%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL117-1 : 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 : n001.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 07:58:02 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 8 unt; 0 def)
% Number of atoms : 20 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 7 |; 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 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(equivalent(VAR_0,VAR_1)) ),
file('theBenchmark.p',condensed_detachment) ).
cnf(c_1,plain,
( is_a_theorem(B)
| ~ is_a_theorem(A)
| ~ is_a_theorem(equivalent(A,B)) ),
inference(clausify,[status(thm)],[condensed_detachment]) ).
fof(yqm,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(equivalent(equivalent(VAR_0,VAR_1),equivalent(equivalent(VAR_2,VAR_1),equivalent(VAR_2,VAR_0)))),
file('theBenchmark.p',yqm) ).
cnf(c_2,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,B),equivalent(C,A)))),
inference(clausify,[status(thm)],[yqm]) ).
fof(prove_qyf,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(a,c)),equivalent(c,b))),
file('theBenchmark.p',prove_qyf) ).
cnf(c_3,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(a,c)),equivalent(c,b))),
inference(clausify,[status(thm)],[prove_qyf]) ).
cnf(c_10,plain,
( is_a_theorem(equivalent(equivalent(C,B),equivalent(C,A)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_4,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(B,D))),equivalent(A,equivalent(D,C)))),
inference(resolve,[status(thm)],[c_10,c_2]) ).
cnf(c_11,plain,
( is_a_theorem(equivalent(A,equivalent(D,C)))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(B,D)))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_7,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(A,B))),
inference(resolve,[status(thm)],[c_11,c_2]) ).
cnf(c_12,plain,
( is_a_theorem(equivalent(A,equivalent(D,C)))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(B,D)))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_8,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(C,B))),
inference(resolve,[status(thm)],[c_12,c_7]) ).
cnf(c_9,plain,
$false,
inference(resolve,[status(thm)],[c_8,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL117-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 21:58:43 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 151313 was started by sandbox2 on n001,
% 0.08/0.36 % Fri Sep 25 21:58:43 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.37
% 0.12/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.37
% 0.12/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.37 % Length of proof is 7.
% 0.12/0.37 % Level of proof is 4.
% 0.12/0.37 % Maximum clause weight is 16.000.
% 0.12/0.37 % Given clauses 5.
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------