%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL131-1 : 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 : n018.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 07:58:04 AM UTC 2026
% Result : Unsatisfiable 0.13s 10.86s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 43 ( 23 unt; 0 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 24 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 144 ( 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(s_6,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : is_a_theorem(equivalent(equivalent(VAR_0,equivalent(equivalent(equivalent(VAR_1,VAR_2),equivalent(VAR_3,VAR_2)),equivalent(VAR_1,VAR_3))),VAR_0)),
file('theBenchmark.p',s_6) ).
cnf(c_2,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(D,C)),equivalent(B,D))),A)),
inference(clausify,[status(thm)],[s_6]) ).
fof(prove_lg_2,axiom,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))),
file('theBenchmark.p',prove_lg_2) ).
cnf(c_3,plain,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))),
inference(clausify,[status(thm)],[prove_lg_2]) ).
cnf(c_2616,plain,
( is_a_theorem(A)
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(D,C)),equivalent(B,D)))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_4,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),equivalent(A,C)),equivalent(equivalent(equivalent(D,E),equivalent(F,E)),equivalent(D,F)))),
inference(resolve,[status(thm)],[c_2616,c_2]) ).
cnf(c_2617,plain,
( is_a_theorem(A)
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(D,C)),equivalent(B,D)))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_5,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),equivalent(A,C))),
inference(resolve,[status(thm)],[c_2617,c_4]) ).
cnf(c_2618,plain,
( is_a_theorem(A)
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(D,C)),equivalent(B,D)))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),D),equivalent(equivalent(A,C),D))),
inference(resolve,[status(thm)],[c_2618,c_5]) ).
cnf(c_2619,plain,
( is_a_theorem(equivalent(A,C))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(C,B))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_7,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),equivalent(equivalent(A,D),equivalent(C,D)))),
inference(resolve,[status(thm)],[c_2619,c_4]) ).
cnf(c_2620,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_6]) ).
cnf(c_8,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(A,D),equivalent(C,equivalent(D,B))))),
inference(resolve,[status(thm)],[c_2620,c_6]) ).
cnf(c_2621,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_6]) ).
cnf(c_10,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(A,B))),
inference(resolve,[status(thm)],[c_2621,c_5]) ).
cnf(c_2622,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_6]) ).
cnf(c_11,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(D,C))),equivalent(A,equivalent(B,D)))),
inference(resolve,[status(thm)],[c_2622,c_2]) ).
cnf(c_2623,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_6]) ).
cnf(c_12,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,C),equivalent(B,C)))),
inference(resolve,[status(thm)],[c_2623,c_10]) ).
cnf(c_2624,plain,
( is_a_theorem(equivalent(A,C))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(C,B))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_13,plain,
is_a_theorem(equivalent(A,A)),
inference(resolve,[status(thm)],[c_2624,c_10]) ).
cnf(c_2625,plain,
( is_a_theorem(equivalent(equivalent(A,C),equivalent(B,C)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_12]) ).
cnf(c_28,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_2625,c_11]) ).
cnf(c_2626,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_11]) ).
cnf(c_29,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(C,D),equivalent(B,D))),equivalent(A,C))),
inference(resolve,[status(thm)],[c_2626,c_11]) ).
cnf(c_2627,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_6]) ).
cnf(c_31,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(A,equivalent(D,C)),equivalent(B,D)))),
inference(resolve,[status(thm)],[c_2627,c_11]) ).
cnf(c_2628,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_7]) ).
cnf(c_64,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,equivalent(C,C)),B))),
inference(resolve,[status(thm)],[c_2628,c_31]) ).
cnf(c_2629,plain,
( is_a_theorem(equivalent(equivalent(A,equivalent(C,C)),B))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_64]) ).
cnf(c_201,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(B,B)),A)),
inference(resolve,[status(thm)],[c_2629,c_13]) ).
cnf(c_2630,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_29]) ).
cnf(c_240,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(C,C),B)),A)),
inference(resolve,[status(thm)],[c_2630,c_201]) ).
cnf(c_2631,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_28]) ).
cnf(c_470,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),equivalent(C,B)),A)),
inference(resolve,[status(thm)],[c_2631,c_240]) ).
cnf(c_2632,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_8]) ).
cnf(c_740,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(B,C)),D),equivalent(A,equivalent(D,equivalent(C,B))))),
inference(resolve,[status(thm)],[c_2632,c_470]) ).
cnf(c_2633,plain,
( is_a_theorem(equivalent(A,equivalent(D,equivalent(C,B))))
| ~ is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),D)) ),
inference(resolve,[status(thm)],[c_1,c_740]) ).
cnf(c_2614,plain,
is_a_theorem(equivalent(A,equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(B,D),equivalent(C,D)))))),
inference(resolve,[status(thm)],[c_2633,c_2]) ).
cnf(c_2615,plain,
$false,
inference(resolve,[status(thm)],[c_2614,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL131-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/10.37 % Computer : n018.cluster.edu
% 0.08/10.37 % Model : x86_64 x86_64
% 0.08/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.37 % Memory : 8046.5625MB
% 0.08/10.37 % OS : Linux 6.8.0-71-generic
% 0.08/10.37 % CPULimit : 300
% 0.08/10.37 % WCLimit : 300
% 0.08/10.37 % DateTime : Fri Sep 25 21:57:01 UTC 2026
% 0.08/10.37 % CPUTime :
% 0.08/10.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/10.37 % Process 2937836 was started by sandbox2 on n018,
% 0.08/10.37 % Fri Sep 25 21:57:01 2026
% 0.08/10.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/10.38
% 0.08/10.38 % From the command line: assign(max_seconds, 300).
% 0.13/10.86
% 0.13/10.86 % SZS status Unsatisfiable for theBenchmark
% 0.13/10.86
% 0.13/10.86 % Proof 1 at 0.33 (+ 0.14) seconds.
% 0.13/10.86 % Length of proof is 22.
% 0.13/10.86 % Level of proof is 12.
% 0.13/10.86 % Maximum clause weight is 99.000.
% 0.13/10.86 % Given clauses 205.
% 0.13/10.86
% 0.13/10.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------