TSTP Solution File: SWV160+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWV160+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n026.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 : Wed May 31 12:40:48 EDT 2023
% Result : Theorem 0.09s 0.31s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 7 unt; 0 def)
% Number of atoms : 79 ( 21 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 82 ( 18 ~; 13 |; 40 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 17 con; 0-3 aty)
% Number of variables : 23 (; 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] : ~ gt(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,C,tptp_sum_index))) = n1 ) ) ),
file('/export/starexec/sandbox/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,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,C,tptp_sum_index))) = n1 ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f106,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f123,plain,
! [X,Y] :
( ( ~ leq(X,pred(Y))
| gt(Y,X) )
& ( leq(X,pred(Y))
| ~ gt(Y,X) ) ),
inference(NNF_transformation,[status(esa)],[f10]) ).
fof(f124,plain,
( ! [X,Y] :
( ~ leq(X,pred(Y))
| gt(Y,X) )
& ! [X,Y] :
( leq(X,pred(Y))
| ~ gt(Y,X) ) ),
inference(miniscoping,[status(esa)],[f123]) ).
fof(f125,plain,
! [X0,X1] :
( ~ leq(X0,pred(X1))
| gt(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f124]) ).
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,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),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,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,sk0_23,tptp_sum_index))) != n1 ),
inference(skolemization,[status(esa)],[f259]) ).
fof(f269,plain,
leq(sk0_23,pred(pv10)),
inference(cnf_transformation,[status(esa)],[f260]) ).
fof(f270,plain,
pv10 = sk0_23,
inference(cnf_transformation,[status(esa)],[f260]) ).
fof(f382,plain,
leq(pv10,pred(pv10)),
inference(forward_demodulation,[status(thm)],[f270,f269]) ).
fof(f383,plain,
gt(pv10,pv10),
inference(resolution,[status(thm)],[f382,f125]) ).
fof(f384,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f383,f106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWV160+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.08/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n026.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 11:55:58 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % Drodi V3.5.1
% 0.09/0.31 % Refutation found
% 0.09/0.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.53 % Elapsed time: 0.014802 seconds
% 0.14/0.53 % CPU time: 0.016557 seconds
% 0.14/0.53 % Memory used: 4.127 MB
%------------------------------------------------------------------------------