%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL018-1 : 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 07:57:46 AM UTC 2026
% Result : Unsatisfiable 54.69s 12.38s
% Output : CNFRefutation 54.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 3
% Syntax : Number of formulae : 77 ( 40 unt; 0 def)
% Number of atoms : 116 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 80 ( 41 ~; 39 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 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 : 286 ( 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(pym,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(equivalent(equivalent(equivalent(VAR_0,equivalent(VAR_1,VAR_2)),VAR_1),equivalent(VAR_2,VAR_0))),
file('theBenchmark.p',pym) ).
cnf(c_2,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),B),equivalent(C,A))),
inference(clausify,[status(thm)],[pym]) ).
fof(prove_pyo,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),c),equivalent(b,a))),
file('theBenchmark.p',prove_pyo) ).
cnf(c_3,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),c),equivalent(b,a))),
inference(clausify,[status(thm)],[prove_pyo]) ).
cnf(c_18036,plain,
( is_a_theorem(equivalent(C,A))
| ~ is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_4,plain,
is_a_theorem(equivalent(A,equivalent(B,equivalent(equivalent(equivalent(C,B),A),C)))),
inference(resolve,[status(thm)],[c_18036,c_2]) ).
cnf(c_18037,plain,
( is_a_theorem(equivalent(B,equivalent(equivalent(equivalent(C,B),A),C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_6,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(B,A),equivalent(equivalent(equivalent(C,equivalent(D,E)),D),equivalent(E,C))),B))),
inference(resolve,[status(thm)],[c_18037,c_2]) ).
cnf(c_18038,plain,
( is_a_theorem(equivalent(equivalent(equivalent(B,A),equivalent(equivalent(equivalent(C,equivalent(D,E)),D),equivalent(E,C))),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_8,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,equivalent(C,D)),C),equivalent(D,B))),equivalent(equivalent(equivalent(E,equivalent(F,V6)),F),equivalent(V6,E))),A)),
inference(resolve,[status(thm)],[c_18038,c_2]) ).
cnf(c_18039,plain,
( is_a_theorem(A)
| ~ is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,equivalent(C,D)),C),equivalent(D,B))),equivalent(equivalent(equivalent(E,equivalent(F,V6)),F),equivalent(V6,E)))) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_11,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,equivalent(B,C)),B),equivalent(C,A)),equivalent(equivalent(equivalent(D,equivalent(E,F)),E),equivalent(F,D)))),
inference(resolve,[status(thm)],[c_18039,c_8]) ).
cnf(c_18040,plain,
( is_a_theorem(equivalent(C,A))
| ~ is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_12,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(B,equivalent(C,A)),C),equivalent(equivalent(equivalent(D,equivalent(E,F)),E),equivalent(F,D))))),
inference(resolve,[status(thm)],[c_18040,c_8]) ).
cnf(c_18041,plain,
( is_a_theorem(A)
| ~ is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,equivalent(C,D)),C),equivalent(D,B))),equivalent(equivalent(equivalent(E,equivalent(F,V6)),F),equivalent(V6,E)))) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_13,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(equivalent(C,equivalent(D,E)),D),equivalent(E,C)),equivalent(equivalent(B,equivalent(F,A)),F)))),
inference(resolve,[status(thm)],[c_18041,c_2]) ).
cnf(c_18042,plain,
( is_a_theorem(A)
| ~ is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,equivalent(C,D)),C),equivalent(D,B))),equivalent(equivalent(equivalent(E,equivalent(F,V6)),F),equivalent(V6,E)))) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_14,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,equivalent(equivalent(B,equivalent(D,A)),D))),C)),
inference(resolve,[status(thm)],[c_18042,c_11]) ).
cnf(c_18043,plain,
( is_a_theorem(C)
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(C,equivalent(equivalent(B,equivalent(D,A)),D)))) ),
inference(resolve,[status(thm)],[c_1,c_14]) ).
cnf(c_17,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,equivalent(equivalent(C,D),equivalent(A,equivalent(equivalent(D,equivalent(E,C)),E))))),B)),
inference(resolve,[status(thm)],[c_18043,c_11]) ).
cnf(c_18044,plain,
( is_a_theorem(C)
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(C,equivalent(equivalent(B,equivalent(D,A)),D)))) ),
inference(resolve,[status(thm)],[c_1,c_14]) ).
cnf(c_19,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,A),C),B)),equivalent(D,C)),D)),
inference(resolve,[status(thm)],[c_18044,c_12]) ).
cnf(c_18045,plain,
( is_a_theorem(equivalent(equivalent(equivalent(B,equivalent(C,A)),C),equivalent(equivalent(equivalent(D,equivalent(E,F)),E),equivalent(F,D))))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_12]) ).
cnf(c_20,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,A),C),B)),equivalent(D,C)),D),equivalent(equivalent(equivalent(E,equivalent(F,V6)),F),equivalent(V6,E)))),
inference(resolve,[status(thm)],[c_18045,c_4]) ).
cnf(c_18046,plain,
( is_a_theorem(D)
| ~ is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,A),C),B)),equivalent(D,C))) ),
inference(resolve,[status(thm)],[c_1,c_19]) ).
cnf(c_25,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(C,equivalent(D,E)),D),equivalent(E,C))),A),equivalent(F,B)),F)),
inference(resolve,[status(thm)],[c_18046,c_12]) ).
cnf(c_18047,plain,
( is_a_theorem(D)
| ~ is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,A),C),B)),equivalent(D,C))) ),
inference(resolve,[status(thm)],[c_1,c_19]) ).
cnf(c_26,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,equivalent(equivalent(equivalent(C,B),A),C))),equivalent(equivalent(equivalent(D,equivalent(E,F)),E),equivalent(F,D)))),
inference(resolve,[status(thm)],[c_18047,c_6]) ).
cnf(c_18048,plain,
( is_a_theorem(equivalent(C,A))
| ~ is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_32,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,equivalent(C,D)),C),equivalent(D,B))),E),A),E)),
inference(resolve,[status(thm)],[c_18048,c_26]) ).
cnf(c_18049,plain,
( is_a_theorem(B)
| ~ is_a_theorem(equivalent(A,equivalent(B,equivalent(equivalent(C,D),equivalent(A,equivalent(equivalent(D,equivalent(E,C)),E)))))) ),
inference(resolve,[status(thm)],[c_1,c_17]) ).
cnf(c_41,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,equivalent(B,C)),B),equivalent(C,A)),equivalent(equivalent(D,equivalent(E,F)),E)),equivalent(V6,equivalent(F,D))),V6)),
inference(resolve,[status(thm)],[c_18049,c_11]) ).
cnf(c_18050,plain,
( is_a_theorem(F)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(C,equivalent(D,E)),D),equivalent(E,C))),A),equivalent(F,B))) ),
inference(resolve,[status(thm)],[c_1,c_25]) ).
cnf(c_65,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,equivalent(equivalent(A,equivalent(equivalent(C,equivalent(D,E)),D)),equivalent(E,C)))),B)),
inference(resolve,[status(thm)],[c_18050,c_20]) ).
cnf(c_18051,plain,
( is_a_theorem(B)
| ~ is_a_theorem(equivalent(A,equivalent(B,equivalent(equivalent(A,equivalent(equivalent(C,equivalent(D,E)),D)),equivalent(E,C))))) ),
inference(resolve,[status(thm)],[c_1,c_65]) ).
cnf(c_75,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(A,equivalent(B,C)),B),C),equivalent(D,A)),D)),
inference(resolve,[status(thm)],[c_18051,c_12]) ).
cnf(c_18052,plain,
( is_a_theorem(D)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,equivalent(B,C)),B),C),equivalent(D,A))) ),
inference(resolve,[status(thm)],[c_1,c_75]) ).
cnf(c_130,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,A),B))),
inference(resolve,[status(thm)],[c_18052,c_32]) ).
cnf(c_18053,plain,
( is_a_theorem(equivalent(equivalent(B,A),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_130]) ).
cnf(c_138,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,equivalent(equivalent(C,B),C))),A)),
inference(resolve,[status(thm)],[c_18053,c_130]) ).
cnf(c_18054,plain,
( is_a_theorem(A)
| ~ is_a_theorem(equivalent(A,equivalent(B,equivalent(equivalent(C,B),C)))) ),
inference(resolve,[status(thm)],[c_1,c_138]) ).
cnf(c_209,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(B,equivalent(C,A)),C))),
inference(resolve,[status(thm)],[c_18054,c_13]) ).
cnf(c_18055,plain,
( is_a_theorem(A)
| ~ is_a_theorem(equivalent(A,equivalent(B,equivalent(equivalent(C,B),C)))) ),
inference(resolve,[status(thm)],[c_1,c_138]) ).
cnf(c_214,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),A),equivalent(C,B)),C)),
inference(resolve,[status(thm)],[c_18055,c_2]) ).
cnf(c_18056,plain,
( is_a_theorem(D)
| ~ is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,A),C),B)),equivalent(D,C))) ),
inference(resolve,[status(thm)],[c_1,c_19]) ).
cnf(c_250,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),A),equivalent(C,B))),
inference(resolve,[status(thm)],[c_18056,c_209]) ).
cnf(c_18057,plain,
( is_a_theorem(C)
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),A),equivalent(C,B))) ),
inference(resolve,[status(thm)],[c_1,c_214]) ).
cnf(c_296,plain,
is_a_theorem(equivalent(A,equivalent(B,equivalent(A,B)))),
inference(resolve,[status(thm)],[c_18057,c_209]) ).
cnf(c_18058,plain,
( is_a_theorem(equivalent(equivalent(B,equivalent(C,A)),C))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_209]) ).
cnf(c_308,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,A)),equivalent(C,B)),C)),
inference(resolve,[status(thm)],[c_18058,c_296]) ).
cnf(c_18059,plain,
( is_a_theorem(equivalent(C,B))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),C),A)) ),
inference(resolve,[status(thm)],[c_1,c_250]) ).
cnf(c_681,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(C,A),B),C))),
inference(resolve,[status(thm)],[c_18059,c_19]) ).
cnf(c_18060,plain,
( is_a_theorem(equivalent(C,B))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),C),A)) ),
inference(resolve,[status(thm)],[c_1,c_250]) ).
cnf(c_815,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(B,A))),
inference(resolve,[status(thm)],[c_18060,c_308]) ).
cnf(c_18061,plain,
( is_a_theorem(equivalent(equivalent(B,equivalent(C,A)),C))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_209]) ).
cnf(c_846,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,equivalent(B,A))),C)),
inference(resolve,[status(thm)],[c_18061,c_815]) ).
cnf(c_18062,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_815]) ).
cnf(c_866,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(C,B),A),C))),
inference(resolve,[status(thm)],[c_18062,c_250]) ).
cnf(c_18063,plain,
( is_a_theorem(equivalent(equivalent(equivalent(C,A),B),C))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_681]) ).
cnf(c_2010,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),equivalent(C,B)),A)),
inference(resolve,[status(thm)],[c_18063,c_815]) ).
cnf(c_18064,plain,
( is_a_theorem(V6)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(A,equivalent(B,C)),B),equivalent(C,A)),equivalent(equivalent(D,equivalent(E,F)),E)),equivalent(V6,equivalent(F,D)))) ),
inference(resolve,[status(thm)],[c_1,c_41]) ).
cnf(c_4472,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(C,A),B))),
inference(resolve,[status(thm)],[c_18064,c_2010]) ).
cnf(c_18065,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_815]) ).
cnf(c_4504,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(B,equivalent(C,A)))),
inference(resolve,[status(thm)],[c_18065,c_4472]) ).
cnf(c_18066,plain,
( is_a_theorem(equivalent(equivalent(C,A),B))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_4472]) ).
cnf(c_4545,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(A,C),B))),
inference(resolve,[status(thm)],[c_18066,c_866]) ).
cnf(c_18067,plain,
( is_a_theorem(equivalent(equivalent(C,A),B))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_4472]) ).
cnf(c_4555,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(A,B),C))),
inference(resolve,[status(thm)],[c_18067,c_681]) ).
cnf(c_18068,plain,
( is_a_theorem(equivalent(B,equivalent(C,A)))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_4504]) ).
cnf(c_4653,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(A,equivalent(C,B)))),
inference(resolve,[status(thm)],[c_18068,c_846]) ).
cnf(c_18069,plain,
( is_a_theorem(equivalent(equivalent(A,C),B))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_4545]) ).
cnf(c_5123,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),C),equivalent(A,B))),
inference(resolve,[status(thm)],[c_18069,c_4555]) ).
cnf(c_18070,plain,
( is_a_theorem(equivalent(A,equivalent(C,B)))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_4653]) ).
cnf(c_18034,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),C),equivalent(B,A))),
inference(resolve,[status(thm)],[c_18070,c_5123]) ).
cnf(c_18035,plain,
$false,
inference(resolve,[status(thm)],[c_18034,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL018-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.42 % Computer : n002.cluster.edu
% 0.15/5.42 % Model : x86_64 x86_64
% 0.15/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.42 % Memory : 8046.5625MB
% 0.15/5.42 % OS : Linux 6.8.0-71-generic
% 0.15/5.42 % CPULimit : 300
% 0.15/5.42 % WCLimit : 300
% 0.15/5.42 % DateTime : Fri Sep 25 21:46:41 UTC 2026
% 0.15/5.43 % CPUTime :
% 0.15/5.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/5.43 % Process 59773 was started by sandbox2 on n002,
% 0.15/5.43 % Fri Sep 25 21:46:41 2026
% 0.15/5.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/5.43
% 0.15/5.43 % From the command line: assign(max_seconds, 300).
% 54.69/12.38
% 54.69/12.38 % SZS status Unsatisfiable for theBenchmark
% 54.69/12.38
% 54.69/12.38 % Proof 1 at 6.02 (+ 0.89) seconds.
% 54.69/12.38 % Length of proof is 39.
% 54.69/12.38 % Level of proof is 21.
% 54.69/12.38 % Maximum clause weight is 92.000.
% 54.69/12.38 % Given clauses 308.
% 54.69/12.38
% 54.69/12.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------