%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV179+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 2.18s 0.75s
% Output : CNFRefutation 2.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 5 unt; 0 def)
% Number of atoms : 62 ( 20 equ)
% Maximal formula atoms : 26 ( 6 avg)
% Number of connectives : 58 ( 5 ~; 3 |; 32 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 12 con; 0-3 aty)
% Number of variables : 17 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cl5_nebula_init_0071,conjecture,
( ( ! [H] :
( ( leq(H,n4)
& leq(n0,H) )
=> a_select2(sigma_init,H) = init )
& ! [G] :
( ( leq(G,n4)
& leq(n0,G) )
=> a_select2(rho_init,G) = init )
& ! [F] :
( ( leq(F,n4)
& leq(n0,F) )
=> a_select2(mu_init,F) = init )
& ! [E] :
( ( leq(E,pred(pv68))
& leq(n0,E) )
=> a_select2(rhoold_init,E) = init )
& ! [D] :
( ( leq(D,n4)
& leq(n0,D) )
=> a_select2(muold_init,D) = init )
& ! [C] :
( ( leq(C,n4)
& leq(n0,C) )
=> a_select3(center_init,C,n0) = init )
& ! [A] :
( ( leq(A,n135299)
& leq(n0,A) )
=> ! [B] :
( ( leq(B,n4)
& leq(n0,B) )
=> a_select3(q_init,A,B) = init ) )
& leq(pv68,n4)
& leq(n0,pv68) )
=> a_select2(rho_init,pv68) = init ),
file('theBenchmark.p',cl5_nebula_init_0071) ).
fof(cl5_nebula_init_0071_neg,negated_conjecture,
~ ( ( ! [H] :
( ( leq(H,n4)
& leq(n0,H) )
=> a_select2(sigma_init,H) = init )
& ! [G] :
( ( leq(G,n4)
& leq(n0,G) )
=> a_select2(rho_init,G) = init )
& ! [F] :
( ( leq(F,n4)
& leq(n0,F) )
=> a_select2(mu_init,F) = init )
& ! [E] :
( ( leq(E,pred(pv68))
& leq(n0,E) )
=> a_select2(rhoold_init,E) = init )
& ! [D] :
( ( leq(D,n4)
& leq(n0,D) )
=> a_select2(muold_init,D) = init )
& ! [C] :
( ( leq(C,n4)
& leq(n0,C) )
=> a_select3(center_init,C,n0) = init )
& ! [A] :
( ( leq(A,n135299)
& leq(n0,A) )
=> ! [B] :
( ( leq(B,n4)
& leq(n0,B) )
=> a_select3(q_init,A,B) = init ) )
& leq(pv68,n4)
& leq(n0,pv68) )
=> a_select2(rho_init,pv68) = init ),
inference(assume_negation,[status(cth)],[cl5_nebula_init_0071]) ).
cnf(c_363,negated_conjecture,
leq(n0,pv68),
inference(clausify,[status(thm)],[cl5_nebula_init_0071_neg]) ).
cnf(c_364,negated_conjecture,
leq(pv68,n4),
inference(clausify,[status(thm)],[cl5_nebula_init_0071_neg]) ).
cnf(c_370,negated_conjecture,
( a_select2(rho_init,A) = init
| ~ leq(A,n4)
| ~ leq(n0,A) ),
inference(clausify,[status(thm)],[cl5_nebula_init_0071_neg]) ).
cnf(c_372,negated_conjecture,
a_select2(rho_init,pv68) != init,
inference(clausify,[status(thm)],[cl5_nebula_init_0071_neg]) ).
cnf(c_2463,negated_conjecture,
( a_select2(rho_init,pv68) = init
| ~ leq(pv68,n4) ),
inference(resolve,[status(thm)],[c_370,c_363]) ).
cnf(c_2464,negated_conjecture,
a_select2(rho_init,pv68) = init,
inference(resolve,[status(thm)],[c_364,c_2463]) ).
cnf(c_2462,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_372,c_2464]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV179+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 13:18:19 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 1406955 was started by sandbox on n019,
% 0.11/0.37 % Sat Sep 26 13:18:19 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.43
% 0.11/0.43 % From the command line: assign(max_seconds, 300).
% 2.18/0.75
% 2.18/0.75 % SZS status Theorem for theBenchmark
% 2.18/0.75
% 2.18/0.75 % Proof 1 at 0.26 (+ 0.04) seconds.
% 2.18/0.75 % Length of proof is 6.
% 2.18/0.75 % Level of proof is 2.
% 2.18/0.75 % Maximum clause weight is 21.000.
% 2.18/0.75 % Given clauses 298.
% 2.18/0.75
% 2.18/0.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------