%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL075-1 : 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 07:57:54 AM UTC 2026
% Result : Unsatisfiable 1.00s 0.63s
% Output : CNFRefutation 1.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 13 unt; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 77 ( 20 sgn 7 !; 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_CAMeredith,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : is_a_theorem(implies(implies(implies(implies(implies(VAR_0,VAR_1),implies(not(VAR_2),not(VAR_3))),VAR_2),VAR_4),implies(implies(VAR_4,VAR_0),implies(VAR_3,VAR_0)))),
file('theBenchmark.p',cn_CAMeredith) ).
cnf(c_2,plain,
is_a_theorem(implies(implies(implies(implies(implies(A,B),implies(not(C),not(D))),C),E),implies(implies(E,A),implies(D,A)))),
inference(clausify,[status(thm)],[cn_CAMeredith]) ).
fof(prove_cn_3,axiom,
~ is_a_theorem(implies(a,implies(not(a),b))),
file('theBenchmark.p',prove_cn_3) ).
cnf(c_3,plain,
~ is_a_theorem(implies(a,implies(not(a),b))),
inference(clausify,[status(thm)],[prove_cn_3]) ).
cnf(c_932,plain,
( is_a_theorem(implies(implies(E,A),implies(D,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(not(C),not(D))),C),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_4,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),implies(B,D)),implies(E,implies(B,D)))),
inference(resolve,[status(thm)],[c_932,c_2]) ).
cnf(c_933,plain,
( is_a_theorem(implies(implies(E,A),implies(D,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(not(C),not(D))),C),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
is_a_theorem(implies(implies(implies(A,implies(not(B),C)),D),implies(B,D))),
inference(resolve,[status(thm)],[c_933,c_4]) ).
cnf(c_934,plain,
( is_a_theorem(implies(implies(E,A),implies(D,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(not(C),not(D))),C),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_15,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_934,c_6]) ).
cnf(c_935,plain,
( is_a_theorem(implies(C,B))
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_1,c_15]) ).
cnf(c_18,plain,
is_a_theorem(implies(A,implies(B,implies(C,C)))),
inference(resolve,[status(thm)],[c_935,c_15]) ).
cnf(c_936,plain,
( is_a_theorem(implies(implies(E,A),implies(D,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(not(C),not(D))),C),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_25,plain,
is_a_theorem(implies(implies(implies(A,implies(B,B)),C),implies(D,C))),
inference(resolve,[status(thm)],[c_936,c_18]) ).
cnf(c_937,plain,
( is_a_theorem(implies(implies(E,A),implies(D,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(not(C),not(D))),C),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_91,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_937,c_25]) ).
cnf(c_938,plain,
( is_a_theorem(implies(implies(E,A),implies(D,A)))
| ~ is_a_theorem(implies(implies(implies(implies(A,B),implies(not(C),not(D))),C),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_97,plain,
is_a_theorem(implies(implies(implies(implies(not(A),not(B)),A),C),implies(B,C))),
inference(resolve,[status(thm)],[c_938,c_91]) ).
cnf(c_939,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(implies(not(A),not(B)),A),C)) ),
inference(resolve,[status(thm)],[c_1,c_97]) ).
cnf(c_930,plain,
is_a_theorem(implies(A,implies(not(A),B))),
inference(resolve,[status(thm)],[c_939,c_91]) ).
cnf(c_931,plain,
$false,
inference(resolve,[status(thm)],[c_930,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL075-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 21:49:14 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 2630317 was started by sandbox2 on n009,
% 0.09/0.37 % Fri Sep 25 21:49:14 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).
% 1.00/0.63
% 1.00/0.63 % Assigning unary symbol not kb_weight 0 and highest precedence (5).
% 1.00/0.63
% 1.00/0.63 % SZS status Unsatisfiable for theBenchmark
% 1.00/0.63
% 1.00/0.63 % Proof 1 at 0.16 (+ 0.08) seconds.
% 1.00/0.63 % Length of proof is 12.
% 1.00/0.63 % Level of proof is 9.
% 1.00/0.63 % Maximum clause weight is 73.000.
% 1.00/0.63 % Given clauses 84.
% 1.00/0.63
% 1.00/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------