%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV157+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 : Thu Sep 24 02:46:46 PM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 10 unt; 0 def)
% Number of atoms : 101 ( 31 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 111 ( 35 ~; 23 |; 41 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 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] :
( ( X != Y
& leq(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,
( ( ! [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,pv47)
& leq(n0,C) )
=> ( 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,
~ ( ( ! [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,pv47)
& leq(n0,C) )
=> ( 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] :
( gt(Y,X)
| X = Y
| ~ leq(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f122,plain,
! [X0,X1] :
( gt(X1,X0)
| X0 = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [X,Y] :
( ( ~ gt(Y,X)
| leq(X,pred(Y)) )
& ( gt(Y,X)
| ~ leq(X,pred(Y)) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f124,plain,
( ! [X,Y] :
( ~ gt(Y,X)
| leq(X,pred(Y)) )
& ! [X,Y] :
( gt(Y,X)
| ~ leq(X,pred(Y)) ) ),
inference(miniscoping,[status(thm)],[f123]) ).
fof(f126,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| leq(X0,pred(X1)) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f259,plain,
( ? [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)))))
& pv47 != C
& leq(C,pv47)
& leq(n0,C) )
& ! [B] :
( sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1
| ~ leq(B,pred(pv10))
| ~ leq(n0,B) )
& ! [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(A,pred(pv47))
| ~ leq(n0,A) )
& 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)))) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f260,plain,
( a_select3(q,pv10,sK23_skl) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK23_skl)),minus(a_select2(x,pv10),a_select2(mu,sK23_skl))),tptp_minus_2),times(a_select2(sigma,sK23_skl),a_select2(sigma,sK23_skl)))),a_select2(rho,sK23_skl)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK23_skl))),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)))))
& pv47 != sK23_skl
& leq(sK23_skl,pv47)
& leq(n0,sK23_skl)
& ! [B] :
( sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1
| ~ leq(B,pred(pv10))
| ~ leq(n0,B) )
& ! [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(A,pred(pv47))
| ~ leq(n0,A) )
& 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)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl]),skolemize(C,sK23_skl)],[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(thm)],[f260]) ).
fof(f266,plain,
! [X0] :
( 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)))))
| ~ leq(X0,pred(pv47))
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f260]) ).
fof(f268,plain,
leq(n0,sK23_skl),
inference(cnf_transformation,[status(thm)],[f260]) ).
fof(f269,plain,
leq(sK23_skl,pv47),
inference(cnf_transformation,[status(thm)],[f260]) ).
fof(f270,plain,
pv47 != sK23_skl,
inference(cnf_transformation,[status(thm)],[f260]) ).
fof(f271,plain,
a_select3(q,pv10,sK23_skl) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK23_skl)),minus(a_select2(x,pv10),a_select2(mu,sK23_skl))),tptp_minus_2),times(a_select2(sigma,sK23_skl),a_select2(sigma,sK23_skl)))),a_select2(rho,sK23_skl)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK23_skl))),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(thm)],[f260]) ).
fof(f371,plain,
! [X0] :
( 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)
| ~ leq(X0,pred(pv47))
| ~ leq(n0,X0) ),
inference(forward_demodulation,[status(thm)],[f261,f266]) ).
fof(f374,plain,
a_select3(q,pv10,sK23_skl) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK23_skl)),minus(a_select2(x,pv10),a_select2(mu,sK23_skl))),tptp_minus_2),times(a_select2(sigma,sK23_skl),a_select2(sigma,sK23_skl)))),a_select2(rho,sK23_skl)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK23_skl))),pv84),
inference(forward_demodulation,[status(thm)],[f261,f271]) ).
fof(f375,plain,
( ~ leq(sK23_skl,pred(pv47))
| ~ leq(n0,sK23_skl) ),
inference(resolution,[status(thm)],[f374,f371]) ).
fof(f376,plain,
~ leq(sK23_skl,pred(pv47)),
inference(forward_subsumption_resolution,[status(thm)],[f375,f268]) ).
fof(f377,plain,
~ gt(pv47,sK23_skl),
inference(resolution,[status(thm)],[f376,f126]) ).
fof(f384,plain,
( sK23_skl = pv47
| ~ leq(sK23_skl,pv47) ),
inference(resolution,[status(thm)],[f377,f122]) ).
fof(f388,plain,
sK23_skl = pv47,
inference(forward_subsumption_resolution,[status(thm)],[f384,f269]) ).
fof(f390,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f388,f270]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV157+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 08:33:12 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.057943 seconds
% 0.13/0.42 % CPU time: 0.167710 seconds
% 0.13/0.42 % Total memory used: 110.545 MB
% 0.13/0.42 % Net memory used: 110.264 MB
%------------------------------------------------------------------------------