TSTP Solution File: SWV157+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWV157+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n012.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 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 9 unt; 0 def)
% Number of atoms : 131 ( 32 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 135 ( 43 ~; 35 |; 41 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 17 con; 0-3 aty)
% Number of variables : 29 (; 28 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X,Y] :
( ( leq(X,Y)
& X != Y )
=> gt(Y,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,pv47) )
=> ( pv47 != C
=> a_select3(q,pv10,C) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,C)),minus(a_select2(x,pv10),a_select2(mu,C))),tptp_minus_2),times(a_select2(sigma,C),a_select2(sigma,C)))),a_select2(rho,C)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,C))),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/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,pv47) )
=> ( pv47 != C
=> a_select3(q,pv10,C) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,C)),minus(a_select2(x,pv10),a_select2(mu,C))),tptp_minus_2),times(a_select2(sigma,C),a_select2(sigma,C)))),a_select2(rho,C)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,C))),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(f121,plain,
! [X,Y] :
( ~ leq(X,Y)
| X = Y
| gt(Y,X) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f122,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| X0 = X1
| gt(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f121]) ).
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(f126,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,pv47)
& pv47 != C
& a_select3(q,pv10,C) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,C)),minus(a_select2(x,pv10),a_select2(mu,C))),tptp_minus_2),times(a_select2(sigma,C),a_select2(sigma,C)))),a_select2(rho,C)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,C))),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,
( 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,pv47)
& pv47 != sk0_23
& 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(f261,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)))),
inference(cnf_transformation,[status(esa)],[f260]) ).
fof(f266,plain,
! [X0] :
( ~ leq(n0,X0)
| ~ leq(X0,pred(pv47))
| a_select3(q,pv10,X0) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X0)),minus(a_select2(x,pv10),a_select2(mu,X0))),tptp_minus_2),times(a_select2(sigma,X0),a_select2(sigma,X0)))),a_select2(rho,X0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X0))),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(cnf_transformation,[status(esa)],[f260]) ).
fof(f268,plain,
leq(n0,sk0_23),
inference(cnf_transformation,[status(esa)],[f260]) ).
fof(f269,plain,
leq(sk0_23,pv47),
inference(cnf_transformation,[status(esa)],[f260]) ).
fof(f270,plain,
pv47 != sk0_23,
inference(cnf_transformation,[status(esa)],[f260]) ).
fof(f271,plain,
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(cnf_transformation,[status(esa)],[f260]) ).
fof(f391,plain,
! [X0] :
( ~ leq(n0,X0)
| ~ leq(X0,pred(pv47))
| a_select3(q,pv10,X0) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X0)),minus(a_select2(x,pv10),a_select2(mu,X0))),tptp_minus_2),times(a_select2(sigma,X0),a_select2(sigma,X0)))),a_select2(rho,X0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X0))),pv84) ),
inference(forward_demodulation,[status(thm)],[f261,f266]) ).
fof(f400,plain,
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))),pv84),
inference(forward_demodulation,[status(thm)],[f261,f271]) ).
fof(f401,plain,
( spl0_0
<=> leq(n0,sk0_23) ),
introduced(split_symbol_definition) ).
fof(f403,plain,
( ~ leq(n0,sk0_23)
| spl0_0 ),
inference(component_clause,[status(thm)],[f401]) ).
fof(f404,plain,
( spl0_1
<=> leq(sk0_23,pred(pv47)) ),
introduced(split_symbol_definition) ).
fof(f406,plain,
( ~ leq(sk0_23,pred(pv47))
| spl0_1 ),
inference(component_clause,[status(thm)],[f404]) ).
fof(f407,plain,
( ~ leq(n0,sk0_23)
| ~ leq(sk0_23,pred(pv47)) ),
inference(resolution,[status(thm)],[f400,f391]) ).
fof(f408,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f407,f401,f404]) ).
fof(f409,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f403,f268]) ).
fof(f410,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f409]) ).
fof(f411,plain,
( ~ gt(pv47,sk0_23)
| spl0_1 ),
inference(resolution,[status(thm)],[f126,f406]) ).
fof(f417,plain,
( spl0_3
<=> sk0_23 = pv47 ),
introduced(split_symbol_definition) ).
fof(f418,plain,
( sk0_23 = pv47
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f417]) ).
fof(f1028,plain,
( spl0_63
<=> gt(pv47,sk0_23) ),
introduced(split_symbol_definition) ).
fof(f1029,plain,
( gt(pv47,sk0_23)
| ~ spl0_63 ),
inference(component_clause,[status(thm)],[f1028]) ).
fof(f1031,plain,
( sk0_23 = pv47
| gt(pv47,sk0_23) ),
inference(resolution,[status(thm)],[f122,f269]) ).
fof(f1032,plain,
( spl0_3
| spl0_63 ),
inference(split_clause,[status(thm)],[f1031,f417,f1028]) ).
fof(f1101,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f418,f270]) ).
fof(f1102,plain,
~ spl0_3,
inference(contradiction_clause,[status(thm)],[f1101]) ).
fof(f1103,plain,
( $false
| spl0_1
| ~ spl0_63 ),
inference(forward_subsumption_resolution,[status(thm)],[f1029,f411]) ).
fof(f1104,plain,
( spl0_1
| ~ spl0_63 ),
inference(contradiction_clause,[status(thm)],[f1103]) ).
fof(f1105,plain,
$false,
inference(sat_refutation,[status(thm)],[f408,f410,f1032,f1102,f1104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : SWV157+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.08/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue May 30 11:36:55 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Drodi V3.5.1
% 0.12/0.36 % Refutation found
% 0.12/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.37 % Elapsed time: 0.035631 seconds
% 0.12/0.37 % CPU time: 0.083308 seconds
% 0.12/0.37 % Memory used: 14.527 MB
%------------------------------------------------------------------------------