%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL116-1 : 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 : n006.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 32.07s 5.22s
% Output : CNFRefutation 32.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 71 ( 40 unt; 0 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 68 ( 35 ~; 33 |; 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 : 183 ( 18 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_50,axiom,
~ is_a_theorem(implies(not(a),implies(b,not(implies(b,a))))),
file('theBenchmark.p',prove_mv_50) ).
cnf(c_6,plain,
~ is_a_theorem(implies(not(a),implies(b,not(implies(b,a))))),
inference(clausify,[status(thm)],[prove_mv_50]) ).
cnf(c_25137,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(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))),
inference(resolve,[status(thm)],[c_25137,c_3]) ).
cnf(c_25138,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(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_25138,c_2]) ).
cnf(c_25139,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_11,plain,
is_a_theorem(implies(implies(implies(implies(A,B),B),C),implies(implies(implies(B,A),A),C))),
inference(resolve,[status(thm)],[c_25139,c_4]) ).
cnf(c_25140,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_13,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(not(B),not(A)),C))),
inference(resolve,[status(thm)],[c_25140,c_5]) ).
cnf(c_25141,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_14,plain,
is_a_theorem(implies(A,implies(implies(not(B),not(C)),implies(C,B)))),
inference(resolve,[status(thm)],[c_25141,c_5]) ).
cnf(c_25142,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_8]) ).
cnf(c_18,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(D,B),implies(A,implies(D,C))))),
inference(resolve,[status(thm)],[c_25142,c_8]) ).
cnf(c_25143,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_8]) ).
cnf(c_21,plain,
is_a_theorem(implies(implies(A,B),implies(implies(implies(A,C),D),implies(implies(B,C),D)))),
inference(resolve,[status(thm)],[c_25143,c_3]) ).
cnf(c_25144,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_28,plain,
is_a_theorem(implies(not(A),implies(A,B))),
inference(resolve,[status(thm)],[c_25144,c_5]) ).
cnf(c_25145,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_29,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_25145,c_4]) ).
cnf(c_25146,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_32,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))),
inference(resolve,[status(thm)],[c_25146,c_28]) ).
cnf(c_25147,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_33,plain,
is_a_theorem(implies(A,implies(not(B),implies(B,C)))),
inference(resolve,[status(thm)],[c_25147,c_28]) ).
cnf(c_25148,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_37,plain,
is_a_theorem(implies(implies(implies(implies(A,B),B),C),implies(A,C))),
inference(resolve,[status(thm)],[c_25148,c_29]) ).
cnf(c_25149,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_11]) ).
cnf(c_87,plain,
is_a_theorem(implies(implies(implies(A,B),B),implies(A,A))),
inference(resolve,[status(thm)],[c_25149,c_10]) ).
cnf(c_25150,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_11]) ).
cnf(c_88,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_25150,c_8]) ).
cnf(c_25151,plain,
( is_a_theorem(implies(A,A))
| ~ is_a_theorem(implies(implies(A,B),B)) ),
inference(resolve,[status(thm)],[c_1,c_87]) ).
cnf(c_120,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_25151,c_33]) ).
cnf(c_25152,plain,
( is_a_theorem(implies(implies(A,B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_29]) ).
cnf(c_123,plain,
is_a_theorem(implies(implies(implies(A,A),B),B)),
inference(resolve,[status(thm)],[c_25152,c_120]) ).
cnf(c_25153,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_13]) ).
cnf(c_133,plain,
is_a_theorem(implies(implies(not(A),not(implies(B,B))),A)),
inference(resolve,[status(thm)],[c_25153,c_123]) ).
cnf(c_25154,plain,
( is_a_theorem(implies(not(A),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_32]) ).
cnf(c_212,plain,
is_a_theorem(implies(not(not(A)),A)),
inference(resolve,[status(thm)],[c_25154,c_133]) ).
cnf(c_25155,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_18]) ).
cnf(c_243,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_25155,c_29]) ).
cnf(c_25156,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_18]) ).
cnf(c_245,plain,
is_a_theorem(implies(implies(A,implies(not(B),not(C))),implies(D,implies(A,implies(C,B))))),
inference(resolve,[status(thm)],[c_25156,c_14]) ).
cnf(c_25157,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_271,plain,
is_a_theorem(implies(A,not(not(A)))),
inference(resolve,[status(thm)],[c_25157,c_212]) ).
cnf(c_25158,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_292,plain,
is_a_theorem(implies(A,implies(B,not(not(B))))),
inference(resolve,[status(thm)],[c_25158,c_271]) ).
cnf(c_25159,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_21]) ).
cnf(c_365,plain,
is_a_theorem(implies(implies(implies(not(not(A)),B),C),implies(implies(A,B),C))),
inference(resolve,[status(thm)],[c_25159,c_212]) ).
cnf(c_25160,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_88]) ).
cnf(c_4698,plain,
is_a_theorem(implies(implies(A,B),implies(A,not(not(B))))),
inference(resolve,[status(thm)],[c_25160,c_292]) ).
cnf(c_25161,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_245]) ).
cnf(c_18503,plain,
is_a_theorem(implies(A,implies(implies(not(B),C),implies(not(C),B)))),
inference(resolve,[status(thm)],[c_25161,c_4698]) ).
cnf(c_25162,plain,
( is_a_theorem(implies(implies(not(B),C),implies(not(C),B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_18503]) ).
cnf(c_18548,plain,
is_a_theorem(implies(implies(not(A),B),implies(not(B),A))),
inference(resolve,[status(thm)],[c_25162,c_18503]) ).
cnf(c_25163,plain,
( is_a_theorem(implies(implies(A,B),C))
| ~ is_a_theorem(implies(implies(not(not(A)),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_365]) ).
cnf(c_24583,plain,
is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))),
inference(resolve,[status(thm)],[c_25163,c_18548]) ).
cnf(c_25164,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(implies(A,B),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_37]) ).
cnf(c_24681,plain,
is_a_theorem(implies(A,implies(not(B),not(implies(A,B))))),
inference(resolve,[status(thm)],[c_25164,c_24583]) ).
cnf(c_25165,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_243]) ).
cnf(c_25135,plain,
is_a_theorem(implies(not(A),implies(B,not(implies(B,A))))),
inference(resolve,[status(thm)],[c_25165,c_24681]) ).
cnf(c_25136,plain,
$false,
inference(resolve,[status(thm)],[c_25135,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL116-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.58 % Computer : n006.cluster.edu
% 0.11/0.58 % Model : x86_64 x86_64
% 0.11/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.58 % Memory : 8046.5625MB
% 0.11/0.58 % OS : Linux 6.8.0-71-generic
% 0.11/0.58 % CPULimit : 300
% 0.11/0.58 % WCLimit : 300
% 0.11/0.58 % DateTime : Fri Sep 25 21:52:26 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.58 % Process 3836087 was started by sandbox2 on n006,
% 0.11/0.58 % Fri Sep 25 21:52:26 2026
% 0.11/0.58 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.58
% 0.11/0.58 % From the command line: assign(max_seconds, 300).
% 32.07/5.22
% 32.07/5.22 % given #500 (W,wt=52): 4926 is_a_theorem(implies(not(implies(A,not(not(implies(B,C))))),not(C))). [hyper(1,a,4690,a,b,440,a)].
% 32.07/5.22
% 32.07/5.22 % SZS status Unsatisfiable for theBenchmark
% 32.07/5.22
% 32.07/5.22 % Proof 1 at 3.14 (+ 1.45) seconds.
% 32.07/5.22 % Length of proof is 36.
% 32.07/5.22 % Level of proof is 16.
% 32.07/5.22 % Maximum clause weight is 85.000.
% 32.07/5.22 % Given clauses 814.
% 32.07/5.22
% 32.07/5.22 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------