%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 07:57:45 AM UTC 2026
% Result : Unsatisfiable 0.14s 10.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 15 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 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 : 74 ( 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(yql,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(equivalent(equivalent(VAR_0,VAR_1),equivalent(equivalent(VAR_2,VAR_1),equivalent(VAR_0,VAR_2)))),
file('theBenchmark.p',yql) ).
cnf(c_2,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,B),equivalent(A,C)))),
inference(clausify,[status(thm)],[yql]) ).
fof(prove_ec_5,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))),
file('theBenchmark.p',prove_ec_5) ).
cnf(c_3,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))),
inference(clausify,[status(thm)],[prove_ec_5]) ).
cnf(c_303,plain,
( is_a_theorem(equivalent(equivalent(C,B),equivalent(A,C)))
| ~ 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(D,B))),equivalent(equivalent(D,C),A))),
inference(resolve,[status(thm)],[c_303,c_2]) ).
cnf(c_304,plain,
( is_a_theorem(equivalent(equivalent(D,C),A))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(D,B)))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_5,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,C),equivalent(equivalent(D,B),equivalent(C,D))))),
inference(resolve,[status(thm)],[c_304,c_4]) ).
cnf(c_305,plain,
( is_a_theorem(equivalent(equivalent(D,C),A))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(D,B)))) ),
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_305,c_2]) ).
cnf(c_306,plain,
( is_a_theorem(equivalent(equivalent(D,C),A))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(D,B)))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_8,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(C,A),B))),
inference(resolve,[status(thm)],[c_306,c_5]) ).
cnf(c_307,plain,
( is_a_theorem(equivalent(equivalent(C,B),equivalent(A,C)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_9,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(D,E),equivalent(C,D)))),equivalent(equivalent(B,E),A))),
inference(resolve,[status(thm)],[c_307,c_5]) ).
cnf(c_308,plain,
( is_a_theorem(equivalent(equivalent(C,A),B))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_22,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),A),B)),
inference(resolve,[status(thm)],[c_308,c_7]) ).
cnf(c_309,plain,
( is_a_theorem(equivalent(equivalent(C,A),B))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_27,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,A)),B)),
inference(resolve,[status(thm)],[c_309,c_22]) ).
cnf(c_310,plain,
( is_a_theorem(B)
| ~ is_a_theorem(equivalent(equivalent(A,B),A)) ),
inference(resolve,[status(thm)],[c_1,c_22]) ).
cnf(c_32,plain,
is_a_theorem(equivalent(A,A)),
inference(resolve,[status(thm)],[c_310,c_27]) ).
cnf(c_311,plain,
( is_a_theorem(equivalent(equivalent(A,C),equivalent(equivalent(D,B),equivalent(C,D))))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_37,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,A),equivalent(B,C)))),
inference(resolve,[status(thm)],[c_311,c_32]) ).
cnf(c_312,plain,
( is_a_theorem(equivalent(equivalent(B,E),A))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(D,E),equivalent(C,D))))) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_301,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(A,equivalent(B,C)))),
inference(resolve,[status(thm)],[c_312,c_37]) ).
cnf(c_302,plain,
$false,
inference(resolve,[status(thm)],[c_301,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/10.38 % Computer : n013.cluster.edu
% 0.08/10.38 % Model : x86_64 x86_64
% 0.08/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.38 % Memory : 8046.5625MB
% 0.08/10.38 % OS : Linux 6.8.0-71-generic
% 0.08/10.38 % CPULimit : 300
% 0.08/10.38 % WCLimit : 300
% 0.08/10.38 % DateTime : Fri Sep 25 21:42:52 UTC 2026
% 0.08/10.38 % CPUTime :
% 0.08/10.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/10.38 % Process 1282673 was started by sandbox on n013,
% 0.08/10.38 % Fri Sep 25 21:42:52 2026
% 0.08/10.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/10.39
% 0.08/10.39 % From the command line: assign(max_seconds, 300).
% 0.14/10.41
% 0.14/10.41 % SZS status Unsatisfiable for theBenchmark
% 0.14/10.41
% 0.14/10.41 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/10.41 % Length of proof is 14.
% 0.14/10.41 % Level of proof is 9.
% 0.14/10.41 % Maximum clause weight is 90.000.
% 0.14/10.41 % Given clauses 30.
% 0.14/10.41
% 0.14/10.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------