%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL011-1 : 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 : n026.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 0.16s 10.61s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% 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 : 81 ( 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(yqj,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(equivalent(equivalent(VAR_0,VAR_1),equivalent(equivalent(VAR_2,VAR_0),equivalent(VAR_1,VAR_2)))),
file('theBenchmark.p',yqj) ).
cnf(c_2,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,A),equivalent(B,C)))),
inference(clausify,[status(thm)],[yqj]) ).
fof(prove_yqf,axiom,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b)))),
file('theBenchmark.p',prove_yqf) ).
cnf(c_3,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(a,c),equivalent(c,b)))),
inference(clausify,[status(thm)],[prove_yqf]) ).
cnf(c_379,plain,
( is_a_theorem(equivalent(equivalent(C,A),equivalent(B,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(B,C)),equivalent(equivalent(equivalent(D,B),equivalent(C,D)),A))),
inference(resolve,[status(thm)],[c_379,c_2]) ).
cnf(c_380,plain,
( is_a_theorem(equivalent(equivalent(C,A),equivalent(B,C)))
| ~ 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,equivalent(C,D))),equivalent(equivalent(equivalent(equivalent(E,C),equivalent(D,E)),B),A))),
inference(resolve,[status(thm)],[c_380,c_4]) ).
cnf(c_381,plain,
( is_a_theorem(equivalent(equivalent(equivalent(D,B),equivalent(C,D)),A))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_7,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(D,B),A)),equivalent(C,D))),
inference(resolve,[status(thm)],[c_381,c_2]) ).
cnf(c_382,plain,
( is_a_theorem(equivalent(equivalent(equivalent(equivalent(E,C),equivalent(D,E)),B),A))
| ~ is_a_theorem(equivalent(A,equivalent(B,equivalent(C,D)))) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_10,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(C,A)),equivalent(equivalent(D,E),equivalent(F,D))),equivalent(equivalent(B,C),equivalent(E,F)))),
inference(resolve,[status(thm)],[c_382,c_4]) ).
cnf(c_383,plain,
( is_a_theorem(equivalent(C,D))
| ~ is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(D,B),A))) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_13,plain,
is_a_theorem(equivalent(A,equivalent(B,equivalent(A,B)))),
inference(resolve,[status(thm)],[c_383,c_4]) ).
cnf(c_384,plain,
( is_a_theorem(equivalent(equivalent(equivalent(equivalent(E,C),equivalent(D,E)),B),A))
| ~ is_a_theorem(equivalent(A,equivalent(B,equivalent(C,D)))) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_15,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(C,A)),C),B)),
inference(resolve,[status(thm)],[c_384,c_13]) ).
cnf(c_385,plain,
( is_a_theorem(B)
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,A)),C)) ),
inference(resolve,[status(thm)],[c_1,c_15]) ).
cnf(c_25,plain,
is_a_theorem(equivalent(A,A)),
inference(resolve,[status(thm)],[c_385,c_7]) ).
cnf(c_386,plain,
( is_a_theorem(equivalent(equivalent(C,A),equivalent(B,C)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_29,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(B,A))),
inference(resolve,[status(thm)],[c_386,c_25]) ).
cnf(c_387,plain,
( is_a_theorem(equivalent(equivalent(B,C),equivalent(E,F)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,A)),equivalent(equivalent(D,E),equivalent(F,D)))) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_57,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(B,C)),equivalent(A,C))),
inference(resolve,[status(thm)],[c_387,c_10]) ).
cnf(c_388,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_29]) ).
cnf(c_377,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,C),equivalent(C,B)))),
inference(resolve,[status(thm)],[c_388,c_57]) ).
cnf(c_378,plain,
$false,
inference(resolve,[status(thm)],[c_377,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL011-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/10.55 % Computer : n026.cluster.edu
% 0.12/10.55 % Model : x86_64 x86_64
% 0.12/10.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.55 % Memory : 8046.5625MB
% 0.12/10.55 % OS : Linux 6.8.0-71-generic
% 0.12/10.55 % CPULimit : 300
% 0.12/10.55 % WCLimit : 300
% 0.12/10.55 % DateTime : Fri Sep 25 21:46:20 UTC 2026
% 0.12/10.56 % CPUTime :
% 0.12/10.56 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/10.56 % Process 3520128 was started by sandbox2 on n026,
% 0.12/10.56 % Fri Sep 25 21:46:20 2026
% 0.12/10.56 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/10.56
% 0.12/10.56 % From the command line: assign(max_seconds, 300).
% 0.16/10.61
% 0.16/10.61 % SZS status Unsatisfiable for theBenchmark
% 0.16/10.61
% 0.16/10.61 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.16/10.61 % Length of proof is 14.
% 0.16/10.61 % Level of proof is 8.
% 0.16/10.61 % Maximum clause weight is 99.000.
% 0.16/10.61 % Given clauses 36.
% 0.16/10.61
% 0.16/10.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------