%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL121-1 : 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 : n009.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 96.26s 22.70s
% Output : CNFRefutation 96.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 3
% Syntax : Number of formulae : 59 ( 31 unt; 0 def)
% Number of atoms : 89 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 32 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 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 : 209 ( 0 sgn 6 !; 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(lg_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : is_a_theorem(equivalent(VAR_0,equivalent(VAR_0,equivalent(equivalent(VAR_1,VAR_2),equivalent(equivalent(VAR_1,VAR_3),equivalent(VAR_2,VAR_3)))))),
file('theBenchmark.p',lg_2) ).
cnf(c_2,plain,
is_a_theorem(equivalent(A,equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(B,D),equivalent(C,D)))))),
inference(clausify,[status(thm)],[lg_2]) ).
fof(prove_lg_1,axiom,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,equivalent(c,c)),b)))),
file('theBenchmark.p',prove_lg_1) ).
cnf(c_3,plain,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,equivalent(c,c)),b)))),
inference(clausify,[status(thm)],[prove_lg_1]) ).
cnf(c_16366,plain,
( is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(B,D),equivalent(C,D)))))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_4,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(B,D),equivalent(C,D))))),equivalent(equivalent(E,F),equivalent(equivalent(E,V6),equivalent(F,V6))))),
inference(resolve,[status(thm)],[c_16366,c_2]) ).
cnf(c_16367,plain,
( is_a_theorem(equivalent(equivalent(E,F),equivalent(equivalent(E,V6),equivalent(F,V6))))
| ~ is_a_theorem(equivalent(A,equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(B,D),equivalent(C,D)))))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_6,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,C),equivalent(B,C)))),
inference(resolve,[status(thm)],[c_16367,c_2]) ).
cnf(c_16368,plain,
( is_a_theorem(equivalent(equivalent(A,C),equivalent(B,C)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_7,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(equivalent(A,D),equivalent(B,D)),C))),
inference(resolve,[status(thm)],[c_16368,c_6]) ).
cnf(c_16369,plain,
( is_a_theorem(equivalent(equivalent(equivalent(A,D),equivalent(B,D)),C))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_14,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),equivalent(equivalent(A,D),equivalent(C,D)))),
inference(resolve,[status(thm)],[c_16369,c_6]) ).
cnf(c_16370,plain,
( is_a_theorem(equivalent(equivalent(A,D),equivalent(C,D)))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(C,B))) ),
inference(resolve,[status(thm)],[c_1,c_14]) ).
cnf(c_17,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(A,B),C))),
inference(resolve,[status(thm)],[c_16370,c_14]) ).
cnf(c_16371,plain,
( is_a_theorem(equivalent(equivalent(equivalent(A,D),equivalent(B,D)),C))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_18,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,B),C)),equivalent(equivalent(A,E),equivalent(D,E)))),
inference(resolve,[status(thm)],[c_16371,c_14]) ).
cnf(c_16372,plain,
( is_a_theorem(equivalent(equivalent(A,D),equivalent(C,D)))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(C,B))) ),
inference(resolve,[status(thm)],[c_1,c_14]) ).
cnf(c_21,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(D,C))),E),equivalent(equivalent(A,equivalent(B,D)),E))),
inference(resolve,[status(thm)],[c_16372,c_4]) ).
cnf(c_16373,plain,
( is_a_theorem(equivalent(equivalent(equivalent(A,D),equivalent(B,D)),C))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_22,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),equivalent(D,C)),equivalent(equivalent(A,B),D))),
inference(resolve,[status(thm)],[c_16373,c_17]) ).
cnf(c_16374,plain,
( is_a_theorem(equivalent(equivalent(A,B),D))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(D,C))) ),
inference(resolve,[status(thm)],[c_1,c_22]) ).
cnf(c_30,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(A,B))),
inference(resolve,[status(thm)],[c_16374,c_17]) ).
cnf(c_16375,plain,
( is_a_theorem(equivalent(equivalent(A,B),D))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(D,C))) ),
inference(resolve,[status(thm)],[c_1,c_22]) ).
cnf(c_31,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(D,C))),equivalent(A,equivalent(B,D)))),
inference(resolve,[status(thm)],[c_16375,c_4]) ).
cnf(c_16376,plain,
( is_a_theorem(equivalent(equivalent(equivalent(A,D),equivalent(B,D)),C))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_32,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),equivalent(A,C))),
inference(resolve,[status(thm)],[c_16376,c_30]) ).
cnf(c_16377,plain,
( is_a_theorem(equivalent(equivalent(A,C),equivalent(B,C)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_35,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),D),equivalent(equivalent(A,C),D))),
inference(resolve,[status(thm)],[c_16377,c_32]) ).
cnf(c_16378,plain,
( is_a_theorem(equivalent(A,C))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(C,B))) ),
inference(resolve,[status(thm)],[c_1,c_32]) ).
cnf(c_37,plain,
is_a_theorem(equivalent(A,A)),
inference(resolve,[status(thm)],[c_16378,c_30]) ).
cnf(c_16379,plain,
( is_a_theorem(equivalent(A,equivalent(B,D)))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(D,C)))) ),
inference(resolve,[status(thm)],[c_1,c_31]) ).
cnf(c_41,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(C,D),equivalent(B,D))),equivalent(A,C))),
inference(resolve,[status(thm)],[c_16379,c_31]) ).
cnf(c_16380,plain,
( is_a_theorem(equivalent(A,equivalent(B,D)))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(D,C)))) ),
inference(resolve,[status(thm)],[c_1,c_31]) ).
cnf(c_44,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,equivalent(B,D))),equivalent(equivalent(A,D),C))),
inference(resolve,[status(thm)],[c_16380,c_7]) ).
cnf(c_16381,plain,
( is_a_theorem(equivalent(equivalent(A,C),D))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),D)) ),
inference(resolve,[status(thm)],[c_1,c_35]) ).
cnf(c_48,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(A,D),equivalent(C,equivalent(D,B))))),
inference(resolve,[status(thm)],[c_16381,c_35]) ).
cnf(c_16382,plain,
( is_a_theorem(equivalent(A,equivalent(B,D)))
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(D,C)))) ),
inference(resolve,[status(thm)],[c_1,c_31]) ).
cnf(c_49,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),equivalent(D,C)),equivalent(A,D))),
inference(resolve,[status(thm)],[c_16382,c_35]) ).
cnf(c_16383,plain,
( is_a_theorem(equivalent(A,D))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),equivalent(D,C))) ),
inference(resolve,[status(thm)],[c_1,c_49]) ).
cnf(c_102,plain,
is_a_theorem(equivalent(A,equivalent(A,equivalent(B,B)))),
inference(resolve,[status(thm)],[c_16383,c_31]) ).
cnf(c_16384,plain,
( is_a_theorem(equivalent(equivalent(A,D),equivalent(C,D)))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(C,B))) ),
inference(resolve,[status(thm)],[c_1,c_14]) ).
cnf(c_127,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,equivalent(C,C)),B))),
inference(resolve,[status(thm)],[c_16384,c_102]) ).
cnf(c_16385,plain,
( is_a_theorem(equivalent(equivalent(A,equivalent(C,C)),B))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_127]) ).
cnf(c_216,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,B)),A)),
inference(resolve,[status(thm)],[c_16385,c_37]) ).
cnf(c_16386,plain,
( is_a_theorem(equivalent(equivalent(A,D),C))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(C,equivalent(B,D)))) ),
inference(resolve,[status(thm)],[c_1,c_44]) ).
cnf(c_235,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(B,B),C)),C),A)),
inference(resolve,[status(thm)],[c_16386,c_216]) ).
cnf(c_16387,plain,
( is_a_theorem(equivalent(A,C))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,D),equivalent(B,D)))) ),
inference(resolve,[status(thm)],[c_1,c_41]) ).
cnf(c_236,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(C,C),B)),A)),
inference(resolve,[status(thm)],[c_16387,c_216]) ).
cnf(c_16388,plain,
( is_a_theorem(equivalent(equivalent(A,D),equivalent(C,equivalent(D,B))))
| ~ is_a_theorem(equivalent(equivalent(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_48]) ).
cnf(c_474,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(B,B),C)),D),equivalent(A,equivalent(D,C)))),
inference(resolve,[status(thm)],[c_16388,c_235]) ).
cnf(c_16389,plain,
( is_a_theorem(equivalent(equivalent(A,equivalent(B,D)),E))
| ~ is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(D,C))),E)) ),
inference(resolve,[status(thm)],[c_1,c_21]) ).
cnf(c_1376,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),equivalent(C,B)),A)),
inference(resolve,[status(thm)],[c_16389,c_236]) ).
cnf(c_16390,plain,
( is_a_theorem(equivalent(equivalent(A,E),equivalent(D,E)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,B),C))) ),
inference(resolve,[status(thm)],[c_1,c_18]) ).
cnf(c_1429,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,equivalent(B,C)),equivalent(C,B)),D),equivalent(A,D))),
inference(resolve,[status(thm)],[c_16390,c_1376]) ).
cnf(c_16391,plain,
( is_a_theorem(equivalent(A,D))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),equivalent(C,B)),D)) ),
inference(resolve,[status(thm)],[c_1,c_1429]) ).
cnf(c_16364,plain,
is_a_theorem(equivalent(A,equivalent(A,equivalent(equivalent(B,equivalent(C,C)),B)))),
inference(resolve,[status(thm)],[c_16391,c_474]) ).
cnf(c_16365,plain,
$false,
inference(resolve,[status(thm)],[c_16364,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL121-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/10.44 % Computer : n009.cluster.edu
% 0.17/10.44 % Model : x86_64 x86_64
% 0.17/10.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.44 % Memory : 8046.5625MB
% 0.17/10.44 % OS : Linux 6.8.0-71-generic
% 0.17/10.44 % CPULimit : 300
% 0.17/10.44 % WCLimit : 300
% 0.17/10.44 % DateTime : Fri Sep 25 21:53:24 UTC 2026
% 0.17/10.45 % CPUTime :
% 0.17/10.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/10.45 % Process 2638657 was started by sandbox2 on n009,
% 0.17/10.45 % Fri Sep 25 21:53:24 2026
% 0.17/10.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/10.46
% 0.17/10.46 % From the command line: assign(max_seconds, 300).
% 96.26/22.70
% 96.26/22.70 % SZS status Unsatisfiable for theBenchmark
% 96.26/22.70
% 96.26/22.70 % Proof 1 at 10.56 (+ 1.61) seconds.
% 96.26/22.70 % Length of proof is 30.
% 96.26/22.70 % Level of proof is 18.
% 96.26/22.70 % Maximum clause weight is 28.000.
% 96.26/22.70 % Given clauses 340.
% 96.26/22.70
% 96.26/22.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------