%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL461+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 : n013.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 07:58:59 AM UTC 2026
% Result : Theorem 51.72s 6.96s
% Output : CNFRefutation 51.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 30
% Syntax : Number of formulae : 202 ( 133 unt; 0 def)
% Number of atoms : 284 ( 70 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 152 ( 70 ~; 61 |; 4 &)
% ( 12 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 18 ( 16 usr; 16 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 374 ( 50 sgn 41 !; 3 ?)
% 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(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> X = Y ) ),
file('theBenchmark.p',substitution_of_equivalents) ).
fof(modus_tollens,axiom,
( modus_tollens
<=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
file('theBenchmark.p',modus_tollens) ).
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(implies_3,axiom,
( implies_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
file('theBenchmark.p',implies_3) ).
fof(and_1,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ),
file('theBenchmark.p',and_1) ).
fof(and_2,axiom,
( and_2
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) ),
file('theBenchmark.p',and_2) ).
fof(and_3,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
file('theBenchmark.p',and_3) ).
fof(or_1,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ),
file('theBenchmark.p',or_1) ).
fof(equivalence_3,axiom,
( equivalence_3
<=> ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ),
file('theBenchmark.p',equivalence_3) ).
fof(kn3,axiom,
( kn3
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),
file('theBenchmark.p',kn3) ).
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(op_equiv,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
file('theBenchmark.p',op_equiv) ).
fof(rosser_kn3,conjecture,
kn3,
file('theBenchmark.p',rosser_kn3) ).
fof(rosser_kn3_neg,negated_conjecture,
~ kn3,
inference(assume_negation,[status(cth)],[rosser_kn3]) ).
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_37,plain,
( B = A
| ~ is_a_theorem(equiv(A,B))
| ~ substitution_of_equivalents ),
inference(clausify,[status(thm)],[substitution_of_equivalents]) ).
cnf(c_40,plain,
( is_a_theorem(implies(implies(not(A),not(B)),implies(B,A)))
| ~ modus_tollens ),
inference(clausify,[status(thm)],[modus_tollens]) ).
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_46,plain,
( is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C))))
| ~ implies_3 ),
inference(clausify,[status(thm)],[implies_3]) ).
cnf(c_48,plain,
( is_a_theorem(implies(and(A,B),A))
| ~ and_1 ),
inference(clausify,[status(thm)],[and_1]) ).
cnf(c_50,plain,
( is_a_theorem(implies(and(A,B),B))
| ~ and_2 ),
inference(clausify,[status(thm)],[and_2]) ).
cnf(c_52,plain,
( is_a_theorem(implies(A,implies(B,and(A,B))))
| ~ and_3 ),
inference(clausify,[status(thm)],[and_3]) ).
cnf(c_54,plain,
( is_a_theorem(implies(A,or(A,B)))
| ~ or_1 ),
inference(clausify,[status(thm)],[or_1]) ).
cnf(c_64,plain,
( is_a_theorem(implies(implies(A,B),implies(implies(B,A),equiv(A,B))))
| ~ equivalence_3 ),
inference(clausify,[status(thm)],[equivalence_3]) ).
fof(nnf_18,plain,
( ( ? [P,Q,R] : ~ is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
| kn3 )
& ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ) ),
inference(fof_nnf,[status(thm)],[kn3]) ).
fof(sk_kn3_sk,plain,
( ( ~ is_a_theorem(implies(implies(sK0,sK1),implies(not(and(sK1,sK2)),not(and(sK2,sK0)))))
| kn3 )
& ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(P,sK0),skolemize(Q,sK1),skolemize(R,sK2)],[nnf_18]) ).
fof(sk_kn3,plain,
( ( ~ is_a_theorem(implies(implies(sK0,sK1),implies(not(and(sK1,sK2)),not(and(sK2,sK0)))))
| kn3 )
& ! [VAR_0,VAR_1,VAR_2] :
( is_a_theorem(implies(implies(VAR_0,VAR_1),implies(not(and(VAR_1,VAR_2)),not(and(VAR_2,VAR_0)))))
| ~ kn3 ) ),
inference(cnf_transformation,[status(thm)],[sk_kn3_sk]) ).
cnf(c_71,plain,
( ~ is_a_theorem(implies(implies(sK0,sK1),implies(not(and(sK1,sK2)),not(and(sK2,sK0)))))
| kn3 ),
inference(split_conjunct,[status(thm)],[sk_kn3]) ).
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]) ).
cnf(c_94,plain,
( and(implies(A,B),implies(B,A)) = equiv(A,B)
| ~ op_equiv ),
inference(clausify,[status(thm)],[op_equiv]) ).
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_op_equiv,axiom,
op_equiv,
file('theBenchmark.p',hilbert_op_equiv) ).
cnf(c_97,plain,
op_equiv,
inference(clausify,[status(thm)],[hilbert_op_equiv]) ).
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_modus_tollens,axiom,
modus_tollens,
file('theBenchmark.p',hilbert_modus_tollens) ).
cnf(c_99,plain,
modus_tollens,
inference(clausify,[status(thm)],[hilbert_modus_tollens]) ).
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_implies_3,axiom,
implies_3,
file('theBenchmark.p',hilbert_implies_3) ).
cnf(c_102,plain,
implies_3,
inference(clausify,[status(thm)],[hilbert_implies_3]) ).
fof(hilbert_and_1,axiom,
and_1,
file('theBenchmark.p',hilbert_and_1) ).
cnf(c_103,plain,
and_1,
inference(clausify,[status(thm)],[hilbert_and_1]) ).
fof(hilbert_and_2,axiom,
and_2,
file('theBenchmark.p',hilbert_and_2) ).
cnf(c_104,plain,
and_2,
inference(clausify,[status(thm)],[hilbert_and_2]) ).
fof(hilbert_and_3,axiom,
and_3,
file('theBenchmark.p',hilbert_and_3) ).
cnf(c_105,plain,
and_3,
inference(clausify,[status(thm)],[hilbert_and_3]) ).
fof(hilbert_or_1,axiom,
or_1,
file('theBenchmark.p',hilbert_or_1) ).
cnf(c_106,plain,
or_1,
inference(clausify,[status(thm)],[hilbert_or_1]) ).
fof(hilbert_equivalence_3,axiom,
equivalence_3,
file('theBenchmark.p',hilbert_equivalence_3) ).
cnf(c_111,plain,
equivalence_3,
inference(clausify,[status(thm)],[hilbert_equivalence_3]) ).
fof(use_substitution_of_equivalents,axiom,
substitution_of_equivalents,
file('theBenchmark.p',use_substitution_of_equivalents) ).
cnf(c_112,plain,
substitution_of_equivalents,
inference(clausify,[status(thm)],[use_substitution_of_equivalents]) ).
cnf(c_113,negated_conjecture,
~ kn3,
inference(clausify,[status(thm)],[rosser_kn3_neg]) ).
cnf(c_114,plain,
not(and(not(A),not(B))) = or(A,B),
inference(resolve,[status(thm)],[c_95,c_89]) ).
cnf(c_115,plain,
not(and(A,not(B))) = implies(A,B),
inference(resolve,[status(thm)],[c_96,c_92]) ).
cnf(c_116,plain,
and(implies(A,B),implies(B,A)) = equiv(A,B),
inference(resolve,[status(thm)],[c_97,c_94]) ).
cnf(c_117,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_118,plain,
is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))),
inference(resolve,[status(thm)],[c_99,c_40]) ).
cnf(c_119,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolve,[status(thm)],[c_100,c_42]) ).
cnf(c_120,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_101,c_44]) ).
cnf(c_121,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_102,c_46]) ).
cnf(c_122,plain,
is_a_theorem(implies(and(A,B),A)),
inference(resolve,[status(thm)],[c_103,c_48]) ).
cnf(c_123,plain,
is_a_theorem(implies(and(A,B),B)),
inference(resolve,[status(thm)],[c_104,c_50]) ).
cnf(c_124,plain,
is_a_theorem(implies(A,implies(B,and(A,B)))),
inference(resolve,[status(thm)],[c_105,c_52]) ).
cnf(c_125,plain,
is_a_theorem(implies(A,or(A,B))),
inference(resolve,[status(thm)],[c_106,c_54]) ).
cnf(c_130,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,A),equiv(A,B)))),
inference(resolve,[status(thm)],[c_111,c_64]) ).
cnf(c_131,plain,
( B = A
| ~ is_a_theorem(equiv(A,B)) ),
inference(resolve,[status(thm)],[c_112,c_37]) ).
cnf(c_132,negated_conjecture,
~ is_a_theorem(implies(implies(sK0,sK1),implies(not(and(sK1,sK2)),not(and(sK2,sK0))))),
inference(resolve,[status(thm)],[c_113,c_71]) ).
cnf(c_42491,plain,
implies(not(A),B) = or(A,B),
inference(paramod,[status(thm)],[c_115,c_114]) ).
cnf(c_133,plain,
or(A,B) = implies(not(A),B),
inference(copy,[status(thm)],[c_42491]) ).
cnf(c_138,plain,
is_a_theorem(implies(A,implies(not(A),B))),
inference(paramod,[status(thm)],[c_133,c_125]) ).
cnf(c_150,plain,
not(and(A,implies(B,C))) = implies(A,and(B,not(C))),
inference(paramod,[status(thm)],[c_115,c_115]) ).
cnf(c_151,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(implies(not(A),not(B))) ),
inference(resolve,[status(thm)],[c_118,c_117]) ).
cnf(c_42492,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,implies(B,A)),C)) ),
inference(resolve,[status(thm)],[c_117,c_119]) ).
cnf(c_158,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_42492,c_120]) ).
cnf(c_42493,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,implies(B,A)),C)) ),
inference(resolve,[status(thm)],[c_117,c_119]) ).
cnf(c_163,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_42493,c_121]) ).
cnf(c_42494,plain,
( is_a_theorem(D)
| ~ is_a_theorem(implies(implies(implies(A,B),implies(implies(B,C),implies(A,C))),D)) ),
inference(resolve,[status(thm)],[c_117,c_121]) ).
cnf(c_165,plain,
is_a_theorem(implies(A,implies(implies(B,C),implies(implies(C,D),implies(B,D))))),
inference(resolve,[status(thm)],[c_42494,c_119]) ).
cnf(c_42495,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(and(A,B),B),C)) ),
inference(resolve,[status(thm)],[c_117,c_123]) ).
cnf(c_174,plain,
is_a_theorem(implies(A,and(implies(and(B,C),C),A))),
inference(resolve,[status(thm)],[c_42495,c_124]) ).
cnf(c_42496,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(and(A,B),A),C)) ),
inference(resolve,[status(thm)],[c_117,c_122]) ).
cnf(c_175,plain,
is_a_theorem(implies(A,and(implies(and(B,C),B),A))),
inference(resolve,[status(thm)],[c_42496,c_124]) ).
cnf(c_42497,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,implies(B,and(A,B))),C)) ),
inference(resolve,[status(thm)],[c_117,c_124]) ).
cnf(c_181,plain,
is_a_theorem(implies(A,and(A,A))),
inference(resolve,[status(thm)],[c_42497,c_120]) ).
cnf(c_42498,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,implies(B,and(A,B))),C)) ),
inference(resolve,[status(thm)],[c_117,c_124]) ).
cnf(c_196,plain,
is_a_theorem(implies(implies(implies(A,and(B,A)),B),equiv(B,implies(A,and(B,A))))),
inference(resolve,[status(thm)],[c_42498,c_130]) ).
cnf(c_42499,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(and(A,B),B),C)) ),
inference(resolve,[status(thm)],[c_117,c_123]) ).
cnf(c_197,plain,
is_a_theorem(implies(implies(A,and(B,A)),equiv(and(B,A),A))),
inference(resolve,[status(thm)],[c_42499,c_130]) ).
cnf(c_42500,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(and(A,B),A),C)) ),
inference(resolve,[status(thm)],[c_117,c_122]) ).
cnf(c_198,plain,
is_a_theorem(implies(implies(A,and(A,B)),equiv(and(A,B),A))),
inference(resolve,[status(thm)],[c_42500,c_130]) ).
cnf(c_42501,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,implies(B,A)),C)) ),
inference(resolve,[status(thm)],[c_117,c_119]) ).
cnf(c_201,plain,
is_a_theorem(implies(implies(implies(A,B),B),equiv(B,implies(A,B)))),
inference(resolve,[status(thm)],[c_42501,c_130]) ).
cnf(c_42502,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(implies(not(A),not(B)),implies(B,A)),C)) ),
inference(resolve,[status(thm)],[c_117,c_118]) ).
cnf(c_202,plain,
is_a_theorem(implies(implies(implies(A,B),implies(not(B),not(A))),equiv(implies(not(B),not(A)),implies(A,B)))),
inference(resolve,[status(thm)],[c_42502,c_130]) ).
cnf(c_42503,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(and(A,B),B),C)) ),
inference(resolve,[status(thm)],[c_117,c_123]) ).
cnf(c_247,plain,
is_a_theorem(implies(not(implies(and(A,B),B)),C)),
inference(resolve,[status(thm)],[c_42503,c_138]) ).
cnf(c_42504,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_117,c_158]) ).
cnf(c_327,plain,
is_a_theorem(implies(not(implies(A,A)),B)),
inference(resolve,[status(thm)],[c_42504,c_138]) ).
cnf(c_42505,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_117,c_158]) ).
cnf(c_329,plain,
is_a_theorem(implies(A,and(implies(B,B),A))),
inference(resolve,[status(thm)],[c_42505,c_124]) ).
cnf(c_42506,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_117,c_158]) ).
cnf(c_330,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_42506,c_119]) ).
cnf(c_42507,plain,
( is_a_theorem(D)
| ~ is_a_theorem(implies(implies(not(implies(and(A,B),B)),C),D)) ),
inference(resolve,[status(thm)],[c_117,c_247]) ).
cnf(c_3492,plain,
~ is_a_theorem(implies(implies(not(implies(and(A,B),B)),C),implies(implies(sK0,sK1),implies(not(and(sK1,sK2)),not(and(sK2,sK0)))))),
inference(resolve,[status(thm)],[c_42507,c_132]) ).
cnf(c_3677,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_163,c_117]) ).
cnf(c_42508,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(A,and(A,A)),B)) ),
inference(resolve,[status(thm)],[c_117,c_181]) ).
cnf(c_7600,plain,
is_a_theorem(and(implies(and(A,B),B),implies(C,and(C,C)))),
inference(resolve,[status(thm)],[c_42508,c_174]) ).
cnf(c_12771,plain,
is_a_theorem(equiv(and(A,A),A)),
inference(paramod,[status(thm)],[c_116,c_7600]) ).
cnf(c_42509,plain,
A = and(A,A),
inference(resolve,[status(thm)],[c_12771,c_131]) ).
cnf(c_13129,plain,
and(A,A) = A,
inference(copy,[status(thm)],[c_42509]) ).
cnf(c_42510,plain,
not(not(A)) = implies(not(A),A),
inference(paramod,[status(thm)],[c_13129,c_115]) ).
cnf(c_13131,plain,
implies(not(A),A) = not(not(A)),
inference(copy,[status(thm)],[c_42510]) ).
cnf(c_42511,plain,
not(implies(A,B)) = implies(implies(A,B),and(A,not(B))),
inference(paramod,[status(thm)],[c_13129,c_150]) ).
cnf(c_13133,plain,
implies(implies(A,B),and(A,not(B))) = not(implies(A,B)),
inference(copy,[status(thm)],[c_42511]) ).
cnf(c_13949,plain,
is_a_theorem(implies(A,not(not(A)))),
inference(paramod,[status(thm)],[c_13131,c_119]) ).
cnf(c_14538,plain,
is_a_theorem(implies(not(not(A)),A)),
inference(resolve,[status(thm)],[c_13949,c_151]) ).
cnf(c_42512,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,implies(B,B)),C)) ),
inference(resolve,[status(thm)],[c_117,c_330]) ).
cnf(c_21104,plain,
is_a_theorem(equiv(implies(A,A),implies(B,and(implies(A,A),B)))),
inference(resolve,[status(thm)],[c_42512,c_196]) ).
cnf(c_42513,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,and(implies(B,B),A)),C)) ),
inference(resolve,[status(thm)],[c_117,c_329]) ).
cnf(c_21697,plain,
is_a_theorem(equiv(and(implies(A,A),B),B)),
inference(resolve,[status(thm)],[c_42513,c_197]) ).
cnf(c_42514,plain,
A = and(implies(B,B),A),
inference(resolve,[status(thm)],[c_21697,c_131]) ).
cnf(c_21982,plain,
and(implies(A,A),B) = B,
inference(copy,[status(thm)],[c_42514]) ).
cnf(c_22176,plain,
is_a_theorem(equiv(implies(A,A),implies(B,B))),
inference(paramod,[status(thm)],[c_21982,c_21104]) ).
cnf(c_42515,plain,
not(not(A)) = implies(implies(B,B),A),
inference(paramod,[status(thm)],[c_21982,c_115]) ).
cnf(c_22195,plain,
implies(implies(A,A),B) = not(not(B)),
inference(copy,[status(thm)],[c_42515]) ).
cnf(c_22701,plain,
implies(A,A) = implies(B,B),
inference(resolve,[status(thm)],[c_22176,c_131]) ).
cnf(c_22985,plain,
is_a_theorem(implies(and(A,B),equiv(and(A,B),A))),
inference(resolve,[status(thm)],[c_198,c_3677]) ).
cnf(c_24156,plain,
( is_a_theorem(equiv(and(A,B),A))
| ~ is_a_theorem(and(A,B)) ),
inference(resolve,[status(thm)],[c_22985,c_117]) ).
cnf(c_42516,plain,
( is_a_theorem(equiv(and(implies(B,B),A),implies(B,B)))
| ~ is_a_theorem(A) ),
inference(paramod,[status(thm)],[c_21982,c_24156]) ).
cnf(c_24260,plain,
( is_a_theorem(equiv(A,implies(B,B)))
| ~ is_a_theorem(A) ),
inference(paramod,[status(thm)],[c_21982,c_42516]) ).
cnf(c_24343,plain,
is_a_theorem(equiv(implies(and(A,B),B),implies(C,C))),
inference(resolve,[status(thm)],[c_24260,c_123]) ).
cnf(c_42517,plain,
implies(A,A) = implies(and(B,C),C),
inference(resolve,[status(thm)],[c_24343,c_131]) ).
cnf(c_24802,plain,
implies(and(A,B),B) = implies(C,C),
inference(copy,[status(thm)],[c_42517]) ).
cnf(c_42518,plain,
and(implies(A,A),implies(B,and(C,B))) = equiv(and(C,B),B),
inference(paramod,[status(thm)],[c_24802,c_116]) ).
cnf(c_42519,plain,
implies(B,and(C,B)) = equiv(and(C,B),B),
inference(paramod,[status(thm)],[c_21982,c_42518]) ).
cnf(c_24901,plain,
equiv(and(A,B),B) = implies(B,and(A,B)),
inference(copy,[status(thm)],[c_42519]) ).
cnf(c_42520,plain,
( A = and(B,A)
| ~ is_a_theorem(implies(A,and(B,A))) ),
inference(paramod,[status(thm)],[c_24901,c_131]) ).
cnf(c_25217,plain,
( and(B,A) = A
| ~ is_a_theorem(implies(A,and(B,A))) ),
inference(copy,[status(thm)],[c_42520]) ).
cnf(c_25231,plain,
( is_a_theorem(equiv(B,implies(A,B)))
| ~ is_a_theorem(implies(implies(A,B),B)) ),
inference(resolve,[status(thm)],[c_201,c_117]) ).
cnf(c_25683,plain,
and(A,not(implies(B,B))) = not(implies(B,B)),
inference(resolve,[status(thm)],[c_25217,c_327]) ).
cnf(c_25692,plain,
and(implies(and(A,B),A),C) = C,
inference(resolve,[status(thm)],[c_25217,c_175]) ).
cnf(c_42521,plain,
implies(A,and(A,B)) = equiv(and(A,B),A),
inference(paramod,[status(thm)],[c_25692,c_116]) ).
cnf(c_25888,plain,
equiv(and(A,B),A) = implies(A,and(A,B)),
inference(copy,[status(thm)],[c_42521]) ).
cnf(c_25915,plain,
( is_a_theorem(equiv(implies(not(B),not(A)),implies(A,B)))
| ~ is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))) ),
inference(resolve,[status(thm)],[c_202,c_117]) ).
cnf(c_42522,plain,
( A = and(A,B)
| ~ is_a_theorem(implies(A,and(A,B))) ),
inference(paramod,[status(thm)],[c_25888,c_131]) ).
cnf(c_26313,plain,
( and(A,B) = A
| ~ is_a_theorem(implies(A,and(A,B))) ),
inference(copy,[status(thm)],[c_42522]) ).
cnf(c_42523,plain,
not(not(implies(A,A))) = implies(B,implies(A,A)),
inference(paramod,[status(thm)],[c_25683,c_115]) ).
cnf(c_27506,plain,
implies(A,implies(B,B)) = not(not(implies(B,B))),
inference(copy,[status(thm)],[c_42523]) ).
cnf(c_42524,plain,
( is_a_theorem(equiv(A,implies(not(A),A)))
| ~ is_a_theorem(implies(not(not(A)),A)) ),
inference(paramod,[status(thm)],[c_13131,c_25231]) ).
cnf(c_42525,plain,
( is_a_theorem(equiv(A,not(not(A))))
| ~ is_a_theorem(implies(not(not(A)),A)) ),
inference(paramod,[status(thm)],[c_13131,c_42524]) ).
cnf(c_29562,plain,
is_a_theorem(equiv(A,not(not(A)))),
inference(resolve,[status(thm)],[c_14538,c_42525]) ).
cnf(c_29568,plain,
not(not(A)) = A,
inference(resolve,[status(thm)],[c_29562,c_131]) ).
cnf(c_29646,plain,
implies(A,implies(B,B)) = implies(B,B),
inference(paramod,[status(thm)],[c_29568,c_27506]) ).
cnf(c_29689,plain,
implies(implies(A,A),B) = B,
inference(paramod,[status(thm)],[c_29568,c_22195]) ).
cnf(c_29725,plain,
implies(not(A),A) = A,
inference(paramod,[status(thm)],[c_29568,c_13131]) ).
cnf(c_42526,plain,
implies(implies(A,B),and(A,not(B))) = and(A,not(B)),
inference(paramod,[status(thm)],[c_115,c_29725]) ).
cnf(c_29785,plain,
not(implies(A,B)) = and(A,not(B)),
inference(paramod,[status(thm)],[c_13133,c_42526]) ).
cnf(c_42527,plain,
not(and(A,B)) = implies(A,and(not(B),not(B))),
inference(paramod,[status(thm)],[c_29725,c_150]) ).
cnf(c_29786,plain,
not(and(A,B)) = implies(A,not(B)),
inference(paramod,[status(thm)],[c_13129,c_42527]) ).
cnf(c_42528,plain,
~ is_a_theorem(implies(implies(and(and(A,B),not(B)),C),implies(implies(sK0,sK1),implies(not(and(sK1,sK2)),not(and(sK2,sK0)))))),
inference(paramod,[status(thm)],[c_29785,c_3492]) ).
cnf(c_42529,plain,
~ is_a_theorem(implies(implies(and(and(A,B),not(B)),C),implies(implies(sK0,sK1),implies(implies(sK1,not(sK2)),not(and(sK2,sK0)))))),
inference(paramod,[status(thm)],[c_29786,c_42528]) ).
cnf(c_31047,plain,
~ is_a_theorem(implies(implies(and(and(A,B),not(B)),C),implies(implies(sK0,sK1),implies(implies(sK1,not(sK2)),implies(sK2,not(sK0)))))),
inference(paramod,[status(thm)],[c_29786,c_42529]) ).
cnf(c_42530,plain,
and(A,implies(A,implies(B,B))) = equiv(implies(B,B),A),
inference(paramod,[status(thm)],[c_29689,c_116]) ).
cnf(c_42531,plain,
and(A,implies(B,B)) = equiv(implies(B,B),A),
inference(paramod,[status(thm)],[c_29646,c_42530]) ).
cnf(c_34729,plain,
equiv(implies(A,A),B) = and(B,implies(A,A)),
inference(copy,[status(thm)],[c_42531]) ).
cnf(c_34731,plain,
is_a_theorem(implies(A,and(A,implies(B,B)))),
inference(paramod,[status(thm)],[c_29689,c_124]) ).
cnf(c_42532,plain,
equiv(implies(A,A),B) = and(B,implies(C,C)),
inference(paramod,[status(thm)],[c_22701,c_34729]) ).
cnf(c_35158,plain,
and(A,implies(B,B)) = and(A,implies(C,C)),
inference(paramod,[status(thm)],[c_34729,c_42532]) ).
cnf(c_42533,plain,
( and(A,implies(C,C)) = A
| ~ is_a_theorem(implies(A,and(A,implies(B,B)))) ),
inference(paramod,[status(thm)],[c_35158,c_26313]) ).
cnf(c_35174,plain,
and(A,implies(B,B)) = A,
inference(resolve,[status(thm)],[c_34731,c_42533]) ).
cnf(c_42534,plain,
not(and(A,implies(B,B))) = implies(A,not(implies(C,C))),
inference(paramod,[status(thm)],[c_35158,c_29786]) ).
cnf(c_42535,plain,
not(A) = implies(A,not(implies(C,C))),
inference(paramod,[status(thm)],[c_35174,c_42534]) ).
cnf(c_42536,plain,
not(A) = implies(A,and(C,not(C))),
inference(paramod,[status(thm)],[c_29785,c_42535]) ).
cnf(c_35178,plain,
implies(A,and(B,not(B))) = not(A),
inference(copy,[status(thm)],[c_42536]) ).
cnf(c_42537,plain,
is_a_theorem(implies(implies(A,B),implies(not(B),implies(A,and(C,not(C)))))),
inference(paramod,[status(thm)],[c_35178,c_121]) ).
cnf(c_37878,plain,
is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))),
inference(paramod,[status(thm)],[c_35178,c_42537]) ).
cnf(c_37890,plain,
is_a_theorem(equiv(implies(not(A),not(B)),implies(B,A))),
inference(resolve,[status(thm)],[c_37878,c_25915]) ).
cnf(c_42538,plain,
implies(A,B) = implies(not(B),not(A)),
inference(resolve,[status(thm)],[c_37890,c_131]) ).
cnf(c_41854,plain,
implies(not(A),not(B)) = implies(B,A),
inference(copy,[status(thm)],[c_42538]) ).
cnf(c_42539,plain,
not(implies(A,B)) = and(not(B),not(not(A))),
inference(paramod,[status(thm)],[c_41854,c_29785]) ).
cnf(c_42540,plain,
and(A,not(B)) = and(not(B),not(not(A))),
inference(paramod,[status(thm)],[c_29785,c_42539]) ).
cnf(c_42541,plain,
and(A,not(B)) = and(not(B),A),
inference(paramod,[status(thm)],[c_29568,c_42540]) ).
cnf(c_42117,plain,
and(not(A),B) = and(B,not(A)),
inference(copy,[status(thm)],[c_42541]) ).
cnf(c_42542,plain,
not(and(A,B)) = implies(not(not(B)),not(A)),
inference(paramod,[status(thm)],[c_41854,c_29786]) ).
cnf(c_42543,plain,
implies(A,not(B)) = implies(not(not(B)),not(A)),
inference(paramod,[status(thm)],[c_29786,c_42542]) ).
cnf(c_42120,plain,
implies(A,not(B)) = implies(B,not(A)),
inference(paramod,[status(thm)],[c_29568,c_42543]) ).
cnf(c_42544,plain,
~ is_a_theorem(implies(implies(and(not(B),and(A,B)),C),implies(implies(sK0,sK1),implies(implies(sK1,not(sK2)),implies(sK2,not(sK0)))))),
inference(paramod,[status(thm)],[c_42117,c_31047]) ).
cnf(c_42545,plain,
~ is_a_theorem(implies(implies(and(not(B),and(A,B)),C),implies(implies(sK0,sK1),implies(implies(sK1,not(sK2)),implies(sK0,not(sK2)))))),
inference(paramod,[status(thm)],[c_42120,c_42544]) ).
cnf(c_42490,plain,
$false,
inference(resolve,[status(thm)],[c_165,c_42545]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL461+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n013.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 25 22:35:52 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 1405691 was started by sandbox on n013,
% 0.11/0.38 % Fri Sep 25 22:35:52 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 51.72/6.96
% 51.72/6.96 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 51.72/6.96
% 51.72/6.96 % given #500 (F,wt=36): 14258 -is_a_theorem(and(equiv(implies(A,A),not(implies(B,B))),C)). [ur(166,b,13137,a)].
% 51.72/6.96
% 51.72/6.96 % SZS status Theorem for theBenchmark
% 51.72/6.96
% 51.72/6.96 % Proof 1 at 5.32 (+ 1.19) seconds.
% 51.72/6.96 % Length of proof is 129.
% 51.72/6.96 % Level of proof is 23.
% 51.72/6.96 % Maximum clause weight is 88.000.
% 51.72/6.96 % Given clauses 769.
% 51.72/6.96
% 51.72/6.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------