%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV159+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 : n015.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 5.32s 1.27s
% Output : CNFRefutation 5.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 9 unt; 0 def)
% Number of atoms : 77 ( 28 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 82 ( 21 ~; 13 |; 38 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 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 : 16 ( 0 sgn 11 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pred_minus_1,axiom,
! [X] : minus(X,n1) = pred(X),
file('theBenchmark.p',pred_minus_1) ).
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(cl5_nebula_norm_0009_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,pred(pv10))
& leq(n0,C) )
=> ( pv10 != C
=> sum(n0,n4,a_select3(q,C,tptp_sum_index)) = n1 ) ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_norm_0009]) ).
cnf(c_302,plain,
minus(A,n1) = pred(A),
inference(clausify,[status(thm)],[pred_minus_1]) ).
cnf(c_303,plain,
pred(A) = minus(A,n1),
inference(copy,[status(thm)],[c_302]) ).
fof(nnf_56,plain,
( ? [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] :
( 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_0009_neg]) ).
fof(sk_cl5_nebula_norm_0009_neg,plain,
( sum(n0,n4,a_select3(q,sK0,tptp_sum_index)) != n1
& pv10 != sK0
& leq(sK0,pred(pv10))
& 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_389,negated_conjecture,
( sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1
| ~ leq(A,pred(pv10))
| ~ leq(n0,A) ),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_norm_0009_neg]) ).
cnf(c_390,negated_conjecture,
( sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1
| ~ leq(A,minus(pv10,n1))
| ~ leq(n0,A) ),
inference(paramod,[status(thm)],[c_303,c_389]) ).
cnf(c_391,negated_conjecture,
leq(n0,sK0),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_norm_0009_neg]) ).
cnf(c_392,negated_conjecture,
leq(sK0,pred(pv10)),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_norm_0009_neg]) ).
cnf(c_393,negated_conjecture,
leq(sK0,minus(pv10,n1)),
inference(paramod,[status(thm)],[c_303,c_392]) ).
cnf(c_396,negated_conjecture,
sum(n0,n4,a_select3(q,sK0,tptp_sum_index)) != n1,
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_norm_0009_neg]) ).
cnf(c_2449,negated_conjecture,
( sum(n0,n4,a_select3(q,sK0,tptp_sum_index)) = n1
| ~ leq(sK0,minus(pv10,n1)) ),
inference(resolve,[status(thm)],[c_391,c_390]) ).
cnf(c_2450,negated_conjecture,
sum(n0,n4,a_select3(q,sK0,tptp_sum_index)) = n1,
inference(resolve,[status(thm)],[c_393,c_2449]) ).
cnf(c_2448,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_396,c_2450]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV159+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n015.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 13:20:14 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 4166346 was started by sandbox on n015,
% 0.17/0.44 % Sat Sep 26 13:20:14 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.26/0.56
% 0.26/0.56 % From the command line: assign(max_seconds, 300).
% 5.32/1.27
% 5.32/1.27 % SZS status Theorem for theBenchmark
% 5.32/1.27
% 5.32/1.27 % Proof 1 at 0.59 (+ 0.09) seconds.
% 5.32/1.27 % Length of proof is 11.
% 5.32/1.27 % Level of proof is 4.
% 5.32/1.27 % Maximum clause weight is 32.000.
% 5.32/1.27 % Given clauses 298.
% 5.32/1.27
% 5.32/1.27 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------