%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV169+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 09:06:57 AM UTC 2026
% Result : Theorem 4.80s 1.21s
% Output : CNFRefutation 4.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 5 unt; 0 def)
% Number of atoms : 66 ( 16 equ)
% Maximal formula atoms : 28 ( 7 avg)
% Number of connectives : 62 ( 5 ~; 3 |; 38 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-3 aty)
% Number of variables : 15 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cl5_nebula_init_0021,conjecture,
( ( ! [G] :
( ( leq(G,n4)
& leq(n0,G) )
=> a_select3(center_init,G,n0) = init )
& ! [E] :
( ( leq(E,pred(pv10))
& leq(n0,E) )
=> ! [F] :
( ( leq(F,n4)
& leq(n0,F) )
=> a_select3(q_init,E,F) = init ) )
& ! [C,D] :
( ( leq(D,n4)
& leq(C,n135299)
& leq(n0,D)
& leq(n0,C) )
=> ( gt(pv10,C)
=> a_select3(q_init,C,D) = init ) )
& ! [A,B] :
( ( leq(B,n4)
& leq(A,n135299)
& leq(n0,B)
& leq(n0,A) )
=> ( ( gt(pv11,B)
& A = pv10 )
=> a_select3(q_init,A,B) = init ) )
& leq(pv65,n4)
& leq(pv11,n4)
& leq(pv10,n135299)
& leq(n0,pv65)
& leq(n0,pv11)
& leq(n0,pv10) )
=> a_select3(center_init,pv65,n0) = init ),
file('theBenchmark.p',cl5_nebula_init_0021) ).
fof(cl5_nebula_init_0021_neg,negated_conjecture,
~ ( ( ! [G] :
( ( leq(G,n4)
& leq(n0,G) )
=> a_select3(center_init,G,n0) = init )
& ! [E] :
( ( leq(E,pred(pv10))
& leq(n0,E) )
=> ! [F] :
( ( leq(F,n4)
& leq(n0,F) )
=> a_select3(q_init,E,F) = init ) )
& ! [C,D] :
( ( leq(D,n4)
& leq(C,n135299)
& leq(n0,D)
& leq(n0,C) )
=> ( gt(pv10,C)
=> a_select3(q_init,C,D) = init ) )
& ! [A,B] :
( ( leq(B,n4)
& leq(A,n135299)
& leq(n0,B)
& leq(n0,A) )
=> ( ( gt(pv11,B)
& A = pv10 )
=> a_select3(q_init,A,B) = init ) )
& leq(pv65,n4)
& leq(pv11,n4)
& leq(pv10,n135299)
& leq(n0,pv65)
& leq(n0,pv11)
& leq(n0,pv10) )
=> a_select3(center_init,pv65,n0) = init ),
inference(assume_negation,[status(cth)],[cl5_nebula_init_0021]) ).
cnf(c_365,negated_conjecture,
leq(n0,pv65),
inference(clausify,[status(thm)],[cl5_nebula_init_0021_neg]) ).
cnf(c_368,negated_conjecture,
leq(pv65,n4),
inference(clausify,[status(thm)],[cl5_nebula_init_0021_neg]) ).
cnf(c_372,negated_conjecture,
( a_select3(center_init,A,n0) = init
| ~ leq(A,n4)
| ~ leq(n0,A) ),
inference(clausify,[status(thm)],[cl5_nebula_init_0021_neg]) ).
cnf(c_373,negated_conjecture,
a_select3(center_init,pv65,n0) != init,
inference(clausify,[status(thm)],[cl5_nebula_init_0021_neg]) ).
cnf(c_3534,negated_conjecture,
( a_select3(center_init,pv65,n0) = init
| ~ leq(pv65,n4) ),
inference(resolve,[status(thm)],[c_372,c_365]) ).
cnf(c_3535,negated_conjecture,
a_select3(center_init,pv65,n0) = init,
inference(resolve,[status(thm)],[c_368,c_3534]) ).
cnf(c_3533,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_373,c_3535]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV169+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n005.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 13:17:31 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 2232826 was started by sandbox2 on n005,
% 0.17/0.43 % Sat Sep 26 13:17:31 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.27/0.53
% 0.27/0.53 % From the command line: assign(max_seconds, 300).
% 4.80/1.21
% 4.80/1.21 % SZS status Theorem for theBenchmark
% 4.80/1.21
% 4.80/1.21 % Proof 1 at 0.54 (+ 0.12) seconds.
% 4.80/1.21 % Length of proof is 6.
% 4.80/1.21 % Level of proof is 2.
% 4.80/1.21 % Maximum clause weight is 22.000.
% 4.80/1.21 % Given clauses 300.
% 4.80/1.21
% 4.80/1.21 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------