%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL463+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 : n026.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 07:59:00 AM UTC 2026
% Result : Theorem 169.31s 22.83s
% Output : CNFRefutation 169.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 33 unt; 0 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 69 ( 33 ~; 26 |; 4 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 6 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 109 ( 16 sgn 16 !; 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(implies_1,axiom,
( implies_1
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) ),
file('theBenchmark.p',implies_1) ).
fof(cn1,axiom,
( cn1
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) ),
file('theBenchmark.p',cn1) ).
fof(cn2,axiom,
( cn2
<=> ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q))) ),
file('theBenchmark.p',cn2) ).
fof(cn3,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
file('theBenchmark.p',cn3) ).
fof(hilbert_implies_1,conjecture,
implies_1,
file('theBenchmark.p',hilbert_implies_1) ).
fof(hilbert_implies_1_neg,negated_conjecture,
~ implies_1,
inference(assume_negation,[status(cth)],[hilbert_implies_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_4,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,X)))
| implies_1 )
& ( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ) ),
inference(fof_nnf,[status(thm)],[implies_1]) ).
fof(sk_implies_1_sk,plain,
( ( ~ is_a_theorem(implies(sK0,implies(sK1,sK0)))
| implies_1 )
& ( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_4]) ).
fof(sk_implies_1,plain,
( ( ~ is_a_theorem(implies(sK0,implies(sK1,sK0)))
| implies_1 )
& ! [VAR_0,VAR_1] :
( is_a_theorem(implies(VAR_0,implies(VAR_1,VAR_0)))
| ~ implies_1 ) ),
inference(cnf_transformation,[status(thm)],[sk_implies_1_sk]) ).
cnf(c_43,plain,
( ~ is_a_theorem(implies(sK0,implies(sK1,sK0)))
| implies_1 ),
inference(split_conjunct,[status(thm)],[sk_implies_1]) ).
cnf(c_72,plain,
( is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C))))
| ~ cn1 ),
inference(clausify,[status(thm)],[cn1]) ).
cnf(c_74,plain,
( is_a_theorem(implies(A,implies(not(A),B)))
| ~ cn2 ),
inference(clausify,[status(thm)],[cn2]) ).
cnf(c_76,plain,
( is_a_theorem(implies(implies(not(A),A),A))
| ~ cn3 ),
inference(clausify,[status(thm)],[cn3]) ).
fof(luka_modus_ponens,axiom,
modus_ponens,
file('theBenchmark.p',luka_modus_ponens) ).
cnf(c_98,plain,
modus_ponens,
inference(clausify,[status(thm)],[luka_modus_ponens]) ).
fof(luka_cn1,axiom,
cn1,
file('theBenchmark.p',luka_cn1) ).
cnf(c_99,plain,
cn1,
inference(clausify,[status(thm)],[luka_cn1]) ).
fof(luka_cn2,axiom,
cn2,
file('theBenchmark.p',luka_cn2) ).
cnf(c_100,plain,
cn2,
inference(clausify,[status(thm)],[luka_cn2]) ).
fof(luka_cn3,axiom,
cn3,
file('theBenchmark.p',luka_cn3) ).
cnf(c_101,plain,
cn3,
inference(clausify,[status(thm)],[luka_cn3]) ).
cnf(c_104,negated_conjecture,
~ implies_1,
inference(clausify,[status(thm)],[hilbert_implies_1_neg]) ).
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(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_99,c_72]) ).
cnf(c_109,plain,
is_a_theorem(implies(A,implies(not(A),B))),
inference(resolve,[status(thm)],[c_100,c_74]) ).
cnf(c_110,plain,
is_a_theorem(implies(implies(not(A),A),A)),
inference(resolve,[status(thm)],[c_101,c_76]) ).
cnf(c_113,negated_conjecture,
~ is_a_theorem(implies(sK0,implies(sK1,sK0))),
inference(resolve,[status(thm)],[c_104,c_43]) ).
cnf(c_132,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_108,c_107]) ).
cnf(c_134,plain,
( is_a_theorem(implies(not(A),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_109,c_107]) ).
cnf(c_137,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(implies(not(A),A),A),B)) ),
inference(resolve,[status(thm)],[c_110,c_107]) ).
cnf(c_20624,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(implies(not(A),A),A),B)) ),
inference(resolve,[status(thm)],[c_107,c_110]) ).
cnf(c_142,plain,
~ is_a_theorem(implies(implies(implies(not(A),A),A),implies(sK0,implies(sK1,sK0)))),
inference(resolve,[status(thm)],[c_20624,c_113]) ).
cnf(c_145,plain,
is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))),
inference(resolve,[status(thm)],[c_132,c_110]) ).
cnf(c_146,plain,
is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))),
inference(resolve,[status(thm)],[c_132,c_109]) ).
cnf(c_147,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))),
inference(resolve,[status(thm)],[c_132,c_108]) ).
cnf(c_152,plain,
~ is_a_theorem(implies(sK0,implies(not(implies(sK1,sK0)),implies(sK1,sK0)))),
inference(resolve,[status(thm)],[c_132,c_142]) ).
cnf(c_466,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_146,c_137]) ).
cnf(c_20625,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(not(A),B),C)) ),
inference(resolve,[status(thm)],[c_107,c_146]) ).
cnf(c_479,plain,
~ is_a_theorem(implies(implies(not(sK0),A),implies(not(implies(sK1,sK0)),implies(sK1,sK0)))),
inference(resolve,[status(thm)],[c_20625,c_152]) ).
cnf(c_507,plain,
is_a_theorem(implies(not(implies(A,A)),B)),
inference(resolve,[status(thm)],[c_466,c_134]) ).
cnf(c_508,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_466,c_107]) ).
cnf(c_596,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(not(implies(A,A)),B),C)) ),
inference(resolve,[status(thm)],[c_507,c_107]) ).
cnf(c_666,plain,
( is_a_theorem(implies(implies(C,A),D))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)) ),
inference(resolve,[status(thm)],[c_147,c_107]) ).
cnf(c_1408,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(D,B),implies(A,implies(D,C))))),
inference(resolve,[status(thm)],[c_666,c_147]) ).
cnf(c_1409,plain,
is_a_theorem(implies(implies(A,not(B)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_666,c_146]) ).
cnf(c_1420,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(implies(B,not(A)),D))),
inference(resolve,[status(thm)],[c_1409,c_132]) ).
cnf(c_14205,plain,
( is_a_theorem(implies(implies(B,not(A)),D))
| ~ is_a_theorem(implies(implies(A,implies(B,C)),D)) ),
inference(resolve,[status(thm)],[c_1420,c_107]) ).
cnf(c_18933,plain,
( is_a_theorem(implies(implies(D,B),implies(A,implies(D,C))))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1408,c_107]) ).
cnf(c_19030,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_18933,c_145]) ).
cnf(c_19469,plain,
is_a_theorem(implies(implies(not(A),not(B)),implies(implies(A,C),implies(B,C)))),
inference(resolve,[status(thm)],[c_19030,c_14205]) ).
cnf(c_19521,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(not(B),not(D)),implies(A,implies(D,C))))),
inference(resolve,[status(thm)],[c_19469,c_18933]) ).
cnf(c_19544,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_19469,c_596]) ).
cnf(c_20091,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_19544,c_508]) ).
cnf(c_20626,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,implies(B,B)),C)) ),
inference(resolve,[status(thm)],[c_107,c_20091]) ).
cnf(c_20622,plain,
~ is_a_theorem(implies(implies(A,implies(B,B)),implies(implies(not(sK0),C),implies(not(implies(sK1,sK0)),implies(sK1,sK0))))),
inference(resolve,[status(thm)],[c_20626,c_479]) ).
cnf(c_20623,plain,
$false,
inference(resolve,[status(thm)],[c_20622,c_19521]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL463+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n026.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 22:38:54 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 3638388 was started by sandbox on n026,
% 0.13/0.36 % Fri Sep 25 22:38:54 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 169.31/22.83
% 169.31/22.83 % Assigning unary symbol not kb_weight 0 and highest precedence (94).
% 169.31/22.83
% 169.31/22.83 % given #500 (F,wt=37): 14228 -is_a_theorem(implies(implies(A,implies(not(c8),B)),not(implies(C,C)))). [ur(107,b,1420,a,c,1494,a)].
% 169.31/22.83
% 169.31/22.83 % SZS status Theorem for theBenchmark
% 169.31/22.83
% 169.31/22.83 % Proof 1 at 4.86 (+ 1.39) seconds.
% 169.31/22.83 % Length of proof is 47.
% 169.31/22.83 % Level of proof is 13.
% 169.31/22.83 % Maximum clause weight is 50.000.
% 169.31/22.83 % Given clauses 759.
% 169.31/22.83
% 169.31/22.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------