%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL457+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 : n026.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 31.38s 4.91s
% Output : CNFRefutation 31.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 30
% Syntax : Number of formulae : 152 ( 97 unt; 0 def)
% Number of atoms : 221 ( 46 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 125 ( 56 ~; 48 |; 4 &)
% ( 11 <=>; 6 =>; 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 : 253 ( 11 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(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(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(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(principia_r4,conjecture,
r4,
file('theBenchmark.p',principia_r4) ).
fof(principia_r4_neg,negated_conjecture,
~ r4,
inference(assume_negation,[status(cth)],[principia_r4]) ).
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_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_25,plain,
( ( ? [P,Q,R] : ~ is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))
| r4 )
& ( ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ) ),
inference(fof_nnf,[status(thm)],[r4]) ).
fof(sk_r4_sk,plain,
( ( ~ is_a_theorem(implies(or(sK0,or(sK1,sK2)),or(sK1,or(sK0,sK2))))
| r4 )
& ( ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(P,sK0),skolemize(Q,sK1),skolemize(R,sK2)],[nnf_25]) ).
fof(sk_r4,plain,
( ( ~ is_a_theorem(implies(or(sK0,or(sK1,sK2)),or(sK1,or(sK0,sK2))))
| r4 )
& ! [VAR_0,VAR_1,VAR_2] :
( is_a_theorem(implies(or(VAR_0,or(VAR_1,VAR_2)),or(VAR_1,or(VAR_0,VAR_2))))
| ~ r4 ) ),
inference(cnf_transformation,[status(thm)],[sk_r4_sk]) ).
cnf(c_85,plain,
( ~ is_a_theorem(implies(or(sK0,or(sK1,sK2)),or(sK1,or(sK0,sK2))))
| r4 ),
inference(split_conjunct,[status(thm)],[sk_r4]) ).
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(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_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_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]) ).
fof(principia_op_implies_or,axiom,
op_implies_or,
file('theBenchmark.p',principia_op_implies_or) ).
cnf(c_113,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_114,plain,
op_and,
inference(clausify,[status(thm)],[principia_op_and]) ).
cnf(c_115,negated_conjecture,
~ r4,
inference(clausify,[status(thm)],[principia_r4_neg]) ).
cnf(c_116,plain,
not(and(not(A),not(B))) = or(A,B),
inference(resolve,[status(thm)],[c_95,c_89]) ).
cnf(c_117,plain,
not(and(A,not(B))) = implies(A,B),
inference(resolve,[status(thm)],[c_96,c_92]) ).
cnf(c_119,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(implies(not(A),not(B)),implies(B,A))),
inference(resolve,[status(thm)],[c_99,c_40]) ).
cnf(c_121,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolve,[status(thm)],[c_100,c_42]) ).
cnf(c_122,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_101,c_44]) ).
cnf(c_123,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_124,plain,
is_a_theorem(implies(and(A,B),A)),
inference(resolve,[status(thm)],[c_103,c_48]) ).
cnf(c_125,plain,
is_a_theorem(implies(and(A,B),B)),
inference(resolve,[status(thm)],[c_104,c_50]) ).
cnf(c_126,plain,
is_a_theorem(implies(A,implies(B,and(A,B)))),
inference(resolve,[status(thm)],[c_105,c_52]) ).
cnf(c_132,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_133,plain,
( B = A
| ~ is_a_theorem(equiv(A,B)) ),
inference(resolve,[status(thm)],[c_112,c_37]) ).
cnf(c_134,plain,
or(not(A),B) = implies(A,B),
inference(resolve,[status(thm)],[c_113,c_93]) ).
cnf(c_29602,plain,
( not(implies(A,not(B))) = and(A,B)
| ~ op_and ),
inference(paramod,[status(thm)],[c_134,c_91]) ).
cnf(c_135,plain,
not(implies(A,not(B))) = and(A,B),
inference(resolve,[status(thm)],[c_114,c_29602]) ).
cnf(c_136,negated_conjecture,
~ is_a_theorem(implies(or(sK0,or(sK1,sK2)),or(sK1,or(sK0,sK2)))),
inference(resolve,[status(thm)],[c_115,c_85]) ).
cnf(c_29603,plain,
implies(not(A),B) = or(A,B),
inference(paramod,[status(thm)],[c_117,c_116]) ).
cnf(c_137,plain,
or(A,B) = implies(not(A),B),
inference(copy,[status(thm)],[c_29603]) ).
cnf(c_29604,negated_conjecture,
~ is_a_theorem(implies(or(sK0,implies(not(sK1),sK2)),or(sK1,or(sK0,sK2)))),
inference(paramod,[status(thm)],[c_137,c_136]) ).
cnf(c_29605,negated_conjecture,
~ is_a_theorem(implies(implies(not(sK0),implies(not(sK1),sK2)),or(sK1,or(sK0,sK2)))),
inference(paramod,[status(thm)],[c_137,c_29604]) ).
cnf(c_29606,negated_conjecture,
~ is_a_theorem(implies(implies(not(sK0),implies(not(sK1),sK2)),or(sK1,implies(not(sK0),sK2)))),
inference(paramod,[status(thm)],[c_137,c_29605]) ).
cnf(c_141,negated_conjecture,
~ is_a_theorem(implies(implies(not(sK0),implies(not(sK1),sK2)),implies(not(sK1),implies(not(sK0),sK2)))),
inference(paramod,[status(thm)],[c_137,c_29606]) ).
cnf(c_142,plain,
implies(not(not(A)),B) = implies(A,B),
inference(paramod,[status(thm)],[c_137,c_134]) ).
cnf(c_152,plain,
not(and(A,implies(B,C))) = implies(A,and(B,not(C))),
inference(paramod,[status(thm)],[c_117,c_117]) ).
cnf(c_29607,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,implies(B,A)),C)) ),
inference(resolve,[status(thm)],[c_119,c_121]) ).
cnf(c_160,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_29607,c_122]) ).
cnf(c_29608,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_119,c_123]) ).
cnf(c_163,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))),
inference(resolve,[status(thm)],[c_29608,c_123]) ).
cnf(c_29609,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,implies(B,and(A,B))),C)) ),
inference(resolve,[status(thm)],[c_119,c_126]) ).
cnf(c_198,plain,
is_a_theorem(implies(implies(implies(A,and(B,A)),B),equiv(B,implies(A,and(B,A))))),
inference(resolve,[status(thm)],[c_29609,c_132]) ).
cnf(c_29610,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(and(A,B),B),C)) ),
inference(resolve,[status(thm)],[c_119,c_125]) ).
cnf(c_199,plain,
is_a_theorem(implies(implies(A,and(B,A)),equiv(and(B,A),A))),
inference(resolve,[status(thm)],[c_29610,c_132]) ).
cnf(c_29611,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(and(A,B),A),C)) ),
inference(resolve,[status(thm)],[c_119,c_124]) ).
cnf(c_200,plain,
is_a_theorem(implies(implies(A,and(A,B)),equiv(and(A,B),A))),
inference(resolve,[status(thm)],[c_29611,c_132]) ).
cnf(c_228,plain,
implies(not(implies(A,B)),C) = implies(and(A,not(B)),C),
inference(paramod,[status(thm)],[c_117,c_142]) ).
cnf(c_231,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(not(not(A))) ),
inference(paramod,[status(thm)],[c_142,c_119]) ).
cnf(c_29612,plain,
not(implies(A,not(B))) = and(not(not(A)),B),
inference(paramod,[status(thm)],[c_142,c_135]) ).
cnf(c_29613,plain,
and(A,B) = and(not(not(A)),B),
inference(paramod,[status(thm)],[c_135,c_29612]) ).
cnf(c_242,plain,
and(not(not(A)),B) = and(A,B),
inference(copy,[status(thm)],[c_29613]) ).
cnf(c_29614,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_119,c_160]) ).
cnf(c_357,plain,
is_a_theorem(implies(A,and(implies(B,B),A))),
inference(resolve,[status(thm)],[c_29614,c_126]) ).
cnf(c_29615,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_119,c_160]) ).
cnf(c_358,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_29615,c_121]) ).
cnf(c_29616,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(not(not(implies(not(A),not(B))))) ),
inference(resolve,[status(thm)],[c_231,c_120]) ).
cnf(c_1823,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(not(and(not(A),B))) ),
inference(paramod,[status(thm)],[c_135,c_29616]) ).
cnf(c_29617,plain,
( is_a_theorem(implies(implies(C,A),D))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)) ),
inference(resolve,[status(thm)],[c_119,c_163]) ).
cnf(c_2909,plain,
~ is_a_theorem(implies(implies(implies(implies(not(sK1),sK2),A),implies(not(sK0),A)),implies(not(sK1),implies(not(sK0),sK2)))),
inference(resolve,[status(thm)],[c_29617,c_141]) ).
cnf(c_4291,plain,
( is_a_theorem(implies(not(B),A))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(paramod,[status(thm)],[c_117,c_1823]) ).
cnf(c_4301,plain,
( is_a_theorem(implies(not(B),not(A)))
| ~ is_a_theorem(implies(A,B)) ),
inference(paramod,[status(thm)],[c_142,c_4291]) ).
cnf(c_29618,plain,
is_a_theorem(implies(not(implies(A,B)),not(implies(not(B),not(A))))),
inference(resolve,[status(thm)],[c_4301,c_120]) ).
cnf(c_29619,plain,
is_a_theorem(implies(not(implies(A,B)),and(not(B),A))),
inference(paramod,[status(thm)],[c_135,c_29618]) ).
cnf(c_4321,plain,
is_a_theorem(implies(and(A,not(B)),and(not(B),A))),
inference(paramod,[status(thm)],[c_228,c_29619]) ).
cnf(c_29620,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,implies(B,B)),C)) ),
inference(resolve,[status(thm)],[c_119,c_358]) ).
cnf(c_20325,plain,
is_a_theorem(equiv(implies(A,A),implies(B,and(implies(A,A),B)))),
inference(resolve,[status(thm)],[c_29620,c_198]) ).
cnf(c_29621,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,and(implies(B,B),A)),C)) ),
inference(resolve,[status(thm)],[c_119,c_357]) ).
cnf(c_20970,plain,
is_a_theorem(equiv(and(implies(A,A),B),B)),
inference(resolve,[status(thm)],[c_29621,c_199]) ).
cnf(c_29622,plain,
A = and(implies(B,B),A),
inference(resolve,[status(thm)],[c_20970,c_133]) ).
cnf(c_21329,plain,
and(implies(A,A),B) = B,
inference(copy,[status(thm)],[c_29622]) ).
cnf(c_21335,plain,
is_a_theorem(equiv(implies(A,A),implies(B,B))),
inference(paramod,[status(thm)],[c_21329,c_20325]) ).
cnf(c_29623,plain,
not(not(A)) = implies(implies(B,B),A),
inference(paramod,[status(thm)],[c_21329,c_117]) ).
cnf(c_21375,plain,
implies(implies(A,A),B) = not(not(B)),
inference(copy,[status(thm)],[c_29623]) ).
cnf(c_29624,plain,
not(implies(implies(A,A),not(B))) = B,
inference(paramod,[status(thm)],[c_21329,c_135]) ).
cnf(c_21376,plain,
not(not(not(not(A)))) = A,
inference(paramod,[status(thm)],[c_21375,c_29624]) ).
cnf(c_21382,plain,
is_a_theorem(implies(not(A),and(not(A),implies(B,B)))),
inference(paramod,[status(thm)],[c_21329,c_4321]) ).
cnf(c_21644,plain,
implies(A,A) = implies(B,B),
inference(resolve,[status(thm)],[c_21335,c_133]) ).
cnf(c_21819,plain,
( is_a_theorem(equiv(and(A,B),A))
| ~ is_a_theorem(implies(A,and(A,B))) ),
inference(resolve,[status(thm)],[c_200,c_119]) ).
cnf(c_29625,plain,
not(implies(A,A)) = and(not(B),B),
inference(paramod,[status(thm)],[c_21644,c_135]) ).
cnf(c_22308,plain,
and(not(A),A) = not(implies(B,B)),
inference(copy,[status(thm)],[c_29625]) ).
cnf(c_22416,plain,
not(implies(A,A)) = not(implies(B,B)),
inference(paramod,[status(thm)],[c_22308,c_22308]) ).
cnf(c_29626,plain,
not(implies(A,not(implies(B,B)))) = and(A,implies(C,C)),
inference(paramod,[status(thm)],[c_22416,c_135]) ).
cnf(c_22461,plain,
and(A,implies(B,B)) = and(A,implies(C,C)),
inference(paramod,[status(thm)],[c_135,c_29626]) ).
cnf(c_22853,plain,
( is_a_theorem(equiv(and(A,implies(C,C)),A))
| ~ is_a_theorem(implies(A,and(A,implies(B,B)))) ),
inference(paramod,[status(thm)],[c_22461,c_21819]) ).
cnf(c_29627,plain,
is_a_theorem(implies(A,and(not(not(A)),implies(B,B)))),
inference(paramod,[status(thm)],[c_142,c_21382]) ).
cnf(c_26371,plain,
is_a_theorem(implies(A,and(A,implies(B,B)))),
inference(paramod,[status(thm)],[c_242,c_29627]) ).
cnf(c_26373,plain,
is_a_theorem(equiv(and(A,implies(B,B)),A)),
inference(resolve,[status(thm)],[c_26371,c_22853]) ).
cnf(c_29628,plain,
A = and(A,implies(B,B)),
inference(resolve,[status(thm)],[c_26373,c_133]) ).
cnf(c_26585,plain,
and(A,implies(B,B)) = A,
inference(copy,[status(thm)],[c_29628]) ).
cnf(c_29629,plain,
not(A) = implies(A,and(B,not(B))),
inference(paramod,[status(thm)],[c_26585,c_152]) ).
cnf(c_26620,plain,
implies(A,and(B,not(B))) = not(A),
inference(copy,[status(thm)],[c_29629]) ).
cnf(c_29630,plain,
not(not(not(A))) = implies(A,and(B,not(B))),
inference(paramod,[status(thm)],[c_26620,c_142]) ).
cnf(c_27143,plain,
not(not(not(A))) = not(A),
inference(paramod,[status(thm)],[c_26620,c_29630]) ).
cnf(c_27219,plain,
not(not(A)) = A,
inference(paramod,[status(thm)],[c_27143,c_21376]) ).
cnf(c_27291,plain,
implies(implies(A,A),B) = B,
inference(paramod,[status(thm)],[c_27219,c_21375]) ).
cnf(c_29631,plain,
is_a_theorem(implies(implies(implies(implies(A,B),B),C),implies(implies(implies(D,D),A),C))),
inference(paramod,[status(thm)],[c_27291,c_163]) ).
cnf(c_29600,plain,
is_a_theorem(implies(implies(implies(implies(A,B),B),C),implies(A,C))),
inference(paramod,[status(thm)],[c_27291,c_29631]) ).
cnf(c_29601,plain,
$false,
inference(resolve,[status(thm)],[c_29600,c_2909]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL457+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 : n026.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 22:38:39 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 3637994 was started by sandbox on n026,
% 0.10/0.37 % Fri Sep 25 22:38:39 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 31.38/4.91
% 31.38/4.91 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 31.38/4.91
% 31.38/4.91 % given #500 (F,wt=28): 12619 -is_a_theorem(equiv(not(implies(A,A)),not(c51))). [ur(190,b,1670,a)].
% 31.38/4.91
% 31.38/4.91 % SZS status Theorem for theBenchmark
% 31.38/4.91
% 31.38/4.91 % Proof 1 at 3.51 (+ 0.88) seconds.
% 31.38/4.91 % Length of proof is 104.
% 31.38/4.91 % Level of proof is 20.
% 31.38/4.91 % Maximum clause weight is 80.000.
% 31.38/4.91 % Given clauses 580.
% 31.38/4.91
% 31.38/4.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------