%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL130-1 : 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 07:58:04 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 16 unt; 0 def)
% Number of atoms : 44 ( 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 93 ( 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(p_4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : is_a_theorem(equivalent(equivalent(VAR_0,equivalent(equivalent(VAR_1,VAR_2),equivalent(equivalent(VAR_1,VAR_3),equivalent(VAR_2,VAR_3)))),VAR_0)),
file('theBenchmark.p',p_4) ).
cnf(c_2,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(B,D),equivalent(C,D)))),A)),
inference(clausify,[status(thm)],[p_4]) ).
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_54,plain,
( is_a_theorem(A)
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(B,D),equivalent(C,D))))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_4,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(A,C),equivalent(B,C))),equivalent(equivalent(D,E),equivalent(equivalent(D,F),equivalent(E,F))))),
inference(resolve,[status(thm)],[c_54,c_2]) ).
cnf(c_55,plain,
( is_a_theorem(A)
| ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(B,D),equivalent(C,D))))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_5,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,C),equivalent(B,C)))),
inference(resolve,[status(thm)],[c_55,c_4]) ).
cnf(c_56,plain,
( is_a_theorem(equivalent(equivalent(A,C),equivalent(B,C)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_6,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(equivalent(A,D),equivalent(B,D)),C))),
inference(resolve,[status(thm)],[c_56,c_5]) ).
cnf(c_57,plain,
( is_a_theorem(equivalent(equivalent(A,C),equivalent(B,C)))
| ~ is_a_theorem(equivalent(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_8,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(B,D),equivalent(C,D)))),E),equivalent(A,E))),
inference(resolve,[status(thm)],[c_57,c_2]) ).
cnf(c_58,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_6]) ).
cnf(c_12,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),equivalent(equivalent(A,D),equivalent(C,D)))),
inference(resolve,[status(thm)],[c_58,c_5]) ).
cnf(c_59,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_12]) ).
cnf(c_21,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(A,B),C))),
inference(resolve,[status(thm)],[c_59,c_12]) ).
cnf(c_60,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_6]) ).
cnf(c_31,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),equivalent(D,C)),equivalent(equivalent(A,B),D))),
inference(resolve,[status(thm)],[c_60,c_21]) ).
cnf(c_61,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_31]) ).
cnf(c_35,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(A,B))),
inference(resolve,[status(thm)],[c_61,c_21]) ).
cnf(c_62,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_6]) ).
cnf(c_36,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(C,B)),equivalent(A,C))),
inference(resolve,[status(thm)],[c_62,c_35]) ).
cnf(c_63,plain,
( is_a_theorem(equivalent(A,C))
| ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(C,B))) ),
inference(resolve,[status(thm)],[c_1,c_36]) ).
cnf(c_40,plain,
is_a_theorem(equivalent(A,A)),
inference(resolve,[status(thm)],[c_63,c_35]) ).
cnf(c_64,plain,
( is_a_theorem(equivalent(A,E))
| ~ is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(B,D),equivalent(C,D)))),E)) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_52,plain,
is_a_theorem(equivalent(A,equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(B,D),equivalent(C,D)))))),
inference(resolve,[status(thm)],[c_64,c_40]) ).
cnf(c_53,plain,
$false,
inference(resolve,[status(thm)],[c_52,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL130-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 21:53:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2639468 was started by sandbox2 on n009,
% 0.10/0.37 % Fri Sep 25 21:53:45 2026
% 0.10/0.37 % 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).
% 0.10/0.39
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.10/0.39 % Length of proof is 15.
% 0.10/0.39 % Level of proof is 11.
% 0.10/0.39 % Maximum clause weight is 24.000.
% 0.10/0.39 % Given clauses 15.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------