%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL485+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 : n002.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 213.82s 29.12s
% Output : CNFRefutation 213.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 26
% Syntax : Number of formulae : 157 ( 105 unt; 0 def)
% Number of atoms : 223 ( 40 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 119 ( 53 ~; 47 |; 4 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 14 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 262 ( 18 sgn 33 !; 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(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> X = Y ) ),
file('theBenchmark.p',substitution_of_equivalents) ).
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(r1,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('theBenchmark.p',r1) ).
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(r4,axiom,
( r4
<=> ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
file('theBenchmark.p',r4) ).
fof(r5,axiom,
( r5
<=> ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
file('theBenchmark.p',r5) ).
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_implies_2,conjecture,
implies_2,
file('theBenchmark.p',hilbert_implies_2) ).
fof(hilbert_implies_2_neg,negated_conjecture,
~ implies_2,
inference(assume_negation,[status(cth)],[hilbert_implies_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]) ).
cnf(c_37,plain,
( B = A
| ~ is_a_theorem(equiv(A,B))
| ~ substitution_of_equivalents ),
inference(clausify,[status(thm)],[substitution_of_equivalents]) ).
fof(nnf_5,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| implies_2 )
& ( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ) ),
inference(fof_nnf,[status(thm)],[implies_2]) ).
fof(sk_implies_2_sk,plain,
( ( ~ is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),implies(sK0,sK1)))
| implies_2 )
& ( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_5]) ).
fof(sk_implies_2,plain,
( ( ~ is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),implies(sK0,sK1)))
| implies_2 )
& ! [VAR_0,VAR_1] :
( is_a_theorem(implies(implies(VAR_0,implies(VAR_0,VAR_1)),implies(VAR_0,VAR_1)))
| ~ implies_2 ) ),
inference(cnf_transformation,[status(thm)],[sk_implies_2_sk]) ).
cnf(c_45,plain,
( ~ is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),implies(sK0,sK1)))
| implies_2 ),
inference(split_conjunct,[status(thm)],[sk_implies_2]) ).
cnf(c_78,plain,
( is_a_theorem(implies(or(A,A),A))
| ~ r1 ),
inference(clausify,[status(thm)],[r1]) ).
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_84,plain,
( is_a_theorem(implies(or(A,or(B,C)),or(B,or(A,C))))
| ~ r4 ),
inference(clausify,[status(thm)],[r4]) ).
cnf(c_86,plain,
( is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B))))
| ~ r5 ),
inference(clausify,[status(thm)],[r5]) ).
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_r1,axiom,
r1,
file('theBenchmark.p',principia_r1) ).
cnf(c_99,plain,
r1,
inference(clausify,[status(thm)],[principia_r1]) ).
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(principia_r4,axiom,
r4,
file('theBenchmark.p',principia_r4) ).
cnf(c_102,plain,
r4,
inference(clausify,[status(thm)],[principia_r4]) ).
fof(principia_r5,axiom,
r5,
file('theBenchmark.p',principia_r5) ).
cnf(c_103,plain,
r5,
inference(clausify,[status(thm)],[principia_r5]) ).
fof(use_substitution_of_equivalents,axiom,
substitution_of_equivalents,
file('theBenchmark.p',use_substitution_of_equivalents) ).
cnf(c_104,plain,
substitution_of_equivalents,
inference(clausify,[status(thm)],[use_substitution_of_equivalents]) ).
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,
~ implies_2,
inference(clausify,[status(thm)],[hilbert_implies_2_neg]) ).
cnf(c_108,plain,
or(not(A),B) = implies(A,B),
inference(resolve,[status(thm)],[c_95,c_93]) ).
cnf(c_27556,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_27556]) ).
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_112,plain,
is_a_theorem(implies(or(A,A),A)),
inference(resolve,[status(thm)],[c_99,c_78]) ).
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_115,plain,
is_a_theorem(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(resolve,[status(thm)],[c_102,c_84]) ).
cnf(c_116,plain,
is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(resolve,[status(thm)],[c_103,c_86]) ).
cnf(c_117,plain,
( B = A
| ~ is_a_theorem(equiv(A,B)) ),
inference(resolve,[status(thm)],[c_104,c_37]) ).
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(implies(sK0,implies(sK0,sK1)),implies(sK0,sK1))),
inference(resolve,[status(thm)],[c_107,c_45]) ).
cnf(c_27557,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_27557]) ).
cnf(c_27558,plain,
is_a_theorem(implies(implies(A,B),implies(implies(not(C),A),or(C,B)))),
inference(paramod,[status(thm)],[c_122,c_116]) ).
cnf(c_123,plain,
is_a_theorem(implies(implies(A,B),implies(implies(not(C),A),implies(not(C),B)))),
inference(paramod,[status(thm)],[c_122,c_27558]) ).
cnf(c_27559,plain,
is_a_theorem(implies(or(A,implies(not(B),C)),or(B,or(A,C)))),
inference(paramod,[status(thm)],[c_122,c_115]) ).
cnf(c_27560,plain,
is_a_theorem(implies(implies(not(A),implies(not(B),C)),or(B,or(A,C)))),
inference(paramod,[status(thm)],[c_122,c_27559]) ).
cnf(c_27561,plain,
is_a_theorem(implies(implies(not(A),implies(not(B),C)),or(B,implies(not(A),C)))),
inference(paramod,[status(thm)],[c_122,c_27560]) ).
cnf(c_124,plain,
is_a_theorem(implies(implies(not(A),implies(not(B),C)),implies(not(B),implies(not(A),C)))),
inference(paramod,[status(thm)],[c_122,c_27561]) ).
cnf(c_27562,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_27562]) ).
cnf(c_126,plain,
is_a_theorem(implies(A,implies(not(B),A))),
inference(paramod,[status(thm)],[c_122,c_113]) ).
cnf(c_127,plain,
is_a_theorem(implies(implies(not(A),A),A)),
inference(paramod,[status(thm)],[c_122,c_112]) ).
cnf(c_128,plain,
implies(not(not(A)),B) = implies(A,B),
inference(paramod,[status(thm)],[c_122,c_108]) ).
cnf(c_135,plain,
not(implies(A,implies(B,C))) = and(A,and(B,not(C))),
inference(paramod,[status(thm)],[c_119,c_109]) ).
cnf(c_137,plain,
not(and(A,implies(B,C))) = implies(A,and(B,not(C))),
inference(paramod,[status(thm)],[c_119,c_119]) ).
cnf(c_143,plain,
( is_a_theorem(implies(not(B),implies(not(A),C)))
| ~ is_a_theorem(implies(not(A),implies(not(B),C))) ),
inference(resolve,[status(thm)],[c_124,c_111]) ).
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_151,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(implies(not(A),B),implies(not(B),A)),C)) ),
inference(resolve,[status(thm)],[c_125,c_111]) ).
cnf(c_155,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(C),and(A,not(B))))),
inference(paramod,[status(thm)],[c_119,c_125]) ).
cnf(c_162,plain,
( is_a_theorem(A)
| ~ is_a_theorem(implies(not(A),A)) ),
inference(resolve,[status(thm)],[c_127,c_111]) ).
cnf(c_27563,plain,
( is_a_theorem(A)
| ~ is_a_theorem(implies(not(A),A)) ),
inference(resolve,[status(thm)],[c_111,c_127]) ).
cnf(c_27564,plain,
~ is_a_theorem(implies(not(implies(implies(sK0,implies(sK0,sK1)),implies(sK0,sK1))),implies(implies(sK0,implies(sK0,sK1)),implies(sK0,sK1)))),
inference(resolve,[status(thm)],[c_27563,c_120]) ).
cnf(c_164,plain,
~ is_a_theorem(implies(and(implies(sK0,implies(sK0,sK1)),and(sK0,not(sK1))),implies(implies(sK0,implies(sK0,sK1)),implies(sK0,sK1)))),
inference(paramod,[status(thm)],[c_135,c_27564]) ).
cnf(c_27565,plain,
not(implies(A,not(B))) = and(not(not(A)),B),
inference(paramod,[status(thm)],[c_128,c_109]) ).
cnf(c_27566,plain,
and(A,B) = and(not(not(A)),B),
inference(paramod,[status(thm)],[c_109,c_27565]) ).
cnf(c_168,plain,
and(not(not(A)),B) = and(A,B),
inference(copy,[status(thm)],[c_27566]) ).
cnf(c_169,plain,
implies(not(and(A,B)),C) = implies(implies(A,not(B)),C),
inference(paramod,[status(thm)],[c_109,c_128]) ).
cnf(c_170,plain,
and(implies(A,B),implies(B,not(not(A)))) = equiv(not(not(A)),B),
inference(paramod,[status(thm)],[c_128,c_110]) ).
cnf(c_172,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(not(not(A))) ),
inference(paramod,[status(thm)],[c_128,c_111]) ).
cnf(c_173,plain,
implies(not(implies(A,B)),C) = implies(and(A,not(B)),C),
inference(paramod,[status(thm)],[c_119,c_128]) ).
cnf(c_27567,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(not(not(C)),B)))),
inference(paramod,[status(thm)],[c_128,c_123]) ).
cnf(c_175,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),
inference(paramod,[status(thm)],[c_128,c_27567]) ).
cnf(c_180,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(paramod,[status(thm)],[c_128,c_126]) ).
cnf(c_182,plain,
is_a_theorem(implies(implies(A,not(A)),not(A))),
inference(paramod,[status(thm)],[c_128,c_127]) ).
cnf(c_224,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_180,c_111]) ).
cnf(c_27568,plain,
is_a_theorem(implies(not(implies(A,not(B))),B)),
inference(resolve,[status(thm)],[c_150,c_180]) ).
cnf(c_263,plain,
is_a_theorem(implies(and(A,B),B)),
inference(paramod,[status(thm)],[c_109,c_27568]) ).
cnf(c_266,plain,
( is_a_theorem(implies(not(B),not(A)))
| ~ is_a_theorem(implies(A,B)) ),
inference(paramod,[status(thm)],[c_128,c_150]) ).
cnf(c_272,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(and(A,B),B),C)) ),
inference(resolve,[status(thm)],[c_263,c_111]) ).
cnf(c_27569,plain,
not(equiv(A,B)) = implies(implies(A,B),and(B,not(A))),
inference(paramod,[status(thm)],[c_110,c_137]) ).
cnf(c_343,plain,
implies(implies(A,B),and(B,not(A))) = not(equiv(A,B)),
inference(copy,[status(thm)],[c_27569]) ).
cnf(c_27570,plain,
is_a_theorem(implies(not(not(A)),not(implies(A,not(A))))),
inference(resolve,[status(thm)],[c_182,c_266]) ).
cnf(c_27571,plain,
is_a_theorem(implies(not(not(A)),and(A,A))),
inference(paramod,[status(thm)],[c_109,c_27570]) ).
cnf(c_543,plain,
is_a_theorem(implies(A,and(A,A))),
inference(paramod,[status(thm)],[c_128,c_27571]) ).
cnf(c_27572,plain,
( is_a_theorem(not(A))
| ~ is_a_theorem(not(not(implies(A,not(A))))) ),
inference(resolve,[status(thm)],[c_182,c_172]) ).
cnf(c_545,plain,
( is_a_theorem(not(A))
| ~ is_a_theorem(not(and(A,A))) ),
inference(paramod,[status(thm)],[c_109,c_27572]) ).
cnf(c_605,plain,
is_a_theorem(implies(implies(A,A),equiv(A,A))),
inference(paramod,[status(thm)],[c_110,c_543]) ).
cnf(c_693,plain,
( is_a_theorem(not(not(A)))
| ~ is_a_theorem(implies(not(A),A)) ),
inference(paramod,[status(thm)],[c_119,c_545]) ).
cnf(c_707,plain,
( is_a_theorem(equiv(A,A))
| ~ is_a_theorem(implies(A,A)) ),
inference(resolve,[status(thm)],[c_605,c_111]) ).
cnf(c_904,plain,
is_a_theorem(implies(not(A),implies(not(B),not(B)))),
inference(resolve,[status(thm)],[c_143,c_180]) ).
cnf(c_1513,plain,
is_a_theorem(implies(not(A),not(A))),
inference(resolve,[status(thm)],[c_904,c_162]) ).
cnf(c_27573,plain,
is_a_theorem(implies(not(not(A)),A)),
inference(resolve,[status(thm)],[c_1513,c_150]) ).
cnf(c_1567,plain,
is_a_theorem(implies(A,A)),
inference(paramod,[status(thm)],[c_128,c_27573]) ).
cnf(c_1614,plain,
is_a_theorem(equiv(A,A)),
inference(resolve,[status(thm)],[c_1567,c_707]) ).
cnf(c_1669,plain,
is_a_theorem(implies(A,equiv(B,B))),
inference(resolve,[status(thm)],[c_1614,c_224]) ).
cnf(c_1818,plain,
is_a_theorem(not(not(equiv(A,A)))),
inference(resolve,[status(thm)],[c_1669,c_693]) ).
cnf(c_27574,plain,
is_a_theorem(implies(not(implies(not(A),B)),and(not(B),not(A)))),
inference(resolve,[status(thm)],[c_155,c_151]) ).
cnf(c_2931,plain,
is_a_theorem(implies(and(not(A),not(B)),and(not(B),not(A)))),
inference(paramod,[status(thm)],[c_173,c_27574]) ).
cnf(c_5242,plain,
is_a_theorem(implies(and(not(A),not(not(B))),and(B,not(A)))),
inference(paramod,[status(thm)],[c_168,c_2931]) ).
cnf(c_5315,plain,
( is_a_theorem(implies(not(C),and(A,B)))
| ~ is_a_theorem(implies(implies(A,not(B)),C)) ),
inference(paramod,[status(thm)],[c_169,c_150]) ).
cnf(c_27575,plain,
not(implies(implies(A,B),not(implies(B,not(not(A)))))) = equiv(not(not(A)),B),
inference(paramod,[status(thm)],[c_170,c_109]) ).
cnf(c_27576,plain,
not(implies(implies(A,B),and(B,not(A)))) = equiv(not(not(A)),B),
inference(paramod,[status(thm)],[c_109,c_27575]) ).
cnf(c_5586,plain,
not(not(equiv(A,B))) = equiv(not(not(A)),B),
inference(paramod,[status(thm)],[c_343,c_27576]) ).
cnf(c_5677,plain,
is_a_theorem(equiv(not(not(A)),A)),
inference(paramod,[status(thm)],[c_5586,c_1818]) ).
cnf(c_27577,plain,
A = not(not(A)),
inference(resolve,[status(thm)],[c_5677,c_117]) ).
cnf(c_5892,plain,
not(not(A)) = A,
inference(copy,[status(thm)],[c_27577]) ).
cnf(c_5901,plain,
is_a_theorem(implies(and(not(A),B),and(B,not(A)))),
inference(paramod,[status(thm)],[c_5892,c_5242]) ).
cnf(c_5918,plain,
not(implies(A,B)) = and(A,not(B)),
inference(paramod,[status(thm)],[c_5892,c_109]) ).
cnf(c_6012,plain,
is_a_theorem(implies(implies(A,and(B,C)),implies(A,C))),
inference(resolve,[status(thm)],[c_175,c_272]) ).
cnf(c_6018,plain,
( is_a_theorem(implies(implies(C,A),implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_175,c_111]) ).
cnf(c_27578,plain,
is_a_theorem(implies(and(A,B),and(B,not(not(A))))),
inference(paramod,[status(thm)],[c_5892,c_5901]) ).
cnf(c_6365,plain,
is_a_theorem(implies(and(A,B),and(B,A))),
inference(paramod,[status(thm)],[c_5892,c_27578]) ).
cnf(c_6944,plain,
is_a_theorem(implies(implies(A,B),implies(A,implies(C,B)))),
inference(resolve,[status(thm)],[c_6018,c_180]) ).
cnf(c_11942,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(A,and(B,C))) ),
inference(resolve,[status(thm)],[c_6012,c_111]) ).
cnf(c_12086,plain,
is_a_theorem(implies(and(A,B),A)),
inference(resolve,[status(thm)],[c_11942,c_6365]) ).
cnf(c_12353,plain,
is_a_theorem(implies(implies(A,and(B,C)),implies(A,B))),
inference(resolve,[status(thm)],[c_12086,c_6018]) ).
cnf(c_19684,plain,
( is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(A,and(B,C))) ),
inference(resolve,[status(thm)],[c_12353,c_111]) ).
cnf(c_27579,plain,
is_a_theorem(implies(not(implies(implies(A,B),implies(A,not(C)))),and(B,C))),
inference(resolve,[status(thm)],[c_5315,c_175]) ).
cnf(c_27580,plain,
is_a_theorem(implies(and(implies(A,B),not(implies(A,not(C)))),and(B,C))),
inference(paramod,[status(thm)],[c_5918,c_27579]) ).
cnf(c_27581,plain,
is_a_theorem(implies(and(implies(A,B),and(A,not(not(C)))),and(B,C))),
inference(paramod,[status(thm)],[c_5918,c_27580]) ).
cnf(c_25228,plain,
is_a_theorem(implies(and(implies(A,B),and(A,C)),and(B,C))),
inference(paramod,[status(thm)],[c_5892,c_27581]) ).
cnf(c_25232,plain,
is_a_theorem(implies(and(implies(A,B),and(A,C)),B)),
inference(resolve,[status(thm)],[c_25228,c_19684]) ).
cnf(c_27582,plain,
( is_a_theorem(implies(A,implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_111,c_6944]) ).
cnf(c_27583,plain,
~ is_a_theorem(implies(and(implies(sK0,implies(sK0,sK1)),and(sK0,not(sK1))),implies(sK0,sK1))),
inference(resolve,[status(thm)],[c_27582,c_164]) ).
cnf(c_27555,plain,
$false,
inference(resolve,[status(thm)],[c_25232,c_27583]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL485+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n002.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % 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 22:41:50 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.39 % Process 188195 was started by sandbox2 on n002,
% 0.11/0.39 % Fri Sep 25 22:41:50 2026
% 0.11/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.40
% 0.11/0.40 % From the command line: assign(max_seconds, 300).
% 213.82/29.12
% 213.82/29.12 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 213.82/29.12
% 213.82/29.12 % given #500 (W,wt=23): 18044 -is_a_theorem(equiv(and(A,c10),implies(B,c9))). [ur(326,b,17873,a)].
% 213.82/29.12
% 213.82/29.12 % SZS status Theorem for theBenchmark
% 213.82/29.12
% 213.82/29.12 % Proof 1 at 3.38 (+ 1.13) seconds.
% 213.82/29.12 % Length of proof is 113.
% 213.82/29.12 % Level of proof is 22.
% 213.82/29.12 % Maximum clause weight is 58.000.
% 213.82/29.12 % Given clauses 947.
% 213.82/29.12
% 213.82/29.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------