%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL498+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 : n002.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 7.36s 11.38s
% Output : CNFRefutation 7.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 66 ( 38 unt; 0 def)
% Number of atoms : 105 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 70 ( 31 ~; 26 |; 4 &)
% ( 7 <=>; 2 =>; 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 : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 93 ( 9 sgn 19 !; 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(cn3,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
file('theBenchmark.p',cn3) ).
fof(r1,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('theBenchmark.p',r1) ).
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(r4,axiom,
( r4
<=> ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
file('theBenchmark.p',r4) ).
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(luka_cn3,conjecture,
cn3,
file('theBenchmark.p',luka_cn3) ).
fof(luka_cn3_neg,negated_conjecture,
~ cn3,
inference(assume_negation,[status(cth)],[luka_cn3]) ).
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_21,plain,
( ( ? [P] : ~ is_a_theorem(implies(implies(not(P),P),P))
| cn3 )
& ( ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0))
| ~ cn3 ) ),
inference(fof_nnf,[status(thm)],[cn3]) ).
fof(sk_cn3_sk,plain,
( ( ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0))
| cn3 )
& ( ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0))
| ~ cn3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(P,sK0)],[nnf_21]) ).
fof(sk_cn3,plain,
( ( ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0))
| cn3 )
& ! [VAR_0] :
( is_a_theorem(implies(implies(not(VAR_0),VAR_0),VAR_0))
| ~ cn3 ) ),
inference(cnf_transformation,[status(thm)],[sk_cn3_sk]) ).
cnf(c_77,plain,
( ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0))
| cn3 ),
inference(split_conjunct,[status(thm)],[sk_cn3]) ).
cnf(c_78,plain,
( is_a_theorem(implies(or(A,A),A))
| ~ r1 ),
inference(clausify,[status(thm)],[r1]) ).
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_84,plain,
( is_a_theorem(implies(or(A,or(B,C)),or(B,or(A,C))))
| ~ r4 ),
inference(clausify,[status(thm)],[r4]) ).
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_r1,axiom,
r1,
file('theBenchmark.p',principia_r1) ).
cnf(c_100,plain,
r1,
inference(clausify,[status(thm)],[principia_r1]) ).
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_r4,axiom,
r4,
file('theBenchmark.p',principia_r4) ).
cnf(c_103,plain,
r4,
inference(clausify,[status(thm)],[principia_r4]) ).
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,
~ cn3,
inference(clausify,[status(thm)],[luka_cn3_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_113,plain,
is_a_theorem(implies(or(A,A),A)),
inference(resolve,[status(thm)],[c_100,c_78]) ).
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_116,plain,
is_a_theorem(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(resolve,[status(thm)],[c_103,c_84]) ).
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_120,negated_conjecture,
~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)),
inference(resolve,[status(thm)],[c_108,c_77]) ).
cnf(c_129,plain,
( is_a_theorem(A)
| ~ is_a_theorem(or(A,A)) ),
inference(resolve,[status(thm)],[c_113,c_112]) ).
cnf(c_132,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(paramod,[status(thm)],[c_109,c_114]) ).
cnf(c_134,plain,
( is_a_theorem(or(B,A))
| ~ is_a_theorem(or(A,B)) ),
inference(resolve,[status(thm)],[c_115,c_112]) ).
cnf(c_137,plain,
( is_a_theorem(or(B,or(A,C)))
| ~ is_a_theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_116,c_112]) ).
cnf(c_140,plain,
is_a_theorem(implies(or(not(A),or(B,C)),or(B,implies(A,C)))),
inference(paramod,[status(thm)],[c_109,c_116]) ).
cnf(c_142,plain,
( is_a_theorem(implies(or(C,A),or(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_117,c_112]) ).
cnf(c_14327,plain,
( is_a_theorem(A)
| ~ is_a_theorem(or(A,A)) ),
inference(resolve,[status(thm)],[c_112,c_113]) ).
cnf(c_154,plain,
~ is_a_theorem(or(implies(implies(not(sK0),sK0),sK0),implies(implies(not(sK0),sK0),sK0))),
inference(resolve,[status(thm)],[c_14327,c_120]) ).
cnf(c_230,plain,
( is_a_theorem(or(B,not(A)))
| ~ is_a_theorem(implies(A,B)) ),
inference(paramod,[status(thm)],[c_109,c_134]) ).
cnf(c_432,plain,
is_a_theorem(or(implies(A,B),not(B))),
inference(resolve,[status(thm)],[c_230,c_132]) ).
cnf(c_436,plain,
is_a_theorem(or(or(A,B),not(B))),
inference(resolve,[status(thm)],[c_230,c_114]) ).
cnf(c_14328,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(or(implies(A,B),not(B)),C)) ),
inference(resolve,[status(thm)],[c_112,c_432]) ).
cnf(c_455,plain,
~ is_a_theorem(implies(or(implies(A,B),not(B)),or(implies(implies(not(sK0),sK0),sK0),implies(implies(not(sK0),sK0),sK0)))),
inference(resolve,[status(thm)],[c_14328,c_154]) ).
cnf(c_464,plain,
is_a_theorem(or(not(A),or(B,A))),
inference(resolve,[status(thm)],[c_436,c_134]) ).
cnf(c_626,plain,
is_a_theorem(or(A,or(not(B),B))),
inference(resolve,[status(thm)],[c_137,c_464]) ).
cnf(c_669,plain,
is_a_theorem(or(not(A),A)),
inference(resolve,[status(thm)],[c_626,c_129]) ).
cnf(c_1402,plain,
( is_a_theorem(or(B,implies(A,C)))
| ~ is_a_theorem(or(not(A),or(B,C))) ),
inference(resolve,[status(thm)],[c_140,c_112]) ).
cnf(c_4442,plain,
is_a_theorem(or(A,implies(or(A,B),B))),
inference(resolve,[status(thm)],[c_1402,c_669]) ).
cnf(c_5926,plain,
is_a_theorem(or(not(A),implies(implies(A,B),B))),
inference(paramod,[status(thm)],[c_109,c_4442]) ).
cnf(c_14304,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(paramod,[status(thm)],[c_109,c_5926]) ).
cnf(c_14325,plain,
is_a_theorem(implies(or(A,B),or(A,implies(implies(B,C),C)))),
inference(resolve,[status(thm)],[c_14304,c_142]) ).
cnf(c_14326,plain,
$false,
inference(resolve,[status(thm)],[c_14325,c_455]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL498+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.36 % Computer : n002.cluster.edu
% 0.10/10.36 % Model : x86_64 x86_64
% 0.10/10.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.36 % Memory : 8046.5625MB
% 0.10/10.36 % OS : Linux 6.8.0-71-generic
% 0.10/10.37 % CPULimit : 300
% 0.10/10.37 % WCLimit : 300
% 0.10/10.37 % DateTime : Fri Sep 25 22:43:02 UTC 2026
% 0.10/10.37 % CPUTime :
% 0.10/10.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/10.37 % Process 189894 was started by sandbox on n002,
% 0.10/10.37 % Fri Sep 25 22:43:02 2026
% 0.10/10.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/10.38
% 0.10/10.38 % From the command line: assign(max_seconds, 300).
% 7.36/11.38
% 7.36/11.38 % SZS status Theorem for theBenchmark
% 7.36/11.38
% 7.36/11.38 % Proof 1 at 0.78 (+ 0.19) seconds.
% 7.36/11.38 % Length of proof is 53.
% 7.36/11.38 % Level of proof is 13.
% 7.36/11.38 % Maximum clause weight is 51.000.
% 7.36/11.38 % Given clauses 337.
% 7.36/11.38
% 7.36/11.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------