%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL077-1 : 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 : n015.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 07:57:55 AM UTC 2026
% Result : Unsatisfiable 0.90s 0.53s
% Output : CNFRefutation 0.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 25 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 22 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 99 ( 21 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(condensed_detachment,axiom,
! [VAR_0,VAR_1] :
( is_a_theorem(VAR_1)
| ~ is_a_theorem(VAR_0)
| ~ is_a_theorem(implies(VAR_0,VAR_1)) ),
file('theBenchmark.p',condensed_detachment) ).
cnf(c_1,plain,
( is_a_theorem(B)
| ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B)) ),
inference(clausify,[status(thm)],[condensed_detachment]) ).
fof(cn_18,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(VAR_0,implies(VAR_1,VAR_0))),
file('theBenchmark.p',cn_18) ).
cnf(c_2,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(clausify,[status(thm)],[cn_18]) ).
fof(cn_35,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(implies(implies(VAR_0,implies(VAR_1,VAR_2)),implies(implies(VAR_0,VAR_1),implies(VAR_0,VAR_2)))),
file('theBenchmark.p',cn_35) ).
cnf(c_3,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))),
inference(clausify,[status(thm)],[cn_35]) ).
fof(cn_49,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(implies(not(VAR_0),not(VAR_1)),implies(VAR_1,VAR_0))),
file('theBenchmark.p',cn_49) ).
cnf(c_4,plain,
is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))),
inference(clausify,[status(thm)],[cn_49]) ).
fof(prove_cn_39,axiom,
~ is_a_theorem(implies(not(not(a)),a)),
file('theBenchmark.p',prove_cn_39) ).
cnf(c_5,plain,
~ is_a_theorem(implies(not(not(a)),a)),
inference(clausify,[status(thm)],[prove_cn_39]) ).
cnf(c_636,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))),
inference(resolve,[status(thm)],[c_636,c_2]) ).
cnf(c_637,plain,
( is_a_theorem(implies(implies(A,B),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_7,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),implies(A,B)),implies(implies(A,implies(B,C)),implies(A,C)))),
inference(resolve,[status(thm)],[c_637,c_3]) ).
cnf(c_638,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_8,plain,
is_a_theorem(implies(A,implies(implies(B,implies(C,D)),implies(implies(B,C),implies(B,D))))),
inference(resolve,[status(thm)],[c_638,c_3]) ).
cnf(c_639,plain,
( is_a_theorem(implies(implies(A,B),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_9,plain,
is_a_theorem(implies(implies(A,B),implies(A,A))),
inference(resolve,[status(thm)],[c_639,c_2]) ).
cnf(c_640,plain,
( is_a_theorem(implies(implies(A,B),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_10,plain,
is_a_theorem(implies(implies(implies(not(A),not(B)),B),implies(implies(not(A),not(B)),A))),
inference(resolve,[status(thm)],[c_640,c_4]) ).
cnf(c_641,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_11,plain,
is_a_theorem(implies(A,implies(implies(not(B),not(C)),implies(C,B)))),
inference(resolve,[status(thm)],[c_641,c_4]) ).
cnf(c_642,plain,
( is_a_theorem(implies(implies(A,implies(B,C)),implies(A,C)))
| ~ is_a_theorem(implies(implies(A,implies(B,C)),implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_16,plain,
is_a_theorem(implies(implies(A,implies(implies(B,A),C)),implies(A,C))),
inference(resolve,[status(thm)],[c_642,c_6]) ).
cnf(c_643,plain,
( is_a_theorem(implies(A,A))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_20,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_643,c_6]) ).
cnf(c_644,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_22,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_644,c_20]) ).
cnf(c_645,plain,
( is_a_theorem(implies(implies(not(A),not(B)),A))
| ~ is_a_theorem(implies(implies(not(A),not(B)),B)) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_51,plain,
is_a_theorem(implies(implies(not(A),not(implies(B,B))),A)),
inference(resolve,[status(thm)],[c_645,c_22]) ).
cnf(c_646,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(A,implies(implies(B,A),C))) ),
inference(resolve,[status(thm)],[c_1,c_16]) ).
cnf(c_173,plain,
is_a_theorem(implies(not(A),implies(A,B))),
inference(resolve,[status(thm)],[c_646,c_11]) ).
cnf(c_647,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(A,implies(implies(B,A),C))) ),
inference(resolve,[status(thm)],[c_1,c_16]) ).
cnf(c_174,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),
inference(resolve,[status(thm)],[c_647,c_8]) ).
cnf(c_648,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_179,plain,
is_a_theorem(implies(A,implies(not(B),implies(B,C)))),
inference(resolve,[status(thm)],[c_648,c_173]) ).
cnf(c_649,plain,
( is_a_theorem(implies(implies(A,B),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_264,plain,
is_a_theorem(implies(implies(implies(A,B),implies(C,A)),implies(implies(A,B),implies(C,B)))),
inference(resolve,[status(thm)],[c_649,c_174]) ).
cnf(c_650,plain,
( is_a_theorem(implies(implies(A,B),implies(C,B)))
| ~ is_a_theorem(implies(implies(A,B),implies(C,A))) ),
inference(resolve,[status(thm)],[c_1,c_264]) ).
cnf(c_406,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))),
inference(resolve,[status(thm)],[c_650,c_179]) ).
cnf(c_651,plain,
( is_a_theorem(implies(not(A),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_406]) ).
cnf(c_634,plain,
is_a_theorem(implies(not(not(A)),A)),
inference(resolve,[status(thm)],[c_651,c_51]) ).
cnf(c_635,plain,
$false,
inference(resolve,[status(thm)],[c_634,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL077-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 21:52:12 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2346078 was started by sandbox2 on n015,
% 0.09/0.36 % Fri Sep 25 21:52:12 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.90/0.53
% 0.90/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.90/0.53
% 0.90/0.53 % Proof 1 at 0.10 (+ 0.06) seconds.
% 0.90/0.53 % Length of proof is 22.
% 0.90/0.53 % Level of proof is 7.
% 0.90/0.53 % Maximum clause weight is 45.000.
% 0.90/0.53 % Given clauses 68.
% 0.90/0.53
% 0.90/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------