%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL257-1 : TPTP v9.3.1. Released v2.0.0.
% 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 07:58:30 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 13 unt; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 12 |; 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 : 61 ( 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_xhn,axiom,
~ is_a_theorem(equivalent(x,equivalent(equivalent(y,z),equivalent(equivalent(z,x),y)))),
file('theBenchmark.p',prove_xhn) ).
cnf(c_3,plain,
~ is_a_theorem(equivalent(x,equivalent(equivalent(y,z),equivalent(equivalent(z,x),y)))),
inference(clausify,[status(thm)],[prove_xhn]) ).
cnf(c_107,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_107,c_2]) ).
cnf(c_108,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_108,c_2]) ).
cnf(c_109,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_109,c_7]) ).
cnf(c_110,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_110,c_8]) ).
cnf(c_111,plain,
( is_a_theorem(equivalent(equivalent(B,C),A))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_12,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(C,equivalent(equivalent(D,B),equivalent(A,D))))),
inference(resolve,[status(thm)],[c_111,c_4]) ).
cnf(c_112,plain,
( is_a_theorem(equivalent(equivalent(B,C),A))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_13,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,A)),equivalent(C,B))),
inference(resolve,[status(thm)],[c_112,c_2]) ).
cnf(c_113,plain,
( is_a_theorem(equivalent(C,B))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(C,A))) ),
inference(resolve,[status(thm)],[c_1,c_13]) ).
cnf(c_46,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),A),B)),
inference(resolve,[status(thm)],[c_113,c_10]) ).
cnf(c_114,plain,
( is_a_theorem(equivalent(C,equivalent(equivalent(D,B),equivalent(A,D))))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_12]) ).
cnf(c_105,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(C,A),B)))),
inference(resolve,[status(thm)],[c_114,c_46]) ).
cnf(c_106,plain,
$false,
inference(resolve,[status(thm)],[c_105,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL257-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n013.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Fri Sep 25 22:08:21 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 1340188 was started by sandbox2 on n013,
% 0.09/0.35 % Fri Sep 25 22:08:21 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.35
% 0.09/0.35 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 12.
% 0.13/0.37 % Level of proof is 7.
% 0.13/0.37 % Maximum clause weight is 16.000.
% 0.13/0.37 % Given clauses 19.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------