%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL494+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 : n001.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 07:59:03 AM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of formulae : 64 ( 38 unt; 0 def)
% Number of atoms : 101 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 63 ( 26 ~; 23 |; 4 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 86 ( 6 sgn 24 !; 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(equivalence_2,axiom,
( equivalence_2
<=> ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(Y,X))) ),
file('theBenchmark.p',equivalence_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(op_equiv,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
file('theBenchmark.p',op_equiv) ).
fof(hilbert_equivalence_2,conjecture,
equivalence_2,
file('theBenchmark.p',hilbert_equivalence_2) ).
fof(hilbert_equivalence_2_neg,negated_conjecture,
~ equivalence_2,
inference(assume_negation,[status(cth)],[hilbert_equivalence_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_14,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(equiv(X,Y),implies(Y,X)))
| equivalence_2 )
& ( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ) ),
inference(fof_nnf,[status(thm)],[equivalence_2]) ).
fof(sk_equivalence_2_sk,plain,
( ( ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK1,sK0)))
| equivalence_2 )
& ( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_14]) ).
fof(sk_equivalence_2,plain,
( ( ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK1,sK0)))
| equivalence_2 )
& ! [VAR_0,VAR_1] :
( is_a_theorem(implies(equiv(VAR_0,VAR_1),implies(VAR_1,VAR_0)))
| ~ equivalence_2 ) ),
inference(cnf_transformation,[status(thm)],[sk_equivalence_2_sk]) ).
cnf(c_63,plain,
( ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK1,sK0)))
| equivalence_2 ),
inference(split_conjunct,[status(thm)],[sk_equivalence_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]) ).
cnf(c_94,plain,
( and(implies(A,B),implies(B,A)) = equiv(A,B)
| ~ op_equiv ),
inference(clausify,[status(thm)],[op_equiv]) ).
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_op_equiv,axiom,
op_equiv,
file('theBenchmark.p',principia_op_equiv) ).
cnf(c_97,plain,
op_equiv,
inference(clausify,[status(thm)],[principia_op_equiv]) ).
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,
~ equivalence_2,
inference(clausify,[status(thm)],[hilbert_equivalence_2_neg]) ).
cnf(c_108,plain,
or(not(A),B) = implies(A,B),
inference(resolve,[status(thm)],[c_95,c_93]) ).
cnf(c_357,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_357]) ).
cnf(c_110,plain,
and(implies(A,B),implies(B,A)) = equiv(A,B),
inference(resolve,[status(thm)],[c_97,c_94]) ).
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(equiv(sK0,sK1),implies(sK1,sK0))),
inference(resolve,[status(thm)],[c_107,c_63]) ).
cnf(c_358,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_358]) ).
cnf(c_359,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_359]) ).
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_150,plain,
( is_a_theorem(implies(not(B),A))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(resolve,[status(thm)],[c_125,c_111]) ).
cnf(c_187,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(paramod,[status(thm)],[c_128,c_126]) ).
cnf(c_360,plain,
is_a_theorem(implies(not(implies(A,not(B))),B)),
inference(resolve,[status(thm)],[c_187,c_150]) ).
cnf(c_276,plain,
is_a_theorem(implies(and(A,B),B)),
inference(paramod,[status(thm)],[c_109,c_360]) ).
cnf(c_355,plain,
is_a_theorem(implies(equiv(A,B),implies(B,A))),
inference(paramod,[status(thm)],[c_110,c_276]) ).
cnf(c_356,plain,
$false,
inference(resolve,[status(thm)],[c_355,c_120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL494+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 22:45:41 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 238661 was started by sandbox on n001,
% 0.10/0.37 % Fri Sep 25 22:45:41 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.44
% 0.10/0.44 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 0.10/0.44
% 0.10/0.44 % SZS status Theorem for theBenchmark
% 0.10/0.44
% 0.10/0.44 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.10/0.44 % Length of proof is 48.
% 0.10/0.44 % Level of proof is 9.
% 0.10/0.44 % Maximum clause weight is 40.000.
% 0.10/0.44 % Given clauses 88.
% 0.10/0.44
% 0.10/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------