%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL392+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 : n016.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 07:58:47 AM UTC 2026
% Result : Theorem 47.07s 6.52s
% Output : CNFRefutation 47.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 5
% Syntax : Number of formulae : 80 ( 44 unt; 0 def)
% Number of atoms : 118 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 76 ( 38 ~; 36 |; 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 : 221 ( 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_56,conjecture,
is_a_theorem(implies(implies(implies(implies(x,y),y),z),implies(implies(not(x),y),z))),
file('theBenchmark.p',prove_cn_56) ).
fof(prove_cn_56_neg,negated_conjecture,
~ is_a_theorem(implies(implies(implies(implies(x,y),y),z),implies(implies(not(x),y),z))),
inference(assume_negation,[status(cth)],[prove_cn_56]) ).
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(implies(x,y),y),z),implies(implies(not(x),y),z))),
inference(clausify,[status(thm)],[prove_cn_56_neg]) ).
cnf(c_22991,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_22991,c_7]) ).
cnf(c_22992,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_22992,c_8]) ).
cnf(c_22993,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_22993,c_9]) ).
cnf(c_22994,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_22994,c_11]) ).
cnf(c_22995,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_25,plain,
is_a_theorem(implies(implies(implies(implies(not(A),A),B),C),implies(implies(A,B),C))),
inference(resolve,[status(thm)],[c_22995,c_12]) ).
cnf(c_22996,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_22996,c_11]) ).
cnf(c_22997,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_22997,c_14]) ).
cnf(c_22998,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_22998,c_8]) ).
cnf(c_22999,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_22999,c_39]) ).
cnf(c_23000,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_23000,c_34]) ).
cnf(c_23001,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_23001,c_41]) ).
cnf(c_23002,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_23002,c_12]) ).
cnf(c_23003,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_23003,c_49]) ).
cnf(c_23004,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_23004,c_12]) ).
cnf(c_23005,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_23005,c_210]) ).
cnf(c_23006,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_23006,c_420]) ).
cnf(c_23007,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_23007,c_912]) ).
cnf(c_23008,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_23008,c_944]) ).
cnf(c_23009,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_23009,c_912]) ).
cnf(c_23010,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_23010,c_1097]) ).
cnf(c_23011,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_23011,c_1116]) ).
cnf(c_23012,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_23012,c_1212]) ).
cnf(c_23013,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_23013,c_1212]) ).
cnf(c_23014,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_23014,c_2854]) ).
cnf(c_23015,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_23015,c_2937]) ).
cnf(c_23016,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_23016,c_3031]) ).
cnf(c_23017,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_23017,c_7]) ).
cnf(c_23018,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_23018,c_2836]) ).
cnf(c_23019,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_23019,c_3785]) ).
cnf(c_23020,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_23020,c_17914]) ).
cnf(c_23021,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_23021,c_18037]) ).
cnf(c_23022,plain,
( is_a_theorem(implies(implies(A,B),C))
| ~ is_a_theorem(implies(implies(implies(not(A),A),B),C)) ),
inference(resolve,[status(thm)],[c_6,c_25]) ).
cnf(c_22732,plain,
is_a_theorem(implies(implies(A,B),implies(implies(not(A),B),B))),
inference(resolve,[status(thm)],[c_23022,c_22563]) ).
cnf(c_23023,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_22770,plain,
is_a_theorem(implies(implies(not(A),B),implies(implies(A,B),B))),
inference(resolve,[status(thm)],[c_23023,c_22732]) ).
cnf(c_23024,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_22989,plain,
is_a_theorem(implies(implies(implies(implies(A,B),B),C),implies(implies(not(A),B),C))),
inference(resolve,[status(thm)],[c_23024,c_22770]) ).
cnf(c_22990,plain,
$false,
inference(resolve,[status(thm)],[c_22989,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL392+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n016.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 22:29:15 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 3458940 was started by sandbox2 on n016,
% 0.17/0.45 % Fri Sep 25 22:29:15 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 47.07/6.52
% 47.07/6.52 % 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)].
% 47.07/6.52
% 47.07/6.52 % SZS status Theorem for theBenchmark
% 47.07/6.52
% 47.07/6.52 % Proof 1 at 4.37 (+ 1.49) seconds.
% 47.07/6.52 % Length of proof is 45.
% 47.07/6.52 % Level of proof is 27.
% 47.07/6.52 % Maximum clause weight is 62.000.
% 47.07/6.52 % Given clauses 569.
% 47.07/6.52
% 47.07/6.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------