TSTP Solution File: SWV164+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWV164+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n003.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 12:40:49 EDT 2023
% Result : Theorem 0.10s 0.33s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 12 unt; 0 def)
% Number of atoms : 72 ( 12 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 70 ( 24 ~; 17 |; 21 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 16 con; 0-3 aty)
% Number of variables : 37 (; 36 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] : ~ gt(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] :
( ( leq(X,Y)
& leq(Y,Z) )
=> leq(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
succ(tptp_minus_1) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [X] : pred(succ(X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
( ( leq(n0,pv10)
& leq(pv10,n135299)
& ! [A] :
( ( leq(n0,A)
& leq(A,pred(pv10)) )
=> sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 ) )
=> ! [B] :
( ( leq(n0,B)
& leq(B,tptp_minus_1) )
=> a_select3(q,pv10,B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,B)),minus(a_select2(x,pv10),a_select2(mu,B))),tptp_minus_2),times(a_select2(sigma,B),a_select2(sigma,B)))),a_select2(rho,B)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,B))),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))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ( ( leq(n0,pv10)
& leq(pv10,n135299)
& ! [A] :
( ( leq(n0,A)
& leq(A,pred(pv10)) )
=> sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 ) )
=> ! [B] :
( ( leq(n0,B)
& leq(B,tptp_minus_1) )
=> a_select3(q,pv10,B) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,B)),minus(a_select2(x,pv10),a_select2(mu,B))),tptp_minus_2),times(a_select2(sigma,B),a_select2(sigma,B)))),a_select2(rho,B)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,B))),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(negated_conjecture,[status(cth)],[f53]) ).
fof(f106,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f108,plain,
! [X,Y,Z] :
( ~ leq(X,Y)
| ~ leq(Y,Z)
| leq(X,Z) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f109,plain,
! [X,Z] :
( ! [Y] :
( ~ leq(X,Y)
| ~ leq(Y,Z) )
| leq(X,Z) ),
inference(miniscoping,[status(esa)],[f108]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ~ leq(X0,X1)
| ~ leq(X1,X2)
| leq(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f109]) ).
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(f214,plain,
succ(tptp_minus_1) = n0,
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f226,plain,
! [X0] : pred(succ(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f259,plain,
( leq(n0,pv10)
& leq(pv10,n135299)
& ! [A] :
( ~ leq(n0,A)
| ~ leq(A,pred(pv10))
| sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 )
& ? [B] :
( leq(n0,B)
& leq(B,tptp_minus_1)
& a_select3(q,pv10,B) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,B)),minus(a_select2(x,pv10),a_select2(mu,B))),tptp_minus_2),times(a_select2(sigma,B),a_select2(sigma,B)))),a_select2(rho,B)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,B))),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(pre_NNF_transformation,[status(esa)],[f54]) ).
fof(f260,plain,
( leq(n0,pv10)
& leq(pv10,n135299)
& ! [A] :
( ~ leq(n0,A)
| ~ leq(A,pred(pv10))
| sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 )
& leq(n0,sk0_23)
& leq(sk0_23,tptp_minus_1)
& a_select3(q,pv10,sk0_23) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sk0_23)),minus(a_select2(x,pv10),a_select2(mu,sk0_23))),tptp_minus_2),times(a_select2(sigma,sk0_23),a_select2(sigma,sk0_23)))),a_select2(rho,sk0_23)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sk0_23))),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(skolemization,[status(esa)],[f259]) ).
fof(f264,plain,
leq(n0,sk0_23),
inference(cnf_transformation,[status(esa)],[f260]) ).
fof(f265,plain,
leq(sk0_23,tptp_minus_1),
inference(cnf_transformation,[status(esa)],[f260]) ).
fof(f350,plain,
! [X0] :
( ~ leq(X0,sk0_23)
| leq(X0,tptp_minus_1) ),
inference(resolution,[status(thm)],[f110,f265]) ).
fof(f355,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| gt(succ(X1),X0) ),
inference(paramodulation,[status(thm)],[f226,f125]) ).
fof(f377,plain,
leq(n0,tptp_minus_1),
inference(resolution,[status(thm)],[f350,f264]) ).
fof(f420,plain,
! [X0] : ~ leq(succ(X0),X0),
inference(resolution,[status(thm)],[f355,f106]) ).
fof(f430,plain,
~ leq(n0,tptp_minus_1),
inference(paramodulation,[status(thm)],[f214,f420]) ).
fof(f431,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f430,f377]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SWV164+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.02/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n003.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue May 30 11:46:53 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.10/0.33 % Drodi V3.5.1
% 0.10/0.33 % Refutation found
% 0.10/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.55 % Elapsed time: 0.019678 seconds
% 0.16/0.55 % CPU time: 0.020172 seconds
% 0.16/0.55 % Memory used: 4.191 MB
%------------------------------------------------------------------------------