%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL513+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 07:59:05 AM UTC 2026
% Result : Theorem 68.28s 20.63s
% Output : CNFRefutation 68.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of formulae : 97 ( 53 unt; 0 def)
% Number of atoms : 161 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 119 ( 55 ~; 47 |; 7 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 168 ( 10 sgn 30 !; 4 ?)
% 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(and_2,axiom,
( and_2
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) ),
file('theBenchmark.p',and_2) ).
fof(equivalence_2,axiom,
( equivalence_2
<=> ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(Y,X))) ),
file('theBenchmark.p',equivalence_2) ).
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(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(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_8,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),Y))
| and_2 )
& ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ) ),
inference(fof_nnf,[status(thm)],[and_2]) ).
fof(sk_and_2_sk,plain,
( ( ~ is_a_theorem(implies(and(sK0,sK1),sK1))
| and_2 )
& ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_8]) ).
fof(sk_and_2,plain,
( ( ~ is_a_theorem(implies(and(sK0,sK1),sK1))
| and_2 )
& ! [VAR_0,VAR_1] :
( is_a_theorem(implies(and(VAR_0,VAR_1),VAR_1))
| ~ and_2 ) ),
inference(cnf_transformation,[status(thm)],[sk_and_2_sk]) ).
cnf(c_50,plain,
( is_a_theorem(implies(and(A,B),B))
| ~ and_2 ),
inference(split_conjunct,[status(thm)],[sk_and_2]) ).
cnf(c_51,plain,
( ~ is_a_theorem(implies(and(sK0,sK1),sK1))
| and_2 ),
inference(split_conjunct,[status(thm)],[sk_and_2]) ).
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(sK2,sK3),implies(sK3,sK2)))
| equivalence_2 )
& ( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X,sK2),skolemize(Y,sK3)],[nnf_14]) ).
fof(sk_equivalence_2,plain,
( ( ~ is_a_theorem(implies(equiv(sK2,sK3),implies(sK3,sK2)))
| 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(sK2,sK3),implies(sK3,sK2)))
| equivalence_2 ),
inference(split_conjunct,[status(thm)],[sk_equivalence_2]) ).
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]) ).
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]) ).
cnf(c_95,plain,
( equiv(A,B) = and(implies(A,B),implies(B,A))
| ~ op_equiv ),
inference(copy,[status(thm)],[c_94]) ).
fof(rosser_op_or,axiom,
op_or,
file('theBenchmark.p',rosser_op_or) ).
cnf(c_96,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_97,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_98,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_99,plain,
modus_ponens,
inference(clausify,[status(thm)],[rosser_modus_ponens]) ).
fof(rosser_kn1,axiom,
kn1,
file('theBenchmark.p',rosser_kn1) ).
cnf(c_100,plain,
kn1,
inference(clausify,[status(thm)],[rosser_kn1]) ).
fof(rosser_kn2,axiom,
kn2,
file('theBenchmark.p',rosser_kn2) ).
cnf(c_101,plain,
kn2,
inference(clausify,[status(thm)],[rosser_kn2]) ).
fof(rosser_kn3,axiom,
kn3,
file('theBenchmark.p',rosser_kn3) ).
cnf(c_102,plain,
kn3,
inference(clausify,[status(thm)],[rosser_kn3]) ).
cnf(c_104,negated_conjecture,
~ equivalence_2,
inference(clausify,[status(thm)],[hilbert_equivalence_2_neg]) ).
cnf(c_105,plain,
not(and(not(A),not(B))) = or(A,B),
inference(resolve,[status(thm)],[c_96,c_89]) ).
cnf(c_106,plain,
not(and(A,not(B))) = implies(A,B),
inference(resolve,[status(thm)],[c_97,c_92]) ).
cnf(c_107,plain,
equiv(A,B) = and(implies(A,B),implies(B,A)),
inference(resolve,[status(thm)],[c_98,c_95]) ).
cnf(c_108,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_99,c_33]) ).
cnf(c_109,plain,
is_a_theorem(implies(A,and(A,A))),
inference(resolve,[status(thm)],[c_100,c_66]) ).
cnf(c_110,plain,
is_a_theorem(implies(and(A,B),A)),
inference(resolve,[status(thm)],[c_101,c_68]) ).
cnf(c_111,plain,
is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))),
inference(resolve,[status(thm)],[c_102,c_70]) ).
cnf(c_10723,plain,
( ~ is_a_theorem(implies(and(implies(sK2,sK3),implies(sK3,sK2)),implies(sK3,sK2)))
| equivalence_2 ),
inference(paramod,[status(thm)],[c_107,c_63]) ).
cnf(c_113,negated_conjecture,
~ is_a_theorem(implies(and(implies(sK2,sK3),implies(sK3,sK2)),implies(sK3,sK2))),
inference(resolve,[status(thm)],[c_104,c_10723]) ).
cnf(c_10724,plain,
implies(not(A),B) = or(A,B),
inference(paramod,[status(thm)],[c_106,c_105]) ).
cnf(c_114,plain,
or(A,B) = implies(not(A),B),
inference(copy,[status(thm)],[c_10724]) ).
cnf(c_123,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),not(and(not(C),A))))),
inference(paramod,[status(thm)],[c_106,c_111]) ).
cnf(c_124,plain,
is_a_theorem(implies(implies(not(A),B),implies(not(and(B,C)),implies(C,A)))),
inference(paramod,[status(thm)],[c_106,c_111]) ).
cnf(c_129,plain,
~ and_2,
inference(resolve,[status(thm)],[c_50,c_113]) ).
cnf(c_130,plain,
~ is_a_theorem(implies(and(sK0,sK1),sK1)),
inference(resolve,[status(thm)],[c_129,c_51]) ).
cnf(c_147,plain,
or(and(A,not(B)),C) = implies(implies(A,B),C),
inference(paramod,[status(thm)],[c_106,c_114]) ).
cnf(c_150,plain,
( is_a_theorem(B)
| ~ is_a_theorem(or(A,B))
| ~ is_a_theorem(not(A)) ),
inference(paramod,[status(thm)],[c_114,c_108]) ).
cnf(c_153,plain,
is_a_theorem(implies(implies(A,B),or(and(B,C),not(and(C,A))))),
inference(paramod,[status(thm)],[c_114,c_111]) ).
cnf(c_10725,plain,
is_a_theorem(implies(implies(not(A),B),implies(not(and(B,not(C))),or(C,A)))),
inference(paramod,[status(thm)],[c_114,c_124]) ).
cnf(c_233,plain,
is_a_theorem(implies(implies(not(A),B),implies(implies(B,C),or(C,A)))),
inference(paramod,[status(thm)],[c_106,c_10725]) ).
cnf(c_234,plain,
is_a_theorem(implies(implies(not(A),B),or(and(B,C),implies(C,A)))),
inference(paramod,[status(thm)],[c_114,c_124]) ).
cnf(c_10726,plain,
or(and(not(A),not(B)),C) = implies(or(A,B),C),
inference(paramod,[status(thm)],[c_114,c_147]) ).
cnf(c_10727,plain,
implies(implies(not(A),B),C) = implies(or(A,B),C),
inference(paramod,[status(thm)],[c_147,c_10726]) ).
cnf(c_278,plain,
implies(or(A,B),C) = implies(implies(not(A),B),C),
inference(copy,[status(thm)],[c_10727]) ).
cnf(c_369,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(not(A),B),C))
| ~ is_a_theorem(or(A,B)) ),
inference(paramod,[status(thm)],[c_278,c_108]) ).
cnf(c_370,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(or(A,B),C))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(paramod,[status(thm)],[c_278,c_108]) ).
cnf(c_496,plain,
is_a_theorem(implies(or(A,B),implies(implies(B,C),or(C,A)))),
inference(paramod,[status(thm)],[c_114,c_233]) ).
cnf(c_592,plain,
is_a_theorem(implies(or(A,not(B)),implies(or(B,C),or(C,A)))),
inference(paramod,[status(thm)],[c_114,c_496]) ).
cnf(c_598,plain,
( is_a_theorem(or(and(B,C),implies(C,A)))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(resolve,[status(thm)],[c_234,c_108]) ).
cnf(c_10728,plain,
( is_a_theorem(implies(implies(B,C),not(and(not(C),not(A)))))
| ~ is_a_theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_369,c_123]) ).
cnf(c_729,plain,
( is_a_theorem(implies(implies(B,C),implies(not(C),A)))
| ~ is_a_theorem(or(A,B)) ),
inference(paramod,[status(thm)],[c_106,c_10728]) ).
cnf(c_763,plain,
( is_a_theorem(implies(or(B,C),or(C,A)))
| ~ is_a_theorem(implies(not(A),not(B))) ),
inference(resolve,[status(thm)],[c_592,c_370]) ).
cnf(c_1209,plain,
( is_a_theorem(or(and(B,C),not(and(C,A))))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_153,c_108]) ).
cnf(c_1404,plain,
is_a_theorem(or(and(and(A,A),B),not(and(B,A)))),
inference(resolve,[status(thm)],[c_1209,c_109]) ).
cnf(c_1413,plain,
( is_a_theorem(not(and(B,A)))
| ~ is_a_theorem(not(and(and(A,A),B))) ),
inference(resolve,[status(thm)],[c_1404,c_150]) ).
cnf(c_1507,plain,
( is_a_theorem(not(and(not(B),A)))
| ~ is_a_theorem(implies(and(A,A),B)) ),
inference(paramod,[status(thm)],[c_106,c_1413]) ).
cnf(c_1512,plain,
is_a_theorem(not(and(not(A),A))),
inference(resolve,[status(thm)],[c_1507,c_110]) ).
cnf(c_10729,plain,
( is_a_theorem(B)
| ~ is_a_theorem(or(and(not(A),A),B)) ),
inference(resolve,[status(thm)],[c_150,c_1512]) ).
cnf(c_1555,plain,
~ is_a_theorem(or(and(not(A),A),implies(and(sK0,sK1),sK1))),
inference(resolve,[status(thm)],[c_10729,c_130]) ).
cnf(c_1605,plain,
is_a_theorem(implies(not(not(A)),A)),
inference(paramod,[status(thm)],[c_106,c_1512]) ).
cnf(c_1750,plain,
~ is_a_theorem(implies(not(sK1),not(and(sK0,sK1)))),
inference(resolve,[status(thm)],[c_598,c_1555]) ).
cnf(c_10730,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(and(A,B),A),C)) ),
inference(resolve,[status(thm)],[c_108,c_110]) ).
cnf(c_1830,plain,
~ is_a_theorem(implies(implies(and(A,B),A),implies(not(sK1),not(and(sK0,sK1))))),
inference(resolve,[status(thm)],[c_10730,c_1750]) ).
cnf(c_10731,plain,
is_a_theorem(or(and(A,B),not(and(B,not(not(A)))))),
inference(resolve,[status(thm)],[c_1605,c_1209]) ).
cnf(c_1857,plain,
is_a_theorem(or(and(A,B),implies(B,not(A)))),
inference(paramod,[status(thm)],[c_106,c_10731]) ).
cnf(c_2269,plain,
( is_a_theorem(implies(B,not(A)))
| ~ is_a_theorem(not(and(A,B))) ),
inference(resolve,[status(thm)],[c_1857,c_150]) ).
cnf(c_2383,plain,
( is_a_theorem(implies(not(B),not(A)))
| ~ is_a_theorem(implies(A,B)) ),
inference(paramod,[status(thm)],[c_106,c_2269]) ).
cnf(c_2402,plain,
is_a_theorem(implies(not(A),not(and(A,B)))),
inference(resolve,[status(thm)],[c_2383,c_110]) ).
cnf(c_2798,plain,
is_a_theorem(implies(or(and(A,B),C),or(C,A))),
inference(resolve,[status(thm)],[c_2402,c_763]) ).
cnf(c_8738,plain,
( is_a_theorem(or(C,A))
| ~ is_a_theorem(or(and(A,B),C)) ),
inference(resolve,[status(thm)],[c_2798,c_108]) ).
cnf(c_8867,plain,
is_a_theorem(or(not(and(A,B)),and(B,B))),
inference(resolve,[status(thm)],[c_8738,c_1404]) ).
cnf(c_10721,plain,
is_a_theorem(implies(implies(and(A,A),B),implies(not(B),not(and(C,A))))),
inference(resolve,[status(thm)],[c_8867,c_729]) ).
cnf(c_10722,plain,
$false,
inference(resolve,[status(thm)],[c_10721,c_1830]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL513+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.41 % Computer : n026.cluster.edu
% 0.08/0.41 % Model : x86_64 x86_64
% 0.08/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.41 % Memory : 8046.5625MB
% 0.08/0.41 % OS : Linux 6.8.0-71-generic
% 0.08/0.41 % CPULimit : 300
% 0.08/0.41 % WCLimit : 300
% 0.08/0.41 % DateTime : Fri Sep 25 22:43:24 UTC 2026
% 0.08/0.42 % CPUTime :
% 0.08/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.42 % Process 3648452 was started by sandbox on n026,
% 0.08/0.42 % Fri Sep 25 22:43:24 2026
% 0.08/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.44
% 0.08/0.44 % From the command line: assign(max_seconds, 300).
% 68.28/20.63
% 68.28/20.63 % SZS status Theorem for theBenchmark
% 68.28/20.63
% 68.28/20.63 % Proof 1 at 1.45 (+ 0.37) seconds.
% 68.28/20.63 % Length of proof is 74.
% 68.28/20.63 % Level of proof is 20.
% 68.28/20.63 % Maximum clause weight is 44.000.
% 68.28/20.63 % Given clauses 309.
% 68.28/20.63
% 68.28/20.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------