%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV157+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 09:06:55 AM UTC 2026
% Result : Theorem 28.20s 4.52s
% Output : CNFRefutation 28.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 9 unt; 0 def)
% Number of atoms : 88 ( 29 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 92 ( 25 ~; 16 |; 39 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 17 con; 0-3 aty)
% Number of variables : 20 ( 0 sgn 14 !; 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_norm_0007,conjecture,
( ( ! [B] :
( ( leq(B,pred(pv10))
& leq(n0,B) )
=> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 )
& ! [A] :
( ( leq(A,pred(pv47))
& leq(n0,A) )
=> a_select3(q,pv10,A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),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))))) )
& leq(pv47,n4)
& leq(pv10,n135299)
& leq(n0,pv47)
& leq(n0,pv10)
& pv84 = 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)))) )
=> ! [C] :
( ( leq(C,pv47)
& leq(n0,C) )
=> ( pv47 != C
=> a_select3(q,pv10,C) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,C)),minus(a_select2(x,pv10),a_select2(mu,C))),tptp_minus_2),times(a_select2(sigma,C),a_select2(sigma,C)))),a_select2(rho,C)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,C))),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_0007) ).
fof(cl5_nebula_norm_0007_neg,negated_conjecture,
~ ( ( ! [B] :
( ( leq(B,pred(pv10))
& leq(n0,B) )
=> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 )
& ! [A] :
( ( leq(A,pred(pv47))
& leq(n0,A) )
=> a_select3(q,pv10,A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),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))))) )
& leq(pv47,n4)
& leq(pv10,n135299)
& leq(n0,pv47)
& leq(n0,pv10)
& pv84 = 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)))) )
=> ! [C] :
( ( leq(C,pv47)
& leq(n0,C) )
=> ( pv47 != C
=> a_select3(q,pv10,C) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,C)),minus(a_select2(x,pv10),a_select2(mu,C))),tptp_minus_2),times(a_select2(sigma,C),a_select2(sigma,C)))),a_select2(rho,C)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,C))),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_0007]) ).
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,
( ? [C] :
( divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,C)),minus(a_select2(x,pv10),a_select2(mu,C))),tptp_minus_2),times(a_select2(sigma,C),a_select2(sigma,C)))),a_select2(rho,C)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,C))),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,C)
& pv47 != C
& leq(C,pv47)
& leq(n0,C) )
& ! [B] :
( sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1
| ~ leq(B,pred(pv10))
| ~ leq(n0,B) )
& ! [A] :
( divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),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,A)
| ~ leq(A,pred(pv47))
| ~ leq(n0,A) )
& leq(pv47,n4)
& leq(pv10,n135299)
& leq(n0,pv47)
& leq(n0,pv10)
& 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)))) = pv84 ),
inference(fof_nnf,[status(thm)],[cl5_nebula_norm_0007_neg]) ).
fof(sk_cl5_nebula_norm_0007_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)
& pv47 != sK0
& leq(sK0,pv47)
& leq(n0,sK0)
& ! [B] :
( sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1
| ~ leq(B,pred(pv10))
| ~ leq(n0,B) )
& ! [A] :
( divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),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,A)
| ~ leq(A,pred(pv47))
| ~ leq(n0,A) )
& leq(pv47,n4)
& leq(pv10,n135299)
& leq(n0,pv47)
& leq(n0,pv10)
& 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)))) = pv84 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0)],[nnf_56]) ).
cnf(c_376,negated_conjecture,
( divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),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,A)
| ~ leq(A,pred(pv47))
| ~ leq(n0,A) ),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_norm_0007_neg]) ).
cnf(c_378,negated_conjecture,
leq(n0,sK0),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_norm_0007_neg]) ).
cnf(c_379,negated_conjecture,
leq(sK0,pv47),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_norm_0007_neg]) ).
cnf(c_380,negated_conjecture,
pv47 != sK0,
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_norm_0007_neg]) ).
cnf(c_381,negated_conjecture,
sK0 != pv47,
inference(copy,[status(thm)],[c_380]) ).
cnf(c_382,negated_conjecture,
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),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_norm_0007_neg]) ).
cnf(c_14890,negated_conjecture,
( 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,pred(pv47)) ),
inference(resolve,[status(thm)],[c_378,c_376]) ).
cnf(c_3013,negated_conjecture,
~ leq(sK0,pred(pv47)),
inference(resolve,[status(thm)],[c_382,c_14890]) ).
cnf(c_14891,negated_conjecture,
( gt(pv47,sK0)
| pv47 = sK0 ),
inference(resolve,[status(thm)],[c_379,c_67]) ).
cnf(c_14892,negated_conjecture,
( gt(pv47,sK0)
| sK0 = pv47 ),
inference(copy,[status(thm)],[c_14891]) ).
cnf(c_3493,negated_conjecture,
gt(pv47,sK0),
inference(resolve,[status(thm)],[c_381,c_14892]) ).
cnf(c_14893,plain,
leq(sK0,pred(pv47)),
inference(resolve,[status(thm)],[c_3493,c_69]) ).
cnf(c_14889,plain,
$false,
inference(resolve,[status(thm)],[c_3013,c_14893]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV157+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 13:17:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1404550 was started by sandbox on n019,
% 0.10/0.37 % Sat Sep 26 13:17:04 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.43
% 0.10/0.43 % From the command line: assign(max_seconds, 300).
% 28.20/4.52
% 28.20/4.52 % given #500 (I,wt=173): 573 leq(n0,f19(A,B,C,D,E,F,n0,V6)) | leq(n0,f21(A,B,C,D,E,F,n0,V6)) | a_select3(F,f24(A,B,C,D,E,F,n0,V6),f23(A,B,C,D,E,F,n0,V6)) != a_select3(F,f23(A,B,C,D,E,F,n0,V6),f24(A,B,C,D,E,F,n0,V6)) | -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(157,d,e),flip(g),unit_del(d,64)].
% 28.20/4.52
% 28.20/4.52 % SZS status Theorem for theBenchmark
% 28.20/4.52
% 28.20/4.52 % Proof 1 at 3.39 (+ 0.63) seconds.
% 28.20/4.52 % Length of proof is 14.
% 28.20/4.52 % Level of proof is 4.
% 28.20/4.52 % Maximum clause weight is 155.000.
% 28.20/4.52 % Given clauses 866.
% 28.20/4.52
% 28.20/4.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------