%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL384+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 : n006.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 07:58:45 AM UTC 2026
% Result : Theorem 7.34s 1.34s
% Output : CNFRefutation 7.34s
% 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 : 216 ( 47 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_45,conjecture,
is_a_theorem(implies(implies(x,implies(y,z)),implies(implies(not(z),y),implies(x,z)))),
file('theBenchmark.p',prove_cn_45) ).
fof(prove_cn_45_neg,negated_conjecture,
~ is_a_theorem(implies(implies(x,implies(y,z)),implies(implies(not(z),y),implies(x,z)))),
inference(assume_negation,[status(cth)],[prove_cn_45]) ).
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(x,implies(y,z)),implies(implies(not(z),y),implies(x,z)))),
inference(clausify,[status(thm)],[prove_cn_45_neg]) ).
cnf(c_5664,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_5664,c_7]) ).
cnf(c_5665,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_5665,c_8]) ).
cnf(c_5666,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_5666,c_9]) ).
cnf(c_5667,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_5667,c_11]) ).
cnf(c_5668,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_5668,c_12]) ).
cnf(c_5669,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_5669,c_11]) ).
cnf(c_5670,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_5670,c_14]) ).
cnf(c_5671,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_5671,c_8]) ).
cnf(c_5672,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_5672,c_42]) ).
cnf(c_5673,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_5673,c_44]) ).
cnf(c_5674,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_5674,c_55]) ).
cnf(c_5675,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_5675,c_22]) ).
cnf(c_5676,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_5676,c_8]) ).
cnf(c_5677,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_5677,c_211]) ).
cnf(c_5678,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_5678,c_210]) ).
cnf(c_5679,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_5679,c_268]) ).
cnf(c_5680,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_5680,c_217]) ).
cnf(c_5681,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_5681,c_418]) ).
cnf(c_5682,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_5682,c_424]) ).
cnf(c_5683,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_5683,c_414]) ).
cnf(c_5684,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_5684,c_726]) ).
cnf(c_5685,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_5685,c_749]) ).
cnf(c_5686,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_5686,c_802]) ).
cnf(c_5687,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_5687,c_441]) ).
cnf(c_5688,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_5688,c_865]) ).
cnf(c_5689,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_5689,c_414]) ).
cnf(c_5690,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_5690,c_926]) ).
cnf(c_5691,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_5691,c_1265]) ).
cnf(c_5692,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_5692,c_1510]) ).
cnf(c_5693,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_1716,plain,
is_a_theorem(implies(not(A),implies(A,B))),
inference(resolve,[status(thm)],[c_5693,c_9]) ).
cnf(c_5694,plain,
( is_a_theorem(implies(C,implies(implies(B,A),A)))
| ~ is_a_theorem(implies(not(A),B)) ),
inference(resolve,[status(thm)],[c_6,c_414]) ).
cnf(c_1746,plain,
is_a_theorem(implies(A,implies(implies(implies(B,C),B),B))),
inference(resolve,[status(thm)],[c_5694,c_1716]) ).
cnf(c_5695,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_5283,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_5695,c_1746]) ).
cnf(c_5696,plain,
( is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_6,c_5283]) ).
cnf(c_5373,plain,
is_a_theorem(implies(implies(not(A),B),implies(implies(B,A),A))),
inference(resolve,[status(thm)],[c_5696,c_414]) ).
cnf(c_5697,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_5662,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(not(C),B),implies(A,C)))),
inference(resolve,[status(thm)],[c_5697,c_5373]) ).
cnf(c_5663,plain,
$false,
inference(resolve,[status(thm)],[c_5662,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL384+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 22:22:56 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3905430 was started by sandbox2 on n006,
% 0.09/0.37 % Fri Sep 25 22:22:56 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 7.34/1.34
% 7.34/1.34 % Assigning unary symbol not kb_weight 0 and highest precedence (6).
% 7.34/1.34
% 7.34/1.34 % SZS status Theorem for theBenchmark
% 7.34/1.34
% 7.34/1.34 % Proof 1 at 0.68 (+ 0.25) seconds.
% 7.34/1.34 % Length of proof is 45.
% 7.34/1.34 % Level of proof is 25.
% 7.34/1.34 % Maximum clause weight is 82.000.
% 7.34/1.34 % Given clauses 205.
% 7.34/1.34
% 7.34/1.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------