%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL507+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 : n014.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 07:59:04 AM UTC 2026
% Result : Theorem 69.26s 20.10s
% Output : CNFRefutation 69.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of formulae : 82 ( 48 unt; 0 def)
% Number of atoms : 130 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 90 ( 42 ~; 36 |; 4 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 148 ( 9 sgn 20 !; 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(and_2,axiom,
( and_2
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) ),
file('theBenchmark.p',and_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(hilbert_and_2,conjecture,
and_2,
file('theBenchmark.p',hilbert_and_2) ).
fof(hilbert_and_2_neg,negated_conjecture,
~ and_2,
inference(assume_negation,[status(cth)],[hilbert_and_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_51,plain,
( ~ is_a_theorem(implies(and(sK0,sK1),sK1))
| and_2 ),
inference(split_conjunct,[status(thm)],[sk_and_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]) ).
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_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,
~ and_2,
inference(clausify,[status(thm)],[hilbert_and_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_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_113,negated_conjecture,
~ is_a_theorem(implies(and(sK0,sK1),sK1)),
inference(resolve,[status(thm)],[c_104,c_51]) ).
cnf(c_10388,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_10388]) ).
cnf(c_125,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_126,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_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_10389,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_126]) ).
cnf(c_241,plain,
is_a_theorem(implies(implies(not(A),B),implies(implies(B,C),or(C,A)))),
inference(paramod,[status(thm)],[c_106,c_10389]) ).
cnf(c_242,plain,
is_a_theorem(implies(implies(not(A),B),or(and(B,C),implies(C,A)))),
inference(paramod,[status(thm)],[c_114,c_126]) ).
cnf(c_10390,plain,
or(and(not(A),not(B)),C) = implies(or(A,B),C),
inference(paramod,[status(thm)],[c_114,c_147]) ).
cnf(c_10391,plain,
implies(implies(not(A),B),C) = implies(or(A,B),C),
inference(paramod,[status(thm)],[c_147,c_10390]) ).
cnf(c_286,plain,
implies(or(A,B),C) = implies(implies(not(A),B),C),
inference(copy,[status(thm)],[c_10391]) ).
cnf(c_363,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_286,c_108]) ).
cnf(c_364,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_286,c_108]) ).
cnf(c_490,plain,
is_a_theorem(implies(or(A,B),implies(implies(B,C),or(C,A)))),
inference(paramod,[status(thm)],[c_114,c_241]) ).
cnf(c_583,plain,
is_a_theorem(implies(or(A,not(B)),implies(or(B,C),or(C,A)))),
inference(paramod,[status(thm)],[c_114,c_490]) ).
cnf(c_589,plain,
( is_a_theorem(or(and(B,C),implies(C,A)))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(resolve,[status(thm)],[c_242,c_108]) ).
cnf(c_10392,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_363,c_125]) ).
cnf(c_794,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_10392]) ).
cnf(c_828,plain,
( is_a_theorem(implies(or(B,C),or(C,A)))
| ~ is_a_theorem(implies(not(A),not(B))) ),
inference(resolve,[status(thm)],[c_583,c_364]) ).
cnf(c_1100,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_1290,plain,
is_a_theorem(or(and(and(A,A),B),not(and(B,A)))),
inference(resolve,[status(thm)],[c_1100,c_109]) ).
cnf(c_1298,plain,
( is_a_theorem(not(and(B,A)))
| ~ is_a_theorem(not(and(and(A,A),B))) ),
inference(resolve,[status(thm)],[c_1290,c_150]) ).
cnf(c_1382,plain,
( is_a_theorem(not(and(not(B),A)))
| ~ is_a_theorem(implies(and(A,A),B)) ),
inference(paramod,[status(thm)],[c_106,c_1298]) ).
cnf(c_1387,plain,
is_a_theorem(not(and(not(A),A))),
inference(resolve,[status(thm)],[c_1382,c_110]) ).
cnf(c_10393,plain,
( is_a_theorem(B)
| ~ is_a_theorem(or(and(not(A),A),B)) ),
inference(resolve,[status(thm)],[c_150,c_1387]) ).
cnf(c_1430,plain,
~ is_a_theorem(or(and(not(A),A),implies(and(sK0,sK1),sK1))),
inference(resolve,[status(thm)],[c_10393,c_113]) ).
cnf(c_1470,plain,
is_a_theorem(implies(not(not(A)),A)),
inference(paramod,[status(thm)],[c_106,c_1387]) ).
cnf(c_1610,plain,
~ is_a_theorem(implies(not(sK1),not(and(sK0,sK1)))),
inference(resolve,[status(thm)],[c_589,c_1430]) ).
cnf(c_10394,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_1689,plain,
~ is_a_theorem(implies(implies(and(A,B),A),implies(not(sK1),not(and(sK0,sK1))))),
inference(resolve,[status(thm)],[c_10394,c_1610]) ).
cnf(c_10395,plain,
is_a_theorem(or(and(A,B),not(and(B,not(not(A)))))),
inference(resolve,[status(thm)],[c_1470,c_1100]) ).
cnf(c_1716,plain,
is_a_theorem(or(and(A,B),implies(B,not(A)))),
inference(paramod,[status(thm)],[c_106,c_10395]) ).
cnf(c_2108,plain,
( is_a_theorem(implies(B,not(A)))
| ~ is_a_theorem(not(and(A,B))) ),
inference(resolve,[status(thm)],[c_1716,c_150]) ).
cnf(c_2212,plain,
( is_a_theorem(implies(not(B),not(A)))
| ~ is_a_theorem(implies(A,B)) ),
inference(paramod,[status(thm)],[c_106,c_2108]) ).
cnf(c_2232,plain,
is_a_theorem(implies(not(A),not(and(A,B)))),
inference(resolve,[status(thm)],[c_2212,c_110]) ).
cnf(c_2622,plain,
is_a_theorem(implies(or(and(A,B),C),or(C,A))),
inference(resolve,[status(thm)],[c_2232,c_828]) ).
cnf(c_8311,plain,
( is_a_theorem(or(C,A))
| ~ is_a_theorem(or(and(A,B),C)) ),
inference(resolve,[status(thm)],[c_2622,c_108]) ).
cnf(c_8437,plain,
is_a_theorem(or(not(and(A,B)),and(B,B))),
inference(resolve,[status(thm)],[c_8311,c_1290]) ).
cnf(c_10386,plain,
is_a_theorem(implies(implies(and(A,A),B),implies(not(B),not(and(C,A))))),
inference(resolve,[status(thm)],[c_8437,c_794]) ).
cnf(c_10387,plain,
$false,
inference(resolve,[status(thm)],[c_10386,c_1689]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL507+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.37 % Computer : n014.cluster.edu
% 0.07/0.37 % Model : x86_64 x86_64
% 0.07/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.37 % Memory : 8046.5625MB
% 0.07/0.37 % OS : Linux 6.8.0-71-generic
% 0.07/0.37 % CPULimit : 300
% 0.07/0.37 % WCLimit : 300
% 0.07/0.37 % DateTime : Fri Sep 25 22:41:02 UTC 2026
% 0.07/0.38 % CPUTime :
% 0.07/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.38 % Process 1300284 was started by sandbox on n014,
% 0.07/0.38 % Fri Sep 25 22:41:02 2026
% 0.07/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.39
% 0.07/0.39 % From the command line: assign(max_seconds, 300).
% 69.26/20.10
% 69.26/20.10 % SZS status Theorem for theBenchmark
% 69.26/20.10
% 69.26/20.10 % Proof 1 at 1.27 (+ 0.31) seconds.
% 69.26/20.10 % Length of proof is 64.
% 69.26/20.10 % Level of proof is 20.
% 69.26/20.10 % Maximum clause weight is 44.000.
% 69.26/20.10 % Given clauses 298.
% 69.26/20.10
% 69.26/20.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------