%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV164+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 : n012.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 5.25s 1.05s
% Output : CNFRefutation 5.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 23 unt; 0 def)
% Number of atoms : 77 ( 23 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 57 ( 17 ~; 12 |; 19 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 16 con; 0-3 aty)
% Number of variables : 29 ( 0 sgn 14 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexivity_gt,axiom,
! [X] : ~ gt(X,X),
file('theBenchmark.p',irreflexivity_gt) ).
fof(leq_succ,axiom,
! [X,Y] :
( leq(X,Y)
=> leq(X,succ(Y)) ),
file('theBenchmark.p',leq_succ) ).
fof(leq_succ_gt_equiv,axiom,
! [X,Y] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
file('theBenchmark.p',leq_succ_gt_equiv) ).
fof(succ_plus_1_r,axiom,
! [X] : plus(X,n1) = succ(X),
file('theBenchmark.p',succ_plus_1_r) ).
fof(succ_plus_1_l,axiom,
! [X] : plus(n1,X) = succ(X),
file('theBenchmark.p',succ_plus_1_l) ).
fof(finite_domain_0,axiom,
! [X] :
( ( leq(X,n0)
& leq(n0,X) )
=> X = n0 ),
file('theBenchmark.p',finite_domain_0) ).
fof(cl5_nebula_norm_0014,conjecture,
( ( ! [A] :
( ( leq(A,pred(pv10))
& leq(n0,A) )
=> sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 )
& leq(pv10,n135299)
& leq(n0,pv10) )
=> ! [B] :
( ( leq(B,tptp_minus_1)
& leq(n0,B) )
=> a_select3(q,pv10,B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,B)),minus(a_select2(x,pv10),a_select2(mu,B))),tptp_minus_2),times(a_select2(sigma,B),a_select2(sigma,B)))),a_select2(rho,B)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,B))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) ) ),
file('theBenchmark.p',cl5_nebula_norm_0014) ).
fof(cl5_nebula_norm_0014_neg,negated_conjecture,
~ ( ( ! [A] :
( ( leq(A,pred(pv10))
& leq(n0,A) )
=> sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 )
& leq(pv10,n135299)
& leq(n0,pv10) )
=> ! [B] :
( ( leq(B,tptp_minus_1)
& leq(n0,B) )
=> a_select3(q,pv10,B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,B)),minus(a_select2(x,pv10),a_select2(mu,B))),tptp_minus_2),times(a_select2(sigma,B),a_select2(sigma,B)))),a_select2(rho,B)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,B))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_norm_0014]) ).
cnf(c_63,plain,
~ gt(A,A),
inference(clausify,[status(thm)],[irreflexivity_gt]) ).
cnf(c_71,plain,
( leq(A,succ(B))
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_succ]) ).
cnf(c_72,plain,
( gt(succ(B),A)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_succ_gt_equiv]) ).
fof(succ_tptp_minus_1,axiom,
succ(tptp_minus_1) = n0,
file('theBenchmark.p',succ_tptp_minus_1) ).
cnf(c_281,plain,
succ(tptp_minus_1) = n0,
inference(clausify,[status(thm)],[succ_tptp_minus_1]) ).
cnf(c_282,plain,
plus(A,n1) = succ(A),
inference(clausify,[status(thm)],[succ_plus_1_r]) ).
cnf(c_283,plain,
succ(A) = plus(A,n1),
inference(copy,[status(thm)],[c_282]) ).
cnf(c_284,plain,
plus(n1,A) = succ(A),
inference(clausify,[status(thm)],[succ_plus_1_l]) ).
cnf(c_285,plain,
plus(n1,A) = plus(A,n1),
inference(paramod,[status(thm)],[c_283,c_284]) ).
cnf(c_368,plain,
( n0 = A
| ~ leq(A,n0)
| ~ leq(n0,A) ),
inference(clausify,[status(thm)],[finite_domain_0]) ).
fof(nnf_56,plain,
( ? [B] :
( divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,B)),minus(a_select2(x,pv10),a_select2(mu,B))),tptp_minus_2),times(a_select2(sigma,B),a_select2(sigma,B)))),a_select2(rho,B)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,B))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) != a_select3(q,pv10,B)
& leq(B,tptp_minus_1)
& leq(n0,B) )
& ! [A] :
( sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1
| ~ leq(A,pred(pv10))
| ~ leq(n0,A) )
& leq(pv10,n135299)
& leq(n0,pv10) ),
inference(fof_nnf,[status(thm)],[cl5_nebula_norm_0014_neg]) ).
fof(sk_cl5_nebula_norm_0014_neg,plain,
( divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK0)),minus(a_select2(x,pv10),a_select2(mu,sK0))),tptp_minus_2),times(a_select2(sigma,sK0),a_select2(sigma,sK0)))),a_select2(rho,sK0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK0))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) != a_select3(q,pv10,sK0)
& leq(sK0,tptp_minus_1)
& leq(n0,sK0)
& ! [A] :
( sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1
| ~ leq(A,pred(pv10))
| ~ leq(n0,A) )
& leq(pv10,n135299)
& leq(n0,pv10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B,sK0)],[nnf_56]) ).
cnf(c_386,negated_conjecture,
leq(n0,sK0),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_norm_0014_neg]) ).
cnf(c_387,negated_conjecture,
leq(sK0,tptp_minus_1),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_norm_0014_neg]) ).
cnf(c_2785,plain,
plus(tptp_minus_1,n1) = n0,
inference(paramod,[status(thm)],[c_283,c_281]) ).
cnf(c_821,plain,
plus(n1,tptp_minus_1) = n0,
inference(paramod,[status(thm)],[c_285,c_2785]) ).
cnf(c_823,plain,
( gt(plus(B,n1),A)
| ~ leq(A,B) ),
inference(paramod,[status(thm)],[c_283,c_72]) ).
cnf(c_824,plain,
( leq(A,plus(B,n1))
| ~ leq(A,B) ),
inference(paramod,[status(thm)],[c_283,c_71]) ).
cnf(c_2786,negated_conjecture,
( n0 = sK0
| ~ leq(sK0,n0) ),
inference(resolve,[status(thm)],[c_386,c_368]) ).
cnf(c_1922,negated_conjecture,
( sK0 = n0
| ~ leq(sK0,n0) ),
inference(copy,[status(thm)],[c_2786]) ).
cnf(c_2787,negated_conjecture,
gt(plus(tptp_minus_1,n1),sK0),
inference(resolve,[status(thm)],[c_823,c_387]) ).
cnf(c_2788,negated_conjecture,
gt(plus(n1,tptp_minus_1),sK0),
inference(paramod,[status(thm)],[c_285,c_2787]) ).
cnf(c_2677,negated_conjecture,
gt(n0,sK0),
inference(paramod,[status(thm)],[c_821,c_2788]) ).
cnf(c_2789,negated_conjecture,
leq(sK0,plus(tptp_minus_1,n1)),
inference(resolve,[status(thm)],[c_824,c_387]) ).
cnf(c_2790,negated_conjecture,
leq(sK0,plus(n1,tptp_minus_1)),
inference(paramod,[status(thm)],[c_285,c_2789]) ).
cnf(c_2681,negated_conjecture,
leq(sK0,n0),
inference(paramod,[status(thm)],[c_821,c_2790]) ).
cnf(c_2783,negated_conjecture,
sK0 = n0,
inference(resolve,[status(thm)],[c_2681,c_1922]) ).
cnf(c_2791,negated_conjecture,
gt(n0,n0),
inference(paramod,[status(thm)],[c_2783,c_2677]) ).
cnf(c_2784,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_63,c_2791]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV164+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Sat Sep 26 13:17:04 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.30 % Process 693510 was started by sandbox2 on n012,
% 0.02/0.30 % Sat Sep 26 13:17:04 2026
% 0.02/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.33
% 0.08/0.33 % From the command line: assign(max_seconds, 300).
% 5.25/1.05
% 5.25/1.05 % given #500 (I,wt=158): 592 leq(n0,f19(A,B,C,D,E,F,V6,V7)) | leq(n0,f22(A,B,C,D,E,F,V6,V7)) | leq(n0,f23(A,B,C,D,E,F,V6,V7)) | -leq(n0,V6) | 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,V6) = 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)))),V6,n0). [factor(163,d,g),unit_del(e,64),unit_del(f,64)].
% 5.25/1.05
% 5.25/1.05 % SZS status Theorem for theBenchmark
% 5.25/1.05
% 5.25/1.05 % Proof 1 at 0.64 (+ 0.07) seconds.
% 5.25/1.05 % Length of proof is 26.
% 5.25/1.05 % Level of proof is 7.
% 5.25/1.05 % Maximum clause weight is 18.000.
% 5.25/1.05 % Given clauses 732.
% 5.25/1.05
% 5.25/1.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------