%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV168+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 : n004.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 25.92s 3.86s
% Output : CNFRefutation 25.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 10 unt; 0 def)
% Number of atoms : 99 ( 30 equ)
% Maximal formula atoms : 35 ( 5 avg)
% Number of connectives : 99 ( 17 ~; 14 |; 42 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 16 con; 0-3 aty)
% Number of variables : 24 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cl5_nebula_init_0016,conjecture,
( ( ( 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,pred(pv40))
& leq(n0,E) )
=> a_select2(sigma_init,E) = init )
& ! [D] :
( ( leq(D,pred(pv40))
& 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(pv46,n135299)
& leq(pv40,n4)
& leq(n0,pv46)
& leq(n0,pv40)
& a_select2(mu_init,pv40) = init )
=> a_select3(q_init,pv46,pv40) = init ),
file('theBenchmark.p',cl5_nebula_init_0016) ).
fof(cl5_nebula_init_0016_neg,negated_conjecture,
~ ( ( ( 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,pred(pv40))
& leq(n0,E) )
=> a_select2(sigma_init,E) = init )
& ! [D] :
( ( leq(D,pred(pv40))
& 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(pv46,n135299)
& leq(pv40,n4)
& leq(n0,pv46)
& leq(n0,pv40)
& a_select2(mu_init,pv40) = init )
=> a_select3(q_init,pv46,pv40) = init ),
inference(assume_negation,[status(cth)],[cl5_nebula_init_0016]) ).
cnf(c_365,negated_conjecture,
a_select2(mu_init,pv40) = init,
inference(clausify,[status(thm)],[cl5_nebula_init_0016_neg]) ).
cnf(c_366,negated_conjecture,
init = a_select2(mu_init,pv40),
inference(copy,[status(thm)],[c_365]) ).
cnf(c_367,negated_conjecture,
leq(n0,pv40),
inference(clausify,[status(thm)],[cl5_nebula_init_0016_neg]) ).
cnf(c_368,negated_conjecture,
leq(n0,pv46),
inference(clausify,[status(thm)],[cl5_nebula_init_0016_neg]) ).
cnf(c_369,negated_conjecture,
leq(pv40,n4),
inference(clausify,[status(thm)],[cl5_nebula_init_0016_neg]) ).
cnf(c_370,negated_conjecture,
leq(pv46,n135299),
inference(clausify,[status(thm)],[cl5_nebula_init_0016_neg]) ).
cnf(c_371,negated_conjecture,
( a_select3(q_init,A,B) = init
| ~ leq(B,n4)
| ~ leq(n0,B)
| ~ leq(A,n135299)
| ~ leq(n0,A) ),
inference(clausify,[status(thm)],[cl5_nebula_init_0016_neg]) ).
cnf(c_372,negated_conjecture,
( a_select3(q_init,A,B) = a_select2(mu_init,pv40)
| ~ leq(B,n4)
| ~ leq(n0,B)
| ~ leq(A,n135299)
| ~ leq(n0,A) ),
inference(paramod,[status(thm)],[c_366,c_371]) ).
cnf(c_387,negated_conjecture,
a_select3(q_init,pv46,pv40) != init,
inference(clausify,[status(thm)],[cl5_nebula_init_0016_neg]) ).
cnf(c_388,negated_conjecture,
a_select3(q_init,pv46,pv40) != a_select2(mu_init,pv40),
inference(paramod,[status(thm)],[c_366,c_387]) ).
cnf(c_2938,negated_conjecture,
( a_select3(q_init,pv46,A) = a_select2(mu_init,pv40)
| ~ leq(A,n4)
| ~ leq(n0,A)
| ~ leq(pv46,n135299) ),
inference(resolve,[status(thm)],[c_372,c_368]) ).
cnf(c_2939,negated_conjecture,
( a_select3(q_init,pv46,A) = a_select2(mu_init,pv40)
| ~ leq(A,n4)
| ~ leq(n0,A) ),
inference(resolve,[status(thm)],[c_2938,c_370]) ).
cnf(c_2940,negated_conjecture,
( a_select3(q_init,pv46,pv40) = a_select2(mu_init,pv40)
| ~ leq(pv40,n4) ),
inference(resolve,[status(thm)],[c_2939,c_367]) ).
cnf(c_2941,negated_conjecture,
a_select3(q_init,pv46,pv40) = a_select2(mu_init,pv40),
inference(resolve,[status(thm)],[c_2940,c_369]) ).
cnf(c_2937,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_388,c_2941]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV168+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n004.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 13:17:21 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 1800723 was started by sandbox2 on n004,
% 0.17/0.44 % Sat Sep 26 13:17:21 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.27/0.55
% 0.27/0.55 % From the command line: assign(max_seconds, 300).
% 25.92/3.86
% 25.92/3.86 % SZS status Theorem for theBenchmark
% 25.92/3.86
% 25.92/3.86 % Proof 1 at 2.99 (+ 0.25) seconds.
% 25.92/3.86 % Length of proof is 12.
% 25.92/3.86 % Level of proof is 4.
% 25.92/3.86 % Maximum clause weight is 30.000.
% 25.92/3.86 % Given clauses 296.
% 25.92/3.86
% 25.92/3.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------