%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL519+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 : n015.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 07:59:05 AM UTC 2026
% Result : Theorem 3.63s 0.91s
% Output : CNFRefutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 22
% Syntax : Number of formulae : 114 ( 76 unt; 0 def)
% Number of atoms : 165 ( 42 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 92 ( 41 ~; 34 |; 4 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 179 ( 7 sgn 28 !; 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(kn1,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('theBenchmark.p',kn1) ).
fof(kn2,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
file('theBenchmark.p',kn2) ).
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(r2,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('theBenchmark.p',r2) ).
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(principia_r2,conjecture,
r2,
file('theBenchmark.p',principia_r2) ).
fof(principia_r2_neg,negated_conjecture,
~ r2,
inference(assume_negation,[status(cth)],[principia_r2]) ).
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_66,plain,
( is_a_theorem(implies(A,and(A,A)))
| ~ kn1 ),
inference(clausify,[status(thm)],[kn1]) ).
cnf(c_68,plain,
( is_a_theorem(implies(and(A,B),A))
| ~ kn2 ),
inference(clausify,[status(thm)],[kn2]) ).
cnf(c_70,plain,
( is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A)))))
| ~ kn3 ),
inference(clausify,[status(thm)],[kn3]) ).
fof(nnf_23,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(Q,or(P,Q)))
| r2 )
& ( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ) ),
inference(fof_nnf,[status(thm)],[r2]) ).
fof(sk_r2_sk,plain,
( ( ~ is_a_theorem(implies(sK0,or(sK1,sK0)))
| r2 )
& ( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(P,sK1),skolemize(Q,sK0)],[nnf_23]) ).
fof(sk_r2,plain,
( ( ~ is_a_theorem(implies(sK0,or(sK1,sK0)))
| r2 )
& ! [VAR_0,VAR_1] :
( is_a_theorem(implies(VAR_0,or(VAR_1,VAR_0)))
| ~ r2 ) ),
inference(cnf_transformation,[status(thm)],[sk_r2_sk]) ).
cnf(c_81,plain,
( ~ is_a_theorem(implies(sK0,or(sK1,sK0)))
| r2 ),
inference(split_conjunct,[status(thm)],[sk_r2]) ).
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(rosser_op_or,axiom,
op_or,
file('theBenchmark.p',rosser_op_or) ).
cnf(c_95,plain,
op_or,
inference(clausify,[status(thm)],[rosser_op_or]) ).
fof(rosser_op_implies_and,axiom,
op_implies_and,
file('theBenchmark.p',rosser_op_implies_and) ).
cnf(c_96,plain,
op_implies_and,
inference(clausify,[status(thm)],[rosser_op_implies_and]) ).
fof(rosser_op_equiv,axiom,
op_equiv,
file('theBenchmark.p',rosser_op_equiv) ).
cnf(c_97,plain,
op_equiv,
inference(clausify,[status(thm)],[rosser_op_equiv]) ).
fof(rosser_modus_ponens,axiom,
modus_ponens,
file('theBenchmark.p',rosser_modus_ponens) ).
cnf(c_98,plain,
modus_ponens,
inference(clausify,[status(thm)],[rosser_modus_ponens]) ).
fof(rosser_kn1,axiom,
kn1,
file('theBenchmark.p',rosser_kn1) ).
cnf(c_99,plain,
kn1,
inference(clausify,[status(thm)],[rosser_kn1]) ).
fof(rosser_kn2,axiom,
kn2,
file('theBenchmark.p',rosser_kn2) ).
cnf(c_100,plain,
kn2,
inference(clausify,[status(thm)],[rosser_kn2]) ).
fof(rosser_kn3,axiom,
kn3,
file('theBenchmark.p',rosser_kn3) ).
cnf(c_101,plain,
kn3,
inference(clausify,[status(thm)],[rosser_kn3]) ).
fof(use_substitution_of_equivalents,axiom,
substitution_of_equivalents,
file('theBenchmark.p',use_substitution_of_equivalents) ).
cnf(c_102,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_103,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_104,plain,
op_and,
inference(clausify,[status(thm)],[principia_op_and]) ).
cnf(c_105,negated_conjecture,
~ r2,
inference(clausify,[status(thm)],[principia_r2_neg]) ).
cnf(c_106,plain,
not(and(not(A),not(B))) = or(A,B),
inference(resolve,[status(thm)],[c_95,c_89]) ).
cnf(c_107,plain,
not(and(A,not(B))) = implies(A,B),
inference(resolve,[status(thm)],[c_96,c_92]) ).
cnf(c_108,plain,
and(implies(A,B),implies(B,A)) = equiv(A,B),
inference(resolve,[status(thm)],[c_97,c_94]) ).
cnf(c_109,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_110,plain,
is_a_theorem(implies(A,and(A,A))),
inference(resolve,[status(thm)],[c_99,c_66]) ).
cnf(c_111,plain,
is_a_theorem(implies(and(A,B),A)),
inference(resolve,[status(thm)],[c_100,c_68]) ).
cnf(c_112,plain,
is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))),
inference(resolve,[status(thm)],[c_101,c_70]) ).
cnf(c_113,plain,
( B = A
| ~ is_a_theorem(equiv(A,B)) ),
inference(resolve,[status(thm)],[c_102,c_37]) ).
cnf(c_114,plain,
or(not(A),B) = implies(A,B),
inference(resolve,[status(thm)],[c_103,c_93]) ).
cnf(c_1609,plain,
( not(implies(A,not(B))) = and(A,B)
| ~ op_and ),
inference(paramod,[status(thm)],[c_114,c_91]) ).
cnf(c_115,plain,
not(implies(A,not(B))) = and(A,B),
inference(resolve,[status(thm)],[c_104,c_1609]) ).
cnf(c_116,negated_conjecture,
~ is_a_theorem(implies(sK0,or(sK1,sK0))),
inference(resolve,[status(thm)],[c_105,c_81]) ).
cnf(c_1610,plain,
implies(not(A),B) = or(A,B),
inference(paramod,[status(thm)],[c_107,c_106]) ).
cnf(c_117,plain,
or(A,B) = implies(not(A),B),
inference(copy,[status(thm)],[c_1610]) ).
cnf(c_119,negated_conjecture,
~ is_a_theorem(implies(sK0,implies(not(sK1),sK0))),
inference(paramod,[status(thm)],[c_117,c_116]) ).
cnf(c_120,plain,
implies(not(not(A)),B) = implies(A,B),
inference(paramod,[status(thm)],[c_117,c_114]) ).
cnf(c_138,plain,
is_a_theorem(implies(implies(A,A),equiv(A,A))),
inference(paramod,[status(thm)],[c_108,c_110]) ).
cnf(c_140,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(and(A,B),A),C)) ),
inference(resolve,[status(thm)],[c_111,c_109]) ).
cnf(c_143,plain,
( is_a_theorem(implies(not(and(B,C)),not(and(C,A))))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_112,c_109]) ).
cnf(c_145,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),not(and(not(C),A))))),
inference(paramod,[status(thm)],[c_107,c_112]) ).
cnf(c_146,plain,
is_a_theorem(implies(implies(not(A),B),implies(not(and(B,C)),implies(C,A)))),
inference(paramod,[status(thm)],[c_107,c_112]) ).
cnf(c_1611,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(and(A,B),A),C)) ),
inference(resolve,[status(thm)],[c_109,c_111]) ).
cnf(c_154,plain,
~ is_a_theorem(implies(implies(and(A,B),A),implies(sK0,implies(not(sK1),sK0)))),
inference(resolve,[status(thm)],[c_1611,c_119]) ).
cnf(c_158,plain,
implies(not(implies(A,B)),C) = implies(and(A,not(B)),C),
inference(paramod,[status(thm)],[c_107,c_120]) ).
cnf(c_160,plain,
and(implies(A,not(not(B))),implies(B,A)) = equiv(A,not(not(B))),
inference(paramod,[status(thm)],[c_120,c_108]) ).
cnf(c_161,plain,
is_a_theorem(implies(A,and(not(not(A)),not(not(A))))),
inference(paramod,[status(thm)],[c_120,c_110]) ).
cnf(c_1612,plain,
not(implies(A,not(B))) = and(not(not(A)),B),
inference(paramod,[status(thm)],[c_120,c_115]) ).
cnf(c_1613,plain,
and(A,B) = and(not(not(A)),B),
inference(paramod,[status(thm)],[c_115,c_1612]) ).
cnf(c_163,plain,
and(not(not(A)),B) = and(A,B),
inference(copy,[status(thm)],[c_1613]) ).
cnf(c_164,plain,
implies(not(and(A,B)),C) = implies(implies(A,not(B)),C),
inference(paramod,[status(thm)],[c_115,c_120]) ).
cnf(c_165,plain,
is_a_theorem(implies(A,and(A,not(not(A))))),
inference(paramod,[status(thm)],[c_163,c_161]) ).
cnf(c_168,plain,
is_a_theorem(implies(implies(not(A),B),implies(implies(B,not(C)),implies(C,A)))),
inference(paramod,[status(thm)],[c_164,c_146]) ).
cnf(c_170,plain,
( is_a_theorem(implies(implies(B,not(C)),not(and(C,A))))
| ~ is_a_theorem(implies(A,B)) ),
inference(paramod,[status(thm)],[c_164,c_143]) ).
cnf(c_185,plain,
( is_a_theorem(equiv(A,A))
| ~ is_a_theorem(implies(A,A)) ),
inference(resolve,[status(thm)],[c_138,c_109]) ).
cnf(c_223,plain,
and(not(and(A,B)),C) = and(implies(A,not(B)),C),
inference(paramod,[status(thm)],[c_115,c_163]) ).
cnf(c_1614,plain,
implies(and(A,B),C) = implies(and(A,not(not(B))),C),
inference(paramod,[status(thm)],[c_115,c_158]) ).
cnf(c_336,plain,
implies(and(A,not(not(B))),C) = implies(and(A,B),C),
inference(copy,[status(thm)],[c_1614]) ).
cnf(c_1615,plain,
and(implies(A,B),C) = and(implies(A,not(not(B))),C),
inference(paramod,[status(thm)],[c_107,c_223]) ).
cnf(c_347,plain,
and(implies(A,not(not(B))),C) = and(implies(A,B),C),
inference(copy,[status(thm)],[c_1615]) ).
cnf(c_1616,plain,
and(implies(A,B),implies(B,A)) = equiv(A,not(not(B))),
inference(paramod,[status(thm)],[c_347,c_160]) ).
cnf(c_1617,plain,
equiv(A,B) = equiv(A,not(not(B))),
inference(paramod,[status(thm)],[c_108,c_1616]) ).
cnf(c_361,plain,
equiv(A,not(not(B))) = equiv(A,B),
inference(copy,[status(thm)],[c_1617]) ).
cnf(c_1618,plain,
is_a_theorem(implies(implies(and(A,not(not(A))),not(B)),not(and(B,A)))),
inference(resolve,[status(thm)],[c_170,c_165]) ).
cnf(c_633,plain,
is_a_theorem(implies(implies(and(A,A),not(B)),not(and(B,A)))),
inference(paramod,[status(thm)],[c_336,c_1618]) ).
cnf(c_1619,plain,
is_a_theorem(not(and(A,not(A)))),
inference(resolve,[status(thm)],[c_633,c_140]) ).
cnf(c_768,plain,
is_a_theorem(implies(A,A)),
inference(paramod,[status(thm)],[c_107,c_1619]) ).
cnf(c_808,plain,
is_a_theorem(equiv(A,A)),
inference(resolve,[status(thm)],[c_768,c_185]) ).
cnf(c_811,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_768,c_109]) ).
cnf(c_868,plain,
is_a_theorem(equiv(not(not(A)),A)),
inference(paramod,[status(thm)],[c_361,c_808]) ).
cnf(c_902,plain,
is_a_theorem(implies(implies(A,B),not(and(not(B),A)))),
inference(resolve,[status(thm)],[c_811,c_145]) ).
cnf(c_1620,plain,
A = not(not(A)),
inference(resolve,[status(thm)],[c_868,c_113]) ).
cnf(c_1019,plain,
not(not(A)) = A,
inference(copy,[status(thm)],[c_1620]) ).
cnf(c_1030,plain,
not(and(A,B)) = implies(A,not(B)),
inference(paramod,[status(thm)],[c_1019,c_107]) ).
cnf(c_1031,plain,
not(implies(A,B)) = and(A,not(B)),
inference(paramod,[status(thm)],[c_107,c_1019]) ).
cnf(c_1038,plain,
is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))),
inference(paramod,[status(thm)],[c_1030,c_902]) ).
cnf(c_1464,plain,
( is_a_theorem(implies(not(B),not(A)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1038,c_109]) ).
cnf(c_1621,plain,
is_a_theorem(implies(not(implies(not(A),not(B))),not(implies(B,A)))),
inference(resolve,[status(thm)],[c_1464,c_1038]) ).
cnf(c_1622,plain,
is_a_theorem(implies(and(not(A),not(not(B))),not(implies(B,A)))),
inference(paramod,[status(thm)],[c_1031,c_1621]) ).
cnf(c_1623,plain,
is_a_theorem(implies(and(not(A),B),not(implies(B,A)))),
inference(paramod,[status(thm)],[c_1019,c_1622]) ).
cnf(c_1515,plain,
is_a_theorem(implies(and(not(A),B),and(B,not(A)))),
inference(paramod,[status(thm)],[c_1031,c_1623]) ).
cnf(c_1624,plain,
( is_a_theorem(implies(implies(B,not(C)),implies(C,A)))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(resolve,[status(thm)],[c_109,c_168]) ).
cnf(c_1625,plain,
~ is_a_theorem(implies(not(implies(not(sK1),sK0)),and(not(sK0),A))),
inference(resolve,[status(thm)],[c_1624,c_154]) ).
cnf(c_1607,plain,
~ is_a_theorem(implies(and(not(sK1),not(sK0)),and(not(sK0),A))),
inference(paramod,[status(thm)],[c_1031,c_1625]) ).
cnf(c_1608,plain,
$false,
inference(resolve,[status(thm)],[c_1607,c_1515]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL519+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 22:44:58 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 2458361 was started by sandbox2 on n015,
% 0.10/0.37 % Fri Sep 25 22:44:58 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 3.63/0.91
% 3.63/0.91 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 3.63/0.91
% 3.63/0.91 % SZS status Theorem for theBenchmark
% 3.63/0.91
% 3.63/0.91 % Proof 1 at 0.29 (+ 0.09) seconds.
% 3.63/0.91 % Length of proof is 83.
% 3.63/0.91 % Level of proof is 17.
% 3.63/0.91 % Maximum clause weight is 50.000.
% 3.63/0.91 % Given clauses 172.
% 3.63/0.91
% 3.63/0.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------