],[sk_and_1]) ).
cnf(c_68,plain,
( is_a_theorem(implies(and(A,B),A))
| ~ kn2 ),
inference(clausify,[status(thm)],[kn2]) ).
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,
~ and_1,
inference(clausify,[status(thm)],[hilbert_and_1_neg]) ).
cnf(c_110,plain,
is_a_theorem(implies(and(A,B),A)),
inference(resolve,[status(thm)],[c_101,c_68]) ).
cnf(c_114,negated_conjecture,
~ is_a_theorem(implies(and(sK0,sK1),sK0)),
inference(resolve,[status(thm)],[c_104,c_49]) ).
cnf(c_113,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_110,c_114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL506+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n005.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 22:40:31 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.34 % Process 443694 was started by sandbox2 on n005,
% 0.08/0.34 % Fri Sep 25 22:40:31 2026
% 0.08/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Theorem for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 9.
% 0.13/0.37 % Level of proof is 3.
% 0.13/0.37 % Maximum clause weight is 7.000.
% 0.13/0.37 % Given clauses 0.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------