%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV053+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 : n010.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 02:46:32 PM UTC 2026
% Result : Theorem 0.13s 0.56s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 80 ( 22 unt; 1 def)
% Number of atoms : 380 ( 88 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 507 ( 207 ~; 217 |; 72 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 15 con; 0-3 aty)
% Number of variables : 88 ( 76 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [Body] : sum(n0,tptp_minus_1,Body) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
succ(tptp_minus_1) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [X] : minus(X,n1) = pred(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [X] : pred(succ(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
( ( ! [C,D] :
( ( leq(C,minus(pv10,n1))
& leq(n0,C) )
=> sum(n0,minus(n5,n1),a_select3(q,C,D)) = n1 )
& ! [A,B] :
( ( leq(A,minus(pv12,n1))
& leq(n0,A) )
=> a_select3(q,pv10,A) = divide(sqrt(times(minus(a_select3(center,A,n0),a_select2(x,pv10)),minus(a_select3(center,A,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,B,n0),a_select2(x,pv10)),minus(a_select3(center,B,n0),a_select2(x,pv10)))))) )
& leq(pv12,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv12)
& leq(n0,pv10) )
=> ( ! [G,H] :
( ( leq(G,minus(pv10,n1))
& leq(n0,G) )
=> sum(n0,minus(n5,n1),a_select3(q,G,H)) = n1 )
& ! [E,F] :
( ( leq(E,minus(pv12,n1))
& leq(n0,E) )
=> a_select3(q,pv10,E) = divide(sqrt(times(minus(a_select3(center,E,n0),a_select2(x,pv10)),minus(a_select3(center,E,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,F,n0),a_select2(x,pv10)),minus(a_select3(center,F,n0),a_select2(x,pv10)))))) )
& leq(pv12,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv12)
& leq(n0,pv10)
& n0 = sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ( ( ! [C,D] :
( ( leq(C,minus(pv10,n1))
& leq(n0,C) )
=> sum(n0,minus(n5,n1),a_select3(q,C,D)) = n1 )
& ! [A,B] :
( ( leq(A,minus(pv12,n1))
& leq(n0,A) )
=> a_select3(q,pv10,A) = divide(sqrt(times(minus(a_select3(center,A,n0),a_select2(x,pv10)),minus(a_select3(center,A,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,B,n0),a_select2(x,pv10)),minus(a_select3(center,B,n0),a_select2(x,pv10)))))) )
& leq(pv12,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv12)
& leq(n0,pv10) )
=> ( ! [G,H] :
( ( leq(G,minus(pv10,n1))
& leq(n0,G) )
=> sum(n0,minus(n5,n1),a_select3(q,G,H)) = n1 )
& ! [E,F] :
( ( leq(E,minus(pv12,n1))
& leq(n0,E) )
=> a_select3(q,pv10,E) = divide(sqrt(times(minus(a_select3(center,E,n0),a_select2(x,pv10)),minus(a_select3(center,E,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,F,n0),a_select2(x,pv10)),minus(a_select3(center,F,n0),a_select2(x,pv10)))))) )
& leq(pv12,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv12)
& leq(n0,pv10)
& n0 = sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10))))) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f204,plain,
! [X0] : sum(n0,tptp_minus_1,X0) = n0,
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f206,plain,
succ(tptp_minus_1) = n0,
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f217,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f218,plain,
! [X0] : pred(succ(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f251,plain,
( ( ? [G,H] :
( sum(n0,minus(n5,n1),a_select3(q,G,H)) != n1
& leq(G,minus(pv10,n1))
& leq(n0,G) )
| ? [E,F] :
( a_select3(q,pv10,E) != divide(sqrt(times(minus(a_select3(center,E,n0),a_select2(x,pv10)),minus(a_select3(center,E,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,F,n0),a_select2(x,pv10)),minus(a_select3(center,F,n0),a_select2(x,pv10))))))
& leq(E,minus(pv12,n1))
& leq(n0,E) )
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| ~ leq(n0,pv10)
| n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10))))) )
& ! [C,D] :
( sum(n0,minus(n5,n1),a_select3(q,C,D)) = n1
| ~ leq(C,minus(pv10,n1))
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(q,pv10,A) = divide(sqrt(times(minus(a_select3(center,A,n0),a_select2(x,pv10)),minus(a_select3(center,A,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,B,n0),a_select2(x,pv10)),minus(a_select3(center,B,n0),a_select2(x,pv10))))))
| ~ leq(A,minus(pv12,n1))
| ~ leq(n0,A) )
& leq(pv12,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv12)
& leq(n0,pv10) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f252,definition,
! [E,F] :
( sP3_prd(F,E)
<=> ( a_select3(q,pv10,E) != divide(sqrt(times(minus(a_select3(center,E,n0),a_select2(x,pv10)),minus(a_select3(center,E,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,F,n0),a_select2(x,pv10)),minus(a_select3(center,F,n0),a_select2(x,pv10))))))
& leq(E,minus(pv12,n1))
& leq(n0,E) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f253,plain,
( ( ? [G,H] :
( sum(n0,minus(n5,n1),a_select3(q,G,H)) != n1
& leq(G,minus(pv10,n1))
& leq(n0,G) )
| ? [E,F] : sP3_prd(F,E)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| ~ leq(n0,pv10)
| n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10))))) )
& ! [C,D] :
( sum(n0,minus(n5,n1),a_select3(q,C,D)) = n1
| ~ leq(C,minus(pv10,n1))
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(q,pv10,A) = divide(sqrt(times(minus(a_select3(center,A,n0),a_select2(x,pv10)),minus(a_select3(center,A,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,B,n0),a_select2(x,pv10)),minus(a_select3(center,B,n0),a_select2(x,pv10))))))
| ~ leq(A,minus(pv12,n1))
| ~ leq(n0,A) )
& leq(pv12,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv12)
& leq(n0,pv10) ),
inference(formula_renaming,[status(thm)],[f251,f252]) ).
fof(f254,plain,
( ( ? [G] :
( ? [H] : sum(n0,minus(n5,n1),a_select3(q,G,H)) != n1
& leq(G,minus(pv10,n1))
& leq(n0,G) )
| ? [E,F] : sP3_prd(F,E)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| ~ leq(n0,pv10)
| n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10))))) )
& ! [C] :
( ! [D] : sum(n0,minus(n5,n1),a_select3(q,C,D)) = n1
| ~ leq(C,minus(pv10,n1))
| ~ leq(n0,C) )
& ! [A] :
( ! [B] : a_select3(q,pv10,A) = divide(sqrt(times(minus(a_select3(center,A,n0),a_select2(x,pv10)),minus(a_select3(center,A,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,B,n0),a_select2(x,pv10)),minus(a_select3(center,B,n0),a_select2(x,pv10))))))
| ~ leq(A,minus(pv12,n1))
| ~ leq(n0,A) )
& leq(pv12,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv12)
& leq(n0,pv10) ),
inference(miniscoping,[status(thm)],[f253]) ).
fof(f255,plain,
( ( ( sum(n0,minus(n5,n1),a_select3(q,sK25_skl,sK26_skl)) != n1
& leq(sK25_skl,minus(pv10,n1))
& leq(n0,sK25_skl) )
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| ~ leq(n0,pv10)
| n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10))))) )
& ! [C] :
( ! [D] : sum(n0,minus(n5,n1),a_select3(q,C,D)) = n1
| ~ leq(C,minus(pv10,n1))
| ~ leq(n0,C) )
& ! [A] :
( ! [B] : a_select3(q,pv10,A) = divide(sqrt(times(minus(a_select3(center,A,n0),a_select2(x,pv10)),minus(a_select3(center,A,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,B,n0),a_select2(x,pv10)),minus(a_select3(center,B,n0),a_select2(x,pv10))))))
| ~ leq(A,minus(pv12,n1))
| ~ leq(n0,A) )
& leq(pv12,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv12)
& leq(n0,pv10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl,sK24_skl,sK25_skl,sK26_skl]),skolemize(E,sK23_skl),skolemize(F,sK24_skl),skolemize(G,sK25_skl),skolemize(H,sK26_skl)],[f254]) ).
fof(f256,plain,
leq(n0,pv10),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f257,plain,
leq(n0,pv12),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f258,plain,
leq(pv10,minus(n135300,n1)),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f259,plain,
leq(pv12,minus(n5,n1)),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f260,plain,
! [X0,X1] :
( a_select3(q,pv10,X0) = divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10))))))
| ~ leq(X0,minus(pv12,n1))
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f261,plain,
! [X0,X1] :
( sum(n0,minus(n5,n1),a_select3(q,X0,X1)) = n1
| ~ leq(X0,minus(pv10,n1))
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f262,plain,
( leq(n0,sK25_skl)
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| ~ leq(n0,pv10)
| n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10))))) ),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f263,plain,
( leq(sK25_skl,minus(pv10,n1))
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| ~ leq(n0,pv10)
| n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10))))) ),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f264,plain,
( sum(n0,minus(n5,n1),a_select3(q,sK25_skl,sK26_skl)) != n1
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| ~ leq(n0,pv10)
| n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10))))) ),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f338,plain,
! [E,F] :
( ( a_select3(q,pv10,E) = divide(sqrt(times(minus(a_select3(center,E,n0),a_select2(x,pv10)),minus(a_select3(center,E,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,F,n0),a_select2(x,pv10)),minus(a_select3(center,F,n0),a_select2(x,pv10))))))
| ~ leq(E,minus(pv12,n1))
| ~ leq(n0,E)
| sP3_prd(F,E) )
& ( ( a_select3(q,pv10,E) != divide(sqrt(times(minus(a_select3(center,E,n0),a_select2(x,pv10)),minus(a_select3(center,E,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,F,n0),a_select2(x,pv10)),minus(a_select3(center,F,n0),a_select2(x,pv10))))))
& leq(E,minus(pv12,n1))
& leq(n0,E) )
| ~ sP3_prd(F,E) ) ),
inference(NNF_transformation,[status(thm)],[f252]) ).
fof(f339,plain,
( ! [E,F] :
( a_select3(q,pv10,E) = divide(sqrt(times(minus(a_select3(center,E,n0),a_select2(x,pv10)),minus(a_select3(center,E,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,F,n0),a_select2(x,pv10)),minus(a_select3(center,F,n0),a_select2(x,pv10))))))
| ~ leq(E,minus(pv12,n1))
| ~ leq(n0,E)
| sP3_prd(F,E) )
& ! [E,F] :
( ( a_select3(q,pv10,E) != divide(sqrt(times(minus(a_select3(center,E,n0),a_select2(x,pv10)),minus(a_select3(center,E,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,F,n0),a_select2(x,pv10)),minus(a_select3(center,F,n0),a_select2(x,pv10))))))
& leq(E,minus(pv12,n1))
& leq(n0,E) )
| ~ sP3_prd(F,E) ) ),
inference(miniscoping,[status(thm)],[f338]) ).
fof(f340,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f339]) ).
fof(f341,plain,
! [X0,X1] :
( leq(X1,minus(pv12,n1))
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f339]) ).
fof(f342,plain,
! [X0,X1] :
( a_select3(q,pv10,X1) != divide(sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10))))))
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f339]) ).
fof(f355,plain,
pred(n0) = tptp_minus_1,
inference(paramodulation,[status(thm)],[f206,f218]) ).
fof(f369,plain,
( leq(n0,sK25_skl)
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10))))) ),
inference(forward_subsumption_resolution,[status(thm)],[f262,f256]) ).
fof(f373,plain,
( leq(sK25_skl,minus(pv10,n1))
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10))))) ),
inference(forward_subsumption_resolution,[status(thm)],[f263,f256]) ).
fof(f374,plain,
( sum(n0,minus(n5,n1),a_select3(q,sK25_skl,sK26_skl)) != n1
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| n0 != sum(n0,minus(n0,n1),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10))))) ),
inference(forward_subsumption_resolution,[status(thm)],[f264,f256]) ).
fof(f814,plain,
( sum(n0,minus(n5,n1),a_select3(q,sK25_skl,sK26_skl)) != n1
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| n0 != sum(n0,pred(n0),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10))))) ),
inference(backward_demodulation,[status(thm)],[f217,f374]) ).
fof(f815,plain,
( leq(sK25_skl,minus(pv10,n1))
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| n0 != sum(n0,pred(n0),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10))))) ),
inference(backward_demodulation,[status(thm)],[f217,f373]) ).
fof(f816,plain,
( leq(n0,sK25_skl)
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| n0 != sum(n0,pred(n0),sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10))))) ),
inference(backward_demodulation,[status(thm)],[f217,f369]) ).
fof(f826,plain,
! [X0,X1] :
( sum(n0,minus(n5,n1),a_select3(q,X0,X1)) = n1
| ~ leq(X0,pred(pv10))
| ~ leq(n0,X0) ),
inference(backward_demodulation,[status(thm)],[f217,f261]) ).
fof(f829,plain,
! [X0,X1] :
( leq(X1,pred(pv12))
| ~ sP3_prd(X0,X1) ),
inference(backward_demodulation,[status(thm)],[f217,f341]) ).
fof(f830,plain,
! [X0,X1] :
( a_select3(q,pv10,X0) = divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,minus(n5,n1),sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10))))))
| ~ leq(X0,pred(pv12))
| ~ leq(n0,X0) ),
inference(backward_demodulation,[status(thm)],[f217,f260]) ).
fof(f831,plain,
! [X0,X1] :
( a_select3(q,pv10,X1) != divide(sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10)))),sum(n0,pred(n5),sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10))))))
| ~ sP3_prd(X0,X1) ),
inference(backward_demodulation,[status(thm)],[f217,f342]) ).
fof(f832,plain,
leq(pv12,pred(n5)),
inference(backward_demodulation,[status(thm)],[f217,f259]) ).
fof(f833,plain,
leq(pv10,pred(n135300)),
inference(backward_demodulation,[status(thm)],[f217,f258]) ).
fof(f846,plain,
( sum(n0,minus(n5,n1),a_select3(q,sK25_skl,sK26_skl)) != n1
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| n0 != sum(n0,tptp_minus_1,sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10))))) ),
inference(forward_demodulation,[status(thm)],[f355,f814]) ).
fof(f847,plain,
( sum(n0,minus(n5,n1),a_select3(q,sK25_skl,sK26_skl)) != n1
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f204,f846]) ).
fof(f848,plain,
( sum(n0,minus(n5,n1),a_select3(q,sK25_skl,sK26_skl)) != n1
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,pred(n135300))
| ~ leq(n0,pv12)
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f217,f847]) ).
fof(f849,plain,
( sum(n0,minus(n5,n1),a_select3(q,sK25_skl,sK26_skl)) != n1
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,pred(n5))
| ~ leq(pv10,pred(n135300))
| ~ leq(n0,pv12)
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f217,f848]) ).
fof(f850,plain,
( sum(n0,pred(n5),a_select3(q,sK25_skl,sK26_skl)) != n1
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,pred(n5))
| ~ leq(pv10,pred(n135300))
| ~ leq(n0,pv12)
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f217,f849]) ).
fof(f851,plain,
( sum(n0,pred(n5),a_select3(q,sK25_skl,sK26_skl)) != n1
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,pred(n5))
| ~ leq(pv10,pred(n135300))
| ~ leq(n0,pv12) ),
inference(trivial_equality_resolution,[status(thm)],[f850]) ).
fof(f852,plain,
( sum(n0,pred(n5),a_select3(q,sK25_skl,sK26_skl)) != n1
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,pred(n5))
| ~ leq(pv10,pred(n135300)) ),
inference(forward_subsumption_resolution,[status(thm)],[f851,f257]) ).
fof(f853,plain,
( leq(sK25_skl,minus(pv10,n1))
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| n0 != sum(n0,tptp_minus_1,sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10))))) ),
inference(forward_demodulation,[status(thm)],[f355,f815]) ).
fof(f854,plain,
( leq(sK25_skl,minus(pv10,n1))
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f204,f853]) ).
fof(f855,plain,
( leq(sK25_skl,minus(pv10,n1))
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,pred(n135300))
| ~ leq(n0,pv12)
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f217,f854]) ).
fof(f856,plain,
( leq(sK25_skl,minus(pv10,n1))
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,pred(n5))
| ~ leq(pv10,pred(n135300))
| ~ leq(n0,pv12)
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f217,f855]) ).
fof(f857,plain,
( leq(sK25_skl,pred(pv10))
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,pred(n5))
| ~ leq(pv10,pred(n135300))
| ~ leq(n0,pv12)
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f217,f856]) ).
fof(f858,plain,
( leq(sK25_skl,pred(pv10))
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,pred(n5))
| ~ leq(pv10,pred(n135300))
| ~ leq(n0,pv12) ),
inference(trivial_equality_resolution,[status(thm)],[f857]) ).
fof(f859,plain,
( leq(sK25_skl,pred(pv10))
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,pred(n5))
| ~ leq(pv10,pred(n135300)) ),
inference(forward_subsumption_resolution,[status(thm)],[f858,f257]) ).
fof(f860,plain,
( leq(n0,sK25_skl)
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| n0 != sum(n0,tptp_minus_1,sqrt(times(minus(a_select3(center,pv71,n0),a_select2(x,pv10)),minus(a_select3(center,pv71,n0),a_select2(x,pv10))))) ),
inference(forward_demodulation,[status(thm)],[f355,f816]) ).
fof(f861,plain,
( leq(n0,sK25_skl)
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv12)
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f204,f860]) ).
fof(f862,plain,
( leq(n0,sK25_skl)
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,minus(n5,n1))
| ~ leq(pv10,pred(n135300))
| ~ leq(n0,pv12)
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f217,f861]) ).
fof(f863,plain,
( leq(n0,sK25_skl)
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,pred(n5))
| ~ leq(pv10,pred(n135300))
| ~ leq(n0,pv12)
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f217,f862]) ).
fof(f864,plain,
( leq(n0,sK25_skl)
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,pred(n5))
| ~ leq(pv10,pred(n135300))
| ~ leq(n0,pv12) ),
inference(trivial_equality_resolution,[status(thm)],[f863]) ).
fof(f865,plain,
( leq(n0,sK25_skl)
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,pred(n5))
| ~ leq(pv10,pred(n135300)) ),
inference(forward_subsumption_resolution,[status(thm)],[f864,f257]) ).
fof(f879,plain,
! [X0,X1] :
( sum(n0,pred(n5),a_select3(q,X0,X1)) = n1
| ~ leq(X0,pred(pv10))
| ~ leq(n0,X0) ),
inference(forward_demodulation,[status(thm)],[f217,f826]) ).
fof(f881,plain,
! [X0,X1] :
( a_select3(q,pv10,X0) = divide(sqrt(times(minus(a_select3(center,X0,n0),a_select2(x,pv10)),minus(a_select3(center,X0,n0),a_select2(x,pv10)))),sum(n0,pred(n5),sqrt(times(minus(a_select3(center,X1,n0),a_select2(x,pv10)),minus(a_select3(center,X1,n0),a_select2(x,pv10))))))
| ~ leq(X0,pred(pv12))
| ~ leq(n0,X0) ),
inference(forward_demodulation,[status(thm)],[f217,f830]) ).
fof(f934,plain,
( sum(n0,pred(n5),a_select3(q,sK25_skl,sK26_skl)) != n1
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,pred(n5)) ),
inference(forward_subsumption_resolution,[status(thm)],[f852,f833]) ).
fof(f955,plain,
( leq(sK25_skl,pred(pv10))
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,pred(n5)) ),
inference(forward_subsumption_resolution,[status(thm)],[f859,f833]) ).
fof(f956,plain,
( leq(n0,sK25_skl)
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv12,pred(n5)) ),
inference(forward_subsumption_resolution,[status(thm)],[f865,f833]) ).
fof(f1091,plain,
! [X0,X1] :
( ~ leq(X1,pred(pv12))
| ~ leq(n0,X1)
| ~ sP3_prd(X0,X1) ),
inference(resolution,[status(thm)],[f831,f881]) ).
fof(f1092,plain,
! [X0,X1] :
( ~ leq(X1,pred(pv12))
| ~ sP3_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1091,f340]) ).
fof(f1131,plain,
( leq(n0,sK25_skl)
| ~ leq(pv12,pred(n5)) ),
inference(backward_subsumption_resolution,[status(thm)],[f956,f1134]) ).
fof(f1132,plain,
( leq(sK25_skl,pred(pv10))
| ~ leq(pv12,pred(n5)) ),
inference(backward_subsumption_resolution,[status(thm)],[f955,f1134]) ).
fof(f1133,plain,
( sum(n0,pred(n5),a_select3(q,sK25_skl,sK26_skl)) != n1
| ~ leq(pv12,pred(n5)) ),
inference(backward_subsumption_resolution,[status(thm)],[f934,f1134]) ).
fof(f1134,plain,
! [X0,X1] : ~ sP3_prd(X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f1092,f829]) ).
fof(f1135,plain,
leq(n0,sK25_skl),
inference(forward_subsumption_resolution,[status(thm)],[f1131,f832]) ).
fof(f1136,plain,
leq(sK25_skl,pred(pv10)),
inference(forward_subsumption_resolution,[status(thm)],[f1132,f832]) ).
fof(f1137,plain,
sum(n0,pred(n5),a_select3(q,sK25_skl,sK26_skl)) != n1,
inference(forward_subsumption_resolution,[status(thm)],[f1133,f832]) ).
fof(f1147,plain,
! [X0] :
( sum(n0,pred(n5),a_select3(q,sK25_skl,X0)) = n1
| ~ leq(n0,sK25_skl) ),
inference(resolution,[status(thm)],[f1136,f879]) ).
fof(f1155,plain,
! [X0] : sum(n0,pred(n5),a_select3(q,sK25_skl,X0)) = n1,
inference(forward_subsumption_resolution,[status(thm)],[f1147,f1135]) ).
fof(f1570,plain,
n1 != n1,
inference(backward_demodulation,[status(thm)],[f1155,f1137]) ).
fof(f1571,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1570]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV053+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.42 % Computer : n010.cluster.edu
% 0.13/0.42 % Model : x86_64 x86_64
% 0.13/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.42 % Memory : 8046.5625MB
% 0.13/0.42 % OS : Linux 6.8.0-71-generic
% 0.13/0.42 % CPULimit : 300
% 0.13/0.42 % WCLimit : 300
% 0.13/0.42 % DateTime : Mon Sep 21 08:29:40 UTC 2026
% 0.13/0.42 % CPUTime :
% 0.13/0.45 % Drodi V4.1.1
% 0.13/0.56 % Refutation found
% 0.13/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.61 % Elapsed time: 0.172593 seconds
% 0.13/0.61 % CPU time: 0.849727 seconds
% 0.13/0.61 % Total memory used: 113.582 MB
% 0.13/0.61 % Net memory used: 112.343 MB
%------------------------------------------------------------------------------