%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV154+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 : n020.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 0.23s 0.63s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 51 unt; 0 def)
% Number of atoms : 111 ( 70 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 87 ( 31 ~; 8 |; 38 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 14 con; 0-3 aty)
% Number of variables : 15 ( 2 sgn 12 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sum_plus_base,axiom,
! [Body] : sum(n0,tptp_minus_1,Body) = n0,
file('theBenchmark.p',sum_plus_base) ).
fof(sum_plus_base_float,axiom,
! [Body] : tptp_float_0_0 = sum(n0,tptp_minus_1,Body),
file('theBenchmark.p',sum_plus_base_float) ).
fof(cl5_nebula_norm_0004,conjecture,
( ( ! [B] :
( ( leq(B,pred(pv10))
& leq(n0,B) )
=> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 )
& ! [A] :
( ( leq(A,pred(pv12))
& leq(n0,A) )
=> a_select3(q,pv10,A) = divide(sqrt(times(minus(a_select3(center,A,n0),a_select2(x,pv10)),minus(a_select3(center,A,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) )
& leq(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,pv10)
& pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) )
=> ! [C] :
( ( leq(C,pv12)
& leq(n0,C) )
=> ( pv12 = C
=> divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) = divide(sqrt(times(minus(a_select3(center,C,n0),a_select2(x,pv10)),minus(a_select3(center,C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ) ),
file('theBenchmark.p',cl5_nebula_norm_0004) ).
fof(cl5_nebula_norm_0004_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(pv12))
& leq(n0,A) )
=> a_select3(q,pv10,A) = divide(sqrt(times(minus(a_select3(center,A,n0),a_select2(x,pv10)),minus(a_select3(center,A,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) )
& leq(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,pv10)
& pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) )
=> ! [C] :
( ( leq(C,pv12)
& leq(n0,C) )
=> ( pv12 = C
=> divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) = divide(sqrt(times(minus(a_select3(center,C,n0),a_select2(x,pv10)),minus(a_select3(center,C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_norm_0004]) ).
cnf(c_283,plain,
sum(n0,tptp_minus_1,A) = n0,
inference(clausify,[status(thm)],[sum_plus_base]) ).
cnf(c_284,plain,
sum(n0,tptp_minus_1,A) = tptp_float_0_0,
inference(clausify,[status(thm)],[sum_plus_base_float]) ).
cnf(c_285,plain,
n0 = tptp_float_0_0,
inference(paramod,[status(thm)],[c_283,c_284]) ).
fof(succ_tptp_minus_1,axiom,
succ(tptp_minus_1) = n0,
file('theBenchmark.p',succ_tptp_minus_1) ).
cnf(c_286,plain,
succ(tptp_minus_1) = n0,
inference(clausify,[status(thm)],[succ_tptp_minus_1]) ).
cnf(c_405,plain,
succ(tptp_minus_1) = tptp_float_0_0,
inference(paramod,[status(thm)],[c_285,c_286]) ).
cnf(c_287,plain,
tptp_float_0_0 = succ(tptp_minus_1),
inference(copy,[status(thm)],[c_405]) ).
fof(successor_4,axiom,
succ(succ(succ(succ(n0)))) = n4,
file('theBenchmark.p',successor_4) ).
cnf(c_375,plain,
succ(succ(succ(succ(n0)))) = n4,
inference(clausify,[status(thm)],[successor_4]) ).
cnf(c_406,plain,
succ(succ(succ(succ(tptp_float_0_0)))) = n4,
inference(paramod,[status(thm)],[c_285,c_375]) ).
cnf(c_407,plain,
succ(succ(succ(succ(succ(tptp_minus_1))))) = n4,
inference(paramod,[status(thm)],[c_287,c_406]) ).
cnf(c_376,plain,
n4 = succ(succ(succ(succ(succ(tptp_minus_1))))),
inference(copy,[status(thm)],[c_407]) ).
fof(successor_1,axiom,
succ(n0) = n1,
file('theBenchmark.p',successor_1) ).
cnf(c_379,plain,
succ(n0) = n1,
inference(clausify,[status(thm)],[successor_1]) ).
cnf(c_408,plain,
succ(tptp_float_0_0) = n1,
inference(paramod,[status(thm)],[c_285,c_379]) ).
cnf(c_380,plain,
succ(succ(tptp_minus_1)) = n1,
inference(paramod,[status(thm)],[c_287,c_408]) ).
fof(nnf_56,plain,
( ? [C] :
( divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,C,n0),a_select2(x,pv10)),minus(a_select3(center,C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
& pv12 = C
& leq(C,pv12)
& leq(n0,C) )
& ! [B] :
( sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1
| ~ leq(B,pred(pv10))
| ~ leq(n0,B) )
& ! [A] :
( divide(sqrt(times(minus(a_select3(center,A,n0),a_select2(x,pv10)),minus(a_select3(center,A,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) = a_select3(q,pv10,A)
| ~ leq(A,pred(pv12))
| ~ leq(n0,A) )
& leq(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,pv10)
& sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) = pv70 ),
inference(fof_nnf,[status(thm)],[cl5_nebula_norm_0004_neg]) ).
fof(sk_cl5_nebula_norm_0004_neg,plain,
( divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,sK0,n0),a_select2(x,pv10)),minus(a_select3(center,sK0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
& pv12 = sK0
& leq(sK0,pv12)
& leq(n0,sK0)
& ! [B] :
( sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1
| ~ leq(B,pred(pv10))
| ~ leq(n0,B) )
& ! [A] :
( divide(sqrt(times(minus(a_select3(center,A,n0),a_select2(x,pv10)),minus(a_select3(center,A,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) = a_select3(q,pv10,A)
| ~ leq(A,pred(pv12))
| ~ leq(n0,A) )
& leq(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,pv10)
& sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) = pv70 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0)],[nnf_56]) ).
cnf(c_385,negated_conjecture,
sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) = pv70,
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_norm_0004_neg]) ).
cnf(c_409,negated_conjecture,
sum(tptp_float_0_0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) = pv70,
inference(paramod,[status(thm)],[c_285,c_385]) ).
cnf(c_410,negated_conjecture,
sum(succ(tptp_minus_1),n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) = pv70,
inference(paramod,[status(thm)],[c_287,c_409]) ).
cnf(c_411,negated_conjecture,
sum(succ(tptp_minus_1),succ(succ(succ(succ(succ(tptp_minus_1))))),sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) = pv70,
inference(paramod,[status(thm)],[c_376,c_410]) ).
cnf(c_412,negated_conjecture,
sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) = pv70,
inference(paramod,[status(thm)],[c_380,c_411]) ).
cnf(c_413,negated_conjecture,
sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,tptp_float_0_0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) = pv70,
inference(paramod,[status(thm)],[c_285,c_412]) ).
cnf(c_414,negated_conjecture,
sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) = pv70,
inference(paramod,[status(thm)],[c_287,c_413]) ).
cnf(c_415,negated_conjecture,
sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,tptp_float_0_0),a_select2(x,pv10))))) = pv70,
inference(paramod,[status(thm)],[c_285,c_414]) ).
cnf(c_416,negated_conjecture,
sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10))))) = pv70,
inference(paramod,[status(thm)],[c_287,c_415]) ).
cnf(c_386,negated_conjecture,
pv70 = sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10))))),
inference(copy,[status(thm)],[c_416]) ).
cnf(c_401,negated_conjecture,
pv12 = sK0,
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_norm_0004_neg]) ).
cnf(c_402,negated_conjecture,
sK0 = pv12,
inference(copy,[status(thm)],[c_401]) ).
cnf(c_403,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,sK0,n0),a_select2(x,pv10)),minus(a_select3(center,sK0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_norm_0004_neg]) ).
cnf(c_417,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,pv12,tptp_float_0_0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,sK0,n0),a_select2(x,pv10)),minus(a_select3(center,sK0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(paramod,[status(thm)],[c_285,c_403]) ).
cnf(c_418,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,sK0,n0),a_select2(x,pv10)),minus(a_select3(center,sK0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(paramod,[status(thm)],[c_287,c_417]) ).
cnf(c_419,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,tptp_float_0_0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,sK0,n0),a_select2(x,pv10)),minus(a_select3(center,sK0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(paramod,[status(thm)],[c_285,c_418]) ).
cnf(c_420,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,sK0,n0),a_select2(x,pv10)),minus(a_select3(center,sK0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(paramod,[status(thm)],[c_287,c_419]) ).
cnf(c_421,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,sK0,n0),a_select2(x,pv10)),minus(a_select3(center,sK0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(paramod,[status(thm)],[c_386,c_420]) ).
cnf(c_422,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,sK0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(paramod,[status(thm)],[c_402,c_421]) ).
cnf(c_423,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,pv12,tptp_float_0_0),a_select2(x,pv10)),minus(a_select3(center,sK0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(paramod,[status(thm)],[c_285,c_422]) ).
cnf(c_424,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,sK0,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(paramod,[status(thm)],[c_287,c_423]) ).
cnf(c_425,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(paramod,[status(thm)],[c_402,c_424]) ).
cnf(c_426,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,tptp_float_0_0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(paramod,[status(thm)],[c_285,c_425]) ).
cnf(c_427,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(paramod,[status(thm)],[c_287,c_426]) ).
cnf(c_428,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(tptp_float_0_0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(paramod,[status(thm)],[c_285,c_427]) ).
cnf(c_429,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(succ(tptp_minus_1),n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(paramod,[status(thm)],[c_287,c_428]) ).
cnf(c_430,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(succ(tptp_minus_1),succ(succ(succ(succ(succ(tptp_minus_1))))),sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(paramod,[status(thm)],[c_376,c_429]) ).
cnf(c_431,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(paramod,[status(thm)],[c_380,c_430]) ).
cnf(c_432,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,tptp_float_0_0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(paramod,[status(thm)],[c_285,c_431]) ).
cnf(c_433,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(paramod,[status(thm)],[c_287,c_432]) ).
cnf(c_434,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,tptp_float_0_0),a_select2(x,pv10)))))),
inference(paramod,[status(thm)],[c_285,c_433]) ).
cnf(c_435,negated_conjecture,
divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,pv12,succ(tptp_minus_1)),a_select2(x,pv10)))),sum(succ(tptp_minus_1),succ(succ(succ(n1))),sqrt(times(minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,succ(tptp_minus_1)),a_select2(x,pv10)))))),
inference(paramod,[status(thm)],[c_287,c_434]) ).
cnf(c_404,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_435]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV154+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n020.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 13:17:05 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 1667295 was started by sandbox on n020,
% 0.17/0.45 % Sat Sep 26 13:17:05 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.23/0.52
% 0.23/0.52 % From the command line: assign(max_seconds, 300).
% 0.23/0.63
% 0.23/0.63 % SZS status Theorem for theBenchmark
% 0.23/0.63
% 0.23/0.63 % Proof 1 at 0.08 (+ 0.01) seconds.
% 0.23/0.63 % Length of proof is 18.
% 0.23/0.63 % Level of proof is 6.
% 0.23/0.63 % Maximum clause weight is 29.000.
% 0.23/0.63 % Given clauses 0.
% 0.23/0.63
% 0.23/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------