%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL369-1 : 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 07:58:41 AM UTC 2026
% Result : Unsatisfiable 3.47s 11.16s
% Output : CNFRefutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 5
% Syntax : Number of formulae : 71 ( 39 unt; 0 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 70 ( 36 ~; 34 |; 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 197 ( 43 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_25,axiom,
~ is_a_theorem(implies(implies(implies(x,y),z),implies(implies(x,u),implies(implies(u,y),z)))),
file('theBenchmark.p',prove_cn_25) ).
cnf(c_5,plain,
~ is_a_theorem(implies(implies(implies(x,y),z),implies(implies(x,u),implies(implies(u,y),z)))),
inference(clausify,[status(thm)],[prove_cn_25]) ).
cnf(c_1710,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_1710,c_2]) ).
cnf(c_1711,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_1711,c_3]) ).
cnf(c_1712,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_1712,c_4]) ).
cnf(c_1713,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_1713,c_6]) ).
cnf(c_1714,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_16,plain,
is_a_theorem(implies(implies(A,B),implies(implies(implies(A,C),D),implies(implies(B,C),D)))),
inference(resolve,[status(thm)],[c_1714,c_2]) ).
cnf(c_1715,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_1715,c_7]) ).
cnf(c_1716,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_1716,c_9]) ).
cnf(c_1717,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_1717,c_3]) ).
cnf(c_1718,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_1718,c_37]) ).
cnf(c_1719,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_1719,c_39]) ).
cnf(c_1720,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_1720,c_50]) ).
cnf(c_1721,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_1721,c_17]) ).
cnf(c_1722,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_1722,c_3]) ).
cnf(c_1723,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_1723,c_206]) ).
cnf(c_1724,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_1724,c_205]) ).
cnf(c_1725,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_1725,c_263]) ).
cnf(c_1726,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_1726,c_212]) ).
cnf(c_1727,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_1727,c_413]) ).
cnf(c_1728,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_1728,c_419]) ).
cnf(c_1729,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_1729,c_409]) ).
cnf(c_1730,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_1730,c_721]) ).
cnf(c_1731,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_1731,c_744]) ).
cnf(c_1732,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_1732,c_797]) ).
cnf(c_1733,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_1733,c_436]) ).
cnf(c_1734,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_1734,c_860]) ).
cnf(c_1735,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_1735,c_409]) ).
cnf(c_1736,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_1736,c_921]) ).
cnf(c_1737,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_1737,c_1260]) ).
cnf(c_1738,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_1738,c_1505]) ).
cnf(c_1739,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_1708,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(A,D),implies(implies(D,B),C)))),
inference(resolve,[status(thm)],[c_1739,c_16]) ).
cnf(c_1709,plain,
$false,
inference(resolve,[status(thm)],[c_1708,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL369-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/10.66 % Computer : n002.cluster.edu
% 0.16/10.66 % Model : x86_64 x86_64
% 0.16/10.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/10.66 % Memory : 8046.5625MB
% 0.16/10.66 % OS : Linux 6.8.0-71-generic
% 0.16/10.66 % CPULimit : 300
% 0.16/10.66 % WCLimit : 300
% 0.16/10.66 % DateTime : Fri Sep 25 22:23:02 UTC 2026
% 0.16/10.66 % CPUTime :
% 0.16/10.66 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/10.66 % Process 147527 was started by sandbox2 on n002,
% 0.16/10.66 % Fri Sep 25 22:23:02 2026
% 0.16/10.66 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/10.67
% 0.16/10.67 % From the command line: assign(max_seconds, 300).
% 3.47/11.16
% 3.47/11.16 % Assigning unary symbol not kb_weight 0 and highest precedence (7).
% 3.47/11.16
% 3.47/11.16 % SZS status Unsatisfiable for theBenchmark
% 3.47/11.16
% 3.47/11.16 % Proof 1 at 0.27 (+ 0.14) seconds.
% 3.47/11.16 % Length of proof is 36.
% 3.47/11.16 % Level of proof is 20.
% 3.47/11.16 % Maximum clause weight is 53.000.
% 3.47/11.16 % Given clauses 96.
% 3.47/11.16
% 3.47/11.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------