%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL008-1 : 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 : 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 0.15s 5.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 12 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 11 |; 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; 2 con; 0-2 aty)
% Number of variables : 50 ( 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_4,axiom,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a))),
file('theBenchmark.p',prove_ec_4) ).
cnf(c_3,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a))),
inference(clausify,[status(thm)],[prove_ec_4]) ).
cnf(c_39,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_39,c_2]) ).
cnf(c_40,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_40,c_2]) ).
cnf(c_41,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_8,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(B,C),A))),
inference(resolve,[status(thm)],[c_41,c_7]) ).
cnf(c_42,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_10,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,C),equivalent(C,B)))),
inference(resolve,[status(thm)],[c_42,c_8]) ).
cnf(c_43,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_17,plain,
is_a_theorem(equivalent(equivalent(A,A),equivalent(B,B))),
inference(resolve,[status(thm)],[c_43,c_10]) ).
cnf(c_44,plain,
( is_a_theorem(equivalent(B,B))
| ~ is_a_theorem(equivalent(A,A)) ),
inference(resolve,[status(thm)],[c_1,c_17]) ).
cnf(c_33,plain,
is_a_theorem(equivalent(A,A)),
inference(resolve,[status(thm)],[c_44,c_17]) ).
cnf(c_45,plain,
( is_a_theorem(equivalent(equivalent(A,C),equivalent(C,B)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_37,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(B,A))),
inference(resolve,[status(thm)],[c_45,c_33]) ).
cnf(c_38,plain,
$false,
inference(resolve,[status(thm)],[c_37,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n013.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Fri Sep 25 21:42:47 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.38 % Process 1282505 was started by sandbox2 on n013,
% 0.09/5.38 % Fri Sep 25 21:42:47 2026
% 0.09/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.39
% 0.09/5.39 % From the command line: assign(max_seconds, 300).
% 0.15/5.40
% 0.15/5.40 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.40
% 0.15/5.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/5.40 % Length of proof is 11.
% 0.15/5.40 % Level of proof is 8.
% 0.15/5.40 % Maximum clause weight is 16.000.
% 0.15/5.40 % Given clauses 11.
% 0.15/5.40
% 0.15/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------