%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL013-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 7 unt; 0 def)
% Number of atoms : 17 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 14 ( 8 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 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 : 26 ( 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(xgf,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(equivalent(VAR_0,equivalent(equivalent(VAR_1,equivalent(VAR_0,VAR_2)),equivalent(VAR_2,VAR_1)))),
file('theBenchmark.p',xgf) ).
cnf(c_2,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,equivalent(A,C)),equivalent(C,B)))),
inference(clausify,[status(thm)],[xgf]) ).
fof(prove_um,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a)))),
file('theBenchmark.p',prove_um) ).
cnf(c_3,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a)))),
inference(clausify,[status(thm)],[prove_um]) ).
cnf(c_9,plain,
( is_a_theorem(equivalent(equivalent(B,equivalent(A,C)),equivalent(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_4,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,equivalent(equivalent(C,equivalent(B,D)),equivalent(D,C))),E)),equivalent(E,A))),
inference(resolve,[status(thm)],[c_9,c_2]) ).
cnf(c_10,plain,
( is_a_theorem(equivalent(E,A))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,equivalent(equivalent(C,equivalent(B,D)),equivalent(D,C))),E))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_7,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(B,equivalent(C,A)))),
inference(resolve,[status(thm)],[c_10,c_2]) ).
cnf(c_8,plain,
$false,
inference(resolve,[status(thm)],[c_7,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.36 % Computer : n015.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Fri Sep 25 21:46:46 UTC 2026
% 0.07/0.37 % CPUTime :
% 0.07/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.37 % Process 2334509 was started by sandbox on n015,
% 0.07/0.37 % Fri Sep 25 21:46:46 2026
% 0.07/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 6.
% 0.13/0.38 % Level of proof is 3.
% 0.13/0.38 % Maximum clause weight is 20.000.
% 0.13/0.38 % Given clauses 4.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------