%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV163+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 : n003.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 02:46:47 PM UTC 2026
% Result : Theorem 0.15s 0.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 11 unt; 0 def)
% Number of atoms : 74 ( 13 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 70 ( 23 ~; 18 |; 20 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-3 aty)
% Number of variables : 31 ( 30 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] : ~ gt(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] :
( ( leq(Y,Z)
& leq(X,Y) )
=> leq(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( gt(Y,X)
=> leq(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
( ( ! [A] :
( ( leq(A,pred(pv10))
& leq(n0,A) )
=> sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 )
& leq(pv10,n135299)
& leq(n0,pv10) )
=> ! [B] :
( ( leq(B,tptp_minus_1)
& leq(n0,B) )
=> a_select3(q,pv10,B) = divide(sqrt(times(minus(a_select3(center,B,n0),a_select2(x,pv10)),minus(a_select3(center,B,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ( ( ! [A] :
( ( leq(A,pred(pv10))
& leq(n0,A) )
=> sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 )
& leq(pv10,n135299)
& leq(n0,pv10) )
=> ! [B] :
( ( leq(B,tptp_minus_1)
& leq(n0,B) )
=> a_select3(q,pv10,B) = divide(sqrt(times(minus(a_select3(center,B,n0),a_select2(x,pv10)),minus(a_select3(center,B,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f61,axiom,
gt(n0,tptp_minus_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [X] :
( ( leq(X,n0)
& leq(n0,X) )
=> X = n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f98,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f100,plain,
! [X,Y,Z] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f101,plain,
! [X,Z] :
( leq(X,Z)
| ! [Y] :
( ~ leq(Y,Z)
| ~ leq(X,Y) ) ),
inference(miniscoping,[status(thm)],[f100]) ).
fof(f102,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f111,plain,
! [X,Y] :
( leq(X,Y)
| ~ gt(Y,X) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f112,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ gt(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f251,plain,
( ? [B] :
( a_select3(q,pv10,B) != divide(sqrt(times(minus(a_select3(center,B,n0),a_select2(x,pv10)),minus(a_select3(center,B,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
& leq(B,tptp_minus_1)
& leq(n0,B) )
& ! [A] :
( sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1
| ~ leq(A,pred(pv10))
| ~ leq(n0,A) )
& leq(pv10,n135299)
& leq(n0,pv10) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f252,plain,
( a_select3(q,pv10,sK23_skl) != divide(sqrt(times(minus(a_select3(center,sK23_skl,n0),a_select2(x,pv10)),minus(a_select3(center,sK23_skl,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
& leq(sK23_skl,tptp_minus_1)
& leq(n0,sK23_skl)
& ! [A] :
( sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1
| ~ leq(A,pred(pv10))
| ~ leq(n0,A) )
& leq(pv10,n135299)
& leq(n0,pv10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl]),skolemize(B,sK23_skl)],[f251]) ).
fof(f256,plain,
leq(n0,sK23_skl),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f257,plain,
leq(sK23_skl,tptp_minus_1),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f265,plain,
gt(n0,tptp_minus_1),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f291,plain,
! [X] :
( X = n0
| ~ leq(X,n0)
| ~ leq(n0,X) ),
inference(pre_NNF_transformation,[status(thm)],[f85]) ).
fof(f292,plain,
! [X0] :
( X0 = n0
| ~ leq(X0,n0)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f291]) ).
fof(f345,plain,
! [X0] :
( leq(X0,tptp_minus_1)
| ~ leq(X0,sK23_skl) ),
inference(resolution,[status(thm)],[f102,f257]) ).
fof(f369,plain,
leq(n0,tptp_minus_1),
inference(resolution,[status(thm)],[f345,f256]) ).
fof(f437,plain,
leq(tptp_minus_1,n0),
inference(resolution,[status(thm)],[f112,f265]) ).
fof(f490,plain,
( tptp_minus_1 = n0
| ~ leq(tptp_minus_1,n0) ),
inference(resolution,[status(thm)],[f292,f369]) ).
fof(f504,plain,
tptp_minus_1 = n0,
inference(forward_subsumption_resolution,[status(thm)],[f490,f437]) ).
fof(f540,plain,
gt(n0,n0),
inference(backward_demodulation,[status(thm)],[f504,f265]) ).
fof(f548,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f540,f98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV163+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.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 08:35:00 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 0.15/0.41 % Refutation found
% 0.15/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.44 % Elapsed time: 0.060599 seconds
% 0.15/0.44 % CPU time: 0.217946 seconds
% 0.15/0.44 % Total memory used: 100.434 MB
% 0.15/0.44 % Net memory used: 100.090 MB
%------------------------------------------------------------------------------