%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV180+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 09:06:58 AM UTC 2026
% Result : Theorem 5.18s 1.41s
% Output : CNFRefutation 5.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 5 unt; 0 def)
% Number of atoms : 92 ( 28 equ)
% Maximal formula atoms : 41 ( 10 avg)
% Number of connectives : 88 ( 5 ~; 3 |; 48 &)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 15 con; 0-3 aty)
% Number of variables : 25 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cl5_nebula_init_0076,conjecture,
( ( ! [L] :
( ( leq(L,n4)
& leq(n0,L) )
=> a_select2(sigmaold_init,L) = init )
& ! [K] :
( ( leq(K,n4)
& leq(n0,K) )
=> a_select2(rhoold_init,K) = init )
& ! [J] :
( ( leq(J,n4)
& leq(n0,J) )
=> a_select2(muold_init,J) = init )
& ( gt(loopcounter,n1)
=> ! [I] :
( ( leq(I,n4)
& leq(n0,I) )
=> a_select2(sigmaold_init,I) = init ) )
& ( gt(loopcounter,n1)
=> ! [H] :
( ( leq(H,n4)
& leq(n0,H) )
=> a_select2(rhoold_init,H) = init ) )
& ( gt(loopcounter,n1)
=> ! [G] :
( ( leq(G,n4)
& leq(n0,G) )
=> a_select2(muold_init,G) = init ) )
& ! [F] :
( ( leq(F,n4)
& leq(n0,F) )
=> a_select3(center_init,F,n0) = init )
& ! [E] :
( ( leq(E,n4)
& leq(n0,E) )
=> a_select2(sigma_init,E) = init )
& ! [D] :
( ( leq(D,n4)
& leq(n0,D) )
=> a_select2(mu_init,D) = init )
& ! [C] :
( ( leq(C,n4)
& leq(n0,C) )
=> a_select2(rho_init,C) = init )
& ! [A] :
( ( leq(A,n135299)
& leq(n0,A) )
=> ! [B] :
( ( leq(B,n4)
& leq(n0,B) )
=> a_select3(q_init,A,B) = init ) )
& leq(pv86,n4)
& leq(n0,pv86) )
=> a_select2(muold_init,pv86) = init ),
file('theBenchmark.p',cl5_nebula_init_0076) ).
fof(cl5_nebula_init_0076_neg,negated_conjecture,
~ ( ( ! [L] :
( ( leq(L,n4)
& leq(n0,L) )
=> a_select2(sigmaold_init,L) = init )
& ! [K] :
( ( leq(K,n4)
& leq(n0,K) )
=> a_select2(rhoold_init,K) = init )
& ! [J] :
( ( leq(J,n4)
& leq(n0,J) )
=> a_select2(muold_init,J) = init )
& ( gt(loopcounter,n1)
=> ! [I] :
( ( leq(I,n4)
& leq(n0,I) )
=> a_select2(sigmaold_init,I) = init ) )
& ( gt(loopcounter,n1)
=> ! [H] :
( ( leq(H,n4)
& leq(n0,H) )
=> a_select2(rhoold_init,H) = init ) )
& ( gt(loopcounter,n1)
=> ! [G] :
( ( leq(G,n4)
& leq(n0,G) )
=> a_select2(muold_init,G) = init ) )
& ! [F] :
( ( leq(F,n4)
& leq(n0,F) )
=> a_select3(center_init,F,n0) = init )
& ! [E] :
( ( leq(E,n4)
& leq(n0,E) )
=> a_select2(sigma_init,E) = init )
& ! [D] :
( ( leq(D,n4)
& leq(n0,D) )
=> a_select2(mu_init,D) = init )
& ! [C] :
( ( leq(C,n4)
& leq(n0,C) )
=> a_select2(rho_init,C) = init )
& ! [A] :
( ( leq(A,n135299)
& leq(n0,A) )
=> ! [B] :
( ( leq(B,n4)
& leq(n0,B) )
=> a_select3(q_init,A,B) = init ) )
& leq(pv86,n4)
& leq(n0,pv86) )
=> a_select2(muold_init,pv86) = init ),
inference(assume_negation,[status(cth)],[cl5_nebula_init_0076]) ).
cnf(c_363,negated_conjecture,
leq(n0,pv86),
inference(clausify,[status(thm)],[cl5_nebula_init_0076_neg]) ).
cnf(c_364,negated_conjecture,
leq(pv86,n4),
inference(clausify,[status(thm)],[cl5_nebula_init_0076_neg]) ).
cnf(c_373,negated_conjecture,
( a_select2(muold_init,A) = init
| ~ leq(A,n4)
| ~ leq(n0,A) ),
inference(clausify,[status(thm)],[cl5_nebula_init_0076_neg]) ).
cnf(c_376,negated_conjecture,
a_select2(muold_init,pv86) != init,
inference(clausify,[status(thm)],[cl5_nebula_init_0076_neg]) ).
cnf(c_2399,negated_conjecture,
( a_select2(muold_init,pv86) = init
| ~ leq(pv86,n4) ),
inference(resolve,[status(thm)],[c_373,c_363]) ).
cnf(c_2400,negated_conjecture,
a_select2(muold_init,pv86) = init,
inference(resolve,[status(thm)],[c_364,c_2399]) ).
cnf(c_2398,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_376,c_2400]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV180+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n005.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sat Sep 26 13:17:47 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.44 % Process 2233221 was started by sandbox2 on n005,
% 0.15/0.44 % Sat Sep 26 13:17:47 2026
% 0.15/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.25/0.56
% 0.25/0.56 % From the command line: assign(max_seconds, 300).
% 5.18/1.41
% 5.18/1.41 % SZS status Theorem for theBenchmark
% 5.18/1.41
% 5.18/1.41 % Proof 1 at 0.69 (+ 0.14) seconds.
% 5.18/1.41 % Length of proof is 6.
% 5.18/1.41 % Level of proof is 2.
% 5.18/1.41 % Maximum clause weight is 21.000.
% 5.18/1.41 % Given clauses 298.
% 5.18/1.41
% 5.18/1.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------