%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL355-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 07:58:39 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.45s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 9 ( 6 unt; 0 def)
% Number of atoms : 14 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 5 !; 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_1,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(implies(implies(VAR_0,VAR_1),implies(implies(VAR_1,VAR_2),implies(VAR_0,VAR_2)))),
file('theBenchmark.p',cn_1) ).
cnf(c_2,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(clausify,[status(thm)],[cn_1]) ).
fof(prove_cn_04,axiom,
~ is_a_theorem(implies(implies(implies(implies(x,y),implies(z,y)),u),implies(implies(z,x),u))),
file('theBenchmark.p',prove_cn_04) ).
cnf(c_5,plain,
~ is_a_theorem(implies(implies(implies(implies(x,y),implies(z,y)),u),implies(implies(z,x),u))),
inference(clausify,[status(thm)],[prove_cn_04]) ).
cnf(c_8,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))),
inference(resolve,[status(thm)],[c_8,c_2]) ).
cnf(c_7,plain,
$false,
inference(resolve,[status(thm)],[c_6,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL355-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.42 % Computer : n006.cluster.edu
% 0.07/0.42 % Model : x86_64 x86_64
% 0.07/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.42 % Memory : 8046.5625MB
% 0.07/0.42 % OS : Linux 6.8.0-71-generic
% 0.07/0.42 % CPULimit : 300
% 0.07/0.42 % WCLimit : 300
% 0.07/0.42 % DateTime : Fri Sep 25 22:18:56 UTC 2026
% 0.07/0.43 % CPUTime :
% 0.07/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.43 % Process 3893207 was started by sandbox on n006,
% 0.07/0.43 % Fri Sep 25 22:18:56 2026
% 0.07/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.43
% 0.07/0.43 % From the command line: assign(max_seconds, 300).
% 0.07/0.45
% 0.07/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.45
% 0.07/0.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.07/0.45 % Length of proof is 5.
% 0.07/0.45 % Level of proof is 2.
% 0.07/0.45 % Maximum clause weight is 16.000.
% 0.07/0.45 % Given clauses 2.
% 0.07/0.45
% 0.07/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------