%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL404-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 : Unsatisfiable 35.37s 5.58s
% Output : CNFRefutation 35.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 5
% Syntax : Number of formulae : 100 ( 62 unt; 0 def)
% Number of atoms : 140 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 82 ( 42 ~; 40 |; 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 : 269 ( 69 sgn 8 !; 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_1,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',cn_1) ).
cnf(c_2,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(clausify,[status(thm)],[cn_1]) ).
fof(cn_2,axiom,
! [VAR_0] : is_a_theorem(implies(implies(not(VAR_0),VAR_0),VAR_0)),
file('theBenchmark.p',cn_2) ).
cnf(c_3,plain,
is_a_theorem(implies(implies(not(A),A),A)),
inference(clausify,[status(thm)],[cn_2]) ).
fof(cn_3,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(VAR_0,implies(not(VAR_0),VAR_1))),
file('theBenchmark.p',cn_3) ).
cnf(c_4,plain,
is_a_theorem(implies(A,implies(not(A),B))),
inference(clausify,[status(thm)],[cn_3]) ).
fof(prove_cn_70,axiom,
~ is_a_theorem(implies(x,implies(y,not(implies(x,not(y)))))),
file('theBenchmark.p',prove_cn_70) ).
cnf(c_5,plain,
~ is_a_theorem(implies(x,implies(y,not(implies(x,not(y)))))),
inference(clausify,[status(thm)],[prove_cn_70]) ).
cnf(c_6,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_2,c_1]) ).
cnf(c_18165,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_7,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))),
inference(resolve,[status(thm)],[c_18165,c_2]) ).
cnf(c_8,plain,
( is_a_theorem(A)
| ~ is_a_theorem(implies(not(A),A)) ),
inference(resolve,[status(thm)],[c_3,c_1]) ).
cnf(c_18166,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_9,plain,
is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))),
inference(resolve,[status(thm)],[c_18166,c_3]) ).
cnf(c_10,plain,
( is_a_theorem(implies(not(A),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
cnf(c_18167,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_12,plain,
is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))),
inference(resolve,[status(thm)],[c_18167,c_4]) ).
cnf(c_23,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_7,c_1]) ).
cnf(c_18168,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_7]) ).
cnf(c_24,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(D,B),implies(A,implies(D,C))))),
inference(resolve,[status(thm)],[c_18168,c_7]) ).
cnf(c_18169,plain,
( is_a_theorem(implies(implies(not(A),A),B))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_36,plain,
is_a_theorem(implies(implies(not(implies(A,B)),implies(A,B)),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_18169,c_2]) ).
cnf(c_43,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(implies(not(A),D),B),C))),
inference(resolve,[status(thm)],[c_12,c_6]) ).
cnf(c_44,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(not(A),B),C)) ),
inference(resolve,[status(thm)],[c_12,c_1]) ).
cnf(c_18170,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_7]) ).
cnf(c_45,plain,
is_a_theorem(implies(implies(A,not(B)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_18170,c_12]) ).
cnf(c_18171,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(not(A),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_12]) ).
cnf(c_48,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_18171,c_3]) ).
cnf(c_50,plain,
is_a_theorem(implies(not(implies(A,A)),B)),
inference(resolve,[status(thm)],[c_48,c_10]) ).
cnf(c_85,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(implies(B,not(A)),D))),
inference(resolve,[status(thm)],[c_45,c_6]) ).
cnf(c_86,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,not(B))) ),
inference(resolve,[status(thm)],[c_45,c_1]) ).
cnf(c_18172,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,not(B))) ),
inference(resolve,[status(thm)],[c_1,c_45]) ).
cnf(c_88,plain,
is_a_theorem(implies(A,implies(not(implies(B,B)),C))),
inference(resolve,[status(thm)],[c_18172,c_50]) ).
cnf(c_95,plain,
is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),implies(D,C))),
inference(resolve,[status(thm)],[c_88,c_6]) ).
cnf(c_176,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_24,c_1]) ).
cnf(c_18173,plain,
( is_a_theorem(implies(D,C))
| ~ is_a_theorem(implies(implies(not(implies(A,A)),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_95]) ).
cnf(c_370,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_18173,c_3]) ).
cnf(c_378,plain,
is_a_theorem(implies(implies(A,B),implies(C,implies(A,B)))),
inference(resolve,[status(thm)],[c_370,c_176]) ).
cnf(c_382,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_370,c_6]) ).
cnf(c_18174,plain,
( is_a_theorem(implies(C,implies(A,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_378]) ).
cnf(c_425,plain,
is_a_theorem(implies(A,implies(implies(not(B),B),B))),
inference(resolve,[status(thm)],[c_18174,c_3]) ).
cnf(c_473,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(C,implies(A,B)))),
inference(resolve,[status(thm)],[c_425,c_176]) ).
cnf(c_669,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(not(implies(A,B)),implies(A,B))) ),
inference(resolve,[status(thm)],[c_36,c_1]) ).
cnf(c_694,plain,
is_a_theorem(implies(implies(not(A),B),implies(C,implies(implies(B,A),A)))),
inference(resolve,[status(thm)],[c_473,c_23]) ).
cnf(c_697,plain,
( is_a_theorem(implies(C,implies(A,B)))
| ~ is_a_theorem(implies(A,implies(not(B),B))) ),
inference(resolve,[status(thm)],[c_473,c_1]) ).
cnf(c_18175,plain,
( is_a_theorem(implies(C,implies(A,B)))
| ~ is_a_theorem(implies(A,implies(not(B),B))) ),
inference(resolve,[status(thm)],[c_1,c_473]) ).
cnf(c_701,plain,
is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))),
inference(resolve,[status(thm)],[c_18175,c_382]) ).
cnf(c_734,plain,
is_a_theorem(implies(implies(implies(A,A),B),B)),
inference(resolve,[status(thm)],[c_701,c_8]) ).
cnf(c_745,plain,
is_a_theorem(implies(A,implies(implies(implies(B,B),not(A)),C))),
inference(resolve,[status(thm)],[c_734,c_86]) ).
cnf(c_746,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_734,c_1]) ).
cnf(c_984,plain,
is_a_theorem(implies(A,implies(B,implies(implies(C,A),A)))),
inference(resolve,[status(thm)],[c_694,c_44]) ).
cnf(c_1016,plain,
is_a_theorem(implies(A,implies(B,implies(implies(C,B),B)))),
inference(resolve,[status(thm)],[c_984,c_697]) ).
cnf(c_1031,plain,
is_a_theorem(implies(A,implies(implies(B,A),A))),
inference(resolve,[status(thm)],[c_1016,c_746]) ).
cnf(c_18176,plain,
( is_a_theorem(implies(implies(implies(not(A),D),B),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_43]) ).
cnf(c_1061,plain,
is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),C)),
inference(resolve,[status(thm)],[c_18176,c_734]) ).
cnf(c_1097,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(C,implies(A,C)))),
inference(resolve,[status(thm)],[c_1031,c_176]) ).
cnf(c_1140,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(not(implies(A,A)),B),C)) ),
inference(resolve,[status(thm)],[c_1061,c_1]) ).
cnf(c_18177,plain,
( is_a_theorem(implies(C,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_1097]) ).
cnf(c_1179,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolve,[status(thm)],[c_18177,c_745]) ).
cnf(c_1193,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_1179,c_6]) ).
cnf(c_18178,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_1193]) ).
cnf(c_1258,plain,
is_a_theorem(implies(A,implies(B,implies(implies(A,C),C)))),
inference(resolve,[status(thm)],[c_18178,c_694]) ).
cnf(c_1650,plain,
is_a_theorem(implies(A,implies(B,implies(implies(B,C),C)))),
inference(resolve,[status(thm)],[c_1258,c_697]) ).
cnf(c_1901,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_1650,c_1140]) ).
cnf(c_1932,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_1901,c_176]) ).
cnf(c_2935,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1932,c_1]) ).
cnf(c_18179,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_1932]) ).
cnf(c_2970,plain,
is_a_theorem(implies(not(A),implies(A,B))),
inference(resolve,[status(thm)],[c_18179,c_4]) ).
cnf(c_2987,plain,
is_a_theorem(implies(A,implies(not(not(B)),B))),
inference(resolve,[status(thm)],[c_2970,c_697]) ).
cnf(c_2994,plain,
is_a_theorem(implies(implies(A,B),implies(not(B),implies(A,C)))),
inference(resolve,[status(thm)],[c_2970,c_176]) ).
cnf(c_3160,plain,
is_a_theorem(implies(not(not(A)),implies(B,A))),
inference(resolve,[status(thm)],[c_2987,c_2935]) ).
cnf(c_3178,plain,
is_a_theorem(implies(implies(A,B),implies(not(not(A)),B))),
inference(resolve,[status(thm)],[c_2987,c_669]) ).
cnf(c_18180,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_1,c_85]) ).
cnf(c_3687,plain,
is_a_theorem(implies(implies(not(A),not(B)),implies(C,implies(B,A)))),
inference(resolve,[status(thm)],[c_18180,c_473]) ).
cnf(c_4803,plain,
is_a_theorem(implies(not(A),implies(implies(B,A),implies(B,C)))),
inference(resolve,[status(thm)],[c_2994,c_2935]) ).
cnf(c_18181,plain,
( is_a_theorem(implies(not(B),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2994]) ).
cnf(c_4850,plain,
is_a_theorem(implies(not(implies(A,B)),implies(not(not(B)),C))),
inference(resolve,[status(thm)],[c_18181,c_3160]) ).
cnf(c_18182,plain,
( is_a_theorem(implies(not(B),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_2994]) ).
cnf(c_4853,plain,
is_a_theorem(implies(not(implies(A,B)),implies(not(A),C))),
inference(resolve,[status(thm)],[c_18182,c_2970]) ).
cnf(c_4939,plain,
is_a_theorem(implies(A,implies(not(implies(B,C)),B))),
inference(resolve,[status(thm)],[c_4853,c_697]) ).
cnf(c_4984,plain,
is_a_theorem(implies(implies(A,B),implies(not(implies(A,C)),B))),
inference(resolve,[status(thm)],[c_4939,c_669]) ).
cnf(c_5872,plain,
is_a_theorem(implies(A,implies(not(implies(B,C)),not(C)))),
inference(resolve,[status(thm)],[c_4850,c_697]) ).
cnf(c_5912,plain,
is_a_theorem(implies(implies(not(A),B),implies(not(implies(C,A)),B))),
inference(resolve,[status(thm)],[c_5872,c_669]) ).
cnf(c_7159,plain,
( is_a_theorem(implies(not(implies(C,A)),B))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(resolve,[status(thm)],[c_5912,c_1]) ).
cnf(c_18183,plain,
( is_a_theorem(implies(not(implies(C,A)),B))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(resolve,[status(thm)],[c_1,c_5912]) ).
cnf(c_7184,plain,
is_a_theorem(implies(not(implies(A,B)),implies(implies(C,B),implies(C,D)))),
inference(resolve,[status(thm)],[c_18183,c_4803]) ).
cnf(c_8500,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_7184,c_8]) ).
cnf(c_8534,plain,
( is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_8500,c_1]) ).
cnf(c_18184,plain,
( is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_1,c_8500]) ).
cnf(c_8539,plain,
is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))),
inference(resolve,[status(thm)],[c_18184,c_3687]) ).
cnf(c_8574,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(implies(not(A),not(B))) ),
inference(resolve,[status(thm)],[c_8539,c_1]) ).
cnf(c_18185,plain,
( is_a_theorem(implies(not(not(A)),B))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_3178]) ).
cnf(c_11414,plain,
is_a_theorem(implies(not(not(implies(A,B))),implies(not(implies(A,C)),B))),
inference(resolve,[status(thm)],[c_18185,c_4984]) ).
cnf(c_12886,plain,
is_a_theorem(implies(not(implies(A,not(implies(B,C)))),implies(not(implies(B,D)),C))),
inference(resolve,[status(thm)],[c_11414,c_7159]) ).
cnf(c_17309,plain,
is_a_theorem(implies(not(implies(A,not(implies(A,B)))),B)),
inference(resolve,[status(thm)],[c_12886,c_8534]) ).
cnf(c_17525,plain,
is_a_theorem(implies(A,implies(B,not(implies(B,not(A)))))),
inference(resolve,[status(thm)],[c_17309,c_8574]) ).
cnf(c_18163,plain,
is_a_theorem(implies(A,implies(B,not(implies(A,not(B)))))),
inference(resolve,[status(thm)],[c_17525,c_2935]) ).
cnf(c_18164,plain,
$false,
inference(resolve,[status(thm)],[c_18163,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL404-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n020.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Fri Sep 25 22:28:33 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.46 % Process 3966239 was started by sandbox on n020,
% 0.18/0.46 % Fri Sep 25 22:28:33 2026
% 0.18/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 35.37/5.58
% 35.37/5.58 % Assigning unary symbol not kb_weight 0 and highest precedence (5).
% 35.37/5.58
% 35.37/5.58 % given #500 (T,wt=42): 7763 -is_a_theorem(not(implies(not(implies(A,B)),C))) | is_a_theorem(not(not(A))). [resolve(6225,a,1,a)].
% 35.37/5.58
% 35.37/5.58 % SZS status Unsatisfiable for theBenchmark
% 35.37/5.58
% 35.37/5.58 % Proof 1 at 3.09 (+ 1.96) seconds.
% 35.37/5.58 % Length of proof is 74.
% 35.37/5.58 % Level of proof is 33.
% 35.37/5.58 % Maximum clause weight is 71.000.
% 35.37/5.58 % Given clauses 850.
% 35.37/5.58
% 35.37/5.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------