%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL098-1 : 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 : n020.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 07:57:58 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.40s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 9 unt; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 8 |; 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 59 ( 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(lg_3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(VAR_0,VAR_1),equivalent(VAR_0,VAR_2)),VAR_3),equivalent(equivalent(VAR_1,VAR_2),VAR_3)),VAR_4),VAR_4)),
file('theBenchmark.p',lg_3) ).
cnf(c_2,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),equivalent(equivalent(B,C),D)),E),E)),
inference(clausify,[status(thm)],[lg_3]) ).
fof(prove_lg_4,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),
file('theBenchmark.p',prove_lg_4) ).
cnf(c_3,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),
inference(clausify,[status(thm)],[prove_lg_4]) ).
cnf(c_4,plain,
( is_a_theorem(E)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),equivalent(equivalent(B,C),D)),E)) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_161,plain,
( is_a_theorem(E)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),D),equivalent(equivalent(B,C),D)),E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_5,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,B),equivalent(equivalent(A,D),C)))),
inference(resolve,[status(thm)],[c_161,c_2]) ).
cnf(c_6,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(equivalent(C,D),equivalent(C,E)),A),equivalent(equivalent(D,E),B)))),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_162,plain,
( is_a_theorem(equivalent(equivalent(equivalent(equivalent(C,D),equivalent(C,E)),A),equivalent(equivalent(D,E),B)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_15,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(equivalent(equivalent(equivalent(equivalent(D,E),equivalent(D,F)),V6),equivalent(equivalent(E,F),V6)),V7)),equivalent(equivalent(B,C),V7))),
inference(resolve,[status(thm)],[c_162,c_2]) ).
cnf(c_163,plain,
( is_a_theorem(equivalent(equivalent(B,C),V7))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(equivalent(equivalent(equivalent(equivalent(D,E),equivalent(D,F)),V6),equivalent(equivalent(E,F),V6)),V7))) ),
inference(resolve,[status(thm)],[c_1,c_15]) ).
cnf(c_159,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),D),equivalent(equivalent(equivalent(A,E),C),equivalent(equivalent(B,E),D)))),
inference(resolve,[status(thm)],[c_163,c_6]) ).
cnf(c_160,plain,
$false,
inference(resolve,[status(thm)],[c_159,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL098-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 21:51:49 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3872538 was started by sandbox on n020,
% 0.08/0.36 % Fri Sep 25 21:51:49 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.40
% 0.08/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.40
% 0.08/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.08/0.40 % Length of proof is 9.
% 0.08/0.40 % Level of proof is 5.
% 0.08/0.40 % Maximum clause weight is 72.000.
% 0.08/0.40 % Given clauses 21.
% 0.08/0.40
% 0.08/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------