%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL024-1 : 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 167.64s 22.73s
% Output : CNFRefutation 167.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 3
% Syntax : Number of formulae : 57 ( 30 unt; 0 def)
% Number of atoms : 86 ( 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 : 193 ( 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(xgk,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(equivalent(VAR_0,equivalent(equivalent(VAR_1,equivalent(VAR_2,VAR_0)),equivalent(VAR_2,VAR_1)))),
file('theBenchmark.p',xgk) ).
cnf(c_2,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,equivalent(C,A)),equivalent(C,B)))),
inference(clausify,[status(thm)],[xgk]) ).
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_31742,plain,
( is_a_theorem(equivalent(equivalent(B,equivalent(C,A)),equivalent(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_4,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,equivalent(C,equivalent(equivalent(D,equivalent(E,C)),equivalent(E,D))))),equivalent(B,A))),
inference(resolve,[status(thm)],[c_31742,c_2]) ).
cnf(c_31743,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,equivalent(B,equivalent(C,equivalent(equivalent(D,equivalent(E,C)),equivalent(E,D)))))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_7,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,equivalent(B,C)),equivalent(B,A)),equivalent(C,D)),D)),
inference(resolve,[status(thm)],[c_31743,c_2]) ).
cnf(c_31744,plain,
( is_a_theorem(D)
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),equivalent(B,A)),equivalent(C,D))) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_8,plain,
is_a_theorem(equivalent(A,A)),
inference(resolve,[status(thm)],[c_31744,c_7]) ).
cnf(c_31745,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,equivalent(B,equivalent(C,equivalent(equivalent(D,equivalent(E,C)),equivalent(E,D)))))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_9,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(B,equivalent(C,D)),equivalent(C,B)),equivalent(D,equivalent(A,equivalent(E,equivalent(equivalent(F,equivalent(V6,E)),equivalent(V6,F)))))))),
inference(resolve,[status(thm)],[c_31745,c_7]) ).
cnf(c_31746,plain,
( is_a_theorem(equivalent(equivalent(B,equivalent(C,A)),equivalent(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_13,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,equivalent(C,C))),equivalent(B,A))),
inference(resolve,[status(thm)],[c_31746,c_8]) ).
cnf(c_31747,plain,
( is_a_theorem(equivalent(equivalent(B,equivalent(C,A)),equivalent(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_17,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,equivalent(equivalent(C,equivalent(D,equivalent(E,E))),equivalent(D,C)))),equivalent(B,A))),
inference(resolve,[status(thm)],[c_31747,c_13]) ).
cnf(c_31748,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,equivalent(B,equivalent(C,C)))) ),
inference(resolve,[status(thm)],[c_1,c_13]) ).
cnf(c_21,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(A,B)),B)),
inference(resolve,[status(thm)],[c_31748,c_2]) ).
cnf(c_31749,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,equivalent(B,equivalent(C,C)))) ),
inference(resolve,[status(thm)],[c_1,c_13]) ).
cnf(c_42,plain,
is_a_theorem(equivalent(A,equivalent(B,equivalent(B,equivalent(A,equivalent(C,C)))))),
inference(resolve,[status(thm)],[c_31749,c_21]) ).
cnf(c_31750,plain,
( is_a_theorem(equivalent(equivalent(B,equivalent(C,A)),equivalent(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_45,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,equivalent(equivalent(C,equivalent(C,D)),D))),equivalent(B,A))),
inference(resolve,[status(thm)],[c_31750,c_21]) ).
cnf(c_31751,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,equivalent(B,equivalent(C,equivalent(equivalent(D,equivalent(E,C)),equivalent(E,D)))))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_101,plain,
is_a_theorem(equivalent(A,equivalent(B,equivalent(B,A)))),
inference(resolve,[status(thm)],[c_31751,c_42]) ).
cnf(c_31752,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,equivalent(B,equivalent(C,equivalent(equivalent(D,equivalent(E,C)),equivalent(E,D)))))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_135,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),equivalent(B,A)),equivalent(equivalent(equivalent(D,equivalent(E,F)),equivalent(E,D)),equivalent(F,C)))),
inference(resolve,[status(thm)],[c_31752,c_9]) ).
cnf(c_31753,plain,
( is_a_theorem(equivalent(equivalent(B,equivalent(C,A)),equivalent(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_159,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,equivalent(C,equivalent(D,equivalent(D,C))))),equivalent(B,A))),
inference(resolve,[status(thm)],[c_31753,c_101]) ).
cnf(c_31754,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,equivalent(B,equivalent(equivalent(C,equivalent(D,equivalent(E,E))),equivalent(D,C))))) ),
inference(resolve,[status(thm)],[c_1,c_17]) ).
cnf(c_741,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(B,equivalent(A,equivalent(C,C))),D)),D)),
inference(resolve,[status(thm)],[c_31754,c_2]) ).
cnf(c_31755,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,equivalent(B,equivalent(equivalent(C,equivalent(C,D)),D)))) ),
inference(resolve,[status(thm)],[c_1,c_45]) ).
cnf(c_796,plain,
is_a_theorem(equivalent(A,equivalent(B,equivalent(B,equivalent(A,equivalent(equivalent(C,equivalent(C,D)),D)))))),
inference(resolve,[status(thm)],[c_31755,c_21]) ).
cnf(c_31756,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,equivalent(B,equivalent(C,equivalent(D,equivalent(D,C)))))) ),
inference(resolve,[status(thm)],[c_1,c_159]) ).
cnf(c_2102,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(A,B)),equivalent(B,C)),C)),
inference(resolve,[status(thm)],[c_31756,c_2]) ).
cnf(c_31757,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,equivalent(B,equivalent(C,equivalent(equivalent(D,equivalent(E,C)),equivalent(E,D)))))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_12246,plain,
is_a_theorem(equivalent(A,equivalent(B,equivalent(equivalent(C,equivalent(C,B)),A)))),
inference(resolve,[status(thm)],[c_31757,c_796]) ).
cnf(c_31758,plain,
( is_a_theorem(C)
| ~ is_a_theorem(equivalent(equivalent(A,equivalent(A,B)),equivalent(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_2102]) ).
cnf(c_12424,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(A,B)),equivalent(C,equivalent(C,B)))),
inference(resolve,[status(thm)],[c_31758,c_12246]) ).
cnf(c_31759,plain,
( is_a_theorem(D)
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(B,equivalent(A,equivalent(C,C))),D))) ),
inference(resolve,[status(thm)],[c_1,c_741]) ).
cnf(c_12664,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,equivalent(C,C))),B)),
inference(resolve,[status(thm)],[c_31759,c_12424]) ).
cnf(c_31760,plain,
( is_a_theorem(B)
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(A,equivalent(C,C)))) ),
inference(resolve,[status(thm)],[c_1,c_12664]) ).
cnf(c_19773,plain,
is_a_theorem(equivalent(A,equivalent(B,equivalent(A,B)))),
inference(resolve,[status(thm)],[c_31760,c_135]) ).
cnf(c_31761,plain,
( is_a_theorem(equivalent(equivalent(B,equivalent(C,A)),equivalent(C,B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_19897,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,equivalent(C,equivalent(D,equivalent(C,D))))),equivalent(B,A))),
inference(resolve,[status(thm)],[c_31761,c_19773]) ).
cnf(c_31762,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,equivalent(B,equivalent(C,equivalent(D,equivalent(C,D)))))) ),
inference(resolve,[status(thm)],[c_1,c_19897]) ).
cnf(c_22297,plain,
is_a_theorem(equivalent(A,equivalent(B,equivalent(B,equivalent(C,equivalent(A,C)))))),
inference(resolve,[status(thm)],[c_31762,c_12424]) ).
cnf(c_31763,plain,
( is_a_theorem(equivalent(B,A))
| ~ is_a_theorem(equivalent(A,equivalent(B,equivalent(equivalent(C,equivalent(D,equivalent(E,E))),equivalent(D,C))))) ),
inference(resolve,[status(thm)],[c_1,c_17]) ).
cnf(c_23118,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(B,equivalent(C,C))),A)),
inference(resolve,[status(thm)],[c_31763,c_22297]) ).
cnf(c_31764,plain,
( is_a_theorem(A)
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(B,equivalent(C,C)))) ),
inference(resolve,[status(thm)],[c_1,c_23118]) ).
cnf(c_24637,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(B,equivalent(A,C)),C))),
inference(resolve,[status(thm)],[c_31764,c_135]) ).
cnf(c_31765,plain,
( is_a_theorem(equivalent(equivalent(B,equivalent(A,C)),C))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_24637]) ).
cnf(c_24886,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,equivalent(B,C)),C),equivalent(equivalent(B,A),D)),D)),
inference(resolve,[status(thm)],[c_31765,c_24637]) ).
cnf(c_31766,plain,
( is_a_theorem(D)
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),C),equivalent(equivalent(B,A),D))) ),
inference(resolve,[status(thm)],[c_1,c_24886]) ).
cnf(c_31740,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),C),equivalent(B,A))),
inference(resolve,[status(thm)],[c_31766,c_19773]) ).
cnf(c_31741,plain,
$false,
inference(resolve,[status(thm)],[c_31740,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL024-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n003.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 25 21:45:53 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 1165250 was started by sandbox2 on n003,
% 0.10/0.38 % Fri Sep 25 21:45:53 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 167.64/22.73
% 167.64/22.73 % given #500 (T,wt=16): 12798 is_a_theorem(equivalent(equivalent(A,A),equivalent(B,equivalent(C,equivalent(C,equivalent(D,equivalent(D,B))))))). [hyper(1,a,9683,a,b,12463,a)].
% 167.64/22.73
% 167.64/22.73 % given #1000 (T,wt=16): 22048 is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,equivalent(B,A)),C)),equivalent(equivalent(D,D),C))). [hyper(1,a,45,a,b,19505,a)].
% 167.64/22.73
% 167.64/22.73 % SZS status Unsatisfiable for theBenchmark
% 167.64/22.73
% 167.64/22.73 % Proof 1 at 15.76 (+ 6.35) seconds.
% 167.64/22.73 % Length of proof is 29.
% 167.64/22.73 % Level of proof is 19.
% 167.64/22.73 % Maximum clause weight is 28.000.
% 167.64/22.73 % Given clauses 1312.
% 167.64/22.73
% 167.64/22.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------