%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL006-1 : 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 : n011.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 07:57:44 AM UTC 2026
% Result : Unsatisfiable 5.72s 1.19s
% Output : CNFRefutation 5.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 13 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 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 : 52 ( 0 sgn 7 !; 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(ec_4,axiom,
! [VAR_0,VAR_1] : is_a_theorem(equivalent(equivalent(VAR_0,VAR_1),equivalent(VAR_1,VAR_0))),
file('theBenchmark.p',ec_4) ).
cnf(c_2,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(B,A))),
inference(clausify,[status(thm)],[ec_4]) ).
fof(ec_5,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(equivalent(equivalent(equivalent(VAR_0,VAR_1),VAR_2),equivalent(VAR_0,equivalent(VAR_1,VAR_2)))),
file('theBenchmark.p',ec_5) ).
cnf(c_3,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(A,equivalent(B,C)))),
inference(clausify,[status(thm)],[ec_5]) ).
fof(prove_ec_1,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,a)),equivalent(b,c))),
file('theBenchmark.p',prove_ec_1) ).
cnf(c_4,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,a)),equivalent(b,c))),
inference(clausify,[status(thm)],[prove_ec_1]) ).
cnf(c_7467,plain,
( is_a_theorem(equivalent(A,equivalent(B,C)))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_5,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(C,equivalent(A,equivalent(B,C))))),
inference(resolve,[status(thm)],[c_7467,c_3]) ).
cnf(c_7468,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(A,B),C))),
inference(resolve,[status(thm)],[c_7468,c_3]) ).
cnf(c_7469,plain,
( is_a_theorem(equivalent(C,equivalent(A,equivalent(B,C))))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_8,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(D,equivalent(B,equivalent(C,D))),A)))),
inference(resolve,[status(thm)],[c_7469,c_5]) ).
cnf(c_7470,plain,
( is_a_theorem(equivalent(C,equivalent(A,equivalent(B,C))))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_14,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,equivalent(C,D)),equivalent(equivalent(equivalent(B,C),D),A)))),
inference(resolve,[status(thm)],[c_7470,c_6]) ).
cnf(c_7471,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_75,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(C,equivalent(A,equivalent(B,C))),D)),D)),
inference(resolve,[status(thm)],[c_7471,c_8]) ).
cnf(c_7472,plain,
( is_a_theorem(D)
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,equivalent(A,equivalent(B,C))),D))) ),
inference(resolve,[status(thm)],[c_1,c_75]) ).
cnf(c_7465,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,A)),equivalent(B,C))),
inference(resolve,[status(thm)],[c_7472,c_14]) ).
cnf(c_7466,plain,
$false,
inference(resolve,[status(thm)],[c_7465,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 21:43:14 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2975687 was started by sandbox2 on n011,
% 0.09/0.37 % Fri Sep 25 21:43:14 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 5.72/1.19
% 5.72/1.19 % SZS status Unsatisfiable for theBenchmark
% 5.72/1.19
% 5.72/1.19 % Proof 1 at 0.64 (+ 0.16) seconds.
% 5.72/1.19 % Length of proof is 11.
% 5.72/1.19 % Level of proof is 5.
% 5.72/1.19 % Maximum clause weight is 51.000.
% 5.72/1.19 % Given clauses 150.
% 5.72/1.19
% 5.72/1.19 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------