TSTP Solution File: SWV159+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWV159+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:46:08 EDT 2024
% Result : Theorem 0.11s 0.35s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 85 ( 25 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 90 ( 24 ~; 16 |; 38 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 17 con; 0-3 aty)
% Number of variables : 12 ( 11 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
( ( 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))))
& leq(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ! [A] :
( ( leq(n0,A)
& leq(A,pred(pv47)) )
=> 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))))) )
& ! [B] :
( ( leq(n0,B)
& leq(B,pred(pv10)) )
=> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) )
=> ! [C] :
( ( leq(n0,C)
& leq(C,pred(pv10)) )
=> ( pv10 != C
=> sum(n0,n4,a_select3(q,C,tptp_sum_index)) = n1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ( ( 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))))
& leq(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ! [A] :
( ( leq(n0,A)
& leq(A,pred(pv47)) )
=> 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))))) )
& ! [B] :
( ( leq(n0,B)
& leq(B,pred(pv10)) )
=> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) )
=> ! [C] :
( ( leq(n0,C)
& leq(C,pred(pv10)) )
=> ( pv10 != C
=> sum(n0,n4,a_select3(q,C,tptp_sum_index)) = n1 ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f259,plain,
( 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))))
& leq(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ! [A] :
( ~ leq(n0,A)
| ~ leq(A,pred(pv47))
| 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))))) )
& ! [B] :
( ~ leq(n0,B)
| ~ leq(B,pred(pv10))
| sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 )
& ? [C] :
( leq(n0,C)
& leq(C,pred(pv10))
& pv10 != C
& sum(n0,n4,a_select3(q,C,tptp_sum_index)) != n1 ) ),
inference(pre_NNF_transformation,[status(esa)],[f54]) ).
fof(f260,plain,
( 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))))
& leq(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ! [A] :
( ~ leq(n0,A)
| ~ leq(A,pred(pv47))
| 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))))) )
& ! [B] :
( ~ leq(n0,B)
| ~ leq(B,pred(pv10))
| sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 )
& leq(n0,sk0_23)
& leq(sk0_23,pred(pv10))
& pv10 != sk0_23
& sum(n0,n4,a_select3(q,sk0_23,tptp_sum_index)) != n1 ),
inference(skolemization,[status(esa)],[f259]) ).
fof(f267,plain,
! [X0] :
( ~ leq(n0,X0)
| ~ leq(X0,pred(pv10))
| sum(n0,n4,a_select3(q,X0,tptp_sum_index)) = n1 ),
inference(cnf_transformation,[status(esa)],[f260]) ).
fof(f268,plain,
leq(n0,sk0_23),
inference(cnf_transformation,[status(esa)],[f260]) ).
fof(f269,plain,
leq(sk0_23,pred(pv10)),
inference(cnf_transformation,[status(esa)],[f260]) ).
fof(f271,plain,
sum(n0,n4,a_select3(q,sk0_23,tptp_sum_index)) != n1,
inference(cnf_transformation,[status(esa)],[f260]) ).
fof(f362,plain,
( spl0_0
<=> leq(n0,sk0_23) ),
introduced(split_symbol_definition) ).
fof(f364,plain,
( ~ leq(n0,sk0_23)
| spl0_0 ),
inference(component_clause,[status(thm)],[f362]) ).
fof(f365,plain,
( spl0_1
<=> sum(n0,n4,a_select3(q,sk0_23,tptp_sum_index)) = n1 ),
introduced(split_symbol_definition) ).
fof(f366,plain,
( sum(n0,n4,a_select3(q,sk0_23,tptp_sum_index)) = n1
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f365]) ).
fof(f368,plain,
( ~ leq(n0,sk0_23)
| sum(n0,n4,a_select3(q,sk0_23,tptp_sum_index)) = n1 ),
inference(resolution,[status(thm)],[f267,f269]) ).
fof(f369,plain,
( ~ spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f368,f362,f365]) ).
fof(f379,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f364,f268]) ).
fof(f380,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f379]) ).
fof(f381,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f366,f271]) ).
fof(f382,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f381]) ).
fof(f383,plain,
$false,
inference(sat_refutation,[status(thm)],[f369,f380,f382]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWV159+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.03/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n029.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Apr 30 01:16:49 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.34 % Drodi V3.6.0
% 0.11/0.35 % Refutation found
% 0.11/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.37 % Elapsed time: 0.027330 seconds
% 0.16/0.37 % CPU time: 0.036419 seconds
% 0.16/0.37 % Total memory used: 14.620 MB
% 0.16/0.37 % Net memory used: 14.598 MB
%------------------------------------------------------------------------------