%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL499+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 : n006.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 07:59:03 AM UTC 2026
% Result : Theorem 0.11s 20.44s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 41 ( 23 unt; 0 def)
% Number of atoms : 70 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 52 ( 23 ~; 18 |; 4 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 13 !; 1 ?)
% 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(kn1,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('theBenchmark.p',kn1) ).
fof(r1,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('theBenchmark.p',r1) ).
fof(r3,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('theBenchmark.p',r3) ).
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_or,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
file('theBenchmark.p',op_implies_or) ).
fof(rosser_kn1,conjecture,
kn1,
file('theBenchmark.p',rosser_kn1) ).
fof(rosser_kn1_neg,negated_conjecture,
~ kn1,
inference(assume_negation,[status(cth)],[rosser_kn1]) ).
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_16,plain,
( ( ? [P] : ~ is_a_theorem(implies(P,and(P,P)))
| kn1 )
& ( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ) ),
inference(fof_nnf,[status(thm)],[kn1]) ).
fof(sk_kn1_sk,plain,
( ( ~ is_a_theorem(implies(sK0,and(sK0,sK0)))
| kn1 )
& ( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(P,sK0)],[nnf_16]) ).
fof(sk_kn1,plain,
( ( ~ is_a_theorem(implies(sK0,and(sK0,sK0)))
| kn1 )
& ! [VAR_0] :
( is_a_theorem(implies(VAR_0,and(VAR_0,VAR_0)))
| ~ kn1 ) ),
inference(cnf_transformation,[status(thm)],[sk_kn1_sk]) ).
cnf(c_67,plain,
( ~ is_a_theorem(implies(sK0,and(sK0,sK0)))
| kn1 ),
inference(split_conjunct,[status(thm)],[sk_kn1]) ).
cnf(c_78,plain,
( is_a_theorem(implies(or(A,A),A))
| ~ r1 ),
inference(clausify,[status(thm)],[r1]) ).
cnf(c_82,plain,
( is_a_theorem(implies(or(A,B),or(B,A)))
| ~ r3 ),
inference(clausify,[status(thm)],[r3]) ).
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_93,plain,
( or(not(A),B) = implies(A,B)
| ~ op_implies_or ),
inference(clausify,[status(thm)],[op_implies_or]) ).
fof(principia_op_implies_or,axiom,
op_implies_or,
file('theBenchmark.p',principia_op_implies_or) ).
cnf(c_96,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_97,plain,
op_and,
inference(clausify,[status(thm)],[principia_op_and]) ).
fof(principia_modus_ponens,axiom,
modus_ponens,
file('theBenchmark.p',principia_modus_ponens) ).
cnf(c_99,plain,
modus_ponens,
inference(clausify,[status(thm)],[principia_modus_ponens]) ).
fof(principia_r1,axiom,
r1,
file('theBenchmark.p',principia_r1) ).
cnf(c_100,plain,
r1,
inference(clausify,[status(thm)],[principia_r1]) ).
fof(principia_r3,axiom,
r3,
file('theBenchmark.p',principia_r3) ).
cnf(c_102,plain,
r3,
inference(clausify,[status(thm)],[principia_r3]) ).
cnf(c_108,negated_conjecture,
~ kn1,
inference(clausify,[status(thm)],[rosser_kn1_neg]) ).
cnf(c_109,plain,
or(not(A),B) = implies(A,B),
inference(resolve,[status(thm)],[c_96,c_93]) ).
cnf(c_110,plain,
not(or(not(A),not(B))) = and(A,B),
inference(resolve,[status(thm)],[c_97,c_91]) ).
cnf(c_112,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_113,plain,
is_a_theorem(implies(or(A,A),A)),
inference(resolve,[status(thm)],[c_100,c_78]) ).
cnf(c_115,plain,
is_a_theorem(implies(or(A,B),or(B,A))),
inference(resolve,[status(thm)],[c_102,c_82]) ).
cnf(c_121,negated_conjecture,
~ is_a_theorem(implies(sK0,and(sK0,sK0))),
inference(resolve,[status(thm)],[c_108,c_67]) ).
cnf(c_123,plain,
or(and(A,B),C) = implies(or(not(A),not(B)),C),
inference(paramod,[status(thm)],[c_110,c_109]) ).
cnf(c_134,plain,
is_a_theorem(implies(or(A,not(B)),implies(B,A))),
inference(paramod,[status(thm)],[c_109,c_115]) ).
cnf(c_249,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(or(A,A),A),B)) ),
inference(resolve,[status(thm)],[c_112,c_113]) ).
cnf(c_165,plain,
~ is_a_theorem(implies(implies(or(A,A),A),implies(sK0,and(sK0,sK0)))),
inference(resolve,[status(thm)],[c_249,c_121]) ).
cnf(c_247,plain,
~ is_a_theorem(implies(or(and(A,A),not(A)),implies(sK0,and(sK0,sK0)))),
inference(paramod,[status(thm)],[c_123,c_165]) ).
cnf(c_248,plain,
$false,
inference(resolve,[status(thm)],[c_247,c_134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL499+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/20.40 % Computer : n006.cluster.edu
% 0.11/20.40 % Model : x86_64 x86_64
% 0.11/20.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/20.40 % Memory : 8046.5625MB
% 0.11/20.40 % OS : Linux 6.8.0-71-generic
% 0.11/20.40 % CPULimit : 300
% 0.11/20.40 % WCLimit : 300
% 0.11/20.40 % DateTime : Fri Sep 25 22:40:22 UTC 2026
% 0.11/20.41 % CPUTime :
% 0.11/20.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/20.41 % Process 3927060 was started by sandbox2 on n006,
% 0.11/20.41 % Fri Sep 25 22:40:22 2026
% 0.11/20.41 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/20.41
% 0.11/20.41 % From the command line: assign(max_seconds, 300).
% 0.11/20.44
% 0.11/20.44 % SZS status Theorem for theBenchmark
% 0.11/20.44
% 0.11/20.44 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.11/20.44 % Length of proof is 31.
% 0.11/20.44 % Level of proof is 6.
% 0.11/20.44 % Maximum clause weight is 33.000.
% 0.11/20.44 % Given clauses 67.
% 0.11/20.44
% 0.11/20.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------