%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL010-1 : 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 : n002.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 0.19s 15.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 14 unt; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 13 |; 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 : 65 ( 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(yqf,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(equivalent(equivalent(VAR_0,VAR_1),equivalent(equivalent(VAR_0,VAR_2),equivalent(VAR_2,VAR_1)))),
file('theBenchmark.p',yqf) ).
cnf(c_2,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,C),equivalent(C,B)))),
inference(clausify,[status(thm)],[yqf]) ).
fof(prove_yql,axiom,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(a,c)))),
file('theBenchmark.p',prove_yql) ).
cnf(c_3,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(a,c)))),
inference(clausify,[status(thm)],[prove_yql]) ).
cnf(c_87,plain,
( is_a_theorem(equivalent(equivalent(A,C),equivalent(C,B)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_4,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(C,equivalent(equivalent(A,D),equivalent(D,B))))),
inference(resolve,[status(thm)],[c_87,c_2]) ).
cnf(c_88,plain,
( is_a_theorem(equivalent(C,equivalent(equivalent(A,D),equivalent(D,B))))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_7,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(B,C)),equivalent(equivalent(A,D),equivalent(D,C)))),
inference(resolve,[status(thm)],[c_88,c_2]) ).
cnf(c_89,plain,
( is_a_theorem(equivalent(equivalent(A,D),equivalent(D,C)))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_8,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,A),B),equivalent(B,equivalent(C,C)))),
inference(resolve,[status(thm)],[c_89,c_7]) ).
cnf(c_90,plain,
( is_a_theorem(equivalent(B,equivalent(C,C)))
| ~ is_a_theorem(equivalent(equivalent(A,A),B)) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_12,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,A),equivalent(B,B)),equivalent(C,C))),
inference(resolve,[status(thm)],[c_90,c_8]) ).
cnf(c_91,plain,
( is_a_theorem(equivalent(C,C))
| ~ is_a_theorem(equivalent(equivalent(A,A),equivalent(B,B))) ),
inference(resolve,[status(thm)],[c_1,c_12]) ).
cnf(c_17,plain,
is_a_theorem(equivalent(A,A)),
inference(resolve,[status(thm)],[c_91,c_12]) ).
cnf(c_92,plain,
( is_a_theorem(equivalent(equivalent(A,D),equivalent(D,C)))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_21,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(B,A))),
inference(resolve,[status(thm)],[c_92,c_17]) ).
cnf(c_93,plain,
( is_a_theorem(equivalent(equivalent(A,C),equivalent(C,B)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_24,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(C,equivalent(B,A)))),
inference(resolve,[status(thm)],[c_93,c_21]) ).
cnf(c_94,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_21]) ).
cnf(c_28,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(B,C)),equivalent(A,C))),
inference(resolve,[status(thm)],[c_94,c_2]) ).
cnf(c_95,plain,
( is_a_theorem(equivalent(C,equivalent(B,A)))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_24]) ).
cnf(c_85,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,B),equivalent(A,C)))),
inference(resolve,[status(thm)],[c_95,c_28]) ).
cnf(c_86,plain,
$false,
inference(resolve,[status(thm)],[c_85,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/15.45 % Computer : n002.cluster.edu
% 0.19/15.45 % Model : x86_64 x86_64
% 0.19/15.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/15.45 % Memory : 8046.5625MB
% 0.19/15.45 % OS : Linux 6.8.0-71-generic
% 0.19/15.45 % CPULimit : 300
% 0.19/15.46 % WCLimit : 300
% 0.19/15.46 % DateTime : Fri Sep 25 21:46:21 UTC 2026
% 0.19/15.46 % CPUTime :
% 0.19/15.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/15.46 % Process 59222 was started by sandbox2 on n002,
% 0.19/15.46 % Fri Sep 25 21:46:21 2026
% 0.19/15.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/15.47
% 0.19/15.47 % From the command line: assign(max_seconds, 300).
% 0.19/15.49
% 0.19/15.49 % SZS status Unsatisfiable for theBenchmark
% 0.19/15.49
% 0.19/15.49 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.19/15.49 % Length of proof is 13.
% 0.19/15.49 % Level of proof is 9.
% 0.19/15.49 % Maximum clause weight is 53.000.
% 0.19/15.49 % Given clauses 19.
% 0.19/15.49
% 0.19/15.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------