%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL371+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 07:58:42 AM UTC 2026
% Result : Theorem 21.61s 3.63s
% Output : CNFRefutation 21.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 5
% Syntax : Number of formulae : 68 ( 38 unt; 0 def)
% Number of atoms : 100 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 64 ( 32 ~; 30 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 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 : 186 ( 33 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_27,conjecture,
is_a_theorem(implies(implies(implies(x,y),y),implies(implies(y,x),x))),
file('theBenchmark.p',prove_cn_27) ).
fof(prove_cn_27_neg,negated_conjecture,
~ is_a_theorem(implies(implies(implies(x,y),y),implies(implies(y,x),x))),
inference(assume_negation,[status(cth)],[prove_cn_27]) ).
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),y),implies(implies(y,x),x))),
inference(clausify,[status(thm)],[prove_cn_27_neg]) ).
cnf(c_17648,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_17648,c_7]) ).
cnf(c_17649,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_17649,c_8]) ).
cnf(c_17650,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_17650,c_9]) ).
cnf(c_17651,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_17651,c_11]) ).
cnf(c_17652,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_26,plain,
is_a_theorem(implies(implies(not(implies(implies(implies(A,B),implies(C,B)),D)),implies(implies(implies(A,B),implies(C,B)),D)),implies(implies(C,A),D))),
inference(resolve,[status(thm)],[c_17652,c_11]) ).
cnf(c_17653,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_17653,c_14]) ).
cnf(c_17654,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_17654,c_8]) ).
cnf(c_17655,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_17655,c_42]) ).
cnf(c_17656,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_51,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(implies(B,not(A)),D))),
inference(resolve,[status(thm)],[c_17656,c_37]) ).
cnf(c_17657,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_52,plain,
is_a_theorem(implies(A,implies(not(implies(B,B)),C))),
inference(resolve,[status(thm)],[c_17657,c_44]) ).
cnf(c_17658,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_85,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_17658,c_12]) ).
cnf(c_17659,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_85]) ).
cnf(c_245,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_17659,c_52]) ).
cnf(c_17660,plain,
( is_a_theorem(implies(C,B))
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_6,c_245]) ).
cnf(c_268,plain,
is_a_theorem(implies(A,implies(implies(not(B),B),B))),
inference(resolve,[status(thm)],[c_17660,c_12]) ).
cnf(c_17661,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_523,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(C,implies(A,B)))),
inference(resolve,[status(thm)],[c_17661,c_268]) ).
cnf(c_17662,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_51]) ).
cnf(c_1050,plain,
is_a_theorem(implies(implies(not(A),not(B)),implies(C,implies(B,A)))),
inference(resolve,[status(thm)],[c_17662,c_523]) ).
cnf(c_17663,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_1085,plain,
is_a_theorem(implies(A,implies(B,implies(C,A)))),
inference(resolve,[status(thm)],[c_17663,c_1050]) ).
cnf(c_17664,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_85]) ).
cnf(c_1210,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_17664,c_1085]) ).
cnf(c_17665,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_6,c_1210]) ).
cnf(c_1333,plain,
is_a_theorem(implies(not(A),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_17665,c_1050]) ).
cnf(c_17666,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_85]) ).
cnf(c_1353,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))),
inference(resolve,[status(thm)],[c_17666,c_1333]) ).
cnf(c_17667,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_523]) ).
cnf(c_1557,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),B))),
inference(resolve,[status(thm)],[c_17667,c_1353]) ).
cnf(c_17668,plain,
( is_a_theorem(implies(implies(implies(B,C),B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_6,c_1557]) ).
cnf(c_3073,plain,
is_a_theorem(implies(implies(implies(A,B),A),A)),
inference(resolve,[status(thm)],[c_17668,c_1557]) ).
cnf(c_17669,plain,
( is_a_theorem(implies(implies(C,A),D))
| ~ is_a_theorem(implies(not(implies(implies(implies(A,B),implies(C,B)),D)),implies(implies(implies(A,B),implies(C,B)),D))) ),
inference(resolve,[status(thm)],[c_6,c_26]) ).
cnf(c_3091,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_17669,c_1557]) ).
cnf(c_17670,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_3177,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_17670,c_3091]) ).
cnf(c_17671,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_6,c_1210]) ).
cnf(c_3399,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_17671,c_3177]) ).
cnf(c_17672,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_3484,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_17672,c_3399]) ).
cnf(c_17673,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_6,c_3484]) ).
cnf(c_3970,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),
inference(resolve,[status(thm)],[c_17673,c_7]) ).
cnf(c_17674,plain,
( is_a_theorem(implies(implies(C,A),implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_3970]) ).
cnf(c_4655,plain,
is_a_theorem(implies(implies(A,implies(implies(B,C),B)),implies(A,B))),
inference(resolve,[status(thm)],[c_17674,c_3073]) ).
cnf(c_17675,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_17646,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(C,A),A))),
inference(resolve,[status(thm)],[c_17675,c_4655]) ).
cnf(c_17647,plain,
$false,
inference(resolve,[status(thm)],[c_17646,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL371+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 22:18:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2059994 was started by sandbox2 on n007,
% 0.10/0.37 % Fri Sep 25 22:18:24 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 21.61/3.63
% 21.61/3.63 % SZS status Theorem for theBenchmark
% 21.61/3.63
% 21.61/3.63 % Proof 1 at 2.47 (+ 0.75) seconds.
% 21.61/3.63 % Length of proof is 39.
% 21.61/3.63 % Level of proof is 22.
% 21.61/3.63 % Maximum clause weight is 62.000.
% 21.61/3.63 % Given clauses 460.
% 21.61/3.63
% 21.61/3.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------