%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL115-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 07:58:02 AM UTC 2026
% Result : Unsatisfiable 0.14s 5.63s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 27 unt; 0 def)
% Number of atoms : 65 ( 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 99 ( 21 sgn 11 !; 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(mv_1,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(VAR_0,implies(VAR_1,VAR_0))),
file('theBenchmark.p',mv_1) ).
cnf(c_2,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(clausify,[status(thm)],[mv_1]) ).
fof(mv_2,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(implies(implies(VAR_0,VAR_1),implies(implies(VAR_1,VAR_2),implies(VAR_0,VAR_2)))),
file('theBenchmark.p',mv_2) ).
cnf(c_3,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(clausify,[status(thm)],[mv_2]) ).
fof(mv_3,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(implies(implies(VAR_0,VAR_1),VAR_1),implies(implies(VAR_1,VAR_0),VAR_0))),
file('theBenchmark.p',mv_3) ).
cnf(c_4,plain,
is_a_theorem(implies(implies(implies(A,B),B),implies(implies(B,A),A))),
inference(clausify,[status(thm)],[mv_3]) ).
fof(mv_5,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(implies(not(VAR_0),not(VAR_1)),implies(VAR_1,VAR_0))),
file('theBenchmark.p',mv_5) ).
cnf(c_5,plain,
is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))),
inference(clausify,[status(thm)],[mv_5]) ).
fof(prove_mv_39,axiom,
~ is_a_theorem(implies(not(implies(a,b)),not(b))),
file('theBenchmark.p',prove_mv_39) ).
cnf(c_6,plain,
~ is_a_theorem(implies(not(implies(a,b)),not(b))),
inference(clausify,[status(thm)],[prove_mv_39]) ).
cnf(c_313,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_7,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))),
inference(resolve,[status(thm)],[c_313,c_2]) ).
cnf(c_314,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_8,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_314,c_2]) ).
cnf(c_315,plain,
( is_a_theorem(implies(implies(B,A),A))
| ~ is_a_theorem(implies(implies(A,B),B)) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_10,plain,
is_a_theorem(implies(implies(implies(A,implies(B,A)),C),C)),
inference(resolve,[status(thm)],[c_315,c_7]) ).
cnf(c_316,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_14,plain,
is_a_theorem(implies(not(A),implies(A,B))),
inference(resolve,[status(thm)],[c_316,c_5]) ).
cnf(c_317,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_15,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_317,c_4]) ).
cnf(c_318,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_18,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))),
inference(resolve,[status(thm)],[c_318,c_14]) ).
cnf(c_319,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_30,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_319,c_10]) ).
cnf(c_320,plain,
( is_a_theorem(implies(implies(A,B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_15]) ).
cnf(c_33,plain,
is_a_theorem(implies(implies(implies(A,A),B),B)),
inference(resolve,[status(thm)],[c_320,c_30]) ).
cnf(c_321,plain,
( is_a_theorem(implies(not(A),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_18]) ).
cnf(c_44,plain,
is_a_theorem(implies(not(implies(A,A)),B)),
inference(resolve,[status(thm)],[c_321,c_33]) ).
cnf(c_322,plain,
( is_a_theorem(implies(not(A),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_18]) ).
cnf(c_50,plain,
is_a_theorem(implies(not(not(A)),implies(B,A))),
inference(resolve,[status(thm)],[c_322,c_5]) ).
cnf(c_323,plain,
( is_a_theorem(implies(implies(A,B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_15]) ).
cnf(c_53,plain,
is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),C)),
inference(resolve,[status(thm)],[c_323,c_44]) ).
cnf(c_324,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_60,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(not(B)),C))),
inference(resolve,[status(thm)],[c_324,c_50]) ).
cnf(c_325,plain,
( is_a_theorem(implies(not(not(B)),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_60]) ).
cnf(c_174,plain,
is_a_theorem(implies(not(not(A)),A)),
inference(resolve,[status(thm)],[c_325,c_53]) ).
cnf(c_326,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(implies(not(A),not(B))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_186,plain,
is_a_theorem(implies(A,not(not(A)))),
inference(resolve,[status(thm)],[c_326,c_174]) ).
cnf(c_327,plain,
( is_a_theorem(implies(not(not(B)),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_60]) ).
cnf(c_194,plain,
is_a_theorem(implies(not(not(A)),not(not(implies(B,A))))),
inference(resolve,[status(thm)],[c_327,c_186]) ).
cnf(c_328,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(implies(not(A),not(B))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_311,plain,
is_a_theorem(implies(not(implies(A,B)),not(B))),
inference(resolve,[status(thm)],[c_328,c_194]) ).
cnf(c_312,plain,
$false,
inference(resolve,[status(thm)],[c_311,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL115-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n018.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Fri Sep 25 21:55:11 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 2933543 was started by sandbox on n018,
% 0.10/5.38 % Fri Sep 25 21:55:11 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.39
% 0.10/5.39 % From the command line: assign(max_seconds, 300).
% 0.14/5.63
% 0.14/5.63 % SZS status Unsatisfiable for theBenchmark
% 0.14/5.63
% 0.14/5.63 % Proof 1 at 0.12 (+ 0.09) seconds.
% 0.14/5.63 % Length of proof is 23.
% 0.14/5.63 % Level of proof is 11.
% 0.14/5.63 % Maximum clause weight is 30.000.
% 0.14/5.63 % Given clauses 123.
% 0.14/5.63
% 0.14/5.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------