%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL403+1 : TPTP v9.3.1. Released v9.1.0.
% 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 07:58:49 AM UTC 2026
% Result : Theorem 158.20s 21.47s
% Output : CNFRefutation 158.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 5
% Syntax : Number of formulae : 88 ( 48 unt; 0 def)
% Number of atoms : 130 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 84 ( 42 ~; 40 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 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 : 234 ( 41 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(condensed_detachment,axiom,
! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ),
file('theBenchmark.p',condensed_detachment) ).
fof(cn_1,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
file('theBenchmark.p',cn_1) ).
fof(cn_2,axiom,
! [X] : is_a_theorem(implies(implies(not(X),X),X)),
file('theBenchmark.p',cn_2) ).
fof(cn_3,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(not(X),Y))),
file('theBenchmark.p',cn_3) ).
fof(prove_cn_69,conjecture,
is_a_theorem(implies(x,implies(not(y),not(implies(x,y))))),
file('theBenchmark.p',prove_cn_69) ).
fof(prove_cn_69_neg,negated_conjecture,
~ is_a_theorem(implies(x,implies(not(y),not(implies(x,y))))),
inference(assume_negation,[status(cth)],[prove_cn_69]) ).
cnf(c_6,plain,
( is_a_theorem(B)
| ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B)) ),
inference(clausify,[status(thm)],[condensed_detachment]) ).
cnf(c_7,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(clausify,[status(thm)],[cn_1]) ).
cnf(c_8,plain,
is_a_theorem(implies(implies(not(A),A),A)),
inference(clausify,[status(thm)],[cn_2]) ).
cnf(c_9,plain,
is_a_theorem(implies(A,implies(not(A),B))),
inference(clausify,[status(thm)],[cn_3]) ).
cnf(c_10,negated_conjecture,
~ is_a_theorem(implies(x,implies(not(y),not(implies(x,y))))),
inference(clausify,[status(thm)],[prove_cn_69_neg]) ).
cnf(c_16699,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_11,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))),
inference(resolve,[status(thm)],[c_16699,c_7]) ).
cnf(c_16700,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_12,plain,
is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))),
inference(resolve,[status(thm)],[c_16700,c_8]) ).
cnf(c_16701,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_14,plain,
is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))),
inference(resolve,[status(thm)],[c_16701,c_9]) ).
cnf(c_16702,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(not(A),B),C)) ),
inference(resolve,[status(thm)],[c_6,c_14]) ).
cnf(c_31,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_16702,c_8]) ).
cnf(c_16703,plain,
( is_a_theorem(implies(not(A),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_6,c_9]) ).
cnf(c_33,plain,
is_a_theorem(implies(not(implies(A,A)),B)),
inference(resolve,[status(thm)],[c_16703,c_31]) ).
cnf(c_16704,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_36,plain,
is_a_theorem(implies(implies(A,B),implies(not(implies(C,C)),B))),
inference(resolve,[status(thm)],[c_16704,c_33]) ).
cnf(c_16705,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(not(A),B),C)) ),
inference(resolve,[status(thm)],[c_6,c_14]) ).
cnf(c_50,plain,
is_a_theorem(implies(A,implies(not(implies(B,B)),C))),
inference(resolve,[status(thm)],[c_16705,c_36]) ).
cnf(c_16706,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_6,c_11]) ).
cnf(c_96,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(D,B),implies(A,implies(D,C))))),
inference(resolve,[status(thm)],[c_16706,c_11]) ).
cnf(c_16707,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_6,c_11]) ).
cnf(c_102,plain,
is_a_theorem(implies(implies(A,not(B)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_16707,c_14]) ).
cnf(c_16708,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_112,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(implies(B,not(A)),D))),
inference(resolve,[status(thm)],[c_16708,c_102]) ).
cnf(c_16709,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_6,c_96]) ).
cnf(c_248,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_16709,c_12]) ).
cnf(c_16710,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(not(B),B))) ),
inference(resolve,[status(thm)],[c_6,c_248]) ).
cnf(c_319,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_16710,c_50]) ).
cnf(c_16711,plain,
( is_a_theorem(implies(C,B))
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_6,c_319]) ).
cnf(c_343,plain,
is_a_theorem(implies(A,implies(implies(not(B),B),B))),
inference(resolve,[status(thm)],[c_16711,c_12]) ).
cnf(c_16712,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_6,c_96]) ).
cnf(c_460,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(C,implies(A,B)))),
inference(resolve,[status(thm)],[c_16712,c_343]) ).
cnf(c_16713,plain,
( is_a_theorem(implies(implies(B,not(A)),D))
| ~ is_a_theorem(implies(implies(A,implies(B,C)),D)) ),
inference(resolve,[status(thm)],[c_6,c_112]) ).
cnf(c_813,plain,
is_a_theorem(implies(implies(not(A),not(B)),implies(C,implies(B,A)))),
inference(resolve,[status(thm)],[c_16713,c_460]) ).
cnf(c_16714,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(not(A),B),C)) ),
inference(resolve,[status(thm)],[c_6,c_14]) ).
cnf(c_840,plain,
is_a_theorem(implies(A,implies(B,implies(C,A)))),
inference(resolve,[status(thm)],[c_16714,c_813]) ).
cnf(c_16715,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(not(B),B))) ),
inference(resolve,[status(thm)],[c_6,c_248]) ).
cnf(c_851,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_16715,c_840]) ).
cnf(c_16716,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_6,c_851]) ).
cnf(c_955,plain,
is_a_theorem(implies(not(A),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_16716,c_813]) ).
cnf(c_16717,plain,
( is_a_theorem(implies(C,implies(A,B)))
| ~ is_a_theorem(implies(A,implies(not(B),B))) ),
inference(resolve,[status(thm)],[c_6,c_460]) ).
cnf(c_969,plain,
is_a_theorem(implies(A,implies(not(B),implies(B,C)))),
inference(resolve,[status(thm)],[c_16717,c_955]) ).
cnf(c_16718,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(not(B),B))) ),
inference(resolve,[status(thm)],[c_6,c_248]) ).
cnf(c_973,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))),
inference(resolve,[status(thm)],[c_16718,c_955]) ).
cnf(c_16719,plain,
( is_a_theorem(implies(not(B),implies(B,C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_6,c_969]) ).
cnf(c_995,plain,
is_a_theorem(implies(not(A),implies(A,B))),
inference(resolve,[status(thm)],[c_16719,c_969]) ).
cnf(c_16720,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,implies(not(B),B))) ),
inference(resolve,[status(thm)],[c_6,c_248]) ).
cnf(c_1014,plain,
is_a_theorem(implies(implies(A,B),implies(not(not(A)),B))),
inference(resolve,[status(thm)],[c_16720,c_995]) ).
cnf(c_16721,plain,
( is_a_theorem(implies(C,implies(A,B)))
| ~ is_a_theorem(implies(A,implies(not(B),B))) ),
inference(resolve,[status(thm)],[c_6,c_460]) ).
cnf(c_1037,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),B))),
inference(resolve,[status(thm)],[c_16721,c_973]) ).
cnf(c_16722,plain,
( is_a_theorem(implies(C,implies(A,B)))
| ~ is_a_theorem(implies(A,implies(not(B),B))) ),
inference(resolve,[status(thm)],[c_6,c_460]) ).
cnf(c_1894,plain,
is_a_theorem(implies(A,implies(implies(B,not(B)),not(B)))),
inference(resolve,[status(thm)],[c_16722,c_1014]) ).
cnf(c_16723,plain,
( is_a_theorem(implies(implies(implies(B,C),B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_6,c_1037]) ).
cnf(c_1968,plain,
is_a_theorem(implies(implies(implies(A,B),A),A)),
inference(resolve,[status(thm)],[c_16723,c_1037]) ).
cnf(c_16724,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_6,c_11]) ).
cnf(c_2005,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_16724,c_1968]) ).
cnf(c_16725,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_6,c_11]) ).
cnf(c_2026,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_16725,c_2005]) ).
cnf(c_16726,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_6,c_851]) ).
cnf(c_2079,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_16726,c_2026]) ).
cnf(c_16727,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_6,c_96]) ).
cnf(c_2131,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_16727,c_2079]) ).
cnf(c_16728,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_2139,plain,
is_a_theorem(implies(implies(implies(implies(A,B),B),C),implies(A,C))),
inference(resolve,[status(thm)],[c_16728,c_2079]) ).
cnf(c_16729,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_6,c_2131]) ).
cnf(c_2351,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),
inference(resolve,[status(thm)],[c_16729,c_7]) ).
cnf(c_16730,plain,
( is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_6,c_2005]) ).
cnf(c_3308,plain,
is_a_theorem(implies(implies(A,not(A)),not(A))),
inference(resolve,[status(thm)],[c_16730,c_1894]) ).
cnf(c_16731,plain,
( is_a_theorem(implies(implies(C,A),implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_2351]) ).
cnf(c_3329,plain,
is_a_theorem(implies(implies(A,implies(B,not(B))),implies(A,not(B)))),
inference(resolve,[status(thm)],[c_16731,c_3308]) ).
cnf(c_16732,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_6,c_11]) ).
cnf(c_12979,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,not(A)),not(A)))),
inference(resolve,[status(thm)],[c_16732,c_3329]) ).
cnf(c_16733,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_6,c_2131]) ).
cnf(c_16404,plain,
is_a_theorem(implies(implies(A,not(B)),implies(implies(B,A),not(B)))),
inference(resolve,[status(thm)],[c_16733,c_12979]) ).
cnf(c_16734,plain,
( is_a_theorem(implies(not(A),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_6,c_973]) ).
cnf(c_16558,plain,
is_a_theorem(implies(not(A),implies(implies(B,A),not(B)))),
inference(resolve,[status(thm)],[c_16734,c_16404]) ).
cnf(c_16735,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_6,c_2131]) ).
cnf(c_16658,plain,
is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))),
inference(resolve,[status(thm)],[c_16735,c_16558]) ).
cnf(c_16736,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(implies(A,B),B),C)) ),
inference(resolve,[status(thm)],[c_6,c_2139]) ).
cnf(c_16697,plain,
is_a_theorem(implies(A,implies(not(B),not(implies(A,B))))),
inference(resolve,[status(thm)],[c_16736,c_16658]) ).
cnf(c_16698,plain,
$false,
inference(resolve,[status(thm)],[c_16697,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL403+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 22:30:27 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2427329 was started by sandbox on n015,
% 0.08/0.36 % Fri Sep 25 22:30:27 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 158.20/21.47
% 158.20/21.47 % Assigning unary symbol not kb_weight 0 and highest precedence (5).
% 158.20/21.47
% 158.20/21.47 % SZS status Theorem for theBenchmark
% 158.20/21.47
% 158.20/21.47 % Proof 1 at 3.59 (+ 1.35) seconds.
% 158.20/21.47 % Length of proof is 49.
% 158.20/21.47 % Level of proof is 28.
% 158.20/21.47 % Maximum clause weight is 41.000.
% 158.20/21.47 % Given clauses 407.
% 158.20/21.47
% 158.20/21.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------