%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL540+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 : n012.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 07:59:08 AM UTC 2026
% Result : Theorem 0.07s 0.48s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 14 unt; 0 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 65 ( 24 ~; 25 |; 11 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 12 !; 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(and_3,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
file('theBenchmark.p',and_3) ).
fof(adjunction,axiom,
( adjunction
<=> ! [X,Y] :
( ( is_a_theorem(Y)
& is_a_theorem(X) )
=> is_a_theorem(and(X,Y)) ) ),
file('theBenchmark.p',adjunction) ).
fof(s1_0_adjunction,conjecture,
adjunction,
file('theBenchmark.p',s1_0_adjunction) ).
fof(s1_0_adjunction_neg,negated_conjecture,
~ adjunction,
inference(assume_negation,[status(cth)],[s1_0_adjunction]) ).
cnf(c_60,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A)
| ~ modus_ponens ),
inference(clausify,[status(thm)],[modus_ponens]) ).
cnf(c_79,plain,
( is_a_theorem(implies(A,implies(B,and(A,B))))
| ~ and_3 ),
inference(clausify,[status(thm)],[and_3]) ).
fof(hilbert_modus_ponens,axiom,
modus_ponens,
file('theBenchmark.p',hilbert_modus_ponens) ).
cnf(c_126,plain,
modus_ponens,
inference(clausify,[status(thm)],[hilbert_modus_ponens]) ).
fof(hilbert_and_3,axiom,
and_3,
file('theBenchmark.p',hilbert_and_3) ).
cnf(c_133,plain,
and_3,
inference(clausify,[status(thm)],[hilbert_and_3]) ).
fof(nnf_34,plain,
( ( ? [X,Y] :
( ~ is_a_theorem(and(X,Y))
& is_a_theorem(Y)
& is_a_theorem(X) )
| adjunction )
& ( ! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) )
| ~ adjunction ) ),
inference(fof_nnf,[status(thm)],[adjunction]) ).
fof(sk_adjunction_sk,plain,
( ( ( ~ is_a_theorem(and(sK0,sK1))
& is_a_theorem(sK1)
& is_a_theorem(sK0) )
| adjunction )
& ( ! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) )
| ~ adjunction ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_34]) ).
fof(sk_adjunction,plain,
( ( ~ is_a_theorem(and(sK0,sK1))
| adjunction )
& ( is_a_theorem(sK1)
| adjunction )
& ( is_a_theorem(sK0)
| adjunction )
& ! [VAR_0,VAR_1] :
( is_a_theorem(and(VAR_0,VAR_1))
| ~ is_a_theorem(VAR_1)
| ~ is_a_theorem(VAR_0)
| ~ adjunction ) ),
inference(cnf_transformation,[status(thm)],[sk_adjunction_sk]) ).
cnf(c_149,plain,
( is_a_theorem(sK0)
| adjunction ),
inference(split_conjunct,[status(thm)],[sk_adjunction]) ).
cnf(c_150,plain,
( is_a_theorem(sK1)
| adjunction ),
inference(split_conjunct,[status(thm)],[sk_adjunction]) ).
cnf(c_151,plain,
( ~ is_a_theorem(and(sK0,sK1))
| adjunction ),
inference(split_conjunct,[status(thm)],[sk_adjunction]) ).
cnf(c_209,negated_conjecture,
~ adjunction,
inference(clausify,[status(thm)],[s1_0_adjunction_neg]) ).
cnf(c_213,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_126,c_60]) ).
cnf(c_220,plain,
is_a_theorem(implies(A,implies(B,and(A,B)))),
inference(resolve,[status(thm)],[c_133,c_79]) ).
cnf(c_236,negated_conjecture,
~ is_a_theorem(and(sK0,sK1)),
inference(resolve,[status(thm)],[c_209,c_151]) ).
cnf(c_237,negated_conjecture,
is_a_theorem(sK1),
inference(resolve,[status(thm)],[c_209,c_150]) ).
cnf(c_238,negated_conjecture,
is_a_theorem(sK0),
inference(resolve,[status(thm)],[c_209,c_149]) ).
cnf(c_259,plain,
( is_a_theorem(implies(B,and(A,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_220,c_213]) ).
cnf(c_781,plain,
is_a_theorem(implies(A,and(sK0,A))),
inference(resolve,[status(thm)],[c_259,c_238]) ).
cnf(c_1937,plain,
( is_a_theorem(and(sK0,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_781,c_213]) ).
cnf(c_2022,plain,
is_a_theorem(and(sK0,sK1)),
inference(resolve,[status(thm)],[c_1937,c_237]) ).
cnf(c_2021,plain,
$false,
inference(resolve,[status(thm)],[c_236,c_2022]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL540+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Fri Sep 25 22:42:20 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.29 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.29 % Process 3245417 was started by sandbox2 on n012,
% 0.03/0.29 % Fri Sep 25 22:42:20 2026
% 0.03/0.29 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.31
% 0.03/0.31 % From the command line: assign(max_seconds, 300).
% 0.07/0.48
% 0.07/0.48 % SZS status Theorem for theBenchmark
% 0.07/0.48
% 0.07/0.48 % Proof 1 at 0.10 (+ 0.05) seconds.
% 0.07/0.48 % Length of proof is 21.
% 0.07/0.48 % Level of proof is 6.
% 0.07/0.48 % Maximum clause weight is 31.000.
% 0.07/0.48 % Given clauses 248.
% 0.07/0.48
% 0.07/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------