%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL484+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 : n007.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 07:59:01 AM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 12 unt; 0 def)
% Number of atoms : 36 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 27 ( 12 ~; 9 |; 3 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 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 ( 3 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(implies_1,axiom,
( implies_1
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) ),
file('theBenchmark.p',implies_1) ).
fof(r2,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('theBenchmark.p',r2) ).
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
file('theBenchmark.p',op_implies_or) ).
fof(hilbert_implies_1,conjecture,
implies_1,
file('theBenchmark.p',hilbert_implies_1) ).
fof(hilbert_implies_1_neg,negated_conjecture,
~ implies_1,
inference(assume_negation,[status(cth)],[hilbert_implies_1]) ).
fof(nnf_4,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,X)))
| implies_1 )
& ( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ) ),
inference(fof_nnf,[status(thm)],[implies_1]) ).
fof(sk_implies_1_sk,plain,
( ( ~ is_a_theorem(implies(sK0,implies(sK1,sK0)))
| implies_1 )
& ( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_4]) ).
fof(sk_implies_1,plain,
( ( ~ is_a_theorem(implies(sK0,implies(sK1,sK0)))
| implies_1 )
& ! [VAR_0,VAR_1] :
( is_a_theorem(implies(VAR_0,implies(VAR_1,VAR_0)))
| ~ implies_1 ) ),
inference(cnf_transformation,[status(thm)],[sk_implies_1_sk]) ).
cnf(c_43,plain,
( ~ is_a_theorem(implies(sK0,implies(sK1,sK0)))
| implies_1 ),
inference(split_conjunct,[status(thm)],[sk_implies_1]) ).
cnf(c_80,plain,
( is_a_theorem(implies(A,or(B,A)))
| ~ r2 ),
inference(clausify,[status(thm)],[r2]) ).
cnf(c_93,plain,
( or(not(A),B) = implies(A,B)
| ~ op_implies_or ),
inference(clausify,[status(thm)],[op_implies_or]) ).
fof(principia_op_implies_or,axiom,
op_implies_or,
file('theBenchmark.p',principia_op_implies_or) ).
cnf(c_96,plain,
op_implies_or,
inference(clausify,[status(thm)],[principia_op_implies_or]) ).
fof(principia_r2,axiom,
r2,
file('theBenchmark.p',principia_r2) ).
cnf(c_101,plain,
r2,
inference(clausify,[status(thm)],[principia_r2]) ).
cnf(c_108,negated_conjecture,
~ implies_1,
inference(clausify,[status(thm)],[hilbert_implies_1_neg]) ).
cnf(c_109,plain,
or(not(A),B) = implies(A,B),
inference(resolve,[status(thm)],[c_96,c_93]) ).
cnf(c_114,plain,
is_a_theorem(implies(A,or(B,A))),
inference(resolve,[status(thm)],[c_101,c_80]) ).
cnf(c_121,negated_conjecture,
~ is_a_theorem(implies(sK0,implies(sK1,sK0))),
inference(resolve,[status(thm)],[c_108,c_43]) ).
cnf(c_130,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(paramod,[status(thm)],[c_109,c_114]) ).
cnf(c_131,plain,
$false,
inference(resolve,[status(thm)],[c_130,c_121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL484+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 22:36:38 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2096382 was started by sandbox2 on n007,
% 0.09/0.37 % Fri Sep 25 22:36:38 2026
% 0.09/0.37 % 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).
% 0.09/0.39
% 0.09/0.39 % SZS status Theorem for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 15.
% 0.09/0.39 % Level of proof is 4.
% 0.09/0.39 % Maximum clause weight is 24.000.
% 0.09/0.39 % Given clauses 53.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------