%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL114-1 : 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 : 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 07:58:01 AM UTC 2026
% Result : Unsatisfiable 57.64s 7.81s
% Output : CNFRefutation 57.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 71 ( 42 unt; 0 def)
% Number of atoms : 102 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 64 ( 33 ~; 31 |; 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 : 186 ( 20 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_36,axiom,
~ is_a_theorem(implies(implies(a,b),implies(not(b),not(a)))),
file('theBenchmark.p',prove_mv_36) ).
cnf(c_6,plain,
~ is_a_theorem(implies(implies(a,b),implies(not(b),not(a)))),
inference(clausify,[status(thm)],[prove_mv_36]) ).
cnf(c_7,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_9,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_3,c_1]) ).
cnf(c_19426,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_10,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))),
inference(resolve,[status(thm)],[c_19426,c_3]) ).
cnf(c_19427,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_12,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_19427,c_2]) ).
cnf(c_19428,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_14,plain,
is_a_theorem(implies(implies(implies(implies(A,B),B),C),implies(implies(implies(B,A),A),C))),
inference(resolve,[status(thm)],[c_19428,c_4]) ).
cnf(c_16,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(implies(not(A),not(B))) ),
inference(resolve,[status(thm)],[c_5,c_1]) ).
cnf(c_19429,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_17,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(not(B),not(A)),C))),
inference(resolve,[status(thm)],[c_19429,c_5]) ).
cnf(c_19430,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_18,plain,
is_a_theorem(implies(A,implies(implies(not(B),not(C)),implies(C,B)))),
inference(resolve,[status(thm)],[c_19430,c_5]) ).
cnf(c_19431,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_12]) ).
cnf(c_25,plain,
is_a_theorem(implies(not(A),implies(A,B))),
inference(resolve,[status(thm)],[c_19431,c_5]) ).
cnf(c_19432,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_12]) ).
cnf(c_26,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_19432,c_4]) ).
cnf(c_29,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))),
inference(resolve,[status(thm)],[c_25,c_9]) ).
cnf(c_30,plain,
is_a_theorem(implies(A,implies(not(B),implies(B,C)))),
inference(resolve,[status(thm)],[c_25,c_7]) ).
cnf(c_19433,plain,
( is_a_theorem(implies(implies(C,A),D))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_35,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(D,B),implies(A,implies(D,C))))),
inference(resolve,[status(thm)],[c_19433,c_10]) ).
cnf(c_19434,plain,
( is_a_theorem(implies(implies(C,A),D))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_36,plain,
is_a_theorem(implies(implies(A,B),implies(implies(implies(A,C),D),implies(implies(B,C),D)))),
inference(resolve,[status(thm)],[c_19434,c_3]) ).
cnf(c_19435,plain,
( is_a_theorem(implies(implies(implies(B,A),A),C))
| ~ is_a_theorem(implies(implies(implies(A,B),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_14]) ).
cnf(c_46,plain,
is_a_theorem(implies(implies(implies(A,B),B),implies(A,A))),
inference(resolve,[status(thm)],[c_19435,c_12]) ).
cnf(c_19436,plain,
( is_a_theorem(implies(implies(implies(B,A),A),C))
| ~ is_a_theorem(implies(implies(implies(A,B),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_14]) ).
cnf(c_47,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),implies(C,B)),implies(implies(A,C),implies(A,B)))),
inference(resolve,[status(thm)],[c_19436,c_10]) ).
cnf(c_54,plain,
( is_a_theorem(implies(implies(A,B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_26,c_1]) ).
cnf(c_110,plain,
is_a_theorem(implies(implies(implies(implies(not(A),not(B)),C),D),implies(implies(implies(B,A),C),D))),
inference(resolve,[status(thm)],[c_17,c_9]) ).
cnf(c_19437,plain,
( is_a_theorem(implies(A,A))
| ~ is_a_theorem(implies(implies(A,B),B)) ),
inference(resolve,[status(thm)],[c_1,c_46]) ).
cnf(c_137,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_19437,c_30]) ).
cnf(c_140,plain,
is_a_theorem(implies(implies(implies(A,A),B),B)),
inference(resolve,[status(thm)],[c_137,c_54]) ).
cnf(c_19438,plain,
( is_a_theorem(implies(implies(not(B),not(A)),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_17]) ).
cnf(c_153,plain,
is_a_theorem(implies(implies(not(A),not(implies(B,B))),A)),
inference(resolve,[status(thm)],[c_19438,c_140]) ).
cnf(c_231,plain,
is_a_theorem(implies(implies(implies(not(A),B),C),implies(implies(implies(A,D),B),C))),
inference(resolve,[status(thm)],[c_29,c_9]) ).
cnf(c_233,plain,
( is_a_theorem(implies(not(A),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_29,c_1]) ).
cnf(c_19439,plain,
( is_a_theorem(implies(implies(D,B),implies(A,implies(D,C))))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_35]) ).
cnf(c_346,plain,
is_a_theorem(implies(implies(A,implies(not(B),not(C))),implies(D,implies(A,implies(C,B))))),
inference(resolve,[status(thm)],[c_19439,c_18]) ).
cnf(c_19440,plain,
( is_a_theorem(implies(implies(implies(A,C),D),implies(implies(B,C),D)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_36]) ).
cnf(c_371,plain,
is_a_theorem(implies(implies(implies(implies(implies(A,A),B),C),D),implies(implies(B,C),D))),
inference(resolve,[status(thm)],[c_19440,c_140]) ).
cnf(c_491,plain,
is_a_theorem(implies(not(not(A)),A)),
inference(resolve,[status(thm)],[c_153,c_233]) ).
cnf(c_507,plain,
is_a_theorem(implies(A,not(not(A)))),
inference(resolve,[status(thm)],[c_491,c_16]) ).
cnf(c_19441,plain,
( is_a_theorem(A)
| ~ is_a_theorem(implies(not(A),not(implies(B,B)))) ),
inference(resolve,[status(thm)],[c_1,c_153]) ).
cnf(c_511,plain,
is_a_theorem(not(not(implies(A,A)))),
inference(resolve,[status(thm)],[c_19441,c_491]) ).
cnf(c_559,plain,
is_a_theorem(implies(A,implies(B,not(not(B))))),
inference(resolve,[status(thm)],[c_507,c_7]) ).
cnf(c_621,plain,
is_a_theorem(implies(implies(not(not(implies(A,A))),B),B)),
inference(resolve,[status(thm)],[c_511,c_54]) ).
cnf(c_19442,plain,
( is_a_theorem(implies(implies(A,C),implies(A,B)))
| ~ is_a_theorem(implies(implies(implies(A,B),implies(C,B)),implies(C,B))) ),
inference(resolve,[status(thm)],[c_1,c_47]) ).
cnf(c_1604,plain,
is_a_theorem(implies(implies(A,B),implies(A,not(not(B))))),
inference(resolve,[status(thm)],[c_19442,c_559]) ).
cnf(c_12307,plain,
( is_a_theorem(implies(implies(implies(A,D),B),C))
| ~ is_a_theorem(implies(implies(not(A),B),C)) ),
inference(resolve,[status(thm)],[c_231,c_1]) ).
cnf(c_17240,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(not(not(implies(A,A))),B)) ),
inference(resolve,[status(thm)],[c_621,c_1]) ).
cnf(c_19443,plain,
( is_a_theorem(implies(D,implies(A,implies(C,B))))
| ~ is_a_theorem(implies(A,implies(not(B),not(C)))) ),
inference(resolve,[status(thm)],[c_1,c_346]) ).
cnf(c_17844,plain,
is_a_theorem(implies(A,implies(implies(not(B),C),implies(not(C),B)))),
inference(resolve,[status(thm)],[c_19443,c_1604]) ).
cnf(c_17873,plain,
is_a_theorem(implies(implies(not(A),B),implies(not(B),A))),
inference(resolve,[status(thm)],[c_17844,c_17240]) ).
cnf(c_17905,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(C),A))),
inference(resolve,[status(thm)],[c_17873,c_12307]) ).
cnf(c_19444,plain,
( is_a_theorem(implies(implies(implies(B,A),C),D))
| ~ is_a_theorem(implies(implies(implies(not(A),not(B)),C),D)) ),
inference(resolve,[status(thm)],[c_1,c_110]) ).
cnf(c_18012,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(C),not(B)))),
inference(resolve,[status(thm)],[c_19444,c_17905]) ).
cnf(c_19445,plain,
( is_a_theorem(implies(implies(B,C),D))
| ~ is_a_theorem(implies(implies(implies(implies(A,A),B),C),D)) ),
inference(resolve,[status(thm)],[c_1,c_371]) ).
cnf(c_19424,plain,
is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))),
inference(resolve,[status(thm)],[c_19445,c_18012]) ).
cnf(c_19425,plain,
$false,
inference(resolve,[status(thm)],[c_19424,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL114-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42 % Computer : n015.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Fri Sep 25 21:55:43 UTC 2026
% 0.18/0.42 % CPUTime :
% 0.18/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.43 % Process 2355144 was started by sandbox on n015,
% 0.18/0.43 % Fri Sep 25 21:55:43 2026
% 0.18/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.43
% 0.18/0.43 % From the command line: assign(max_seconds, 300).
% 57.64/7.81
% 57.64/7.81 % given #500 (W,wt=42): 561 is_a_theorem(not(not(implies(A,not(not(A)))))). [hyper(1,a,507,a,b,507,a)].
% 57.64/7.81
% 57.64/7.81 % SZS status Unsatisfiable for theBenchmark
% 57.64/7.81
% 57.64/7.81 % Proof 1 at 4.36 (+ 2.96) seconds.
% 57.64/7.81 % Length of proof is 45.
% 57.64/7.81 % Level of proof is 16.
% 57.64/7.81 % Maximum clause weight is 61.000.
% 57.64/7.81 % Given clauses 835.
% 57.64/7.81
% 57.64/7.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------