%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL071-1 : 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 : n019.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 07:57:54 AM UTC 2026
% Result : Unsatisfiable 18.90s 4.18s
% Output : CNFRefutation 18.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 93 ( 50 unt; 0 def)
% Number of atoms : 138 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 92 ( 47 ~; 45 |; 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 : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 260 ( 41 sgn 12 !; 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_19,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(implies(implies(implies(VAR_0,VAR_1),VAR_2),implies(VAR_1,VAR_2))),
file('theBenchmark.p',cn_19) ).
cnf(c_2,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(clausify,[status(thm)],[cn_19]) ).
fof(cn_37,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(implies(implies(implies(VAR_0,VAR_1),VAR_2),implies(not(VAR_0),VAR_2))),
file('theBenchmark.p',cn_37) ).
cnf(c_3,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))),
inference(clausify,[status(thm)],[cn_37]) ).
fof(cn_60,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : is_a_theorem(implies(implies(VAR_0,implies(not(VAR_1),VAR_2)),implies(VAR_0,implies(implies(VAR_3,VAR_2),implies(implies(VAR_1,VAR_3),VAR_2))))),
file('theBenchmark.p',cn_60) ).
cnf(c_4,plain,
is_a_theorem(implies(implies(A,implies(not(B),C)),implies(A,implies(implies(D,C),implies(implies(B,D),C))))),
inference(clausify,[status(thm)],[cn_60]) ).
fof(prove_cn_2,axiom,
~ is_a_theorem(implies(implies(not(a),a),a)),
file('theBenchmark.p',prove_cn_2) ).
cnf(c_5,plain,
~ is_a_theorem(implies(implies(not(a),a),a)),
inference(clausify,[status(thm)],[prove_cn_2]) ).
cnf(c_10110,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolve,[status(thm)],[c_10110,c_2]) ).
cnf(c_10111,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_11,plain,
is_a_theorem(implies(implies(not(A),B),implies(C,implies(implies(D,B),implies(implies(A,D),B))))),
inference(resolve,[status(thm)],[c_10111,c_4]) ).
cnf(c_10112,plain,
( is_a_theorem(implies(A,implies(implies(D,C),implies(implies(B,D),C))))
| ~ is_a_theorem(implies(A,implies(not(B),C))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_12,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(D,C),implies(implies(A,D),C)))),
inference(resolve,[status(thm)],[c_10112,c_3]) ).
cnf(c_10113,plain,
( is_a_theorem(implies(A,implies(implies(D,C),implies(implies(B,D),C))))
| ~ is_a_theorem(implies(A,implies(not(B),C))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_13,plain,
is_a_theorem(implies(implies(implies(A,not(B)),C),implies(implies(D,C),implies(implies(B,D),C)))),
inference(resolve,[status(thm)],[c_10113,c_2]) ).
cnf(c_10114,plain,
( is_a_theorem(implies(not(A),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_16,plain,
is_a_theorem(implies(not(A),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_10114,c_6]) ).
cnf(c_10115,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_17,plain,
is_a_theorem(implies(A,implies(B,implies(C,A)))),
inference(resolve,[status(thm)],[c_10115,c_6]) ).
cnf(c_10116,plain,
( is_a_theorem(implies(implies(D,C),implies(implies(A,D),C)))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_12]) ).
cnf(c_99,plain,
is_a_theorem(implies(implies(A,implies(B,implies(C,implies(D,E)))),implies(implies(D,A),implies(B,implies(C,implies(D,E)))))),
inference(resolve,[status(thm)],[c_10116,c_17]) ).
cnf(c_10117,plain,
( is_a_theorem(implies(implies(D,C),implies(implies(A,D),C)))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_12]) ).
cnf(c_101,plain,
is_a_theorem(implies(implies(A,implies(B,implies(C,D))),implies(implies(C,A),implies(B,implies(C,D))))),
inference(resolve,[status(thm)],[c_10117,c_6]) ).
cnf(c_10118,plain,
( is_a_theorem(implies(implies(D,C),implies(implies(A,D),C)))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_12]) ).
cnf(c_104,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(implies(D,B),A),implies(B,C)))),
inference(resolve,[status(thm)],[c_10118,c_2]) ).
cnf(c_10119,plain,
( is_a_theorem(implies(implies(implies(D,B),A),implies(B,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_104]) ).
cnf(c_124,plain,
is_a_theorem(implies(implies(implies(A,B),not(C)),implies(B,implies(C,D)))),
inference(resolve,[status(thm)],[c_10119,c_16]) ).
cnf(c_10120,plain,
( is_a_theorem(implies(implies(implies(D,B),A),implies(B,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_104]) ).
cnf(c_133,plain,
is_a_theorem(implies(implies(implies(A,B),implies(implies(C,B),D)),implies(B,D))),
inference(resolve,[status(thm)],[c_10120,c_2]) ).
cnf(c_10121,plain,
( is_a_theorem(implies(B,D))
| ~ is_a_theorem(implies(implies(A,B),implies(implies(C,B),D))) ),
inference(resolve,[status(thm)],[c_1,c_133]) ).
cnf(c_204,plain,
is_a_theorem(implies(not(A),implies(A,B))),
inference(resolve,[status(thm)],[c_10121,c_124]) ).
cnf(c_10122,plain,
( is_a_theorem(implies(B,D))
| ~ is_a_theorem(implies(implies(A,B),implies(implies(C,B),D))) ),
inference(resolve,[status(thm)],[c_1,c_133]) ).
cnf(c_207,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_10122,c_2]) ).
cnf(c_10123,plain,
( is_a_theorem(implies(implies(D,C),implies(implies(A,D),C)))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_12]) ).
cnf(c_211,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(B,A),implies(B,C)))),
inference(resolve,[status(thm)],[c_10123,c_207]) ).
cnf(c_10124,plain,
( is_a_theorem(implies(A,implies(implies(D,C),implies(implies(B,D),C))))
| ~ is_a_theorem(implies(A,implies(not(B),C))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_222,plain,
is_a_theorem(implies(not(not(A)),implies(implies(B,C),implies(implies(A,B),C)))),
inference(resolve,[status(thm)],[c_10124,c_204]) ).
cnf(c_10125,plain,
( is_a_theorem(implies(implies(B,A),implies(B,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_211]) ).
cnf(c_253,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_10125,c_207]) ).
cnf(c_10126,plain,
( is_a_theorem(implies(implies(B,A),implies(B,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_211]) ).
cnf(c_269,plain,
is_a_theorem(implies(implies(A,B),implies(A,implies(C,B)))),
inference(resolve,[status(thm)],[c_10126,c_17]) ).
cnf(c_10127,plain,
( is_a_theorem(implies(implies(B,A),implies(B,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_211]) ).
cnf(c_285,plain,
is_a_theorem(implies(implies(A,implies(A,implies(A,B))),implies(A,B))),
inference(resolve,[status(thm)],[c_10127,c_253]) ).
cnf(c_10128,plain,
( is_a_theorem(implies(A,implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_269]) ).
cnf(c_303,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(C,implies(A,B)))),
inference(resolve,[status(thm)],[c_10128,c_253]) ).
cnf(c_10129,plain,
( is_a_theorem(implies(implies(B,A),implies(B,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_211]) ).
cnf(c_355,plain,
is_a_theorem(implies(implies(A,implies(B,implies(B,C))),implies(A,implies(B,C)))),
inference(resolve,[status(thm)],[c_10129,c_303]) ).
cnf(c_10130,plain,
( is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(A,implies(A,implies(A,B)))) ),
inference(resolve,[status(thm)],[c_1,c_285]) ).
cnf(c_463,plain,
is_a_theorem(implies(implies(not(A),B),implies(implies(A,not(A)),B))),
inference(resolve,[status(thm)],[c_10130,c_11]) ).
cnf(c_10131,plain,
( is_a_theorem(implies(implies(A,not(A)),B))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(resolve,[status(thm)],[c_1,c_463]) ).
cnf(c_532,plain,
is_a_theorem(implies(implies(A,not(A)),not(A))),
inference(resolve,[status(thm)],[c_10131,c_207]) ).
cnf(c_10132,plain,
( is_a_theorem(implies(implies(A,not(A)),B))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(resolve,[status(thm)],[c_1,c_463]) ).
cnf(c_538,plain,
is_a_theorem(implies(implies(A,not(A)),implies(B,not(A)))),
inference(resolve,[status(thm)],[c_10132,c_6]) ).
cnf(c_10133,plain,
( is_a_theorem(implies(implies(D,C),implies(implies(B,D),C)))
| ~ is_a_theorem(implies(implies(A,not(B)),C)) ),
inference(resolve,[status(thm)],[c_1,c_13]) ).
cnf(c_542,plain,
is_a_theorem(implies(implies(A,not(B)),implies(implies(B,A),not(B)))),
inference(resolve,[status(thm)],[c_10133,c_532]) ).
cnf(c_10134,plain,
( is_a_theorem(implies(implies(B,A),implies(B,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_211]) ).
cnf(c_546,plain,
is_a_theorem(implies(implies(A,implies(B,not(B))),implies(A,not(B)))),
inference(resolve,[status(thm)],[c_10134,c_538]) ).
cnf(c_10135,plain,
( is_a_theorem(implies(A,implies(B,C)))
| ~ is_a_theorem(implies(A,implies(B,implies(B,C)))) ),
inference(resolve,[status(thm)],[c_1,c_355]) ).
cnf(c_1627,plain,
is_a_theorem(implies(not(not(A)),implies(implies(A,A),A))),
inference(resolve,[status(thm)],[c_10135,c_222]) ).
cnf(c_10136,plain,
( is_a_theorem(implies(implies(D,A),implies(B,implies(C,implies(D,E)))))
| ~ is_a_theorem(implies(A,implies(B,implies(C,implies(D,E))))) ),
inference(resolve,[status(thm)],[c_1,c_99]) ).
cnf(c_2250,plain,
is_a_theorem(implies(implies(A,not(B)),implies(B,implies(C,implies(A,D))))),
inference(resolve,[status(thm)],[c_10136,c_204]) ).
cnf(c_10137,plain,
( is_a_theorem(implies(A,implies(B,C)))
| ~ is_a_theorem(implies(A,implies(B,implies(B,C)))) ),
inference(resolve,[status(thm)],[c_1,c_355]) ).
cnf(c_2399,plain,
is_a_theorem(implies(implies(A,not(B)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_10137,c_2250]) ).
cnf(c_10138,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,not(B))) ),
inference(resolve,[status(thm)],[c_1,c_2399]) ).
cnf(c_2466,plain,
is_a_theorem(implies(A,implies(not(A),B))),
inference(resolve,[status(thm)],[c_10138,c_207]) ).
cnf(c_10139,plain,
( is_a_theorem(implies(A,not(B)))
| ~ is_a_theorem(implies(A,implies(B,not(B)))) ),
inference(resolve,[status(thm)],[c_1,c_546]) ).
cnf(c_2471,plain,
is_a_theorem(implies(A,not(not(A)))),
inference(resolve,[status(thm)],[c_10139,c_2466]) ).
cnf(c_10140,plain,
( is_a_theorem(implies(implies(B,A),not(B)))
| ~ is_a_theorem(implies(A,not(B))) ),
inference(resolve,[status(thm)],[c_1,c_542]) ).
cnf(c_2741,plain,
is_a_theorem(implies(implies(not(A),A),not(not(A)))),
inference(resolve,[status(thm)],[c_10140,c_2471]) ).
cnf(c_10141,plain,
( is_a_theorem(implies(implies(C,A),implies(B,implies(C,D))))
| ~ is_a_theorem(implies(A,implies(B,implies(C,D)))) ),
inference(resolve,[status(thm)],[c_1,c_101]) ).
cnf(c_3095,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_10141,c_269]) ).
cnf(c_10142,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_3095]) ).
cnf(c_3522,plain,
is_a_theorem(implies(implies(A,A),implies(not(not(A)),A))),
inference(resolve,[status(thm)],[c_10142,c_1627]) ).
cnf(c_10143,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_3095]) ).
cnf(c_3552,plain,
is_a_theorem(implies(A,implies(implies(A,B),implies(C,B)))),
inference(resolve,[status(thm)],[c_10143,c_269]) ).
cnf(c_10144,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_3095]) ).
cnf(c_3563,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_10144,c_207]) ).
cnf(c_10145,plain,
( is_a_theorem(implies(implies(A,B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_3563]) ).
cnf(c_3780,plain,
is_a_theorem(implies(implies(implies(A,A),B),B)),
inference(resolve,[status(thm)],[c_10145,c_207]) ).
cnf(c_10146,plain,
( is_a_theorem(implies(implies(C,A),implies(B,implies(C,D))))
| ~ is_a_theorem(implies(A,implies(B,implies(C,D)))) ),
inference(resolve,[status(thm)],[c_1,c_101]) ).
cnf(c_4117,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_10146,c_3552]) ).
cnf(c_10147,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_3095]) ).
cnf(c_4533,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),
inference(resolve,[status(thm)],[c_10147,c_4117]) ).
cnf(c_10148,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_1,c_3780]) ).
cnf(c_7962,plain,
is_a_theorem(implies(not(not(A)),A)),
inference(resolve,[status(thm)],[c_10148,c_3522]) ).
cnf(c_10149,plain,
( is_a_theorem(implies(implies(C,A),implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_4533]) ).
cnf(c_7982,plain,
is_a_theorem(implies(implies(A,not(not(B))),implies(A,B))),
inference(resolve,[status(thm)],[c_10149,c_7962]) ).
cnf(c_10150,plain,
( is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(A,not(not(B)))) ),
inference(resolve,[status(thm)],[c_1,c_7982]) ).
cnf(c_10108,plain,
is_a_theorem(implies(implies(not(A),A),A)),
inference(resolve,[status(thm)],[c_10150,c_2741]) ).
cnf(c_10109,plain,
$false,
inference(resolve,[status(thm)],[c_10108,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL071-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.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 21:49:04 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3805576 was started by sandbox on n019,
% 0.09/0.37 % Fri Sep 25 21:49:04 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 18.90/4.18
% 18.90/4.18 % SZS status Unsatisfiable for theBenchmark
% 18.90/4.18
% 18.90/4.18 % Proof 1 at 1.59 (+ 0.80) seconds.
% 18.90/4.18 % Length of proof is 47.
% 18.90/4.18 % Level of proof is 14.
% 18.90/4.18 % Maximum clause weight is 52.000.
% 18.90/4.18 % Given clauses 362.
% 18.90/4.18
% 18.90/4.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------