%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWV159+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 : Thu Sep 24 09:02:50 AM UTC 2026
% Result : Theorem 4.56s 14.88s
% Output : Proof 4.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 105 ( 34 equ)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 121 ( 33 ~; 20 |; 59 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 17 con; 0-3 aty)
% Number of variables : 17 ( 0 sgn 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cl5_nebula_norm_0009,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,pred(pv10))
& leq(n0,C) )
=> ( pv10 != C
=> sum(n0,n4,a_select3(q,C,tptp_sum_index)) = n1 ) ) ),
file('theBenchmark.p',cl5_nebula_norm_0009) ).
fof(f_53_1,negated_conjecture,
( ~ ! [C] :
( ( leq(C,pred(pv10))
& leq(n0,C) )
=> ( pv10 != C
=> sum(n0,n4,a_select3(q,C,tptp_sum_index)) = n1 ) )
& ! [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)))) ),
inference(negate,[status(cth)],[cl5_nebula_norm_0009]) ).
fof(f_53_2,negated_conjecture,
( ? [C] :
( sum(n0,n4,a_select3(q,C,tptp_sum_index)) != n1
& pv10 != C
& leq(C,pred(pv10))
& leq(n0,C) )
& ! [B] :
( sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1
| ~ leq(B,pred(pv10))
| ~ leq(n0,B) )
& ! [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(A,pred(pv47))
| ~ leq(n0,A) )
& 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)))) ),
inference(fof_nnf,[status(thm)],[f_53_1]) ).
fof(f_53_3,negated_conjecture,
( ? [U_184] :
( sum(n0,n4,a_select3(q,U_184,tptp_sum_index)) != n1
& pv10 != U_184
& leq(U_184,pred(pv10))
& leq(n0,U_184) )
& ! [U_183] :
( sum(n0,n4,a_select3(q,U_183,tptp_sum_index)) = n1
| ~ leq(U_183,pred(pv10))
| ~ leq(n0,U_183) )
& ! [U_182] :
( a_select3(q,pv10,U_182) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,U_182)),minus(a_select2(x,pv10),a_select2(mu,U_182))),tptp_minus_2),times(a_select2(sigma,U_182),a_select2(sigma,U_182)))),a_select2(rho,U_182)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,U_182))),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(U_182,pred(pv47))
| ~ leq(n0,U_182) )
& 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)))) ),
inference(variable_rename,[status(thm)],[f_53_2]) ).
fof(f_53_4,negated_conjecture,
( sum(n0,n4,a_select3(q,sK28,tptp_sum_index)) != n1
& pv10 != sK28
& leq(sK28,pred(pv10))
& leq(n0,sK28)
& ! [U_183] :
( sum(n0,n4,a_select3(q,U_183,tptp_sum_index)) = n1
| ~ leq(U_183,pred(pv10))
| ~ leq(n0,U_183) )
& ! [U_182] :
( a_select3(q,pv10,U_182) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,U_182)),minus(a_select2(x,pv10),a_select2(mu,U_182))),tptp_minus_2),times(a_select2(sigma,U_182),a_select2(sigma,U_182)))),a_select2(rho,U_182)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,U_182))),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(U_182,pred(pv47))
| ~ leq(n0,U_182) )
& 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)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_184,sK28)],[f_53_3]) ).
fof(f_53_5,negated_conjecture,
( sum(n0,n4,a_select3(q,sK28,tptp_sum_index)) != n1
& pv10 != sK28
& leq(sK28,pred(pv10))
& leq(n0,sK28)
& ! [U_183] :
( sum(n0,n4,a_select3(q,U_183,tptp_sum_index)) = n1
| ~ leq(U_183,pred(pv10))
| ~ leq(n0,U_183) )
& ! [U_182] :
( a_select3(q,pv10,U_182) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,U_182)),minus(a_select2(x,pv10),a_select2(mu,U_182))),tptp_minus_2),times(a_select2(sigma,U_182),a_select2(sigma,U_182)))),a_select2(rho,U_182)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,U_182))),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(U_182,pred(pv47))
| ~ leq(n0,U_182) )
& 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)))) ),
inference(definitional_conversion,[status(esa)],[f_53_4]) ).
cnf(f_53_12,negated_conjecture,
( sum(n0,n4,a_select3(q,U_183,tptp_sum_index)) = n1
| ~ leq(U_183,pred(pv10))
| ~ leq(n0,U_183) ),
inference(clausify,[status(thm)],[f_53_5]) ).
cnf(f_53_13,negated_conjecture,
leq(n0,sK28),
inference(clausify,[status(thm)],[f_53_5]) ).
cnf(f_53_14,negated_conjecture,
leq(sK28,pred(pv10)),
inference(clausify,[status(thm)],[f_53_5]) ).
cnf(f_53_16,negated_conjecture,
sum(n0,n4,a_select3(q,sK28,tptp_sum_index)) != n1,
inference(clausify,[status(thm)],[f_53_5]) ).
cnf(t1,plain,
sum(n0,n4,a_select3(q,sK28,tptp_sum_index)) != n1,
inference(start,[status(thm),parent(0:0)],[f_53_16]) ).
cnf(t2,plain,
( ~ leq(sK28,pred(pv10))
| ~ leq(n0,sK28)
| sum(n0,n4,a_select3(q,sK28,tptp_sum_index)) = n1 ),
inference(extension,[status(thm),parent(t1:1)],[f_53_12]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
leq(n0,sK28),
inference(extension,[status(thm),parent(t2:2)],[f_53_13]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
leq(sK28,pred(pv10)),
inference(extension,[status(thm),parent(t2:3)],[f_53_14]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV159+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/10.37 % Computer : n010.cluster.edu
% 0.08/10.37 % Model : x86_64 x86_64
% 0.08/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.37 % Memory : 8046.5625MB
% 0.08/10.37 % OS : Linux 6.8.0-71-generic
% 0.08/10.37 % CPULimit : 300
% 0.08/10.37 % WCLimit : 300
% 0.08/10.37 % DateTime : Sun Sep 20 03:07:38 UTC 2026
% 0.08/10.37 % CPUTime :
% 4.56/14.88 % SZS status Theorem for theBenchmark
% 4.56/14.88 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------