%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV167+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 : n009.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 09:06:56 AM UTC 2026
% Result : Theorem 34.44s 5.49s
% Output : CNFRefutation 34.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 210 ( 67 equ)
% Maximal formula atoms : 36 ( 9 avg)
% Number of connectives : 263 ( 76 ~; 72 |; 85 &)
% ( 1 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 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 : 57 ( 0 sgn 51 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(leq_gt2,axiom,
! [X,Y] :
( ( X != Y
& leq(X,Y) )
=> gt(Y,X) ),
file('theBenchmark.p',leq_gt2) ).
fof(leq_gt_pred,axiom,
! [X,Y] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
file('theBenchmark.p',leq_gt_pred) ).
fof(cl5_nebula_init_0011,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(pv40,n4)
& leq(n0,pv40)
& a_select2(sigma_init,pv40) = init
& a_select2(mu_init,pv40) = init )
=> ! [J] :
( ( leq(J,pv40)
& leq(n0,J) )
=> a_select2(mu_init,J) = init ) ),
file('theBenchmark.p',cl5_nebula_init_0011) ).
fof(cl5_nebula_init_0011_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(pv40,n4)
& leq(n0,pv40)
& a_select2(sigma_init,pv40) = init
& a_select2(mu_init,pv40) = init )
=> ! [J] :
( ( leq(J,pv40)
& leq(n0,J) )
=> a_select2(mu_init,J) = init ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_init_0011]) ).
cnf(c_67,plain,
( gt(B,A)
| B = A
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_gt2]) ).
cnf(c_69,plain,
( ~ gt(B,A)
| leq(A,pred(B)) ),
inference(clausify,[status(thm)],[leq_gt_pred]) ).
fof(nnf_56,plain,
( ? [J] :
( a_select2(mu_init,J) != init
& leq(J,pv40)
& 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) )
& leq(pv40,n4)
& leq(n0,pv40)
& a_select2(sigma_init,pv40) = init
& a_select2(mu_init,pv40) = init ),
inference(fof_nnf,[status(thm)],[cl5_nebula_init_0011_neg]) ).
fof(sk_cl5_nebula_init_0011_neg_sk,plain,
( a_select2(mu_init,sK0) != init
& leq(sK0,pv40)
& 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) )
& leq(pv40,n4)
& leq(n0,pv40)
& a_select2(sigma_init,pv40) = init
& a_select2(mu_init,pv40) = init ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(J,sK0)],[nnf_56]) ).
fof(sk_cl5_nebula_init_0011_neg,plain,
( a_select2(mu_init,sK0) != init
& leq(sK0,pv40)
& 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) )
& leq(pv40,n4)
& leq(n0,pv40)
& a_select2(sigma_init,pv40) = init
& a_select2(mu_init,pv40) = init ),
inference(cnf_transformation,[status(thm)],[sk_cl5_nebula_init_0011_neg_sk]) ).
cnf(c_363,negated_conjecture,
a_select2(mu_init,pv40) = init,
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0011_neg]) ).
cnf(c_364,negated_conjecture,
init = a_select2(mu_init,pv40),
inference(copy,[status(thm)],[c_363]) ).
cnf(c_371,negated_conjecture,
( a_select2(mu_init,A) = init
| ~ leq(A,pred(pv40))
| ~ leq(n0,A) ),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0011_neg]) ).
cnf(c_377,negated_conjecture,
leq(n0,sK0),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0011_neg]) ).
cnf(c_378,negated_conjecture,
leq(sK0,pv40),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0011_neg]) ).
cnf(c_379,negated_conjecture,
a_select2(mu_init,sK0) != init,
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_init_0011_neg]) ).
cnf(c_15222,negated_conjecture,
( a_select2(mu_init,sK0) = init
| ~ leq(sK0,pred(pv40)) ),
inference(resolve,[status(thm)],[c_377,c_371]) ).
cnf(c_2482,negated_conjecture,
~ leq(sK0,pred(pv40)),
inference(resolve,[status(thm)],[c_379,c_15222]) ).
cnf(c_15223,negated_conjecture,
( gt(pv40,sK0)
| pv40 = sK0 ),
inference(resolve,[status(thm)],[c_378,c_67]) ).
cnf(c_2965,negated_conjecture,
( gt(pv40,sK0)
| sK0 = pv40 ),
inference(copy,[status(thm)],[c_15223]) ).
cnf(c_15224,plain,
( leq(sK0,pred(pv40))
| sK0 = pv40 ),
inference(resolve,[status(thm)],[c_2965,c_69]) ).
cnf(c_15129,plain,
sK0 = pv40,
inference(resolve,[status(thm)],[c_2482,c_15224]) ).
cnf(c_15225,plain,
a_select2(mu_init,pv40) != init,
inference(paramod,[status(thm)],[c_15129,c_379]) ).
cnf(c_15221,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_364,c_15225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV167+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 : n009.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 13:17:29 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 236739 was started by sandbox2 on n009,
% 0.10/0.35 % Sat Sep 26 13:17:29 2026
% 0.10/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.47
% 0.13/0.47 % From the command line: assign(max_seconds, 300).
% 34.44/5.49
% 34.44/5.49 % given #500 (I,wt=143): 574 leq(n0,f19(A,B,C,D,E,F,n0,V6)) | leq(f21(A,B,C,D,E,F,n0,V6),n0) | leq(f23(A,B,C,D,E,F,n0,V6),n0) | -leq(n0,V7) | -leq(V7,n0) | a_select3(tptp_madd(A,tptp_mmul(B,tptp_mmul(tptp_madd(tptp_mmul(C,tptp_mmul(D,trans(C))),tptp_mmul(E,tptp_mmul(F,trans(E)))),trans(B)))),n0,V7) = a_select3(tptp_madd(A,tptp_mmul(B,tptp_mmul(tptp_madd(tptp_mmul(C,tptp_mmul(D,trans(C))),tptp_mmul(E,tptp_mmul(F,trans(E)))),trans(B)))),V7,n0). [factor(159,d,e),flip(g),unit_del(d,64)].
% 34.44/5.49
% 34.44/5.49 % SZS status Theorem for theBenchmark
% 34.44/5.49
% 34.44/5.49 % Proof 1 at 4.17 (+ 0.77) seconds.
% 34.44/5.49 % Length of proof is 15.
% 34.44/5.49 % Level of proof is 4.
% 34.44/5.49 % Maximum clause weight is 22.000.
% 34.44/5.49 % Given clauses 971.
% 34.44/5.49
% 34.44/5.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------