%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL014-1 : 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 : n017.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 19.26s 2.92s
% Output : CNFRefutation 19.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 3
% Syntax : Number of formulae : 65 ( 34 unt; 0 def)
% Number of atoms : 98 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 68 ( 35 ~; 33 |; 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 : 185 ( 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(wn,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(equivalent(equivalent(VAR_0,equivalent(VAR_1,VAR_2)),equivalent(VAR_2,equivalent(VAR_0,VAR_1)))),
file('theBenchmark.p',wn) ).
cnf(c_2,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(C,equivalent(A,B)))),
inference(clausify,[status(thm)],[wn]) ).
fof(prove_xgf,axiom,
~ is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(a,c)),equivalent(c,b)))),
file('theBenchmark.p',prove_xgf) ).
cnf(c_3,plain,
~ is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(a,c)),equivalent(c,b)))),
inference(clausify,[status(thm)],[prove_xgf]) ).
cnf(c_16853,plain,
( is_a_theorem(equivalent(C,equivalent(A,B)))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_4,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,equivalent(B,C)),C))),
inference(resolve,[status(thm)],[c_16853,c_2]) ).
cnf(c_16854,plain,
( is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),C))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_5,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(A,equivalent(B,C)),C),D)),D)),
inference(resolve,[status(thm)],[c_16854,c_4]) ).
cnf(c_16855,plain,
( is_a_theorem(equivalent(C,equivalent(A,B)))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(B,equivalent(C,A))))),
inference(resolve,[status(thm)],[c_16855,c_4]) ).
cnf(c_16856,plain,
( is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),C))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_7,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(C,equivalent(A,B)),D)),D)),
inference(resolve,[status(thm)],[c_16856,c_2]) ).
cnf(c_16857,plain,
( is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),C))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_8,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(A,equivalent(B,C)),C),D)),equivalent(D,E)),E)),
inference(resolve,[status(thm)],[c_16857,c_5]) ).
cnf(c_16858,plain,
( is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),C))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_11,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(B,equivalent(C,A))),D)),D)),
inference(resolve,[status(thm)],[c_16858,c_6]) ).
cnf(c_16859,plain,
( is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),C))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_16,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(C,equivalent(A,B)),D)),equivalent(D,E)),E)),
inference(resolve,[status(thm)],[c_16859,c_7]) ).
cnf(c_16860,plain,
( is_a_theorem(D)
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(B,equivalent(C,A))),D))) ),
inference(resolve,[status(thm)],[c_1,c_11]) ).
cnf(c_21,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,A),B))),
inference(resolve,[status(thm)],[c_16860,c_4]) ).
cnf(c_16861,plain,
( is_a_theorem(equivalent(equivalent(B,A),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_21]) ).
cnf(c_22,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,equivalent(equivalent(C,B),C))),A)),
inference(resolve,[status(thm)],[c_16861,c_21]) ).
cnf(c_16862,plain,
( is_a_theorem(D)
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(A,equivalent(B,C)),C),D))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_24,plain,
is_a_theorem(equivalent(A,equivalent(B,equivalent(A,B)))),
inference(resolve,[status(thm)],[c_16862,c_21]) ).
cnf(c_16863,plain,
( is_a_theorem(equivalent(C,equivalent(A,B)))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_36,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(A,B))),
inference(resolve,[status(thm)],[c_16863,c_24]) ).
cnf(c_16864,plain,
( is_a_theorem(equivalent(B,equivalent(A,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_24]) ).
cnf(c_44,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(B,C)),A))),
inference(resolve,[status(thm)],[c_16864,c_36]) ).
cnf(c_16865,plain,
( is_a_theorem(E)
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(A,equivalent(B,C)),C),D)),equivalent(D,E))) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_53,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),C),equivalent(A,B))),
inference(resolve,[status(thm)],[c_16865,c_36]) ).
cnf(c_16866,plain,
( is_a_theorem(equivalent(C,equivalent(A,B)))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_77,plain,
is_a_theorem(equivalent(A,equivalent(A,equivalent(equivalent(B,C),equivalent(B,C))))),
inference(resolve,[status(thm)],[c_16866,c_44]) ).
cnf(c_16867,plain,
( is_a_theorem(equivalent(C,equivalent(A,B)))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_127,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,B)),equivalent(C,C))),
inference(resolve,[status(thm)],[c_16867,c_77]) ).
cnf(c_16868,plain,
( is_a_theorem(equivalent(C,C))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_127]) ).
cnf(c_196,plain,
is_a_theorem(equivalent(A,A)),
inference(resolve,[status(thm)],[c_16868,c_127]) ).
cnf(c_16869,plain,
( is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),C))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_213,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(A,B)),B)),
inference(resolve,[status(thm)],[c_16869,c_196]) ).
cnf(c_16870,plain,
( is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),C))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_269,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(A,B)),equivalent(B,C)),C)),
inference(resolve,[status(thm)],[c_16870,c_213]) ).
cnf(c_16871,plain,
( is_a_theorem(E)
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(C,equivalent(A,B)),D)),equivalent(D,E))) ),
inference(resolve,[status(thm)],[c_1,c_16]) ).
cnf(c_502,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(B,equivalent(C,A)))),
inference(resolve,[status(thm)],[c_16871,c_196]) ).
cnf(c_16872,plain,
( is_a_theorem(equivalent(B,equivalent(C,A)))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_502]) ).
cnf(c_532,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(C,equivalent(A,B))))),
inference(resolve,[status(thm)],[c_16872,c_502]) ).
cnf(c_16873,plain,
( is_a_theorem(equivalent(A,B))
| ~ is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),C)) ),
inference(resolve,[status(thm)],[c_1,c_53]) ).
cnf(c_1132,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),A),B)),
inference(resolve,[status(thm)],[c_16873,c_22]) ).
cnf(c_16874,plain,
( is_a_theorem(B)
| ~ is_a_theorem(equivalent(equivalent(A,B),A)) ),
inference(resolve,[status(thm)],[c_1,c_1132]) ).
cnf(c_1410,plain,
is_a_theorem(equivalent(A,equivalent(B,equivalent(B,A)))),
inference(resolve,[status(thm)],[c_16874,c_269]) ).
cnf(c_16875,plain,
( is_a_theorem(equivalent(C,equivalent(A,B)))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_1453,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(B,A))),
inference(resolve,[status(thm)],[c_16875,c_1410]) ).
cnf(c_16876,plain,
( is_a_theorem(equivalent(B,equivalent(B,A)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_1410]) ).
cnf(c_1506,plain,
is_a_theorem(equivalent(A,equivalent(A,equivalent(equivalent(B,C),equivalent(C,B))))),
inference(resolve,[status(thm)],[c_16876,c_1453]) ).
cnf(c_16877,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_1453]) ).
cnf(c_3476,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(B,equivalent(C,A))),C)),
inference(resolve,[status(thm)],[c_16877,c_532]) ).
cnf(c_16878,plain,
( is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(C,B))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_1506]) ).
cnf(c_7707,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(B,A)),equivalent(equivalent(C,D),equivalent(D,C)))),
inference(resolve,[status(thm)],[c_16878,c_1453]) ).
cnf(c_16879,plain,
( is_a_theorem(D)
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(A,equivalent(B,C)),C),D))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_8264,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(C,B),A)))),
inference(resolve,[status(thm)],[c_16879,c_7707]) ).
cnf(c_16880,plain,
( is_a_theorem(equivalent(C,equivalent(A,B)))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_16502,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(C,equivalent(B,A)))),
inference(resolve,[status(thm)],[c_16880,c_8264]) ).
cnf(c_16881,plain,
( is_a_theorem(equivalent(C,equivalent(B,A)))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_16502]) ).
cnf(c_16851,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,equivalent(A,C)),equivalent(C,B)))),
inference(resolve,[status(thm)],[c_16881,c_3476]) ).
cnf(c_16852,plain,
$false,
inference(resolve,[status(thm)],[c_16851,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL014-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 21:38:49 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3259551 was started by sandbox2 on n017,
% 0.10/0.37 % Fri Sep 25 21:38:49 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 19.26/2.92
% 19.26/2.92 % SZS status Unsatisfiable for theBenchmark
% 19.26/2.92
% 19.26/2.92 % Proof 1 at 2.23 (+ 0.30) seconds.
% 19.26/2.92 % Length of proof is 33.
% 19.26/2.92 % Level of proof is 20.
% 19.26/2.92 % Maximum clause weight is 60.000.
% 19.26/2.92 % Given clauses 248.
% 19.26/2.92
% 19.26/2.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------