%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL509+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 : n013.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 18.68s 3.13s
% Output : CNFRefutation 18.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of formulae : 85 ( 50 unt; 0 def)
% Number of atoms : 137 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 97 ( 45 ~; 36 |; 7 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 129 ( 14 sgn 28 !; 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(or_1,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ),
file('theBenchmark.p',or_1) ).
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(cn2,axiom,
( cn2
<=> ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q))) ),
file('theBenchmark.p',cn2) ).
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_or_1,conjecture,
or_1,
file('theBenchmark.p',hilbert_or_1) ).
fof(hilbert_or_1_neg,negated_conjecture,
~ or_1,
inference(assume_negation,[status(cth)],[hilbert_or_1]) ).
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_10,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,or(X,Y)))
| or_1 )
& ( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ) ),
inference(fof_nnf,[status(thm)],[or_1]) ).
fof(sk_or_1_sk,plain,
( ( ~ is_a_theorem(implies(sK0,or(sK0,sK1)))
| or_1 )
& ( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_10]) ).
fof(sk_or_1,plain,
( ( ~ is_a_theorem(implies(sK0,or(sK0,sK1)))
| or_1 )
& ! [VAR_0,VAR_1] :
( is_a_theorem(implies(VAR_0,or(VAR_0,VAR_1)))
| ~ or_1 ) ),
inference(cnf_transformation,[status(thm)],[sk_or_1_sk]) ).
cnf(c_55,plain,
( ~ is_a_theorem(implies(sK0,or(sK0,sK1)))
| or_1 ),
inference(split_conjunct,[status(thm)],[sk_or_1]) ).
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_20,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(P,implies(not(P),Q)))
| cn2 )
& ( ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1)))
| ~ cn2 ) ),
inference(fof_nnf,[status(thm)],[cn2]) ).
fof(sk_cn2_sk,plain,
( ( ~ is_a_theorem(implies(sK2,implies(not(sK2),sK3)))
| cn2 )
& ( ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1)))
| ~ cn2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(P,sK2),skolemize(Q,sK3)],[nnf_20]) ).
fof(sk_cn2,plain,
( ( ~ is_a_theorem(implies(sK2,implies(not(sK2),sK3)))
| cn2 )
& ! [VAR_0,VAR_1] :
( is_a_theorem(implies(VAR_0,implies(not(VAR_0),VAR_1)))
| ~ cn2 ) ),
inference(cnf_transformation,[status(thm)],[sk_cn2_sk]) ).
cnf(c_74,plain,
( is_a_theorem(implies(A,implies(not(A),B)))
| ~ cn2 ),
inference(split_conjunct,[status(thm)],[sk_cn2]) ).
cnf(c_75,plain,
( ~ is_a_theorem(implies(sK2,implies(not(sK2),sK3)))
| cn2 ),
inference(split_conjunct,[status(thm)],[sk_cn2]) ).
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_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_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]) ).
cnf(c_103,negated_conjecture,
~ or_1,
inference(clausify,[status(thm)],[hilbert_or_1_neg]) ).
cnf(c_104,plain,
not(and(not(A),not(B))) = or(A,B),
inference(resolve,[status(thm)],[c_95,c_89]) ).
cnf(c_105,plain,
not(and(A,not(B))) = implies(A,B),
inference(resolve,[status(thm)],[c_96,c_92]) ).
cnf(c_107,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_108,plain,
is_a_theorem(implies(A,and(A,A))),
inference(resolve,[status(thm)],[c_99,c_66]) ).
cnf(c_109,plain,
is_a_theorem(implies(and(A,B),A)),
inference(resolve,[status(thm)],[c_100,c_68]) ).
cnf(c_110,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_112,negated_conjecture,
~ is_a_theorem(implies(sK0,or(sK0,sK1))),
inference(resolve,[status(thm)],[c_103,c_55]) ).
cnf(c_12495,plain,
implies(not(A),B) = or(A,B),
inference(paramod,[status(thm)],[c_105,c_104]) ).
cnf(c_113,plain,
or(A,B) = implies(not(A),B),
inference(copy,[status(thm)],[c_12495]) ).
cnf(c_115,negated_conjecture,
~ is_a_theorem(implies(sK0,implies(not(sK0),sK1))),
inference(paramod,[status(thm)],[c_113,c_112]) ).
cnf(c_134,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(A,and(A,A)),B)) ),
inference(resolve,[status(thm)],[c_108,c_107]) ).
cnf(c_137,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(and(A,B),A),C)) ),
inference(resolve,[status(thm)],[c_109,c_107]) ).
cnf(c_140,plain,
( is_a_theorem(implies(not(and(B,C)),not(and(C,A))))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_110,c_107]) ).
cnf(c_142,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),not(and(not(C),A))))),
inference(paramod,[status(thm)],[c_105,c_110]) ).
cnf(c_143,plain,
is_a_theorem(implies(implies(not(A),B),implies(not(and(B,C)),implies(C,A)))),
inference(paramod,[status(thm)],[c_105,c_110]) ).
cnf(c_150,plain,
~ cn2,
inference(resolve,[status(thm)],[c_74,c_115]) ).
cnf(c_151,plain,
~ is_a_theorem(implies(sK2,implies(not(sK2),sK3))),
inference(resolve,[status(thm)],[c_150,c_75]) ).
cnf(c_186,plain,
is_a_theorem(implies(not(and(and(A,A),B)),not(and(B,A)))),
inference(resolve,[status(thm)],[c_134,c_110]) ).
cnf(c_294,plain,
is_a_theorem(implies(implies(and(A,A),B),not(and(not(B),A)))),
inference(paramod,[status(thm)],[c_105,c_186]) ).
cnf(c_434,plain,
is_a_theorem(not(and(not(A),A))),
inference(resolve,[status(thm)],[c_294,c_137]) ).
cnf(c_12496,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(not(and(not(A),A)),B)) ),
inference(resolve,[status(thm)],[c_107,c_434]) ).
cnf(c_474,plain,
~ is_a_theorem(implies(not(and(not(A),A)),implies(sK2,implies(not(sK2),sK3)))),
inference(resolve,[status(thm)],[c_12496,c_151]) ).
cnf(c_478,plain,
is_a_theorem(implies(not(not(A)),A)),
inference(paramod,[status(thm)],[c_105,c_434]) ).
cnf(c_12497,plain,
is_a_theorem(implies(not(and(A,B)),not(and(B,not(not(A)))))),
inference(resolve,[status(thm)],[c_478,c_140]) ).
cnf(c_586,plain,
is_a_theorem(implies(not(and(A,B)),implies(B,not(A)))),
inference(paramod,[status(thm)],[c_105,c_12497]) ).
cnf(c_588,plain,
( is_a_theorem(A)
| ~ is_a_theorem(not(not(A))) ),
inference(resolve,[status(thm)],[c_478,c_107]) ).
cnf(c_680,plain,
is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))),
inference(paramod,[status(thm)],[c_105,c_586]) ).
cnf(c_884,plain,
is_a_theorem(implies(not(A),not(and(A,B)))),
inference(resolve,[status(thm)],[c_680,c_137]) ).
cnf(c_885,plain,
is_a_theorem(implies(not(and(A,A)),not(A))),
inference(resolve,[status(thm)],[c_680,c_134]) ).
cnf(c_12498,plain,
( is_a_theorem(implies(not(and(B,C)),implies(C,A)))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(resolve,[status(thm)],[c_107,c_143]) ).
cnf(c_959,plain,
~ is_a_theorem(implies(not(implies(not(sK2),sK3)),not(sK2))),
inference(resolve,[status(thm)],[c_12498,c_474]) ).
cnf(c_1106,plain,
is_a_theorem(implies(not(A),implies(A,B))),
inference(paramod,[status(thm)],[c_105,c_884]) ).
cnf(c_1114,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(not(A),implies(A,B)),C)) ),
inference(resolve,[status(thm)],[c_1106,c_107]) ).
cnf(c_1442,plain,
is_a_theorem(implies(implies(not(A),A),not(not(A)))),
inference(paramod,[status(thm)],[c_105,c_885]) ).
cnf(c_2104,plain,
( is_a_theorem(not(not(A)))
| ~ is_a_theorem(implies(not(A),A)) ),
inference(resolve,[status(thm)],[c_1442,c_107]) ).
cnf(c_12499,plain,
is_a_theorem(implies(implies(implies(A,B),C),not(and(not(C),not(A))))),
inference(resolve,[status(thm)],[c_1114,c_142]) ).
cnf(c_3531,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(C),A))),
inference(paramod,[status(thm)],[c_105,c_12499]) ).
cnf(c_5343,plain,
( is_a_theorem(implies(not(C),A))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_3531,c_107]) ).
cnf(c_12500,plain,
( is_a_theorem(implies(not(C),A))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_107,c_3531]) ).
cnf(c_5347,plain,
~ is_a_theorem(implies(implies(not(sK2),A),implies(not(sK2),sK3))),
inference(resolve,[status(thm)],[c_12500,c_959]) ).
cnf(c_5617,plain,
is_a_theorem(implies(not(implies(not(A),B)),implies(B,C))),
inference(resolve,[status(thm)],[c_5343,c_3531]) ).
cnf(c_12168,plain,
is_a_theorem(not(not(implies(not(A),not(A))))),
inference(resolve,[status(thm)],[c_5617,c_2104]) ).
cnf(c_12252,plain,
is_a_theorem(implies(not(A),not(A))),
inference(resolve,[status(thm)],[c_12168,c_588]) ).
cnf(c_12501,plain,
is_a_theorem(implies(implies(A,B),not(and(A,not(B))))),
inference(paramod,[status(thm)],[c_105,c_12252]) ).
cnf(c_12493,plain,
is_a_theorem(implies(implies(A,B),implies(A,B))),
inference(paramod,[status(thm)],[c_105,c_12501]) ).
cnf(c_12494,plain,
$false,
inference(resolve,[status(thm)],[c_12493,c_5347]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL509+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n013.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 22:40:37 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 1410564 was started by sandbox2 on n013,
% 0.09/0.38 % Fri Sep 25 22:40:37 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.40
% 0.14/0.40 % From the command line: assign(max_seconds, 300).
% 18.68/3.13
% 18.68/3.13 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 18.68/3.13
% 18.68/3.13 % SZS status Theorem for theBenchmark
% 18.68/3.13
% 18.68/3.13 % Proof 1 at 2.03 (+ 0.65) seconds.
% 18.68/3.13 % Length of proof is 65.
% 18.68/3.13 % Level of proof is 19.
% 18.68/3.13 % Maximum clause weight is 50.000.
% 18.68/3.13 % Given clauses 343.
% 18.68/3.13
% 18.68/3.13 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------