%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV159+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 : n004.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 0.07s 0.38s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 6 unt; 2 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,
( ( ! [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,pred(pv10))
& leq(n0,C) )
=> ( pv10 != C
=> sum(n0,n4,a_select3(q,C,tptp_sum_index)) = n1 ) ) ),
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,pred(pv10))
& leq(n0,C) )
=> ( pv10 != C
=> sum(n0,n4,a_select3(q,C,tptp_sum_index)) = n1 ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f259,plain,
( ? [C] :
( sum(n0,n4,a_select3(q,C,tptp_sum_index)) != n1
& pv10 != C
& leq(C,pred(pv10))
& 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,
( sum(n0,n4,a_select3(q,sK23_skl,tptp_sum_index)) != n1
& pv10 != sK23_skl
& leq(sK23_skl,pred(pv10))
& 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(f267,plain,
! [X0] :
( sum(n0,n4,a_select3(q,X0,tptp_sum_index)) = n1
| ~ leq(X0,pred(pv10))
| ~ 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,pred(pv10)),
inference(cnf_transformation,[status(thm)],[f260]) ).
fof(f271,plain,
sum(n0,n4,a_select3(q,sK23_skl,tptp_sum_index)) != n1,
inference(cnf_transformation,[status(thm)],[f260]) ).
fof(f371,plain,
( sum(n0,n4,a_select3(q,sK23_skl,tptp_sum_index)) = n1
| ~ leq(n0,sK23_skl) ),
inference(resolution,[status(thm)],[f267,f269]) ).
fof(f374,definition,
( sQ0_spl
<=> leq(n0,sK23_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f376,plain,
( sQ0_spl
| ~ leq(n0,sK23_skl) ),
inference(component_clause,[status(thm)],[f374]) ).
fof(f377,definition,
( sQ1_spl
<=> sum(n0,n4,a_select3(q,sK23_skl,tptp_sum_index)) = n1 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f378,plain,
( ~ sQ1_spl
| sum(n0,n4,a_select3(q,sK23_skl,tptp_sum_index)) = n1 ),
inference(component_clause,[status(thm)],[f377]) ).
fof(f380,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f371,f374,f377]) ).
fof(f388,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f376,f268]) ).
fof(f389,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f388]) ).
fof(f390,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f378,f271]) ).
fof(f391,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f390]) ).
fof(f392,plain,
$false,
inference(sat_refutation,[status(thm)],[f380,f389,f391]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV159+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.33 % Computer : n004.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 08:33:19 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.07/0.38 % Refutation found
% 0.07/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.077986 seconds
% 0.13/0.43 % CPU time: 0.205357 seconds
% 0.13/0.43 % Total memory used: 109.797 MB
% 0.13/0.43 % Net memory used: 109.632 MB
%------------------------------------------------------------------------------