%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL065-1 : 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 : 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 07:57:53 AM UTC 2026
% Result : Unsatisfiable 0.51s 0.50s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 24 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 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 : 94 ( 20 sgn 9 !; 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(prove_cn_2,axiom,
~ is_a_theorem(implies(implies(not(a),a),a)),
file('theBenchmark.p',prove_cn_2) ).
cnf(c_5,plain,
~ is_a_theorem(implies(implies(not(a),a),a)),
inference(clausify,[status(thm)],[prove_cn_2]) ).
cnf(c_1765,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))),
inference(resolve,[status(thm)],[c_1765,c_2]) ).
cnf(c_1766,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_7,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_1766,c_3]) ).
cnf(c_1767,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_8,plain,
is_a_theorem(implies(A,implies(implies(B,implies(C,D)),implies(implies(B,C),implies(B,D))))),
inference(resolve,[status(thm)],[c_1767,c_3]) ).
cnf(c_1768,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_9,plain,
is_a_theorem(implies(implies(A,B),implies(A,A))),
inference(resolve,[status(thm)],[c_1768,c_2]) ).
cnf(c_1769,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_11,plain,
is_a_theorem(implies(A,implies(implies(not(B),not(C)),implies(C,B)))),
inference(resolve,[status(thm)],[c_1769,c_4]) ).
cnf(c_1770,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_7]) ).
cnf(c_16,plain,
is_a_theorem(implies(implies(A,implies(implies(B,A),C)),implies(A,C))),
inference(resolve,[status(thm)],[c_1770,c_6]) ).
cnf(c_1771,plain,
( is_a_theorem(implies(A,A))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_23,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_1771,c_8]) ).
cnf(c_1772,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_25,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_1772,c_23]) ).
cnf(c_1773,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_26,plain,
is_a_theorem(implies(A,implies(B,implies(C,C)))),
inference(resolve,[status(thm)],[c_1773,c_25]) ).
cnf(c_1774,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_7]) ).
cnf(c_27,plain,
is_a_theorem(implies(implies(A,implies(implies(B,B),C)),implies(A,C))),
inference(resolve,[status(thm)],[c_1774,c_26]) ).
cnf(c_1775,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_57,plain,
is_a_theorem(implies(implies(A,implies(not(B),not(C))),implies(A,implies(C,B)))),
inference(resolve,[status(thm)],[c_1775,c_11]) ).
cnf(c_1776,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(A,implies(implies(B,A),C))) ),
inference(resolve,[status(thm)],[c_1,c_16]) ).
cnf(c_107,plain,
is_a_theorem(implies(not(A),implies(A,B))),
inference(resolve,[status(thm)],[c_1776,c_11]) ).
cnf(c_1777,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_111,plain,
is_a_theorem(implies(implies(not(A),A),implies(not(A),B))),
inference(resolve,[status(thm)],[c_1777,c_107]) ).
cnf(c_1778,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_57]) ).
cnf(c_1701,plain,
is_a_theorem(implies(implies(not(A),A),implies(B,A))),
inference(resolve,[status(thm)],[c_1778,c_111]) ).
cnf(c_1779,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(A,implies(implies(B,B),C))) ),
inference(resolve,[status(thm)],[c_1,c_27]) ).
cnf(c_1763,plain,
is_a_theorem(implies(implies(not(A),A),A)),
inference(resolve,[status(thm)],[c_1779,c_1701]) ).
cnf(c_1764,plain,
$false,
inference(resolve,[status(thm)],[c_1763,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL065-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.33 % Computer : n007.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Fri Sep 25 21:45:54 UTC 2026
% 0.07/0.33 % CPUTime :
% 0.07/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.34 % Process 1994857 was started by sandbox2 on n007,
% 0.07/0.34 % Fri Sep 25 21:45:54 2026
% 0.07/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.34
% 0.07/0.34 % From the command line: assign(max_seconds, 300).
% 0.51/0.50
% 0.51/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.51/0.50
% 0.51/0.50 % Proof 1 at 0.10 (+ 0.05) seconds.
% 0.51/0.50 % Length of proof is 21.
% 0.51/0.50 % Level of proof is 7.
% 0.51/0.50 % Maximum clause weight is 45.000.
% 0.51/0.50 % Given clauses 119.
% 0.51/0.50
% 0.51/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------