%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV177+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 : n003.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 8.37s 6.63s
% Output : CNFRefutation 8.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 6 unt; 0 def)
% Number of atoms : 200 ( 50 equ)
% Maximal formula atoms : 37 ( 14 avg)
% Number of connectives : 260 ( 74 ~; 69 |; 89 &)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 17 con; 0-3 aty)
% Number of variables : 50 ( 0 sgn 47 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cl5_nebula_init_0061,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 ) )
& gt(loopcounter,n1)
& leq(pv45,n135299)
& leq(pv40,n4)
& leq(n0,pv45)
& leq(n0,pv40) )
=> ! [J] :
( ( leq(J,n4)
& leq(n0,J) )
=> a_select2(rhoold_init,J) = init ) ),
file('theBenchmark.p',cl5_nebula_init_0061) ).
fof(cl5_nebula_init_0061_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 ) )
& gt(loopcounter,n1)
& leq(pv45,n135299)
& leq(pv40,n4)
& leq(n0,pv45)
& leq(n0,pv40) )
=> ! [J] :
( ( leq(J,n4)
& leq(n0,J) )
=> a_select2(rhoold_init,J) = init ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_init_0061]) ).
fof(nnf_56,plain,
( ? [J] :
( a_select2(rhoold_init,J) != init
& leq(J,n4)
& leq(n0,J) )
& ( ! [I] :
( a_select2(sigmaold_init,I) = init
| ~ leq(I,n4)
| ~ leq(n0,I) )
| ~ gt(loopcounter,n1) )
& ( ! [H] :
( a_select2(rhoold_init,H) = init
| ~ leq(H,n4)
| ~ leq(n0,H) )
| ~ gt(loopcounter,n1) )
& ( ! [G] :
( a_select2(muold_init,G) = init
| ~ leq(G,n4)
| ~ leq(n0,G) )
| ~ gt(loopcounter,n1) )
& ! [F] :
( a_select3(center_init,F,n0) = init
| ~ leq(F,n4)
| ~ leq(n0,F) )
& ! [E] :
( a_select2(sigma_init,E) = init
| ~ leq(E,pred(pv40))
| ~ leq(n0,E) )
& ! [D] :
( a_select2(mu_init,D) = init
| ~ leq(D,pred(pv40))
| ~ leq(n0,D) )
& ! [C] :
( a_select2(rho_init,C) = init
| ~ leq(C,n4)
| ~ leq(n0,C) )
& ! [A] :
( ! [B] :
( a_select3(q_init,A,B) = init
| ~ leq(B,n4)
| ~ leq(n0,B) )
| ~ leq(A,n135299)
| ~ leq(n0,A) )
& gt(loopcounter,n1)
& leq(pv45,n135299)
& leq(pv40,n4)
& leq(n0,pv45)
& leq(n0,pv40) ),
inference(fof_nnf,[status(thm)],[cl5_nebula_init_0061_neg]) ).
fof(sk_cl5_nebula_init_0061_neg_sk,plain,
( a_select2(rhoold_init,sK0) != init
& leq(sK0,n4)
& leq(n0,sK0)
& ( ! [I] :
( a_select2(sigmaold_init,I) = init
| ~ leq(I,n4)
| ~ leq(n0,I) )
| ~ gt(loopcounter,n1) )
& ( ! [H] :
( a_select2(rhoold_init,H) = init
| ~ leq(H,n4)
| ~ leq(n0,H) )
| ~ gt(loopcounter,n1) )
& ( ! [G] :
( a_select2(muold_init,G) = init
| ~ leq(G,n4)
| ~ leq(n0,G) )
| ~ gt(loopcounter,n1) )
& ! [F] :
( a_select3(center_init,F,n0) = init
| ~ leq(F,n4)
| ~ leq(n0,F) )
& ! [E] :
( a_select2(sigma_init,E) = init
| ~ leq(E,pred(pv40))
| ~ leq(n0,E) )
& ! [D] :
( a_select2(mu_init,D) = init
| ~ leq(D,pred(pv40))
| ~ leq(n0,D) )
& ! [C] :
( a_select2(rho_init,C) = init
| ~ leq(C,n4)
| ~ leq(n0,C) )
& ! [A] :
( ! [B] :
( a_select3(q_init,A,B) = init
| ~ leq(B,n4)
| ~ leq(n0,B) )
| ~ leq(A,n135299)
| ~ leq(n0,A) )
& gt(loopcounter,n1)
& leq(pv45,n135299)
& leq(pv40,n4)
& leq(n0,pv45)
& leq(n0,pv40) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(J,sK0)],[nnf_56]) ).
fof(sk_cl5_nebula_init_0061_neg,plain,
( a_select2(rhoold_init,sK0) != init
& leq(sK0,n4)
& leq(n0,sK0)
& ! [VAR_0] :
( a_select2(sigmaold_init,VAR_0) = init
| ~ leq(VAR_0,n4)
| ~ leq(n0,VAR_0)
| ~ gt(loopcounter,n1) )
& ! [VAR_0] :
( a_select2(rhoold_init,VAR_0) = init
| ~ leq(VAR_0,n4)
| ~ leq(n0,VAR_0)
| ~ gt(loopcounter,n1) )
& ! [VAR_0] :
( a_select2(muold_init,VAR_0) = init
| ~ leq(VAR_0,n4)
| ~ leq(n0,VAR_0)
| ~ gt(loopcounter,n1) )
& ! [VAR_0] :
( a_select3(center_init,VAR_0,n0) = init
| ~ leq(VAR_0,n4)
| ~ leq(n0,VAR_0) )
& ! [VAR_0] :
( a_select2(sigma_init,VAR_0) = init
| ~ leq(VAR_0,pred(pv40))
| ~ leq(n0,VAR_0) )
& ! [VAR_0] :
( a_select2(mu_init,VAR_0) = init
| ~ leq(VAR_0,pred(pv40))
| ~ leq(n0,VAR_0) )
& ! [VAR_0] :
( a_select2(rho_init,VAR_0) = init
| ~ leq(VAR_0,n4)
| ~ leq(n0,VAR_0) )
& ! [VAR_0,VAR_1] :
( a_select3(q_init,VAR_0,VAR_1) = init
| ~ leq(VAR_1,n4)
| ~ leq(n0,VAR_1)
| ~ leq(VAR_0,n135299)
| ~ leq(n0,VAR_0) )
& gt(loopcounter,n1)
& leq(pv45,n135299)
& leq(pv40,n4)
& leq(n0,pv45)
& leq(n0,pv40) ),
inference(cnf_transformation,[status(thm)],[sk_cl5_nebula_init_0061_neg_sk]) ).
cnf(c_367,negated_conjecture,
gt(loopcounter,n1),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0061_neg]) ).
cnf(c_375,negated_conjecture,
( a_select2(rhoold_init,A) = init
| ~ leq(A,n4)
| ~ leq(n0,A)
| ~ gt(loopcounter,n1) ),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0061_neg]) ).
cnf(c_376,negated_conjecture,
( a_select2(rhoold_init,A) = init
| ~ leq(A,n4)
| ~ leq(n0,A) ),
inference(resolve,[status(thm)],[c_367,c_375]) ).
cnf(c_379,negated_conjecture,
leq(n0,sK0),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0061_neg]) ).
cnf(c_380,negated_conjecture,
leq(sK0,n4),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0061_neg]) ).
cnf(c_381,negated_conjecture,
a_select2(rhoold_init,sK0) != init,
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0061_neg]) ).
cnf(c_2955,negated_conjecture,
( a_select2(rhoold_init,sK0) = init
| ~ leq(sK0,n4) ),
inference(resolve,[status(thm)],[c_379,c_376]) ).
cnf(c_2956,negated_conjecture,
a_select2(rhoold_init,sK0) = init,
inference(resolve,[status(thm)],[c_380,c_2955]) ).
cnf(c_2954,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_381,c_2956]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV177+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.44 % Computer : n003.cluster.edu
% 0.15/5.44 % Model : x86_64 x86_64
% 0.15/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.44 % Memory : 8046.5625MB
% 0.15/5.44 % OS : Linux 6.8.0-71-generic
% 0.15/5.44 % CPULimit : 300
% 0.15/5.44 % WCLimit : 300
% 0.15/5.44 % DateTime : Sat Sep 26 13:20:00 UTC 2026
% 0.15/5.45 % CPUTime :
% 0.15/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/5.45 % Process 2985383 was started by sandbox2 on n003,
% 0.15/5.45 % Sat Sep 26 13:20:00 2026
% 0.15/5.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.21/5.57
% 0.21/5.57 % From the command line: assign(max_seconds, 300).
% 8.37/6.63
% 8.37/6.63 % SZS status Theorem for theBenchmark
% 8.37/6.63
% 8.37/6.63 % Proof 1 at 0.85 (+ 0.17) seconds.
% 8.37/6.63 % Length of proof is 8.
% 8.37/6.63 % Level of proof is 3.
% 8.37/6.63 % Maximum clause weight is 21.000.
% 8.37/6.63 % Given clauses 304.
% 8.37/6.63
% 8.37/6.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------