%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV183+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 : n011.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 09:06:59 AM UTC 2026
% Result : Theorem 3.09s 0.89s
% Output : CNFRefutation 3.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 220 ( 64 equ)
% Maximal formula atoms : 42 ( 18 avg)
% Number of connectives : 297 ( 89 ~; 84 |; 90 &)
% ( 0 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 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 : 64 ( 0 sgn 62 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cl5_nebula_init_0091,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 ) )
& gt(loopcounter,n0) )
=> ! [M] :
( ( leq(M,n4)
& leq(n0,M) )
=> a_select2(mu_init,M) = init ) ),
file('theBenchmark.p',cl5_nebula_init_0091) ).
fof(cl5_nebula_init_0091_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 ) )
& gt(loopcounter,n0) )
=> ! [M] :
( ( leq(M,n4)
& leq(n0,M) )
=> a_select2(mu_init,M) = init ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_init_0091]) ).
fof(nnf_56,plain,
( ? [M] :
( a_select2(mu_init,M) != init
& leq(M,n4)
& leq(n0,M) )
& ! [L] :
( a_select2(sigmaold_init,L) = init
| ~ leq(L,n4)
| ~ leq(n0,L) )
& ! [K] :
( a_select2(rhoold_init,K) = init
| ~ leq(K,n4)
| ~ leq(n0,K) )
& ! [J] :
( a_select2(muold_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,n4)
| ~ leq(n0,E) )
& ! [D] :
( a_select2(mu_init,D) = init
| ~ leq(D,n4)
| ~ 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,n0) ),
inference(fof_nnf,[status(thm)],[cl5_nebula_init_0091_neg]) ).
fof(sk_cl5_nebula_init_0091_neg_sk,plain,
( a_select2(mu_init,sK0) != init
& leq(sK0,n4)
& leq(n0,sK0)
& ! [L] :
( a_select2(sigmaold_init,L) = init
| ~ leq(L,n4)
| ~ leq(n0,L) )
& ! [K] :
( a_select2(rhoold_init,K) = init
| ~ leq(K,n4)
| ~ leq(n0,K) )
& ! [J] :
( a_select2(muold_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,n4)
| ~ leq(n0,E) )
& ! [D] :
( a_select2(mu_init,D) = init
| ~ leq(D,n4)
| ~ 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,n0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(M,sK0)],[nnf_56]) ).
fof(sk_cl5_nebula_init_0091_neg,plain,
( a_select2(mu_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) )
& ! [VAR_0] :
( a_select2(rhoold_init,VAR_0) = init
| ~ leq(VAR_0,n4)
| ~ leq(n0,VAR_0) )
& ! [VAR_0] :
( a_select2(muold_init,VAR_0) = init
| ~ leq(VAR_0,n4)
| ~ leq(n0,VAR_0) )
& ! [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,n4)
| ~ leq(n0,VAR_0) )
& ! [VAR_0] :
( a_select2(mu_init,VAR_0) = init
| ~ leq(VAR_0,n4)
| ~ 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,n0) ),
inference(cnf_transformation,[status(thm)],[sk_cl5_nebula_init_0091_neg_sk]) ).
cnf(c_368,negated_conjecture,
( a_select2(mu_init,A) = init
| ~ leq(A,n4)
| ~ leq(n0,A) ),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0091_neg]) ).
cnf(c_377,negated_conjecture,
leq(n0,sK0),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0091_neg]) ).
cnf(c_378,negated_conjecture,
leq(sK0,n4),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0091_neg]) ).
cnf(c_379,negated_conjecture,
a_select2(mu_init,sK0) != init,
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0091_neg]) ).
cnf(c_1404,negated_conjecture,
( a_select2(mu_init,sK0) = init
| ~ leq(sK0,n4) ),
inference(resolve,[status(thm)],[c_377,c_368]) ).
cnf(c_1405,negated_conjecture,
a_select2(mu_init,sK0) = init,
inference(resolve,[status(thm)],[c_378,c_1404]) ).
cnf(c_1403,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_379,c_1405]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV183+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n011.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 13:18:29 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.35 % Process 646451 was started by sandbox2 on n011,
% 0.10/0.35 % Sat Sep 26 13:18:29 2026
% 0.10/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.41
% 0.14/0.41 % From the command line: assign(max_seconds, 300).
% 3.09/0.89
% 3.09/0.89 % SZS status Theorem for theBenchmark
% 3.09/0.89
% 3.09/0.89 % Proof 1 at 0.38 (+ 0.07) seconds.
% 3.09/0.89 % Length of proof is 6.
% 3.09/0.89 % Level of proof is 2.
% 3.09/0.89 % Maximum clause weight is 21.000.
% 3.09/0.89 % Given clauses 300.
% 3.09/0.89
% 3.09/0.89 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------