%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL039-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 07:57:49 AM UTC 2026
% Result : Unsatisfiable 89.24s 12.22s
% Output : CNFRefutation 89.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 30 unt; 0 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 52 ( 30 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 93 ( 13 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(condensed_detachment,axiom,
! [VAR_0,VAR_1] :
( is_a_theorem(VAR_1)
| ~ is_a_theorem(VAR_0)
| ~ is_a_theorem(implies(VAR_0,VAR_1)) ),
file('theBenchmark.p',condensed_detachment) ).
cnf(c_1,plain,
( is_a_theorem(B)
| ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B)) ),
inference(clausify,[status(thm)],[condensed_detachment]) ).
fof(cn_18,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(VAR_0,implies(VAR_1,VAR_0))),
file('theBenchmark.p',cn_18) ).
cnf(c_2,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(clausify,[status(thm)],[cn_18]) ).
fof(cn_35,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(implies(implies(VAR_0,implies(VAR_1,VAR_2)),implies(implies(VAR_0,VAR_1),implies(VAR_0,VAR_2)))),
file('theBenchmark.p',cn_35) ).
cnf(c_3,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))),
inference(clausify,[status(thm)],[cn_35]) ).
fof(cn_49,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(implies(not(VAR_0),not(VAR_1)),implies(VAR_1,VAR_0))),
file('theBenchmark.p',cn_49) ).
cnf(c_4,plain,
is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))),
inference(clausify,[status(thm)],[cn_49]) ).
fof(necessitation1,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(necessary(implies(VAR_0,VAR_1)),implies(necessary(VAR_0),necessary(VAR_1)))),
file('theBenchmark.p',necessitation1) ).
cnf(c_5,plain,
is_a_theorem(implies(necessary(implies(A,B)),implies(necessary(A),necessary(B)))),
inference(clausify,[status(thm)],[necessitation1]) ).
fof(necessitation2,axiom,
! [VAR_0] : is_a_theorem(implies(necessary(VAR_0),VAR_0)),
file('theBenchmark.p',necessitation2) ).
cnf(c_6,plain,
is_a_theorem(implies(necessary(A),A)),
inference(clausify,[status(thm)],[necessitation2]) ).
fof(axiom_of_necessitation,axiom,
! [VAR_0] :
( is_a_theorem(necessary(VAR_0))
| ~ is_a_theorem(VAR_0) ),
file('theBenchmark.p',axiom_of_necessitation) ).
cnf(c_7,plain,
( is_a_theorem(necessary(A))
| ~ is_a_theorem(A) ),
inference(clausify,[status(thm)],[axiom_of_necessitation]) ).
fof(prove_this,axiom,
~ is_a_theorem(implies(necessary(a),not(necessary(not(a))))),
file('theBenchmark.p',prove_this) ).
cnf(c_8,plain,
~ is_a_theorem(implies(necessary(a),not(necessary(not(a))))),
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_14705,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_9,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))),
inference(resolve,[status(thm)],[c_14705,c_2]) ).
cnf(c_14706,plain,
( is_a_theorem(implies(implies(A,B),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_10,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),implies(A,B)),implies(implies(A,implies(B,C)),implies(A,C)))),
inference(resolve,[status(thm)],[c_14706,c_3]) ).
cnf(c_14707,plain,
( is_a_theorem(implies(implies(A,B),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_12,plain,
is_a_theorem(implies(implies(A,B),implies(A,A))),
inference(resolve,[status(thm)],[c_14707,c_2]) ).
cnf(c_14708,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_14,plain,
is_a_theorem(implies(A,implies(implies(not(B),not(C)),implies(C,B)))),
inference(resolve,[status(thm)],[c_14708,c_4]) ).
cnf(c_14709,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_18,plain,
is_a_theorem(implies(A,implies(necessary(B),B))),
inference(resolve,[status(thm)],[c_14709,c_6]) ).
cnf(c_24,plain,
( ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,implies(necessary(a),not(necessary(not(a)))))) ),
inference(resolve,[status(thm)],[c_8,c_1]) ).
cnf(c_14710,plain,
( is_a_theorem(implies(implies(A,implies(B,C)),implies(A,C)))
| ~ is_a_theorem(implies(implies(A,implies(B,C)),implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_40,plain,
is_a_theorem(implies(implies(A,implies(implies(B,A),C)),implies(A,C))),
inference(resolve,[status(thm)],[c_14710,c_9]) ).
cnf(c_14711,plain,
( is_a_theorem(implies(implies(A,B),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_96,plain,
is_a_theorem(implies(implies(A,necessary(B)),implies(A,B))),
inference(resolve,[status(thm)],[c_14711,c_18]) ).
cnf(c_14712,plain,
( is_a_theorem(implies(implies(A,implies(B,C)),implies(A,C)))
| ~ is_a_theorem(implies(implies(A,implies(B,C)),implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_120,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_14712,c_12]) ).
cnf(c_14713,plain,
( is_a_theorem(implies(implies(A,B),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_144,plain,
is_a_theorem(implies(implies(A,implies(not(B),not(C))),implies(A,implies(C,B)))),
inference(resolve,[status(thm)],[c_14713,c_14]) ).
cnf(c_1031,plain,
~ is_a_theorem(implies(necessary(a),necessary(not(necessary(not(a)))))),
inference(resolve,[status(thm)],[c_96,c_24]) ).
cnf(c_14714,plain,
( is_a_theorem(implies(necessary(A),necessary(B)))
| ~ is_a_theorem(necessary(implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_1288,plain,
~ is_a_theorem(necessary(implies(a,not(necessary(not(a)))))),
inference(resolve,[status(thm)],[c_14714,c_1031]) ).
cnf(c_1290,plain,
~ is_a_theorem(implies(a,not(necessary(not(a))))),
inference(resolve,[status(thm)],[c_1288,c_7]) ).
cnf(c_14715,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(implies(not(A),not(B))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_1538,plain,
~ is_a_theorem(implies(not(not(necessary(not(a)))),not(a))),
inference(resolve,[status(thm)],[c_14715,c_1290]) ).
cnf(c_14716,plain,
( is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(A,necessary(B))) ),
inference(resolve,[status(thm)],[c_1,c_96]) ).
cnf(c_1793,plain,
~ is_a_theorem(implies(not(not(necessary(not(a)))),necessary(not(a)))),
inference(resolve,[status(thm)],[c_14716,c_1538]) ).
cnf(c_14717,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(A,implies(implies(B,A),C))) ),
inference(resolve,[status(thm)],[c_1,c_40]) ).
cnf(c_2125,plain,
is_a_theorem(implies(not(A),implies(A,B))),
inference(resolve,[status(thm)],[c_14717,c_14]) ).
cnf(c_14718,plain,
( is_a_theorem(implies(A,implies(C,B)))
| ~ is_a_theorem(implies(A,implies(not(B),not(C)))) ),
inference(resolve,[status(thm)],[c_1,c_144]) ).
cnf(c_14574,plain,
is_a_theorem(implies(not(not(A)),implies(B,A))),
inference(resolve,[status(thm)],[c_14718,c_2125]) ).
cnf(c_14719,plain,
( is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_120]) ).
cnf(c_14703,plain,
is_a_theorem(implies(not(not(A)),A)),
inference(resolve,[status(thm)],[c_14719,c_14574]) ).
cnf(c_14704,plain,
$false,
inference(resolve,[status(thm)],[c_14703,c_1793]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 21:46:19 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3856245 was started by sandbox on n020,
% 0.10/0.37 % Fri Sep 25 21:46:19 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 89.24/12.22
% 89.24/12.22 % SZS status Unsatisfiable for theBenchmark
% 89.24/12.22
% 89.24/12.22 % Proof 1 at 2.53 (+ 1.09) seconds.
% 89.24/12.22 % Length of proof is 27.
% 89.24/12.22 % Level of proof is 8.
% 89.24/12.22 % Maximum clause weight is 20.000.
% 89.24/12.22 % Given clauses 412.
% 89.24/12.22
% 89.24/12.22 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------