%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL077-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 07:57:55 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 15 unt; 0 def)
% Number of atoms : 39 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 53 ( 6 sgn 12 !; 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(transitivity,axiom,
! [VAR_0,VAR_1,VAR_2] :
( is_a_theorem(implies(VAR_0,VAR_2))
| ~ is_a_theorem(implies(VAR_1,VAR_2))
| ~ is_a_theorem(implies(VAR_0,VAR_1)) ),
file('theBenchmark.p',transitivity) ).
cnf(c_5,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(A,B)) ),
inference(clausify,[status(thm)],[transitivity]) ).
fof(prove_cn_39,axiom,
~ is_a_theorem(implies(not(not(a)),a)),
file('theBenchmark.p',prove_cn_39) ).
cnf(c_6,plain,
~ is_a_theorem(implies(not(not(a)),a)),
inference(clausify,[status(thm)],[prove_cn_39]) ).
cnf(c_235,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_8,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_235,c_3]) ).
cnf(c_236,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(A,B),implies(A,A))),
inference(resolve,[status(thm)],[c_236,c_2]) ).
cnf(c_237,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_5,c_2]) ).
cnf(c_18,plain,
is_a_theorem(implies(not(A),implies(A,B))),
inference(resolve,[status(thm)],[c_237,c_4]) ).
cnf(c_238,plain,
( is_a_theorem(implies(not(A),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_5,c_18]) ).
cnf(c_32,plain,
is_a_theorem(implies(not(not(A)),implies(B,A))),
inference(resolve,[status(thm)],[c_238,c_4]) ).
cnf(c_239,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_8]) ).
cnf(c_41,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_239,c_10]) ).
cnf(c_240,plain,
( is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_41]) ).
cnf(c_233,plain,
is_a_theorem(implies(not(not(A)),A)),
inference(resolve,[status(thm)],[c_240,c_32]) ).
cnf(c_234,plain,
$false,
inference(resolve,[status(thm)],[c_233,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL077-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 21:48:59 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2629544 was started by sandbox2 on n009,
% 0.09/0.37 % Fri Sep 25 21:48:59 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.40
% 0.09/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.40
% 0.09/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.09/0.40 % Length of proof is 13.
% 0.09/0.40 % Level of proof is 4.
% 0.09/0.40 % Maximum clause weight is 45.000.
% 0.09/0.40 % Given clauses 28.
% 0.09/0.40
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------