%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL453+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 : n014.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 0.10s 0.46s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 50 ( 28 unt; 0 def)
% Number of atoms : 83 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 58 ( 25 ~; 21 |; 4 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 64 ( 3 sgn 17 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('theBenchmark.p',modus_ponens) ).
fof(implies_1,axiom,
( implies_1
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) ),
file('theBenchmark.p',implies_1) ).
fof(implies_2,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
file('theBenchmark.p',implies_2) ).
fof(or_3,axiom,
( or_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) ),
file('theBenchmark.p',or_3) ).
fof(cn3,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
file('theBenchmark.p',cn3) ).
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_cn3,conjecture,
cn3,
file('theBenchmark.p',luka_cn3) ).
fof(luka_cn3_neg,negated_conjecture,
~ cn3,
inference(assume_negation,[status(cth)],[luka_cn3]) ).
cnf(c_33,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A)
| ~ modus_ponens ),
inference(clausify,[status(thm)],[modus_ponens]) ).
cnf(c_42,plain,
( is_a_theorem(implies(A,implies(B,A)))
| ~ implies_1 ),
inference(clausify,[status(thm)],[implies_1]) ).
cnf(c_44,plain,
( is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B)))
| ~ implies_2 ),
inference(clausify,[status(thm)],[implies_2]) ).
cnf(c_58,plain,
( is_a_theorem(implies(implies(A,B),implies(implies(C,B),implies(or(A,C),B))))
| ~ or_3 ),
inference(clausify,[status(thm)],[or_3]) ).
fof(nnf_21,plain,
( ( ? [P] : ~ is_a_theorem(implies(implies(not(P),P),P))
| cn3 )
& ( ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0))
| ~ cn3 ) ),
inference(fof_nnf,[status(thm)],[cn3]) ).
fof(sk_cn3_sk,plain,
( ( ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0))
| cn3 )
& ( ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0))
| ~ cn3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(P,sK0)],[nnf_21]) ).
fof(sk_cn3,plain,
( ( ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0))
| cn3 )
& ! [VAR_0] :
( is_a_theorem(implies(implies(not(VAR_0),VAR_0),VAR_0))
| ~ cn3 ) ),
inference(cnf_transformation,[status(thm)],[sk_cn3_sk]) ).
cnf(c_77,plain,
( ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0))
| cn3 ),
inference(split_conjunct,[status(thm)],[sk_cn3]) ).
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_95,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_96,plain,
op_implies_and,
inference(clausify,[status(thm)],[hilbert_op_implies_and]) ).
fof(hilbert_modus_ponens,axiom,
modus_ponens,
file('theBenchmark.p',hilbert_modus_ponens) ).
cnf(c_98,plain,
modus_ponens,
inference(clausify,[status(thm)],[hilbert_modus_ponens]) ).
fof(hilbert_implies_1,axiom,
implies_1,
file('theBenchmark.p',hilbert_implies_1) ).
cnf(c_100,plain,
implies_1,
inference(clausify,[status(thm)],[hilbert_implies_1]) ).
fof(hilbert_implies_2,axiom,
implies_2,
file('theBenchmark.p',hilbert_implies_2) ).
cnf(c_101,plain,
implies_2,
inference(clausify,[status(thm)],[hilbert_implies_2]) ).
fof(hilbert_or_3,axiom,
or_3,
file('theBenchmark.p',hilbert_or_3) ).
cnf(c_108,plain,
or_3,
inference(clausify,[status(thm)],[hilbert_or_3]) ).
cnf(c_114,negated_conjecture,
~ cn3,
inference(clausify,[status(thm)],[luka_cn3_neg]) ).
cnf(c_115,plain,
not(and(not(A),not(B))) = or(A,B),
inference(resolve,[status(thm)],[c_95,c_89]) ).
cnf(c_116,plain,
not(and(A,not(B))) = implies(A,B),
inference(resolve,[status(thm)],[c_96,c_92]) ).
cnf(c_118,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_98,c_33]) ).
cnf(c_120,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolve,[status(thm)],[c_100,c_42]) ).
cnf(c_121,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_101,c_44]) ).
cnf(c_128,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,B),implies(or(A,C),B)))),
inference(resolve,[status(thm)],[c_108,c_58]) ).
cnf(c_133,negated_conjecture,
~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)),
inference(resolve,[status(thm)],[c_114,c_77]) ).
cnf(c_320,plain,
implies(not(A),B) = or(A,B),
inference(paramod,[status(thm)],[c_116,c_115]) ).
cnf(c_134,plain,
or(A,B) = implies(not(A),B),
inference(copy,[status(thm)],[c_320]) ).
cnf(c_138,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,B),implies(implies(not(A),C),B)))),
inference(paramod,[status(thm)],[c_134,c_128]) ).
cnf(c_321,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,implies(B,A)),C)) ),
inference(resolve,[status(thm)],[c_118,c_120]) ).
cnf(c_159,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_321,c_121]) ).
cnf(c_322,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_118,c_159]) ).
cnf(c_312,plain,
is_a_theorem(implies(implies(A,B),implies(implies(not(B),A),B))),
inference(resolve,[status(thm)],[c_322,c_138]) ).
cnf(c_323,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_118,c_159]) ).
cnf(c_318,plain,
~ is_a_theorem(implies(implies(A,A),implies(implies(not(sK0),sK0),sK0))),
inference(resolve,[status(thm)],[c_323,c_133]) ).
cnf(c_319,plain,
$false,
inference(resolve,[status(thm)],[c_318,c_312]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL453+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.37 % Computer : n014.cluster.edu
% 0.06/0.37 % Model : x86_64 x86_64
% 0.06/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.37 % Memory : 8046.5625MB
% 0.06/0.37 % OS : Linux 6.8.0-71-generic
% 0.06/0.37 % CPULimit : 300
% 0.06/0.37 % WCLimit : 300
% 0.06/0.37 % DateTime : Fri Sep 25 22:35:33 UTC 2026
% 0.06/0.37 % CPUTime :
% 0.06/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.06/0.37 % Process 1289684 was started by sandbox on n014,
% 0.06/0.37 % Fri Sep 25 22:35:33 2026
% 0.06/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.06/0.38
% 0.06/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.46
% 0.10/0.46 % Assigning unary symbol not kb_weight 0 and highest precedence (94).
% 0.10/0.46
% 0.10/0.46 % SZS status Theorem for theBenchmark
% 0.10/0.46
% 0.10/0.46 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/0.46 % Length of proof is 36.
% 0.10/0.46 % Level of proof is 7.
% 0.10/0.46 % Maximum clause weight is 70.000.
% 0.10/0.46 % Given clauses 63.
% 0.10/0.46
% 0.10/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------