%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL462+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 : n007.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 07:58:59 AM UTC 2026
% Result : Theorem 168.59s 22.90s
% Output : CNFRefutation 168.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 56 ( 32 unt; 0 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 66 ( 31 ~; 25 |; 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 : 104 ( 13 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(modus_tollens,axiom,
( modus_tollens
<=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
file('theBenchmark.p',modus_tollens) ).
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_modus_tollens,conjecture,
modus_tollens,
file('theBenchmark.p',hilbert_modus_tollens) ).
fof(hilbert_modus_tollens_neg,negated_conjecture,
~ modus_tollens,
inference(assume_negation,[status(cth)],[hilbert_modus_tollens]) ).
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_3,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| modus_tollens )
& ( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ) ),
inference(fof_nnf,[status(thm)],[modus_tollens]) ).
fof(sk_modus_tollens_sk,plain,
( ( ~ is_a_theorem(implies(implies(not(sK0),not(sK1)),implies(sK1,sK0)))
| modus_tollens )
& ( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK1),skolemize(Y,sK0)],[nnf_3]) ).
fof(sk_modus_tollens,plain,
( ( ~ is_a_theorem(implies(implies(not(sK0),not(sK1)),implies(sK1,sK0)))
| modus_tollens )
& ! [VAR_0,VAR_1] :
( is_a_theorem(implies(implies(not(VAR_0),not(VAR_1)),implies(VAR_1,VAR_0)))
| ~ modus_tollens ) ),
inference(cnf_transformation,[status(thm)],[sk_modus_tollens_sk]) ).
cnf(c_41,plain,
( ~ is_a_theorem(implies(implies(not(sK0),not(sK1)),implies(sK1,sK0)))
| modus_tollens ),
inference(split_conjunct,[status(thm)],[sk_modus_tollens]) ).
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,
~ modus_tollens,
inference(clausify,[status(thm)],[hilbert_modus_tollens_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(implies(not(sK0),not(sK1)),implies(sK1,sK0))),
inference(resolve,[status(thm)],[c_104,c_41]) ).
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_20651,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(implies(not(sK0),not(sK1)),implies(sK1,sK0)))),
inference(resolve,[status(thm)],[c_20651,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_148,plain,
~ is_a_theorem(implies(implies(not(sK0),not(sK1)),implies(not(implies(sK1,sK0)),implies(sK1,sK0)))),
inference(resolve,[status(thm)],[c_132,c_142]) ).
cnf(c_461,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_146,c_137]) ).
cnf(c_502,plain,
is_a_theorem(implies(not(implies(A,A)),B)),
inference(resolve,[status(thm)],[c_461,c_134]) ).
cnf(c_503,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_461,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_502,c_107]) ).
cnf(c_872,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_1248,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(D,B),implies(A,implies(D,C))))),
inference(resolve,[status(thm)],[c_872,c_147]) ).
cnf(c_1249,plain,
is_a_theorem(implies(implies(A,not(B)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_872,c_146]) ).
cnf(c_1260,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(implies(B,not(A)),D))),
inference(resolve,[status(thm)],[c_1249,c_132]) ).
cnf(c_14215,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_1260,c_107]) ).
cnf(c_19155,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_1248,c_107]) ).
cnf(c_19254,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_19155,c_145]) ).
cnf(c_19855,plain,
is_a_theorem(implies(implies(not(A),not(B)),implies(implies(A,C),implies(B,C)))),
inference(resolve,[status(thm)],[c_19254,c_14215]) ).
cnf(c_19897,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_19855,c_19155]) ).
cnf(c_19920,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_19855,c_596]) ).
cnf(c_20144,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_19920,c_503]) ).
cnf(c_20652,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,implies(B,B)),C)) ),
inference(resolve,[status(thm)],[c_107,c_20144]) ).
cnf(c_20649,plain,
~ is_a_theorem(implies(implies(A,implies(B,B)),implies(implies(not(sK0),not(sK1)),implies(not(implies(sK1,sK0)),implies(sK1,sK0))))),
inference(resolve,[status(thm)],[c_20652,c_148]) ).
cnf(c_20650,plain,
$false,
inference(resolve,[status(thm)],[c_20649,c_19897]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL462+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.44 % Computer : n007.cluster.edu
% 0.12/0.44 % Model : x86_64 x86_64
% 0.12/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.44 % Memory : 8046.5625MB
% 0.12/0.44 % OS : Linux 6.8.0-71-generic
% 0.12/0.44 % CPULimit : 300
% 0.12/0.44 % WCLimit : 300
% 0.12/0.44 % DateTime : Fri Sep 25 22:34:08 UTC 2026
% 0.12/0.45 % CPUTime :
% 0.12/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.45 % Process 2090527 was started by sandbox on n007,
% 0.12/0.45 % Fri Sep 25 22:34:08 2026
% 0.12/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.46
% 0.12/0.46 % From the command line: assign(max_seconds, 300).
% 168.59/22.90
% 168.59/22.90 % Assigning unary symbol not kb_weight 0 and highest precedence (94).
% 168.59/22.90
% 168.59/22.90 % given #500 (F,wt=39): 2581 -is_a_theorem(implies(implies(A,implies(not(A),B)),implies(c5,implies(not(c6),c6)))). [ur(135,b,2551,a)].
% 168.59/22.90
% 168.59/22.90 % SZS status Theorem for theBenchmark
% 168.59/22.90
% 168.59/22.90 % Proof 1 at 4.99 (+ 1.31) seconds.
% 168.59/22.90 % Length of proof is 46.
% 168.59/22.90 % Level of proof is 13.
% 168.59/22.90 % Maximum clause weight is 51.000.
% 168.59/22.90 % Given clauses 736.
% 168.59/22.90
% 168.59/22.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------