%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL369+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 : Theorem 2.09s 0.65s
% Output : CNFRefutation 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 5
% Syntax : Number of formulae : 72 ( 40 unt; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 68 ( 34 ~; 32 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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,
! [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_25,conjecture,
is_a_theorem(implies(implies(implies(x,y),z),implies(implies(x,u),implies(implies(u,y),z)))),
file('theBenchmark.p',prove_cn_25) ).
fof(prove_cn_25_neg,negated_conjecture,
~ is_a_theorem(implies(implies(implies(x,y),z),implies(implies(x,u),implies(implies(u,y),z)))),
inference(assume_negation,[status(cth)],[prove_cn_25]) ).
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(implies(implies(x,y),z),implies(implies(x,u),implies(implies(u,y),z)))),
inference(clausify,[status(thm)],[prove_cn_25_neg]) ).
cnf(c_1715,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_1715,c_7]) ).
cnf(c_1716,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_1716,c_8]) ).
cnf(c_1717,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_1717,c_9]) ).
cnf(c_1718,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_17,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(D,B),implies(A,implies(D,C))))),
inference(resolve,[status(thm)],[c_1718,c_11]) ).
cnf(c_1719,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_21,plain,
is_a_theorem(implies(implies(A,B),implies(implies(implies(A,C),D),implies(implies(B,C),D)))),
inference(resolve,[status(thm)],[c_1719,c_7]) ).
cnf(c_1720,plain,
( is_a_theorem(implies(implies(not(A),A),B))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_12]) ).
cnf(c_22,plain,
is_a_theorem(implies(implies(not(implies(A,B)),implies(A,B)),implies(implies(not(A),A),B))),
inference(resolve,[status(thm)],[c_1720,c_12]) ).
cnf(c_1721,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_37,plain,
is_a_theorem(implies(implies(A,not(B)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_1721,c_14]) ).
cnf(c_1722,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_42,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_1722,c_8]) ).
cnf(c_1723,plain,
( is_a_theorem(implies(not(A),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_6,c_9]) ).
cnf(c_44,plain,
is_a_theorem(implies(not(implies(A,A)),B)),
inference(resolve,[status(thm)],[c_1723,c_42]) ).
cnf(c_1724,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,not(B))) ),
inference(resolve,[status(thm)],[c_6,c_37]) ).
cnf(c_55,plain,
is_a_theorem(implies(A,implies(not(implies(B,B)),C))),
inference(resolve,[status(thm)],[c_1724,c_44]) ).
cnf(c_1725,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_59,plain,
is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),implies(D,C))),
inference(resolve,[status(thm)],[c_1725,c_55]) ).
cnf(c_1726,plain,
( is_a_theorem(implies(D,C))
| ~ is_a_theorem(implies(implies(not(implies(A,A)),B),C)) ),
inference(resolve,[status(thm)],[c_6,c_59]) ).
cnf(c_210,plain,
is_a_theorem(implies(A,implies(implies(not(B),B),B))),
inference(resolve,[status(thm)],[c_1726,c_22]) ).
cnf(c_1727,plain,
( is_a_theorem(implies(D,C))
| ~ is_a_theorem(implies(implies(not(implies(A,A)),B),C)) ),
inference(resolve,[status(thm)],[c_6,c_59]) ).
cnf(c_211,plain,
is_a_theorem(implies(A,implies(B,B))),
inference(resolve,[status(thm)],[c_1727,c_8]) ).
cnf(c_1728,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_217,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_1728,c_211]) ).
cnf(c_1729,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_17]) ).
cnf(c_268,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(C,implies(A,B)))),
inference(resolve,[status(thm)],[c_1729,c_210]) ).
cnf(c_1730,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_414,plain,
is_a_theorem(implies(implies(not(A),B),implies(C,implies(implies(B,A),A)))),
inference(resolve,[status(thm)],[c_1730,c_268]) ).
cnf(c_1731,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_268]) ).
cnf(c_418,plain,
is_a_theorem(implies(A,implies(implies(implies(B,B),C),C))),
inference(resolve,[status(thm)],[c_1731,c_217]) ).
cnf(c_1732,plain,
( is_a_theorem(implies(implies(implies(B,B),C),C))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_6,c_418]) ).
cnf(c_424,plain,
is_a_theorem(implies(implies(implies(A,A),B),B)),
inference(resolve,[status(thm)],[c_1732,c_418]) ).
cnf(c_1733,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,not(B))) ),
inference(resolve,[status(thm)],[c_6,c_37]) ).
cnf(c_441,plain,
is_a_theorem(implies(A,implies(implies(implies(B,B),not(A)),C))),
inference(resolve,[status(thm)],[c_1733,c_424]) ).
cnf(c_1734,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_726,plain,
is_a_theorem(implies(A,implies(B,implies(implies(C,A),A)))),
inference(resolve,[status(thm)],[c_1734,c_414]) ).
cnf(c_1735,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_268]) ).
cnf(c_749,plain,
is_a_theorem(implies(A,implies(B,implies(implies(C,B),B)))),
inference(resolve,[status(thm)],[c_1735,c_726]) ).
cnf(c_1736,plain,
( is_a_theorem(implies(B,implies(implies(C,B),B)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_6,c_749]) ).
cnf(c_802,plain,
is_a_theorem(implies(A,implies(implies(B,A),A))),
inference(resolve,[status(thm)],[c_1736,c_749]) ).
cnf(c_1737,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_17]) ).
cnf(c_826,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(C,implies(A,C)))),
inference(resolve,[status(thm)],[c_1737,c_802]) ).
cnf(c_1738,plain,
( is_a_theorem(implies(C,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_6,c_826]) ).
cnf(c_865,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolve,[status(thm)],[c_1738,c_441]) ).
cnf(c_1739,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_877,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_1739,c_865]) ).
cnf(c_1740,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_6,c_877]) ).
cnf(c_926,plain,
is_a_theorem(implies(A,implies(B,implies(implies(A,C),C)))),
inference(resolve,[status(thm)],[c_1740,c_414]) ).
cnf(c_1741,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_268]) ).
cnf(c_1265,plain,
is_a_theorem(implies(A,implies(B,implies(implies(B,C),C)))),
inference(resolve,[status(thm)],[c_1741,c_926]) ).
cnf(c_1742,plain,
( is_a_theorem(implies(B,implies(implies(B,C),C)))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_6,c_1265]) ).
cnf(c_1510,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_1742,c_1265]) ).
cnf(c_1743,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_17]) ).
cnf(c_1546,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_1743,c_1510]) ).
cnf(c_1744,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_6,c_1546]) ).
cnf(c_1713,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(A,D),implies(implies(D,B),C)))),
inference(resolve,[status(thm)],[c_1744,c_21]) ).
cnf(c_1714,plain,
$false,
inference(resolve,[status(thm)],[c_1713,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL369+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 22:18:09 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.37 % Process 2059194 was started by sandbox2 on n007,
% 0.13/0.37 % Fri Sep 25 22:18:09 2026
% 0.13/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 2.09/0.65
% 2.09/0.65 % Assigning unary symbol not kb_weight 0 and highest precedence (7).
% 2.09/0.65
% 2.09/0.65 % SZS status Theorem for theBenchmark
% 2.09/0.65
% 2.09/0.65 % Proof 1 at 0.19 (+ 0.07) seconds.
% 2.09/0.65 % Length of proof is 41.
% 2.09/0.65 % Level of proof is 21.
% 2.09/0.65 % Maximum clause weight is 53.000.
% 2.09/0.65 % Given clauses 96.
% 2.09/0.65
% 2.09/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------