%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL490+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 : n016.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 07:59:02 AM UTC 2026
% Result : Theorem 0.15s 0.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 41 ( 23 unt; 0 def)
% Number of atoms : 70 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 52 ( 23 ~; 18 |; 4 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 61 ( 5 sgn 19 !; 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(or_1,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ),
file('theBenchmark.p',or_1) ).
fof(r2,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('theBenchmark.p',r2) ).
fof(r3,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('theBenchmark.p',r3) ).
fof(r5,axiom,
( r5
<=> ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
file('theBenchmark.p',r5) ).
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
file('theBenchmark.p',op_implies_or) ).
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_80,plain,
( is_a_theorem(implies(A,or(B,A)))
| ~ r2 ),
inference(clausify,[status(thm)],[r2]) ).
cnf(c_82,plain,
( is_a_theorem(implies(or(A,B),or(B,A)))
| ~ r3 ),
inference(clausify,[status(thm)],[r3]) ).
cnf(c_86,plain,
( is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B))))
| ~ r5 ),
inference(clausify,[status(thm)],[r5]) ).
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_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_r2,axiom,
r2,
file('theBenchmark.p',principia_r2) ).
cnf(c_101,plain,
r2,
inference(clausify,[status(thm)],[principia_r2]) ).
fof(principia_r3,axiom,
r3,
file('theBenchmark.p',principia_r3) ).
cnf(c_102,plain,
r3,
inference(clausify,[status(thm)],[principia_r3]) ).
fof(principia_r5,axiom,
r5,
file('theBenchmark.p',principia_r5) ).
cnf(c_104,plain,
r5,
inference(clausify,[status(thm)],[principia_r5]) ).
cnf(c_108,negated_conjecture,
~ or_1,
inference(clausify,[status(thm)],[hilbert_or_1_neg]) ).
cnf(c_109,plain,
or(not(A),B) = implies(A,B),
inference(resolve,[status(thm)],[c_96,c_93]) ).
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_114,plain,
is_a_theorem(implies(A,or(B,A))),
inference(resolve,[status(thm)],[c_101,c_80]) ).
cnf(c_115,plain,
is_a_theorem(implies(or(A,B),or(B,A))),
inference(resolve,[status(thm)],[c_102,c_82]) ).
cnf(c_117,plain,
is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(resolve,[status(thm)],[c_104,c_86]) ).
cnf(c_121,negated_conjecture,
~ is_a_theorem(implies(sK0,or(sK0,sK1))),
inference(resolve,[status(thm)],[c_108,c_55]) ).
cnf(c_250,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),or(not(C),B)))),
inference(paramod,[status(thm)],[c_109,c_117]) ).
cnf(c_144,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),
inference(paramod,[status(thm)],[c_109,c_250]) ).
cnf(c_251,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,or(B,A)),C)) ),
inference(resolve,[status(thm)],[c_112,c_114]) ).
cnf(c_153,plain,
~ is_a_theorem(implies(implies(A,or(B,A)),implies(sK0,or(sK0,sK1)))),
inference(resolve,[status(thm)],[c_251,c_121]) ).
cnf(c_252,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(or(A,B),or(B,A)),C)) ),
inference(resolve,[status(thm)],[c_112,c_115]) ).
cnf(c_248,plain,
~ is_a_theorem(implies(implies(or(A,B),or(B,A)),implies(implies(C,or(D,C)),implies(sK0,or(sK0,sK1))))),
inference(resolve,[status(thm)],[c_252,c_153]) ).
cnf(c_249,plain,
$false,
inference(resolve,[status(thm)],[c_248,c_144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL490+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 22:44:29 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 3485882 was started by sandbox2 on n016,
% 0.08/0.37 % Fri Sep 25 22:44:29 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.38
% 0.15/0.38 % From the command line: assign(max_seconds, 300).
% 0.15/0.40
% 0.15/0.40 % SZS status Theorem for theBenchmark
% 0.15/0.40
% 0.15/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.15/0.40 % Length of proof is 29.
% 0.15/0.40 % Level of proof is 5.
% 0.15/0.40 % Maximum clause weight is 20.000.
% 0.15/0.40 % Given clauses 73.
% 0.15/0.40
% 0.15/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------