%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL123-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 42.35s 5.86s
% Output : CNFRefutation 42.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 17 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 15 |; 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 110 ( 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_4,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(e,equivalent(b,f))),equivalent(a,equivalent(e,equivalent(c,f))))),
file('theBenchmark.p',prove_lg_4) ).
cnf(c_3,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(e,equivalent(b,f))),equivalent(a,equivalent(e,equivalent(c,f))))),
inference(clausify,[status(thm)],[prove_lg_4]) ).
cnf(c_6807,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_5,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_6807,c_2]) ).
cnf(c_6808,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_5,c_1]) ).
cnf(c_6,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,C),equivalent(B,C)))),
inference(resolve,[status(thm)],[c_2,c_6808]) ).
cnf(c_8,plain,
( is_a_theorem(equivalent(equivalent(A,C),equivalent(B,C)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_1]) ).
cnf(c_6809,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_9,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(equivalent(A,D),equivalent(B,D)),C))),
inference(resolve,[status(thm)],[c_6809,c_6]) ).
cnf(c_14,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_9,c_1]) ).
cnf(c_6810,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_9]) ).
cnf(c_16,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),equivalent(equivalent(A,D),equivalent(C,D)))),
inference(resolve,[status(thm)],[c_6810,c_6]) ).
cnf(c_6811,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_16]) ).
cnf(c_23,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(A,B),C))),
inference(resolve,[status(thm)],[c_6811,c_16]) ).
cnf(c_6812,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_16]) ).
cnf(c_24,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_6812,c_5]) ).
cnf(c_25,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),equivalent(D,C)),equivalent(equivalent(A,B),D))),
inference(resolve,[status(thm)],[c_23,c_14]) ).
cnf(c_6813,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_25]) ).
cnf(c_46,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(A,B))),
inference(resolve,[status(thm)],[c_6813,c_23]) ).
cnf(c_48,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),equivalent(A,C))),
inference(resolve,[status(thm)],[c_46,c_14]) ).
cnf(c_152,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(D,C))),E),F),equivalent(equivalent(equivalent(A,equivalent(B,D)),E),F))),
inference(resolve,[status(thm)],[c_24,c_8]) ).
cnf(c_6814,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_24]) ).
cnf(c_161,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),equivalent(D,B)),equivalent(A,equivalent(D,C)))),
inference(resolve,[status(thm)],[c_6814,c_48]) ).
cnf(c_6815,plain,
( is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,D)),E),F))
| ~ is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(D,C))),E),F)) ),
inference(resolve,[status(thm)],[c_1,c_152]) ).
cnf(c_6805,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),equivalent(D,equivalent(B,E))),equivalent(A,equivalent(D,equivalent(C,E))))),
inference(resolve,[status(thm)],[c_6815,c_161]) ).
cnf(c_6806,plain,
$false,
inference(resolve,[status(thm)],[c_6805,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL123-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n008.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Fri Sep 25 21:53:41 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 1996794 was started by sandbox2 on n008,
% 0.19/0.45 % Fri Sep 25 21:53:41 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 42.35/5.86
% 42.35/5.86 % SZS status Unsatisfiable for theBenchmark
% 42.35/5.86
% 42.35/5.86 % Proof 1 at 3.89 (+ 1.47) seconds.
% 42.35/5.86 % Length of proof is 18.
% 42.35/5.86 % Level of proof is 11.
% 42.35/5.86 % Maximum clause weight is 87.000.
% 42.35/5.86 % Given clauses 328.
% 42.35/5.86
% 42.35/5.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------