%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL373+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 : n026.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 07:58:43 AM UTC 2026
% Result : Theorem 40.69s 5.59s
% Output : CNFRefutation 40.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% 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 : 7 ( 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 : 199 ( 35 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_29,conjecture,
is_a_theorem(implies(implies(implies(x,y),z),implies(implies(x,z),z))),
file('theBenchmark.p',prove_cn_29) ).
fof(prove_cn_29_neg,negated_conjecture,
~ is_a_theorem(implies(implies(implies(x,y),z),implies(implies(x,z),z))),
inference(assume_negation,[status(cth)],[prove_cn_29]) ).
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,z),z))),
inference(clausify,[status(thm)],[prove_cn_29_neg]) ).
cnf(c_22565,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_22565,c_7]) ).
cnf(c_22566,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_22566,c_8]) ).
cnf(c_22567,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_22567,c_9]) ).
cnf(c_22568,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_22568,c_11]) ).
cnf(c_22569,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_22569,c_11]) ).
cnf(c_22570,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_34,plain,
is_a_theorem(implies(implies(A,not(B)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_22570,c_14]) ).
cnf(c_22571,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_39,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_22571,c_8]) ).
cnf(c_22572,plain,
( is_a_theorem(implies(not(A),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_6,c_9]) ).
cnf(c_41,plain,
is_a_theorem(implies(not(implies(A,A)),B)),
inference(resolve,[status(thm)],[c_22572,c_39]) ).
cnf(c_22573,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_48,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(implies(B,not(A)),D))),
inference(resolve,[status(thm)],[c_22573,c_34]) ).
cnf(c_22574,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,not(B))) ),
inference(resolve,[status(thm)],[c_6,c_34]) ).
cnf(c_49,plain,
is_a_theorem(implies(A,implies(not(implies(B,B)),C))),
inference(resolve,[status(thm)],[c_22574,c_41]) ).
cnf(c_22575,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_132,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_22575,c_12]) ).
cnf(c_22576,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_132]) ).
cnf(c_189,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),
inference(resolve,[status(thm)],[c_22576,c_49]) ).
cnf(c_22577,plain,
( is_a_theorem(implies(C,B))
| ~ is_a_theorem(implies(implies(A,A),B)) ),
inference(resolve,[status(thm)],[c_6,c_189]) ).
cnf(c_210,plain,
is_a_theorem(implies(A,implies(implies(not(B),B),B))),
inference(resolve,[status(thm)],[c_22577,c_12]) ).
cnf(c_22578,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_420,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(C,implies(A,B)))),
inference(resolve,[status(thm)],[c_22578,c_210]) ).
cnf(c_22579,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_48]) ).
cnf(c_912,plain,
is_a_theorem(implies(implies(not(A),not(B)),implies(C,implies(B,A)))),
inference(resolve,[status(thm)],[c_22579,c_420]) ).
cnf(c_22580,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_944,plain,
is_a_theorem(implies(A,implies(B,implies(C,A)))),
inference(resolve,[status(thm)],[c_22580,c_912]) ).
cnf(c_22581,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_132]) ).
cnf(c_985,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),
inference(resolve,[status(thm)],[c_22581,c_944]) ).
cnf(c_22582,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_6,c_985]) ).
cnf(c_1097,plain,
is_a_theorem(implies(not(A),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_22582,c_912]) ).
cnf(c_22583,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_132]) ).
cnf(c_1116,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))),
inference(resolve,[status(thm)],[c_22583,c_1097]) ).
cnf(c_22584,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_420]) ).
cnf(c_1212,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),B))),
inference(resolve,[status(thm)],[c_22584,c_1116]) ).
cnf(c_22585,plain,
( is_a_theorem(implies(implies(implies(B,C),B),B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_6,c_1212]) ).
cnf(c_2836,plain,
is_a_theorem(implies(implies(implies(A,B),A),A)),
inference(resolve,[status(thm)],[c_22585,c_1212]) ).
cnf(c_22586,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_2854,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_22586,c_1212]) ).
cnf(c_22587,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_2937,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_22587,c_2854]) ).
cnf(c_22588,plain,
( is_a_theorem(implies(B,C))
| ~ is_a_theorem(implies(implies(A,B),C)) ),
inference(resolve,[status(thm)],[c_6,c_985]) ).
cnf(c_3031,plain,
is_a_theorem(implies(A,implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_22588,c_2937]) ).
cnf(c_22589,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_3105,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(B,implies(A,C)))),
inference(resolve,[status(thm)],[c_22589,c_3031]) ).
cnf(c_22590,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_6,c_3105]) ).
cnf(c_3395,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),
inference(resolve,[status(thm)],[c_22590,c_7]) ).
cnf(c_22591,plain,
( is_a_theorem(implies(implies(C,A),implies(C,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_3395]) ).
cnf(c_3785,plain,
is_a_theorem(implies(implies(A,implies(implies(B,C),B)),implies(A,B))),
inference(resolve,[status(thm)],[c_22591,c_2836]) ).
cnf(c_22592,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_17914,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(C,A),A))),
inference(resolve,[status(thm)],[c_22592,c_3785]) ).
cnf(c_22593,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_18037,plain,
is_a_theorem(implies(implies(A,B),implies(implies(implies(A,C),B),B))),
inference(resolve,[status(thm)],[c_22593,c_17914]) ).
cnf(c_22594,plain,
( is_a_theorem(implies(B,implies(A,C)))
| ~ is_a_theorem(implies(A,implies(B,C))) ),
inference(resolve,[status(thm)],[c_6,c_3105]) ).
cnf(c_22563,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(A,C),C))),
inference(resolve,[status(thm)],[c_22594,c_18037]) ).
cnf(c_22564,plain,
$false,
inference(resolve,[status(thm)],[c_22563,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL373+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n026.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 22:23:24 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 3612694 was started by sandbox2 on n026,
% 0.10/0.36 % Fri Sep 25 22:23:24 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 40.69/5.59
% 40.69/5.59 % given #500 (W,wt=37): 11279 is_a_theorem(implies(not(implies(A,implies(B,C))),implies(D,not(C)))). [hyper(6,a,3336,a,b,11221,a)].
% 40.69/5.59
% 40.69/5.59 % SZS status Theorem for theBenchmark
% 40.69/5.59
% 40.69/5.59 % Proof 1 at 3.79 (+ 1.37) seconds.
% 40.69/5.59 % Length of proof is 41.
% 40.69/5.59 % Level of proof is 24.
% 40.69/5.59 % Maximum clause weight is 62.000.
% 40.69/5.59 % Given clauses 564.
% 40.69/5.59
% 40.69/5.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------