%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL022-1 : 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 : n016.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 07:57:46 AM UTC 2026
% Result : Unsatisfiable 0.09s 5.39s
% Output : CNFRefutation 0.09s
% 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 : 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 : 70 ( 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_1,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,a)),equivalent(b,c))),
file('theBenchmark.p',prove_ec_1) ).
cnf(c_3,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,a)),equivalent(b,c))),
inference(clausify,[status(thm)],[prove_ec_1]) ).
cnf(c_371,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_371,c_2]) ).
cnf(c_372,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_372,c_4]) ).
cnf(c_373,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_373,c_2]) ).
cnf(c_374,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_374,c_7]) ).
cnf(c_375,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_375,c_8]) ).
cnf(c_376,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_376,c_10]) ).
cnf(c_377,plain,
( is_a_theorem(equivalent(B,B))
| ~ is_a_theorem(equivalent(A,A)) ),
inference(resolve,[status(thm)],[c_1,c_17]) ).
cnf(c_22,plain,
is_a_theorem(equivalent(A,A)),
inference(resolve,[status(thm)],[c_377,c_17]) ).
cnf(c_378,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_25,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(B,A))),
inference(resolve,[status(thm)],[c_378,c_22]) ).
cnf(c_379,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_30,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,A),equivalent(B,C)))),
inference(resolve,[status(thm)],[c_379,c_22]) ).
cnf(c_380,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_25]) ).
cnf(c_369,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,A)),equivalent(B,C))),
inference(resolve,[status(thm)],[c_380,c_30]) ).
cnf(c_370,plain,
$false,
inference(resolve,[status(thm)],[c_369,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL022-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n016.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Fri Sep 25 21:49:20 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.36 % Process 3373122 was started by sandbox2 on n016,
% 0.09/5.36 % Fri Sep 25 21:49:20 2026
% 0.09/5.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.37
% 0.09/5.37 % From the command line: assign(max_seconds, 300).
% 0.09/5.39
% 0.09/5.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/5.39
% 0.09/5.39 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.09/5.39 % Length of proof is 14.
% 0.09/5.39 % Level of proof is 9.
% 0.09/5.39 % Maximum clause weight is 53.000.
% 0.09/5.39 % Given clauses 33.
% 0.09/5.39
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------