%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL120-1 : 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 : n005.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 07:58:03 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 17 unt; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 18 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 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 : 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(qyf,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(equivalent(equivalent(equivalent(VAR_0,VAR_1),equivalent(VAR_0,VAR_2)),equivalent(VAR_2,VAR_1))),
file('theBenchmark.p',qyf) ).
cnf(c_2,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(C,B))),
inference(clausify,[status(thm)],[qyf]) ).
fof(prove_xgj,axiom,
~ is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(c,a)),equivalent(b,c)))),
file('theBenchmark.p',prove_xgj) ).
cnf(c_3,plain,
~ is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(c,a)),equivalent(b,c)))),
inference(clausify,[status(thm)],[prove_xgj]) ).
cnf(c_916,plain,
( is_a_theorem(equivalent(C,B))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(A,C))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_4,plain,
is_a_theorem(equivalent(A,equivalent(B,equivalent(B,A)))),
inference(resolve,[status(thm)],[c_916,c_2]) ).
cnf(c_917,plain,
( is_a_theorem(equivalent(B,equivalent(B,A)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_5,plain,
is_a_theorem(equivalent(A,equivalent(A,equivalent(B,equivalent(C,equivalent(C,B)))))),
inference(resolve,[status(thm)],[c_917,c_4]) ).
cnf(c_918,plain,
( is_a_theorem(equivalent(C,B))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(A,C))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(A,B)),B)),
inference(resolve,[status(thm)],[c_918,c_4]) ).
cnf(c_919,plain,
( is_a_theorem(equivalent(B,equivalent(B,A)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_7,plain,
is_a_theorem(equivalent(A,equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(B,D)),equivalent(D,C))))),
inference(resolve,[status(thm)],[c_919,c_2]) ).
cnf(c_920,plain,
( is_a_theorem(equivalent(B,equivalent(B,A)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_9,plain,
is_a_theorem(equivalent(A,equivalent(A,equivalent(B,equivalent(B,equivalent(C,equivalent(D,equivalent(D,C)))))))),
inference(resolve,[status(thm)],[c_920,c_5]) ).
cnf(c_921,plain,
( is_a_theorem(B)
| ~ is_a_theorem(equivalent(A,equivalent(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_14,plain,
is_a_theorem(equivalent(A,A)),
inference(resolve,[status(thm)],[c_921,c_4]) ).
cnf(c_922,plain,
( is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(B,D)),equivalent(D,C))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_42,plain,
is_a_theorem(equivalent(equivalent(A,A),equivalent(equivalent(equivalent(B,C),equivalent(B,D)),equivalent(D,C)))),
inference(resolve,[status(thm)],[c_922,c_14]) ).
cnf(c_923,plain,
( is_a_theorem(equivalent(A,equivalent(B,equivalent(B,equivalent(C,equivalent(D,equivalent(D,C)))))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_49,plain,
is_a_theorem(equivalent(equivalent(A,A),equivalent(B,equivalent(B,equivalent(C,equivalent(D,equivalent(D,C))))))),
inference(resolve,[status(thm)],[c_923,c_14]) ).
cnf(c_924,plain,
( is_a_theorem(equivalent(C,B))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(A,C))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_332,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,B),equivalent(C,A)))),
inference(resolve,[status(thm)],[c_924,c_42]) ).
cnf(c_925,plain,
( is_a_theorem(equivalent(equivalent(C,B),equivalent(C,A)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_332]) ).
cnf(c_333,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(B,D))),equivalent(A,equivalent(D,C)))),
inference(resolve,[status(thm)],[c_925,c_332]) ).
cnf(c_926,plain,
( is_a_theorem(equivalent(C,B))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(A,C))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_879,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,equivalent(C,equivalent(C,B)))),A)),
inference(resolve,[status(thm)],[c_926,c_49]) ).
cnf(c_927,plain,
( is_a_theorem(A)
| ~ is_a_theorem(equivalent(A,equivalent(B,equivalent(C,equivalent(C,B))))) ),
inference(resolve,[status(thm)],[c_1,c_879]) ).
cnf(c_914,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,equivalent(C,A)),equivalent(B,C)))),
inference(resolve,[status(thm)],[c_927,c_333]) ).
cnf(c_915,plain,
$false,
inference(resolve,[status(thm)],[c_914,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL120-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n005.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Fri Sep 25 21:53:02 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.11/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.35 % Process 337919 was started by sandbox on n005,
% 0.11/0.35 % Fri Sep 25 21:53:02 2026
% 0.11/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.35
% 0.11/0.35 % From the command line: assign(max_seconds, 300).
% 0.13/0.45
% 0.13/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.45
% 0.13/0.45 % Proof 1 at 0.06 (+ 0.03) seconds.
% 0.13/0.45 % Length of proof is 16.
% 0.13/0.45 % Level of proof is 8.
% 0.13/0.45 % Maximum clause weight is 86.000.
% 0.13/0.45 % Given clauses 111.
% 0.13/0.45
% 0.13/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------