%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL016-1 : 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 : n003.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 35.71s 5.60s
% Output : CNFRefutation 35.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 3
% Syntax : Number of formulae : 63 ( 36 unt; 0 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 60 ( 31 ~; 29 |; 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 : 228 ( 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(yro,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(equivalent(equivalent(VAR_0,VAR_1),equivalent(VAR_2,equivalent(equivalent(VAR_2,VAR_1),VAR_0)))),
file('theBenchmark.p',yro) ).
cnf(c_2,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(C,equivalent(equivalent(C,B),A)))),
inference(clausify,[status(thm)],[yro]) ).
fof(prove_yrm,axiom,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(c,equivalent(equivalent(b,c),a)))),
file('theBenchmark.p',prove_yrm) ).
cnf(c_3,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(c,equivalent(equivalent(b,c),a)))),
inference(clausify,[status(thm)],[prove_yrm]) ).
cnf(c_4,plain,
( is_a_theorem(equivalent(C,equivalent(equivalent(C,B),A)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_9748,plain,
( is_a_theorem(equivalent(C,equivalent(equivalent(C,B),A)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_5,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(A,equivalent(B,equivalent(equivalent(B,C),D))),equivalent(D,C)))),
inference(resolve,[status(thm)],[c_9748,c_2]) ).
cnf(c_6,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(A,equivalent(equivalent(B,equivalent(C,equivalent(equivalent(C,D),E))),equivalent(E,D))),B))),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_7,plain,
( is_a_theorem(equivalent(equivalent(A,equivalent(B,equivalent(equivalent(B,C),D))),equivalent(D,C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_5,c_1]) ).
cnf(c_9749,plain,
( is_a_theorem(equivalent(equivalent(A,equivalent(B,equivalent(equivalent(B,C),D))),equivalent(D,C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_9,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(C,equivalent(equivalent(C,B),A))),equivalent(D,equivalent(equivalent(D,E),F))),equivalent(F,E))),
inference(resolve,[status(thm)],[c_9749,c_2]) ).
cnf(c_11,plain,
( is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,equivalent(C,equivalent(equivalent(C,D),E))),equivalent(E,D))),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_6,c_1]) ).
cnf(c_9750,plain,
( is_a_theorem(equivalent(F,E))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,equivalent(equivalent(C,B),A))),equivalent(D,equivalent(equivalent(D,E),F)))) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_15,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),C),B),A),C)),
inference(resolve,[status(thm)],[c_9750,c_9]) ).
cnf(c_16,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),C),B),A),C),equivalent(equivalent(D,equivalent(E,equivalent(equivalent(E,F),V6))),equivalent(V6,F))),D)),
inference(resolve,[status(thm)],[c_15,c_11]) ).
cnf(c_17,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),C),B),A),C),equivalent(D,equivalent(equivalent(D,E),F))),equivalent(F,E))),
inference(resolve,[status(thm)],[c_15,c_7]) ).
cnf(c_18,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(A,B),equivalent(equivalent(equivalent(equivalent(C,D),B),D),C)))),
inference(resolve,[status(thm)],[c_15,c_4]) ).
cnf(c_19,plain,
( is_a_theorem(C)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),B),A)) ),
inference(resolve,[status(thm)],[c_15,c_1]) ).
cnf(c_20,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(A,B),equivalent(equivalent(equivalent(equivalent(C,D),B),D),C))),equivalent(E,equivalent(equivalent(E,F),V6))),equivalent(V6,F))),
inference(resolve,[status(thm)],[c_18,c_7]) ).
cnf(c_9751,plain,
( is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(equivalent(C,D),B),D),C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_18]) ).
cnf(c_26,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(C,equivalent(equivalent(C,B),A))),D),equivalent(equivalent(equivalent(equivalent(E,F),D),F),E))),
inference(resolve,[status(thm)],[c_9751,c_2]) ).
cnf(c_31,plain,
( is_a_theorem(equivalent(equivalent(equivalent(equivalent(E,F),D),F),E))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,equivalent(equivalent(C,B),A))),D)) ),
inference(resolve,[status(thm)],[c_26,c_1]) ).
cnf(c_9752,plain,
( is_a_theorem(equivalent(equivalent(equivalent(equivalent(E,F),D),F),E))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,equivalent(equivalent(C,B),A))),D)) ),
inference(resolve,[status(thm)],[c_1,c_26]) ).
cnf(c_33,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(C,D),equivalent(E,equivalent(equivalent(E,D),C)))),B),A)),
inference(resolve,[status(thm)],[c_9752,c_9]) ).
cnf(c_9753,plain,
( is_a_theorem(A)
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(C,D),equivalent(E,equivalent(equivalent(E,D),C)))),B)) ),
inference(resolve,[status(thm)],[c_1,c_33]) ).
cnf(c_38,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(C,equivalent(equivalent(C,B),A))),D),D)),
inference(resolve,[status(thm)],[c_9753,c_15]) ).
cnf(c_41,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(A,B),B))),
inference(resolve,[status(thm)],[c_38,c_19]) ).
cnf(c_48,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(equivalent(equivalent(C,D),E),D),C),E)),B),A)),
inference(resolve,[status(thm)],[c_17,c_31]) ).
cnf(c_49,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(D,E),F),E),D),F),equivalent(V6,equivalent(equivalent(V6,C),B)))))),
inference(resolve,[status(thm)],[c_17,c_4]) ).
cnf(c_56,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(A,equivalent(equivalent(B,C),C)),B))),
inference(resolve,[status(thm)],[c_41,c_4]) ).
cnf(c_9754,plain,
( is_a_theorem(equivalent(equivalent(A,B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_41]) ).
cnf(c_58,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(A,B),B)),C),C)),
inference(resolve,[status(thm)],[c_9754,c_41]) ).
cnf(c_9755,plain,
( is_a_theorem(equivalent(equivalent(A,B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_41]) ).
cnf(c_64,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),C),B),A),C),D),D)),
inference(resolve,[status(thm)],[c_9755,c_15]) ).
cnf(c_85,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,A),B),B)),
inference(resolve,[status(thm)],[c_58,c_19]) ).
cnf(c_9756,plain,
( is_a_theorem(B)
| ~ is_a_theorem(equivalent(equivalent(A,A),B)) ),
inference(resolve,[status(thm)],[c_1,c_85]) ).
cnf(c_100,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,A),equivalent(equivalent(B,C),C)),B)),
inference(resolve,[status(thm)],[c_9756,c_56]) ).
cnf(c_9757,plain,
( is_a_theorem(A)
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(C,D),equivalent(E,equivalent(equivalent(E,D),C)))),B)) ),
inference(resolve,[status(thm)],[c_1,c_33]) ).
cnf(c_108,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(equivalent(C,D),A),D),C)),B)),
inference(resolve,[status(thm)],[c_9757,c_20]) ).
cnf(c_9758,plain,
( is_a_theorem(B)
| ~ is_a_theorem(equivalent(equivalent(A,A),equivalent(equivalent(B,C),C))) ),
inference(resolve,[status(thm)],[c_1,c_100]) ).
cnf(c_209,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(A,B),C)),equivalent(C,B))),
inference(resolve,[status(thm)],[c_9758,c_16]) ).
cnf(c_9759,plain,
( is_a_theorem(equivalent(F,E))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),C),B),A),C),equivalent(D,equivalent(equivalent(D,E),F)))) ),
inference(resolve,[status(thm)],[c_1,c_17]) ).
cnf(c_726,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(A,B),equivalent(C,B))),C)),
inference(resolve,[status(thm)],[c_9759,c_49]) ).
cnf(c_9760,plain,
( is_a_theorem(A)
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(equivalent(equivalent(C,D),E),D),C),E)),B)) ),
inference(resolve,[status(thm)],[c_1,c_48]) ).
cnf(c_1036,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(B,A))),
inference(resolve,[status(thm)],[c_9760,c_726]) ).
cnf(c_1057,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(A,equivalent(B,C)),equivalent(C,B)))),
inference(resolve,[status(thm)],[c_1036,c_4]) ).
cnf(c_1058,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1036,c_1]) ).
cnf(c_2286,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),equivalent(C,B)),A)),
inference(resolve,[status(thm)],[c_1057,c_1058]) ).
cnf(c_9761,plain,
( is_a_theorem(B)
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(equivalent(C,D),A),D),C))) ),
inference(resolve,[status(thm)],[c_1,c_108]) ).
cnf(c_4716,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(B,C),A),C))),
inference(resolve,[status(thm)],[c_9761,c_209]) ).
cnf(c_9762,plain,
( is_a_theorem(D)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),C),B),A),C),D)) ),
inference(resolve,[status(thm)],[c_1,c_64]) ).
cnf(c_5165,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),equivalent(B,A)),C)),
inference(resolve,[status(thm)],[c_9762,c_2286]) ).
cnf(c_9763,plain,
( is_a_theorem(C)
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(B,A))) ),
inference(resolve,[status(thm)],[c_1,c_5165]) ).
cnf(c_8616,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(B,A),C))),
inference(resolve,[status(thm)],[c_9763,c_726]) ).
cnf(c_9764,plain,
( is_a_theorem(equivalent(equivalent(B,A),C))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_8616]) ).
cnf(c_8660,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(C,B),A))),
inference(resolve,[status(thm)],[c_9764,c_8616]) ).
cnf(c_9765,plain,
( is_a_theorem(equivalent(equivalent(C,B),A))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_8660]) ).
cnf(c_9032,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(A,equivalent(C,B)))),
inference(resolve,[status(thm)],[c_9765,c_8660]) ).
cnf(c_9766,plain,
( is_a_theorem(equivalent(A,equivalent(C,B)))
| ~ is_a_theorem(equivalent(A,equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_9032]) ).
cnf(c_9746,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(C,equivalent(equivalent(B,C),A)))),
inference(resolve,[status(thm)],[c_9766,c_4716]) ).
cnf(c_9747,plain,
$false,
inference(resolve,[status(thm)],[c_9746,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n003.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 21:45:23 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 1164394 was started by sandbox2 on n003,
% 0.12/0.38 % Fri Sep 25 21:45:23 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 35.71/5.60
% 35.71/5.60 % SZS status Unsatisfiable for theBenchmark
% 35.71/5.60
% 35.71/5.60 % Proof 1 at 3.75 (+ 1.26) seconds.
% 35.71/5.60 % Length of proof is 41.
% 35.71/5.60 % Level of proof is 16.
% 35.71/5.60 % Maximum clause weight is 97.000.
% 35.71/5.60 % Given clauses 372.
% 35.71/5.60
% 35.71/5.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------