%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL488+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 : n020.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 07:59:02 AM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 58 ( 34 unt; 0 def)
% Number of atoms : 93 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 62 ( 27 ~; 22 |; 4 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 6 sgn 22 !; 2 ?)
% 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(and_2,axiom,
( and_2
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) ),
file('theBenchmark.p',and_2) ).
fof(r2,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('theBenchmark.p',r2) ).
fof(r3,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('theBenchmark.p',r3) ).
fof(op_or,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('theBenchmark.p',op_or) ).
fof(op_and,axiom,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
file('theBenchmark.p',op_and) ).
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(op_implies_or,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
file('theBenchmark.p',op_implies_or) ).
fof(hilbert_and_2,conjecture,
and_2,
file('theBenchmark.p',hilbert_and_2) ).
fof(hilbert_and_2_neg,negated_conjecture,
~ and_2,
inference(assume_negation,[status(cth)],[hilbert_and_2]) ).
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]) ).
fof(nnf_8,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),Y))
| and_2 )
& ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ) ),
inference(fof_nnf,[status(thm)],[and_2]) ).
fof(sk_and_2_sk,plain,
( ( ~ is_a_theorem(implies(and(sK0,sK1),sK1))
| and_2 )
& ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_8]) ).
fof(sk_and_2,plain,
( ( ~ is_a_theorem(implies(and(sK0,sK1),sK1))
| and_2 )
& ! [VAR_0,VAR_1] :
( is_a_theorem(implies(and(VAR_0,VAR_1),VAR_1))
| ~ and_2 ) ),
inference(cnf_transformation,[status(thm)],[sk_and_2_sk]) ).
cnf(c_51,plain,
( ~ is_a_theorem(implies(and(sK0,sK1),sK1))
| and_2 ),
inference(split_conjunct,[status(thm)],[sk_and_2]) ).
cnf(c_80,plain,
( is_a_theorem(implies(A,or(B,A)))
| ~ r2 ),
inference(clausify,[status(thm)],[r2]) ).
cnf(c_82,plain,
( is_a_theorem(implies(or(A,B),or(B,A)))
| ~ r3 ),
inference(clausify,[status(thm)],[r3]) ).
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_90,plain,
( and(A,B) = not(or(not(A),not(B)))
| ~ op_and ),
inference(clausify,[status(thm)],[op_and]) ).
cnf(c_91,plain,
( not(or(not(A),not(B))) = and(A,B)
| ~ op_and ),
inference(copy,[status(thm)],[c_90]) ).
cnf(c_92,plain,
( not(and(A,not(B))) = implies(A,B)
| ~ op_implies_and ),
inference(clausify,[status(thm)],[op_implies_and]) ).
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_95,plain,
op_implies_or,
inference(clausify,[status(thm)],[principia_op_implies_or]) ).
fof(principia_op_and,axiom,
op_and,
file('theBenchmark.p',principia_op_and) ).
cnf(c_96,plain,
op_and,
inference(clausify,[status(thm)],[principia_op_and]) ).
fof(principia_modus_ponens,axiom,
modus_ponens,
file('theBenchmark.p',principia_modus_ponens) ).
cnf(c_98,plain,
modus_ponens,
inference(clausify,[status(thm)],[principia_modus_ponens]) ).
fof(principia_r2,axiom,
r2,
file('theBenchmark.p',principia_r2) ).
cnf(c_100,plain,
r2,
inference(clausify,[status(thm)],[principia_r2]) ).
fof(principia_r3,axiom,
r3,
file('theBenchmark.p',principia_r3) ).
cnf(c_101,plain,
r3,
inference(clausify,[status(thm)],[principia_r3]) ).
fof(hilbert_op_or,axiom,
op_or,
file('theBenchmark.p',hilbert_op_or) ).
cnf(c_105,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_106,plain,
op_implies_and,
inference(clausify,[status(thm)],[hilbert_op_implies_and]) ).
cnf(c_107,negated_conjecture,
~ and_2,
inference(clausify,[status(thm)],[hilbert_and_2_neg]) ).
cnf(c_108,plain,
or(not(A),B) = implies(A,B),
inference(resolve,[status(thm)],[c_95,c_93]) ).
cnf(c_210,plain,
( not(implies(A,not(B))) = and(A,B)
| ~ op_and ),
inference(paramod,[status(thm)],[c_108,c_91]) ).
cnf(c_109,plain,
not(implies(A,not(B))) = and(A,B),
inference(resolve,[status(thm)],[c_96,c_210]) ).
cnf(c_111,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_113,plain,
is_a_theorem(implies(A,or(B,A))),
inference(resolve,[status(thm)],[c_100,c_80]) ).
cnf(c_114,plain,
is_a_theorem(implies(or(A,B),or(B,A))),
inference(resolve,[status(thm)],[c_101,c_82]) ).
cnf(c_118,plain,
not(and(not(A),not(B))) = or(A,B),
inference(resolve,[status(thm)],[c_105,c_89]) ).
cnf(c_119,plain,
not(and(A,not(B))) = implies(A,B),
inference(resolve,[status(thm)],[c_106,c_92]) ).
cnf(c_120,negated_conjecture,
~ is_a_theorem(implies(and(sK0,sK1),sK1)),
inference(resolve,[status(thm)],[c_107,c_51]) ).
cnf(c_211,plain,
implies(not(A),B) = or(A,B),
inference(paramod,[status(thm)],[c_119,c_118]) ).
cnf(c_122,plain,
or(A,B) = implies(not(A),B),
inference(copy,[status(thm)],[c_211]) ).
cnf(c_212,plain,
is_a_theorem(implies(implies(not(A),B),or(B,A))),
inference(paramod,[status(thm)],[c_122,c_114]) ).
cnf(c_125,plain,
is_a_theorem(implies(implies(not(A),B),implies(not(B),A))),
inference(paramod,[status(thm)],[c_122,c_212]) ).
cnf(c_126,plain,
is_a_theorem(implies(A,implies(not(B),A))),
inference(paramod,[status(thm)],[c_122,c_113]) ).
cnf(c_128,plain,
implies(not(not(A)),B) = implies(A,B),
inference(paramod,[status(thm)],[c_122,c_108]) ).
cnf(c_154,plain,
is_a_theorem(implies(implies(not(A),implies(B,not(C))),implies(and(B,C),A))),
inference(paramod,[status(thm)],[c_109,c_125]) ).
cnf(c_213,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,implies(not(B),A)),C)) ),
inference(resolve,[status(thm)],[c_111,c_126]) ).
cnf(c_165,plain,
~ is_a_theorem(implies(implies(A,implies(not(B),A)),implies(and(sK0,sK1),sK1))),
inference(resolve,[status(thm)],[c_213,c_120]) ).
cnf(c_208,plain,
~ is_a_theorem(implies(implies(A,implies(B,A)),implies(and(sK0,sK1),sK1))),
inference(paramod,[status(thm)],[c_128,c_165]) ).
cnf(c_209,plain,
$false,
inference(resolve,[status(thm)],[c_208,c_154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL488+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.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 22:40:20 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3992037 was started by sandbox2 on n020,
% 0.09/0.36 % Fri Sep 25 22:40:20 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.40
% 0.14/0.40 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 0.14/0.40
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40
% 0.14/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.14/0.40 % Length of proof is 43.
% 0.14/0.40 % Level of proof is 8.
% 0.14/0.40 % Maximum clause weight is 54.000.
% 0.14/0.40 % Given clauses 63.
% 0.14/0.40
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------