%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL455+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 : n003.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 0.08s 0.38s
% Output : CNFRefutation 0.08s
% 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(or_2,axiom,
( or_2
<=> ! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) ),
file('theBenchmark.p',or_2) ).
fof(r2,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('theBenchmark.p',r2) ).
fof(principia_r2,conjecture,
r2,
file('theBenchmark.p',principia_r2) ).
fof(principia_r2_neg,negated_conjecture,
~ r2,
inference(assume_negation,[status(cth)],[principia_r2]) ).
cnf(c_56,plain,
( is_a_theorem(implies(A,or(B,A)))
| ~ or_2 ),
inference(clausify,[status(thm)],[or_2]) ).
fof(nnf_23,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(Q,or(P,Q)))
| r2 )
& ( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ) ),
inference(fof_nnf,[status(thm)],[r2]) ).
fof(sk_r2_sk,plain,
( ( ~ is_a_theorem(implies(sK0,or(sK1,sK0)))
| r2 )
& ( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(P,sK1),skolemize(Q,sK0)],[nnf_23]) ).
fof(sk_r2,plain,
( ( ~ is_a_theorem(implies(sK0,or(sK1,sK0)))
| r2 )
& ! [VAR_0,VAR_1] :
( is_a_theorem(implies(VAR_0,or(VAR_1,VAR_0)))
| ~ r2 ) ),
inference(cnf_transformation,[status(thm)],[sk_r2_sk]) ).
cnf(c_81,plain,
( ~ is_a_theorem(implies(sK0,or(sK1,sK0)))
| r2 ),
inference(split_conjunct,[status(thm)],[sk_r2]) ).
fof(hilbert_or_2,axiom,
or_2,
file('theBenchmark.p',hilbert_or_2) ).
cnf(c_108,plain,
or_2,
inference(clausify,[status(thm)],[hilbert_or_2]) ).
cnf(c_116,negated_conjecture,
~ r2,
inference(clausify,[status(thm)],[principia_r2_neg]) ).
cnf(c_129,plain,
is_a_theorem(implies(A,or(B,A))),
inference(resolve,[status(thm)],[c_108,c_56]) ).
cnf(c_135,negated_conjecture,
~ is_a_theorem(implies(sK0,or(sK1,sK0))),
inference(resolve,[status(thm)],[c_116,c_81]) ).
cnf(c_134,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_129,c_135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL455+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 22:37:23 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1306950 was started by sandbox on n003,
% 0.08/0.36 % Fri Sep 25 22:37:23 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.38
% 0.08/0.38 % SZS status Theorem for theBenchmark
% 0.08/0.38
% 0.08/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.08/0.38 % Length of proof is 9.
% 0.08/0.38 % Level of proof is 3.
% 0.08/0.38 % Maximum clause weight is 7.000.
% 0.08/0.38 % Given clauses 0.
% 0.08/0.38
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------