%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL388-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 07:58:46 AM UTC 2026
% Result : Unsatisfiable 25.16s 13.86s
% Output : CNFRefutation 25.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 247 ( 52 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_51,axiom,
~ is_a_theorem(implies(implies(x,implies(y,z)),implies(x,implies(not(z),not(y))))),
file('theBenchmark.p',prove_cn_51) ).
cnf(c_5,plain,
~ is_a_theorem(implies(implies(x,implies(y,z)),implies(x,implies(not(z),not(y))))),
inference(clausify,[status(thm)],[prove_cn_51]) ).
cnf(c_20873,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_6,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))),
inference(resolve,[status(thm)],[c_20873,c_2]) ).
cnf(c_20874,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(A,B),implies(implies(not(A),A),B))),
inference(resolve,[status(thm)],[c_20874,c_3]) ).
cnf(c_20875,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(implies(not(A),B),C),implies(A,C))),
inference(resolve,[status(thm)],[c_20875,c_4]) ).
cnf(c_20876,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_6]) ).
cnf(c_12,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(D,B),implies(A,implies(D,C))))),
inference(resolve,[status(thm)],[c_20876,c_6]) ).
cnf(c_20877,plain,
( is_a_theorem(implies(implies(not(A),A),B))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_17,plain,
is_a_theorem(implies(implies(not(implies(A,B)),implies(A,B)),implies(implies(not(A),A),B))),
inference(resolve,[status(thm)],[c_20877,c_7]) ).
cnf(c_20878,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_6]) ).
cnf(c_32,plain,
is_a_theorem(implies(implies(A,not(B)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_20878,c_9]) ).
cnf(c_20879,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(not(A),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_37,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_20879,c_3]) ).
cnf(c_20880,plain,
( is_a_theorem(implies(not(A),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_39,plain,
is_a_theorem(implies(not(implies(A,A)),B)),
inference(resolve,[status(thm)],[c_20880,c_37]) ).
cnf(c_20881,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,not(B))) ),
inference(resolve,[status(thm)],[c_1,c_32]) ).
cnf(c_50,plain,
is_a_theorem(implies(A,implies(not(implies(B,B)),C))),
inference(resolve,[status(thm)],[c_20881,c_39]) ).
cnf(c_20882,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_54,plain,
is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),implies(D,C))),
inference(resolve,[status(thm)],[c_20882,c_50]) ).
cnf(c_20883,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_54]) ).
cnf(c_205,plain,
is_a_theorem(implies(A,implies(implies(not(B),B),B))),
inference(resolve,[status(thm)],[c_20883,c_17]) ).
cnf(c_20884,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_54]) ).
cnf(c_206,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_20884,c_3]) ).
cnf(c_20885,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_212,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_20885,c_206]) ).
cnf(c_20886,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_12]) ).
cnf(c_263,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(C,implies(A,B)))),
inference(resolve,[status(thm)],[c_20886,c_205]) ).
cnf(c_20887,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_6]) ).
cnf(c_409,plain,
is_a_theorem(implies(implies(not(A),B),implies(C,implies(implies(B,A),A)))),
inference(resolve,[status(thm)],[c_20887,c_263]) ).
cnf(c_20888,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_263]) ).
cnf(c_413,plain,
is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))),
inference(resolve,[status(thm)],[c_20888,c_212]) ).
cnf(c_20889,plain,
( is_a_theorem(implies(implies(implies(B,B),C),C))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_413]) ).
cnf(c_419,plain,
is_a_theorem(implies(implies(implies(A,A),B),B)),
inference(resolve,[status(thm)],[c_20889,c_413]) ).
cnf(c_20890,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,not(B))) ),
inference(resolve,[status(thm)],[c_1,c_32]) ).
cnf(c_436,plain,
is_a_theorem(implies(A,implies(implies(implies(B,B),not(A)),C))),
inference(resolve,[status(thm)],[c_20890,c_419]) ).
cnf(c_20891,plain,
( is_a_theorem(implies(A,C))
| ~ is_a_theorem(implies(implies(not(A),B),C)) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_721,plain,
is_a_theorem(implies(A,implies(B,implies(implies(C,A),A)))),
inference(resolve,[status(thm)],[c_20891,c_409]) ).
cnf(c_20892,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_263]) ).
cnf(c_744,plain,
is_a_theorem(implies(A,implies(B,implies(implies(C,B),B)))),
inference(resolve,[status(thm)],[c_20892,c_721]) ).
cnf(c_20893,plain,
( is_a_theorem(implies(B,implies(implies(C,B),B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_744]) ).
cnf(c_797,plain,
is_a_theorem(implies(A,implies(implies(B,A),A))),
inference(resolve,[status(thm)],[c_20893,c_744]) ).
cnf(c_20894,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_12]) ).
cnf(c_821,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(C,implies(A,C)))),
inference(resolve,[status(thm)],[c_20894,c_797]) ).
cnf(c_20895,plain,
( is_a_theorem(implies(C,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_821]) ).
cnf(c_860,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolve,[status(thm)],[c_20895,c_436]) ).
cnf(c_20896,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_872,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_20896,c_860]) ).
cnf(c_20897,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_872]) ).
cnf(c_921,plain,
is_a_theorem(implies(A,implies(B,implies(implies(A,C),C)))),
inference(resolve,[status(thm)],[c_20897,c_409]) ).
cnf(c_20898,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_263]) ).
cnf(c_1260,plain,
is_a_theorem(implies(A,implies(B,implies(implies(B,C),C)))),
inference(resolve,[status(thm)],[c_20898,c_921]) ).
cnf(c_20899,plain,
( is_a_theorem(implies(B,implies(implies(B,C),C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_1260]) ).
cnf(c_1505,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_20899,c_1260]) ).
cnf(c_20900,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_12]) ).
cnf(c_1541,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_20900,c_1505]) ).
cnf(c_20901,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_1541]) ).
cnf(c_1711,plain,
is_a_theorem(implies(not(A),implies(A,B))),
inference(resolve,[status(thm)],[c_20901,c_4]) ).
cnf(c_20902,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_1541]) ).
cnf(c_1713,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),
inference(resolve,[status(thm)],[c_20902,c_2]) ).
cnf(c_20903,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_263]) ).
cnf(c_1742,plain,
is_a_theorem(implies(A,implies(not(not(B)),B))),
inference(resolve,[status(thm)],[c_20903,c_1711]) ).
cnf(c_20904,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_1751,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))),
inference(resolve,[status(thm)],[c_20904,c_1711]) ).
cnf(c_20905,plain,
( is_a_theorem(implies(not(not(B)),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_1742]) ).
cnf(c_1929,plain,
is_a_theorem(implies(not(not(A)),A)),
inference(resolve,[status(thm)],[c_20905,c_1742]) ).
cnf(c_20906,plain,
( is_a_theorem(implies(C,implies(implies(B,A),A)))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(resolve,[status(thm)],[c_1,c_409]) ).
cnf(c_1958,plain,
is_a_theorem(implies(A,implies(implies(B,not(B)),not(B)))),
inference(resolve,[status(thm)],[c_20906,c_1929]) ).
cnf(c_20907,plain,
( is_a_theorem(implies(implies(B,not(B)),not(B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_1,c_1958]) ).
cnf(c_2367,plain,
is_a_theorem(implies(implies(A,not(A)),not(A))),
inference(resolve,[status(thm)],[c_20907,c_1958]) ).
cnf(c_20908,plain,
( is_a_theorem(implies(implies(C,A),implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_1713]) ).
cnf(c_3439,plain,
is_a_theorem(implies(implies(A,implies(B,not(B))),implies(A,not(B)))),
inference(resolve,[status(thm)],[c_20908,c_2367]) ).
cnf(c_20909,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_6]) ).
cnf(c_16781,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,not(A)),not(A)))),
inference(resolve,[status(thm)],[c_20909,c_3439]) ).
cnf(c_20910,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_1541]) ).
cnf(c_20411,plain,
is_a_theorem(implies(implies(A,not(B)),implies(implies(B,A),not(B)))),
inference(resolve,[status(thm)],[c_20910,c_16781]) ).
cnf(c_20911,plain,
( is_a_theorem(implies(not(A),C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_1,c_1751]) ).
cnf(c_20649,plain,
is_a_theorem(implies(not(A),implies(implies(B,A),not(B)))),
inference(resolve,[status(thm)],[c_20911,c_20411]) ).
cnf(c_20912,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_1,c_1541]) ).
cnf(c_20828,plain,
is_a_theorem(implies(implies(A,B),implies(not(B),not(A)))),
inference(resolve,[status(thm)],[c_20912,c_20649]) ).
cnf(c_20913,plain,
( is_a_theorem(implies(implies(C,A),implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_1,c_1713]) ).
cnf(c_20871,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(A,implies(not(C),not(B))))),
inference(resolve,[status(thm)],[c_20913,c_20828]) ).
cnf(c_20872,plain,
$false,
inference(resolve,[status(thm)],[c_20871,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL388-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/10.59 % Computer : n002.cluster.edu
% 0.11/10.59 % Model : x86_64 x86_64
% 0.11/10.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.59 % Memory : 8046.5625MB
% 0.11/10.59 % OS : Linux 6.8.0-71-generic
% 0.11/10.59 % CPULimit : 300
% 0.11/10.59 % WCLimit : 300
% 0.11/10.59 % DateTime : Fri Sep 25 22:27:17 UTC 2026
% 0.11/10.59 % CPUTime :
% 0.11/10.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/10.59 % Process 159874 was started by sandbox2 on n002,
% 0.11/10.59 % Fri Sep 25 22:27:17 2026
% 0.11/10.59 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/10.60
% 0.15/10.60 % From the command line: assign(max_seconds, 300).
% 25.16/13.86
% 25.16/13.86 % Assigning unary symbol not kb_weight 0 and highest precedence (6).
% 25.16/13.86
% 25.16/13.86 % given #500 (T,wt=43): 11707 is_a_theorem(implies(implies(not(not(A)),implies(A,not(A))),not(A))). [hyper(1,a,5637,a,b,2367,a)].
% 25.16/13.86
% 25.16/13.86 % SZS status Unsatisfiable for theBenchmark
% 25.16/13.86
% 25.16/13.86 % Proof 1 at 2.37 (+ 0.82) seconds.
% 25.16/13.86 % Length of proof is 47.
% 25.16/13.86 % Level of proof is 30.
% 25.16/13.86 % Maximum clause weight is 53.000.
% 25.16/13.86 % Given clauses 518.
% 25.16/13.86
% 25.16/13.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------